STUDY OF PULSE LENGTH LIMITATIONS AND CURRENT DENSITY MEASUREMENT OPTIMIZATION FOR LOW-β ELECTRON BEAMS By Madison Renae Howard A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Physics — Doctor of Philosophy 2025 ABSTRACT Velvet cathodes are a popular emitter choice for high current electron beams and are utilized at several high dose radiography facilities, such as the Dual Axis Radiographic Hydrodynamic Test facility. Electron emission from a velvet surface has been studied for nearly 40 years and is shown to be a result of surface flashover. These cathodes produce stable, high current pulses on timescales less than 0.3µs. After this time frame is exceeded, cathode performance is altered and becomes increasingly unreliable. A test stand has been developed to investigate the emission characteristics of a variety of cathodes with pulse lengths up to 2.2µs. In this thesis, we evaluate the temporal evolution of velvet cathodes over pulse durations ranging from 0.3 - 1.5µs and explore the dependence on diode geometry. Charge accumula- tion on the velvet surface results in excess electron emission that presents as intense transients or arcs in the measured current. Additionally, the expansion of the hydrogen plasma formed on the face of the cathode causes a decrease in the gap distance between the cathode and anode shrouds. The combination of these effects makes velvet an unreliable emitter choice for long pulse applications. For future radiographic facilities, cathode candidates should produce stable current pulses up to 3µs with current densities on the order of 100A/cm2. A critical element for diagnosing the quality of a particle source is measuring the extracted current density. Popular methods utilize invasive diagnostic screens. Electron beams pro- duced on the cathode test stand are non-relativistic, where β = 0.5 - 0.75, and the resulting current density measurements are strongly affected by electron scatter and Cherenkov lim- its. Various measurement methods are evaluated including X-ray scintillation and Cherenkov emission. The limits for each measurement method and optimal measurement range are dis- cussed for each technique and are confirmed with Monte Carlo modeling. ACKNOWLEDGMENTS I would like to begin by thanking both my advisors: Steve Lidia and Joshua Coleman. Thank you for your unwavering support and constant guidance over the past 5 years. I would also like to thank the remaining members of my committee for their invaluable support: Scott Pratt, Artemis Spyrou, and Sergey Baryshev. Additional thanks to the faculty that keep the accelerator program at Michigan State alive. This project would not have been possible without ASET and I will be forever grateful for the opportunities provided to me. And of course, thank you to the faculty at Morehead State University that encouraged me to pursue this path and never stopped believing in me: Dr. Ignacio Birriel, Dr. Jennifer Birriel, Dr. Kevin Adkins, and Dr. Joshua Qualls. I cannot begin to thank my entire family enough for sticking by me over the years, especially my parents and sister: Lori, Brad, and Kelsey Howard. (To anyone who was told to look at this by my mother: 1.) I apologize and 2.) despite what she may have told you, I do not make laser beams out of velvet.) I also want to thank my extremely supportive and incredible friends: Regan, Emily, Jeremiah, Jared, Danielle, Cayman, Austin, Roy, Mostafa, Artemis, Julia, James, and of course Samuel. My sincerest thanks to everyone at LANL I have had the opportunity to work with over the past 3 years: Michael Jaworski, Howard Bender, Martin Taccetti, Jason Koglin, James Maslow, Tyler Mix, and the entirety of J-6. Special thanks to Jeffery Bull and Colin Josey for their support with MCNP6® and to Alex Edgar for his assistance with SEM imaging. Finally, I would like the three feline coworkers that helped keep me sane and motivated throughout this journey. From them I learned that it is okay to take a break, as long as that break involves treats. iv Work supported by Triad National Security, LLC for the National Nuclear Security Admin- istration of U.S. Department of Energy under contract 89233218CNA000001. v TABLE OF CONTENTS LIST OF SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii LIST OF ABBREVIATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Chapter 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Electron sources and applications . . . . . . . . . . . . . . . . . . . . . . . . 1.2 . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Research overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction to velvet cathodes Chapter 2. Relevant Electron Physics . . . . . . . . . . . . . . . . . . . . . . . 2.1 Diode transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Transverse phase space and emittance . . . . . . . . . . . . . . . . . . . . . . 2.3 Transverse envelope equation . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Electron emission mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Electron scattering physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Cherenkov emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 3. Experimental Design and Diagnostic Methods . . . . . . . . . . . 3.1 The cathode test stand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Current and voltage diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Current density and emission diagnostics . . . . . . . . . . . . . . . . . . . . Chapter 4. Numerical Simulation Tools . . . . . . . . . . . . . . . . . . . . . . 4.1 Trak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 MCNP6® . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 4 5 12 12 15 18 20 31 34 37 37 44 49 62 62 70 76 Chapter 5. Emission Characterization . . . . . . . . . . . . . . . . . . . . . . . 76 5.1 Conditioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.2 Cathode light emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.3 Cathode plasma lifetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Varying emitter diameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 Chapter 6. Characterizing Excess Emission . . . . . . . . . . . . . . . . . . . . 101 6.1 Long pulse emission measurements . . . . . . . . . . . . . . . . . . . . . . . 102 6.2 Excess emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 Chapter 7. Evaluating AK gap closure rates . . . . . . . . . . . . . . . . . . . 121 . . . . . . . . . . . . . . . . . . . . . . . . . 122 7.1 Expansion velocity calculations 7.2 AK gap imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 7.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 vi Chapter 8. Optimizing Current Density Measurements . . . . . . . . . . . . 140 8.1 Electron ranging studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 8.2 Cherenkov emitter studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 8.3 Discussion on optimal configuration . . . . . . . . . . . . . . . . . . . . . . . 159 Chapter 9. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 9.1 Recommendations for future work . . . . . . . . . . . . . . . . . . . . . . . . 163 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 vii LIST OF SYMBOLS dcath: cathode diameter ϵ: emittance J: current density ρ : charge density ε0: permittivity of free space ϕ: electric potential me : rest mass of an electron q: charge of an electron Kgun: gun perveance Kdiode: diode perveance K: dimensionless perveance ϵn: normalized emittance Bn: normalized brightness ne: plasma density (cid:10)Θ2 W (cid:11)1/2 : average scattering angle θc: Cherenkov angle ˜n: index of refraction θL: limiting angle γ: Lorentz factor β: v c (cid:16) velocity (cid:17) speed of light εr: relative dielectric constant Ethresh: electron emission threshold Z(t): beam impedance Z: atomic number νexp: plasma expansion velocity viii LIST OF ABBREVIATIONS CEBAF: Continuous Electron Beam Accelerator Facility DARHT: Dual Axis Hydrodynamic Test Facility LANL: Los Alamos National Laboratory LCLS: Linear Coherent Light Source SLAC: Stanford Linear Accelerator Center APS: Advanced Photon Source ANL: Argonne National Laboratory HPM: High Power Microwave Linac: Linear Accelerator RF: Radio Frequency FRIB: Facility for Rare Isotope Beams LIA: Linear Induction Accelerator FXR: Flash X-ray Linear Induction Accelerator FEL: Free Electron Laser Vircator: VIrtual CAthode oscillatOR AK Gap: Anode-Cathode Gap PFN: Pulse Forming Network DRD: Diamond Radiation Detector 1-D CL: 1-Dimensional Child Langmuir Law QE: Quantum Efficiency BPM: Beam Position Monitor ICCD: Intensified Charged Coupled Device TIR: Total Internal Reflection SEM: Scanning Electron Microscope EE: Excess Emission FWHM: Full Width at Half Maximum RMS: Root Mean Square ix Chapter 1. Introduction 1.1 Electron sources and applications Electron source development is a well established and crucial force for various fields. Table 1.1 lists various facilities using different electron sources. Electron sources are commonly used for electron acceleration for a wide range of applications. The Continuous Electron Beam Accelerator Facility (CEBAF) at Thomas Jefferson National Laboratory (J-Lab) generates a 15nA electron beam that is used for nuclear physics experiments [1, 2, 3]. X-ray flash radiography facilities, such as DARHT [4, 5, 6] at Los Alamos National Laboratory (LANL) require sources capable of producing high electron currents in order to produce quality images of the object of interest. Accelerators such as the Linear Coherent Light Source (LCLS) [7, 8] at the Stanford Linear Accelerator Center (SLAC) or the Advanced Photon Source (APS) [9, 10, 11] at Argonne National Laboratory (ANL) are examples of light sources that produce a specific spectrum of photons. Another popular use for electron sources is High Power Microwave (HPM) source development, like the KALI-5000 coaxial vircator [12, 13]. The electron source design depends on the experimental needs and facility requirements. The facilities listed in Tab. 1.1 produce wildly different beam properties (beam current, emittance, pulse length, etc.) and use differing cathode types. The primary electron emission mechanisms are thermionic emission, photoemission, field emission, and explosive emission (cold cathodes). The physical process behind each mechanism is explained in Ch. 2. This thesis describes the characteristics of intense electron beams produced by cold cathodes over extended pulse lengths. However, it is worth discussing popular uses and applications of electron sources mentioned in Tab. 1.1 . 1 Table 1.1: List of various facilities utilizing electron sources. The cathode diameter is noted by dcath, ϵ refers to the emittance of the beam, Vinj is the diode voltage, and Ibeam is the beam current. The cathode types listed will be described in Ch. 2. Note that vircator facilities are not concerned with the emittance of the beam, therefore no value is listed for the KALI-5000. Facility/Application Cathode Vinj [MV] Ibeam [A] dcath [cm] ϵ [mm-mrad] Pulse Length [ns] CEBAF [1, 2, 3]/ Photocathode: 0.13 1.5 × 10−8 Not listed 0.5 3 × 10−4 Electron linac GaAs DARHT-I [4]/ Explosive emitter: 3.8 1750 5cm 800 60 X-ray radiography Velvet DARHT-II [5, 6]/ Thermionic cathode: 2.2 1600 16.5cm 200-300 1600 X-ray radiography Tungsten LCLS [7, 8]/ Photocathode: 135 100 1.3mm FEL Copper APS [9, 10, 11]/ Thermionic cathode: 4.5 ∼1 6mm 1 7 9 × 10−3 5000 Synchrotron light source barium-tungsten KALI 5000 [12, 13]/ Explosive emitter: 0.312/0.306 2400/2050 13.7 outer, 11-12.3 inner N/A 100 Coaxial vircator Velvet/graphite 2-length There are various categories of particle accelerators determined by the acceleration mech- anism, design, and application. Linear accelerators, also known as linacs, are a relatively simple accelerator type in which particles are accelerated down a straight beam line. The majority of linac facilities utilize radio frequency (RF) fields to accelerate charged particles. These accelerators, or RF linacs, fall into the “resonant accelerator” category, as resonant structures called cavities are used to create the acceleration fields. The accelerating fields vary sinusoidally in order to continuously accelerate the charged particles. An example of an RF linac is the Facility for Rare Isotope Beams (FRIB), which uses super conducting RF cavities with operating frequencies ranging from 80.5 MHz - 322 MHz [14] that will accelerate 2 heavy uranium ions up to 200 MeV [15]. Linear induction accelerators, or LIAs, do not rely on these resonant structures and are driven by pulsed power drivers, relying on structures called induction cells. Induction accelerators are used to transport high current, space charge dominated beams due to the “nested” focusing structure. (A complete comparison between RF and induction accelerators can be found in Ref. [16].) Electron LIAs are commonly used for high-resolution radiography of hydrodynamic exper- iments [17, 18]. The high current electron beam is used to generate a pulse of bremsstrahlung photons. The photons illuminate the experiment and produce an X-ray image. A high X-ray dose is required for high-quality imaging, which is directly dependent on the electron beam current, energy, the dose, and spot size [17]. Because of the high current requirements, LIAs are an ideal choice for this application and are utilized at major flash radiography facili- ties such as DARHT and the Flash X-Ray linear induction accelerator (FXR) [19, 20] at Lawrence Livermore National Laboratory (LLNL). Light sources are a class of particle accelerator type that produce a specific spectrum of photons. There are over 50 light sources worldwide [21] which are classified into generations based on design, beam emittance, and the photon brilliance. Synchrotron light sources, such as the APS [9], are circular accelerators that generate electromagnetic radiation, or “synchrotron light” throughout the circular orbit. Beam insertion devices such as wigglers and undulators are composed of magnets with alternating dipole fields that produce high brilliance photons as the charged particle propagates through [22]. APS generates X-ray energies of up to 100keV and can additionally generate soft X-rays with energies of 3.5 keV [23]. These devices are utilized in 3rd and 4th generation light sources. An example of a 4th generation light source is the LCLS, a Free Electron Laser (FEL) capable of producing 3 X-rays with brightness 1010 times that of a 3rd generation light source [7]. LCLS is capable of producing photon energies over the range 0.8 - 8.3keV [7]. A relevant example of an HPM source is the VIrtual CAthode oscillatOR, also known as the vircator [24]. These are popular HPM sources due to a simple configuration and a high output power. Vircators are composed of a cold cathode, an anode mesh, and a virtual cathode. The virtual cathode is formed behind the anode mesh as the beam exceeds the space charge limit [25]. Microwaves are generated through the following process: A uniform electron beam is injected toward the virtual cathode, where a fraction of the beam current is reflected back towards the injection position. The initial beam energy is modulated by an external oscillating electric field, and energy is extracted from the oscillations in the reflected current [26, 27]. Injection parameters for the KALI-5000 vircator are listed in Table 1.1. Vircator experiments are most concerned with a high microwave power output, thus the emittance is not measured and therefore not listed in Tab. 1.1. 1.2 Introduction to velvet cathodes Velvet cathodes have been utilized as an electron source for high current density beams for nearly 40 years [28, 29, 30]. Initial experiments detail that high current densities of 200A/cm2 were produced for a diode voltage of 40kV [28]. Cold cathodes are a popular choice for electron sources and it was shown in Ref. [31] that the produced beam brightness greatly exceeds that of the standard thermionic cathode. When compared to other cold cathode materials, such as graphite, the velvet cathode produced a more uniform beam with a low emittance at low applied fields (100 - 200 kV/cm) [32]. In addition to high producible current, velvet cathodes are favored because they are 4 inexpensive and relatively simple to implement and maintain. Table 1.2 lists major X-ray radiography facilities utilizing these cathodes as the electron source. These cathodes are also favored for vircator applications as the expansion velocity is lower than other cold cathode materials and the modulated beam current is constant [30]. Table 1.2: Tabulated list of accelerator facilities utilizing velvet cathodes for high dose radiography. Note that the values listed for FXR refer to standard operations and do not reflect the parameters for dual-pulse mode. Facility AK-Gap [cm] dcath [cm] Vinj [MV] Ibeam [kA] J(x,y) [A/cm2] ϵ [mm-mrad] Pulse length [ns] DARHT-I [33] 17.8 FXR (standard ops.[19]) 10.0 EPURE-I [34] ATA [35] 17.2 22.4 5.08 5.60 6.35 13 3.8 2.5 3.8 2.5 1.75 2.80 2.60 10 86.5 113.9 82 ∼75 800 1300 ∼1030 ∼3000 60 50 80 75 The emission mechanism for velvet cathodes was first outlined in Ref. [30] and was determined to be a result of surface flashover. The step-by-step process and emission details are explained further in Ch. 2. 1.3 Research overview 1.3.1 Experimental motivation and goals The Dual Axis Radiographic Hydrodynamic Testing facility (DARHT), shown in Fig. 1.1, is an accelerator facility used for high resolution imaging of hydrotests and is coined “the worlds most powerful X-ray machine” [36]. DARHT consists of two LIAs placed perpendicularly to one another: Axis-I and Axis-II. The dual-axis configuration allows for imaging at two different angles simultaneously, which provides information on the symmetry of the test 5 object [37]. In total, five images are taken: one from Axis-I and four from Axis-II. Figure 1.1: An aerial view of the Dual Axis Radiographic Hydrodynamic Test (DARHT) Facility at Los Alamos National Laboratory with labeled components, including the diodes, pulsed power, and firing point. Fig. 1.1 shows a cut-out of the facility with labeled components. The injector parameters are listed in Table 1.1. Axis-I is a single pulse machine that provides an 80ns FWHM electron beam pulse generated by a velvet cathode. Axis-I produces 1.75kA with a 5-cm-diameter cathode at a diode voltage of 3.8MV. Axis-II is a long pulse machine, producing a 1.6µs pulse generated by a 16.5-cm-diameter thermionic cathode with an injector energy of 2.2 MeV. The 1.7 kA beam is systematically kicked into shorter pulses downstream, allowing for up to four images at the interaction point [37]. In order to reach the current levels desired by the DARHT facility, the Axis-II cathode is relatively complex. The 16.5-cm-diameter 311X-M cathode is composed of a porous sintered 6 tungsten substrate that is impregnated with barium oxide, calcium oxide, and aluminate [38, 39, 40]. Scandate is added to improve the emission at low temperatures and the osmium- ruthenium M coating reduces the overall work function and emissivity, a measure of the energy radiated from a material [38, 39, 40]. In order to form a space charge limited current, the cathode must be heated to 1150oC. To avoid poisoning or degradation of the cathode, the injector must be kept under high vacuum (less than 3×10−7 Torr). Because of the complexity of designing, operating, and maintaining the Axis-II cathode, it becomes necessary to explore other possible emission sources for long pulse, high current applications. 1.3.2 Radiographic cathode requirements Future radiographic facilities and upgrades to existing facilities will benefit greatly from an electron emitter capable of producing a large current density on extended timescales. Table 1.3 lists various characteristics for the present Axis-II thermionic cathode along with the desired metrics for future radiographic facilities. The desired characteristics include a current density on the order of 100A/cm2, a current of 2kA, total pulse length of 3µs, and a total charge of 6mC. The desired emittance and brightness remain in a similar range as that for the Axis-II cathode. As mentioned in the previous section, the current pulse generated by the Axis-II cathode is kicked into smaller pulses each with a pulse width of 20 - 100ns [41]. Future facilities would either use a steady pulse with a total charge of 6mC, or generate 2 - n pulses with individual pulse durations ranging from 20 - 100ns. Though thermionic cathodes can produce the desired pulse length, the requirements for J are not realistic for this emission type. Other cathode types, such as field emission cathodes or photocathodes, are not capable of producing the desired current density and as 7 such are poor candidates for future facilities. However, explosive emitters, such as velvet cathodes, have been shown to produce current densities of this magnitude, as demonstrated in Table 1.2. As such, cold cathodes may be a suitable choice for electron injectors in future radiographic facilities. The experiment described throughout this dissertation was developed to test candidate cathodes for the above applications. As velvet is highly documented for timescales <0.2µs and a popular emitter choice for radiographic applications, it is vital to observe the char- acteristics on extended pulse lengths and determine appropriate operational parameters. Throughout this dissertation, various diagnostics were developed to monitor excess emis- sion, plasma growth, and the extracted current density. Table 1.3: Metrics for Axis-II cathode and future requirements. Note that the pulse length refers to the total pulse length. The pulse on Axis-II is kicked into smaller pulses with individual pulse durations of 20 - 100ns [41]. J [A/cm2] ϵ [mm-mrads] B [A/(mm-mrad)2] Ibeam [kA] Total Pulse [µs] Q [mC] Axis-II 10 200 - 300 0.020 - 0.045 Future 100 200 - 300 0.022 - 0.050 1.6 2.0 1.6-1.7 3 ∼3 6 1.3.3 Experimental configuration A model of the experimental test bed is shown in Fig. 1.2 with various components pointed out for reference. The test stand is driven by a 4-stage Pulse Forming Network Marx [42, 43, 44, 45] capable of providing a 2.2µs pulse at 300kV to the cathode shroud [46]. The test stand and the insulator are designed to withstand fields up to 200kV/cm over the full PFN voltage pulse. The final pulse length is determined by a spark-gap driven crowbar that 8 can reduce the voltage pulse to approximately 300ns. More details on the voltage input and pulsed power components, as well as the deployed diagnostics not listed in Fig. 1.2, are in Ch. 3. Figure 1.2: Model of the test bed with the compensation can, insulator, current density diagnostic, and AK gap pointed out. More detail on the diode design is found in Ch. 3. The maximum diode voltage is ∼275kV and the extracted current is dependent on the emitter area. For a 25-mm-diameter velvet cathode, the maximum current at the head of the pulse is 200A. The electron beams lie within the energy range of γ = 1.2-1.5 and β = 0.5-0.75. Emission is initiated for fields E >∼40kV/cm. The length of the current pulse varies between 0.3 - 2.2µs, with a large suite of data collected over the range 0.3 - 1.2µs. The anode and cathode shrouds are both composed of polished stainless steel. The AK 9 gap is held constant at 22-mm the cathode plug is recessed an additional 3-mm into the cathode shroud. The aluminum cathode plug is designed to hold emitters up to 25-mm in diameter. The electron beam is terminated with a current density diagnostic shown in Fig. 1.2. The diagnostic is mounted such that it can be moved axially between 14 - 16cm from the cathode shroud. The mount can hold screen diagnostics either 3.7” or 4.5” in diameter with viewing areas of 88-mm-ϕ and 108-mm-ϕ. The current density diagnostic configuration varies by experiment. The emission characteristics are monitored with a full diagnostic suite to monitor the emission off the velvet, current density, excess emission, plasma growth, and the electron scatter within the diode. The emission off the velvet is monitored through gated imaging and with current and voltage measurements made in the diode. Diamond Radiation Detec- tors, or DRDs, are used to measure the electron scatter and quantify the excess emission. Additional gated cameras are used to monitor plasma growth and the current density distri- bution measured on a screen diagnostic downstream of the anode. Full explanations of each diagnostic and the corresponding analysis methods will be described in Ch. 3. 1.3.4 Results reported The results reported are split into two major categories. First is the documentation of pulse length limitations and resulting emission characteristics for velvet cathodes. The electric field thresholds in the context of the experimental configuration above are documented in Ch. 5. This chapter also details the morphological changes in the velvet through SEM imaging and comments on the overall shot lifetime. Velvet cathodes are subject to excess electron emission and arcing on the material surface 10 which results in large current fluctuations, impedance collapse, and beam loading. Evidence of excess emission can be seen in all diagnostic waveforms, particularly the diode voltage and extracted beam current. This has been documented in work such as Ref. [29] for 1µs-long current pulses, though it was not fully diagnosed. To fully explore this effect, experiments were performed on the above test stand with current pulse lengths ranging from 0.3µs - 1.5µs. It is found that once the collected charge exceeds a given threshold, dependent on cathode size, excess emission is initiated. This threshold is typically reached approximately 150 - 200ns into the voltage pulse. The experiments and findings are detailed in Ch. 6. The expansion velocity for the given diode geometry has been calculated from the ex- tracted current measurements, through the simulation software TRAK [47, 48], and further observed through optical diagnostics. These experiments are detailed in Ch. 7. It is found that this expansion velocity is dependent on pulse duration, diode voltage, and emission area. The second category of reported results concerns the optimization of current density mea- surements. The electron beams produced are within the sub-relativistic energy regime with a Lorentz factor, γ, ranging from 1.2 - 1.5. At low energy, current density and beam profile measurements taken with diagnostic screens are confused by electron scatter and Cherenkov emission effects. Chapter 8 discusses diagnostic variations and the optimal configuration for current density measurements for high current, low-beta electron beams. The Monte Carlo code MCNP6® [49] is used to simulate and further quantify the effects from Cherenkov ra- diation and electron scatter. Recommendations will be made concerning optimal diagnostic configurations for current density measurements of intense, low-beta electron beams. 11 Chapter 2. Relevant Electron Physics In this chapter, I discuss the relevant parameters and characteristics when discussing electron injection, including emittance, and brightness. Additionally, the major emission mechanisms will be described in detail: thermionic emission, photoemission, field emission, and explosive emission. Lastly, electron scattering and Cherenkov physics are explained. Understanding these processes are critical when measuring the current density distribution for low-β electron beams on diagnostic screens, and is particularly relevant for Ch. 8. 2.1 Diode transport Let us begin discussion on diode transport by considering a one-dimensional diode consisting of two infinite parallel plates. The plates are biased by a voltage of V0 and separated by a distance d, as shown in Fig. 2.1. The face of the cathode (the black rectangle) is located at z = 0 and the anode (yellow rectangle) at z = d. Assume that the cathode is negatively biased and that electrons flow from the cathode and towards the anode along the z-axis only. Figure 2.1: A one-dimensional diode with infinite parallel plates separated by a distance d. To fully understand the electron flow and derive the maximum extracted current levels 12 for the above scenario, we consider Poisson’s equation: d2 dz2 ϕ = − ρ ε0 , (2.1) where ρ is the charge density and ε0 is the permittivity of free space (8.85 x 10−12 F/m). The potential ϕ is assumed to be zero where z = 0 (the face of the cathode). The relationship between ρ, the current density (J), and the electron velocity in the z-direction (vz) can be derived by introducing the continuity equation: Jz = ρvz = const. . (2.2) Assuming that the motion is non-relativistic, the kinetic energy of the electrons is modeled by KE = 1 2 mev2 z , where me = 511keV /c2 is the rest mass of an electron. The potential energy is defined as qϕ, where q is the charge of an electron. Equating the kinetic and potential energies results in the following equation of motion: vz = (cid:114) 2 q me ϕ. Combining equations 2.1, 2.2, and 2.3 results in the following: d2ϕ dz2 = J ε0 1 (cid:112)2q/me ϕ−1/2 , (2.3) (2.4) where we define −Jz = J as a positive quantity. By integrating both sides of Eq. 2.4 and assuming that when z = d, ϕ = V0, the following relation is derived: 13 J = 4ε0 9 (cid:114) 2q me 3/2 V 0 d2 . (2.5) Equation 2.5 is referred to as the Child-Langmuir law [50, 51] and represents the max- imum current density that can be extracted from the source [52]. Child’s law is one of the most fundamental equations regarding microwave tubes and electron gun design. It is im- portant to note that for the 1-D case, this relation is dependent only on the diode voltage, V, and the gap separation, d. The constant 4ε0 9 Note that the units, (cid:113) 2q me (cid:104) A V 3/2 = 2.33 ∗ 10−6 A/V 3/2 is known as the gun perveance constant. (cid:105) , are often called “pervs”. In general, perveance quantifies the space-charge effects within the charged particle beam [53]. The diode or gun perveance of an electron beam can be defined as: Kgun = Kdiode = I V 3/2 , where I is the beam current [54]. The gun perveance may also be defined as follows: Kgun = Id2 πr2V 3/2 , (2.6) (2.7) where r is the radius of the cathode. This definition more accurately includes the diode geometry. The dimensionless perveance is defined as: K = qI 2πε0me(γβc)3 , (2.8) 14 where β is the ratio of the particle velocity to the speed of light, c, and γ is the Lorentz factor. It is helpful to think of the above definition as the ratio of space charge forces in the beam to the beam’s inertial forces. The Child-Langmuir law from Eq. 2.5 is based off a 1-dimensional model with non- relativistic particles. The relationship between current density, voltage, and diode geometry becomes more complex when those assumptions cannot be made. Let us consider the 1D diode with ultra-relativistic electrons: vz ∼ c. Making this substitution and following the derivation above, the approximate ultra-relativistic solution [55] is derived as: J ≃ 2V0ε0c d2 . (2.9) However, this solution has high error at lower energies. This led to the derivation of the exact relativistic solution, known as the Jory-Trivelpiece equation [56], which holds for all energies greater than 0.5 MeV: J ≃ (cid:20)2εmec3 qd2 (cid:21) (cid:34)(cid:18) 1 + qVo mec2 (cid:19)1/2 (cid:35)2 − 0.8471 . (2.10) The exact relativistic solution above does not apply to the work presented in this thesis as the maximum electron beam energy produced is 275 keV with β = 0.75. 2.2 Transverse phase space and emittance An important parameter when discussing charged particle transport is the beam emittance. In the simplest terms, emittance is a measure of the parallelism of the beam: where a larger value corresponds to a larger overall divergence and lower beam quality [57, 58]. A more 15 exact description of this value concerns the concept of phase space: a six-dimensional space with axes in x(t), y(t), z(t), vx(t), vy(t), and vz(t). Viewing the particles in this space provides a more accurate description of the particle motion and overall beam dynamics. We can the define the beam emittance as the volume encompassed by the beam’s trajectory plotted in phase space. The one-dimensional rms-emittance is defined by the following: ϵ4rms = (cid:113)(cid:10)x2(cid:11) (cid:10)x′2(cid:11) − ⟨xx′⟩2 , (2.11) where x′ is the transverse angle coordinate with respect to the axis of symmetry to highlight small changes in the transverse motion: x′ = dx dx = vx vz , (2.12) The term (cid:10)xx′(cid:11) is the “correlation term”, which is nonzero when the beam is either converg- ing or diverging. This term is zero when measuring the waist on an ideal beam or at the particle source. In this case, the dimensions of the ellipse are a and a′ and the emittance is defined as: ϵ4rms = aa′ . (2.13) The units for all definitions of the transverse emittance are π-mm-mrads. Rather than defining the position and transverse angle as a function of time, it is simpler to discuss the variables as a function of the axial coordinate z, which defines the trace space. An example of the emittance plotted in trace space is shown in Fig. 2.2a. The value of the emittance generally decreases as the beam is accelerated. However, by 16 Figure 2.2: (a.) The emittance plotted in trace space. correlation term equates to zero and the spread in x′ is the thermal spread a′ (b.) The emittance where the th. Liouville’s theorem, the number of particles within a given volume must remain constant, thus the emittance must be a conserved quantity within an ideal system. The normalized emittance defined as ϵn = βγϵ , (2.14) and ensures that the quantity remains invariant throughout the acceleration of the beam. We can redefine the emittance in terms of the thermal spread, as depicted in Fig. 2.2b, where we utilize the definition a′ th = ∆vx vz , (2.15) where ∆vx is the rms spread in the transverse velocity, related to the thermal velocity spread as follows: ∆vx = vT x = (cid:114) Tx m . (2.16) where Tx is the transverse beam temperature in eV and m is the mass in eV/c2. Thus, we 17 can define the normalized thermal emittance for a particle source of radius r as: ϵn = 2πrvT x . (2.17) The introduction of the beam emittance leads to the definition of the beam brightness. Brightness is described as the “current density per unit solid angle in the axial direction” [59] and is defined by B = I π2ϵxϵy . (2.18) A high brightness beam is critical for both light source and radiography applications. As a result, producing a low emittance beam while maintaining a reasonably high current density is of the upmost importance. As with the emittance, the brightness is a conserved quantity in an ideal system. To ensure consistency throughout acceleration, the normalized brightness is defined as Bn = I π2ϵ2 n , (2.19) where we utilize the definition of normalized emittance. 2.3 Transverse envelope equation The transport of cylindrical charged particle beams is characterized by the paraxial ray equation [60], also known as the “envelope equation”: R′′ = − γ′R′ β2γ − γ′′ 2β2γ R − (cid:21)2 (cid:20) qBz 2βγmc R + ϵ2 R3 + (cid:20) Pϕ βγmc (cid:21)2 1 R3 + K R , (2.20) 18 where γ′ and γ′′ are the first and second derivatives of the Lorentz factor with respect to z, Bz is the azimuthal magnetic field, ϵ is the beam emittance, pϕ is the canonical momentum, and K is the dimensionless perveance defined in Eq. 2.8. R refers to the envelope radius and R′ and R′′ are the first and second derivatives with respect to position along the z-axis. Each term in Eq. 2.20 points to a different focusing/defocusing mechanism [60, 61]. The first term on the right-hand side of Eq. 2.20 results from the acceleration of the beam where γ is dependent on position. This is a focusing term: the envelope angle decreases as the particles are accelerated. The second term represents focusing as a result from an external electric field. If the kinetic energy of the beam is high enough, this term an be neglected. Term 3 represents magnetic focusing that arises from solenoidal fields and must be modified for different magnetic focusing elements. The final three terms in the envelope equation are defocusing terms. The fourth term is the emittance described above. Term 5 is the canonical angular momentum term. In order for this term to contribute to beam defocusing, the particle source must be subject to an external magnetic field. If the magnetic field surrounds the source, then the momentum is defined as Pϕ = 1 2qBr2, where r is the radius of the cathode. For term 5 to be considered relevant, the following condition must be met: Pϕ βγmc ≥ ϵ. (2.21) The final term, K R , points to beam defocusing as a result of the space charge forces within the charged particle beam. The work described throughout this dissertation focuses on sub-relativistic electron beam 19 injection, where the source is not subject to external focusing fields. Inside the AK-gap, the beam is being accelerated and is subject to focusing from the axial and radial electric fields in the first two terms of the envelope equation. Once the electron beam passes through the diode, γ holds somewhat constant throughout the pulse, meaning γ′ ≃ 0. Therefore, the only contributing terms to the beam envelope after leaving the diode are those concerning the emittance and the space charge forces (terms 4 and 6). 2.4 Electron emission mechanisms J. R. Pierce, under the pseudonym J. J. Coupling, described the “ideal cathode” as having the following characteristics [62, 63]: • The material should emit electrons freely, essentially leaking off the surface without any outside assistance. • The cathode produces an unlimited current density. • The cathode has an unlimited lifetime and the emission is constant and consistent throughout the entirety of operations. • The material should emit electrons uniformly. Realistically, cathodes do not exhibit any of the above characteristics. All cathodes re- quire persuasion in order to emit electrons through an external electric field and in some cases an external power source. Each of these methods produce different beam characteristics in terms of current density, uniformity, and lifetime, depending on operation environment. Ultimately, the choice of emission mechanism for an electron gun depends on the desired 20 characteristics: emittance and extracted current density. Additionally, the external require- ments, i.e. the power input, must be taken into consideration. 2.4.1 Thermionic emission At absolute zero (T = 0 K), all electrons have energy < E0 at the top of the conduction band, called the Fermi level [64] (see Fig. 2.3). When T > 0K, some electrons will exceed E0. If the total energy of the electron exceeds the sum of this energy and the work function, E0 + W , then the electron can be emitted from the material surface. The work function, W, represents the amount of energy necessary to remove an electron from a given solid: in this case, the surface of the cathode material. Table 2.1 lists various materials, the corresponding work function, and the material’s melting point. The process of heating the material such that the electrons have enough energy to overcome the potential barrier and escape the surface is referred to as thermionic emission. Figure 2.3: The energy level diagram for metals [64]. The current density that can be extracted from a thermionic cathode for a given tem- 21 Table 2.1: A tabulated list of various metals, their corresponding work function, and the melting point in oC. Values compiled from Refs. [65, 66]. Atomic Number Z Metal Work Function W [eV] Melting Point [oC] 55 56 20 12 31 13 51 74 44 29 76 Cesium (Cs) Barium (Ba) Calcium (Ca) Magnesium (Mg) Gallium (Ga) Aluminum (Al) Antimony (Sb) Tungsten (W) Ruthenium (Ru) Copper (Cu) Osmium (Os) 2.1 2.7 2.9 3.7 4.2 4.3 4.6 4.6 4.7 4.7 5.4 28 725 839 649 30 660 631 3410 2334 1085 3045 perature is defined by the Richardson-Dushman equation [67, 68]: JRD = (cid:32) 4πqmk2 B h3 (cid:33) −W kB T , T 2e (2.22) where kB is the Boltzmann constant (8.61 ∗ 10−5 eV/K), h is Plank’s constant (4.14 ∗ 10−15 eV-s), and T is the cathode temperature in K. The extracted current density from a thermionic cathode can be modeled with the Miram curve [69, 70, 71]. Computational, analytical, and experimental data show that once a certain temperature is reached, the extracted current is no longer limited by the temperature applied to the cathode face. At this point, the current enters the space charge limited regime and follows the Child Langmuir relation in Eq. 2.5. Once JRD = JCL, increasing the applied temperature will no longer increase the current density. An example of the Miram curve 22 for three different desired current densities is shown in Fig. 2.4: where the percentage of total current J/JCL is plotted as a function of temperature. To generate this curve, a work function of W = 1.8eV was assumed. Figure 2.4: The Miram curve [69, 70] for 3 different desired current densities. The work function is taken to be 1.8eV. When considering potential cathode materials, a thermionic emitter must be chosen such that the heat required to extract a space charge limited current does not exceed the material’s melting point. For example: cesium has a very low work function (W = 2.1eV). If this were to be considered as an emitter for DARHT-II, which requires a current density of J = 7.5A/cm2, the required temperature is T ≃ 1140oC (calculated using Eq. 2.22). This far exceeds the melting point for Cs, making it a poor choice for a high-current electron source. Materials with high melting points, such as Tungsten or Osmium, have higher work 23 functions. However, certain metals with low W, such as Barium can be used to coat cathodes with a high work function to decrease the effective W on the surface and thus the amount of heat required to extract large currents. Thermionic cathodes are favorable for applications where a continuous or long electron beam pulse (> 500ns) is necessary. Assuming that high vacuum is maintained, the cathode will emit electrons as long as it is heated, lasting for 100s of hours. Thermionic cathodes are commonly used for long-pulse electron injection, such as on DARHT Axis-II [72, 73], and vacuum tubes [62]. 2.4.2 Photoemission Figure 2.5: The three steps necessary for photo-emission according to the Three-Step Model. (a.) Step 1: a laser pulse excites the electrons, giving the electrons enough energy to overcome the potential barrier and escape the metal cathode. (b.) Step 2: the electrons move to the surface of the metal. (c.) Step 3: the electron escapes the metal into the vacuum. The process of initiating electron emission by utilizing a high energy laser to excite the electrons is called photoemission. A laser pulse is directed on the surface of a low-work function material. The photons are absorbed, which excite the electrons such that they overcome the work function and escape the material, as shown in Fig. 2.5. Unlike thermionic and field emission cathodes, photocathodes are characterized by the quantum efficiency, or QE, rather than by achievable current density. The QE is defined as the ratio of electrons emitted from the material to the amount of photons absorbed by the material. This can be 24 considered further as a product of the probability of each step, detailed in Fig. 2.5: 1.) The electrons are excited to a higher energy state by the incoming laser pulse, such that Eγ > W , 2.) the electrons move to the material’s surface, 3.) the electrons overcome the potential barrier and escape into the vacuum. Assuming that the potential barrier is a step-function with no electrons occupying states above the Fermi level and that the emitted electrons are moving perpendicularly to the material surface, the Three-Step Model (TSM) [74, 75] can be used to define the quantum efficiency: QE = [1 − R(ω)] Fe−e (EF + ¯h) 2¯hω (cid:34) 1 + EF + W EF + ¯hω − 2 (cid:114)EF + W E + ¯hω (cid:35) , (2.23) where EF is the metal’s Fermi level, R(ω) is the reflectivity at frequency ω, and Fe−e is the probability that the electrons survive the electron-electron (e-e) scattering while moving through the material and reach the surface. There are two primary categories of photocathodes: metal and semiconductors. Metal cathodes, such as copper, aluminum, or magnesium, can withstand low vacuum levels (∼ 10−6 Torr) and have lifetimes exceeding 1 year. However, these cathodes tend to have low quantum efficiencies, on the order of 0.001%, meaning that the required laser power can exceed 10kW/cm2 [76, 77, 78]. On the other hand, semiconductor photocathodes have much higher quantum efficiencies, in some cases reaching up to 10%, and require less laser power than the metal cathodes. Common semiconductor materials for this accelerator applications include Cs2T e, GaAs, and K2CsSb. Unfortunately, the semiconductors require ultra high vacuum levels: ∼ 10−9. Even at high vacuum, the cathode lifetime is typically less than 100-hours [76]. There 25 have been developments in developing an air-stable photocathode, shown in Refs. [79, 80], meaning that the cathodes are more resilient in poor vacuum and have reasonable lifetimes. Photocathodes are desirable for FELs, such as LCLS, as the extracted beams have a low emittance and thus a high brightness. Additionally, the beam pulses can be easily shaped. When implemented in an RF photoinjector, these cathodes typically produce pulses on the picosecond scale (see Tab. 1.1), and are not suitable for longer pulse applications. 2.4.3 Field emission The process of introducing an external electric field to a material surface to initiate electron emission is known as field-emission. Field emission cathodes are commonly used for electron microscopy devices, X-ray sources, RF sources, and as sources for vacuum electronics. These cathodes are preferred over both thermionic and photocathodes as they are simpler and less expensive to operate. In short, the field emission mechanism relies on the electrons tunneling through the potential barrier, rather than raising the energy to exceed the barrier like with thermionic and photo-emission. To understand the full process: we once again discuss the energy diagram and the potential barrier, shown in Fig. 2.6. After the application of a high electric field, ∼ 104 kV /cm, the electron’s energy profile is altered and the potential well is significantly narrowed. There is a non-zero probability that electrons are able to exit the material despite the fact that the energy is lower than what is needed to cross the potential wall: this is called tunneling. As the field strength is increased, the potential barrier narrows and the probability of an electron tunneling through the barrier into the vacuum increases. The amount of electrons that can be extracted in this manner increases exponentially with 26 an increase in electric field strength, as modeled by the Fowler-Nordheim equation [81]: J = K1E2 ϕ  exp − 3 2   , K2ϕ E (2.24) where E is the electric field strength in V/cm, K1 = 1.54 × 10−6 A–eV /V 2 and K2 = 6.83 × 107 V /(cm–eV 3 2 ). Figure 2.6: The energy diagram for the field emission mechanism [82, 83]. The amount of current extracted for a given field strength can be increased by altering the material surface such that the applied field is enhanced on manufactured microprotru- sions or “tips”. A successful example of utilizing the field enhancement by the addition of small fibers are cathodes composed of carbon nanotube arrays. These fibers have been utilized to produce currents >1mA for several hours [84, 85] for electric field strengths of ∼2kV/cm. Additionally, recent work [86] has shown success with pyramid shaped diamond 27 emitter arrays. This cathode type was implemented in an RF electron gun and produced an intrinsically shaped 6µs beam pulse where each tip contributed a current of ∼1.25µA. 2.4.4 Explosive emission (1.) An Figure 2.7: The emission mechanism for velvet cathodes, based off Ref. electric field is applied between the cathode and anode. (2.) The electric field creates primary electrons. (3.) The liberated electrons interact with other free electrons and gases on the cathode surface causing an electron avalanche. The dissociated H2O vapor is ionized and an H+ plasma is formed. (4.) A space charge limited current is formed as the electrons are accelerated through the anode-cathode gap (AK gap). (5.) The plasma heats with added voltage and current, causing an expansion of the cathode plasma into the AK gap throughout the pulse. [30]. The concept of explosive electron emission was briefly introduced in Ch. 1. These cold cathodes are often referred to as field emission cathodes as the electron emission is initiated by the application of an external electric field. The emission mechanism for cold cathodes, specifically the velvet cathode is outlined in Fig. 2.7 and is as follows: An electric field is applied between an anode and cathode. The electric field is enhanced on the each of the velvet fibers or “tufts”. The application of the electric field creates primary electrons that dissociate the H2O vapor on the surface of the cathode. The liberated electrons interact with other free electrons and gases on the surface of the cathode causing an electron avalanche. The electrons ionize the dissociated H2O vapor resulting in an H+ plasma. This process is known as surface flashover or surface discharge. The continuous application of the electric 28 field extracts a space charge limited current as the electrons are accelerated through the anode-cathode gap (AK gap). As the electric field is applied and beam current is extracted, the plasma heats and subsequently expands into the AK gap throughout the pulse. For all explosive emitters, the electrons are extracted from a plasma that forms on the surface. The extracted current is immediately within the space-charge limited regime, rather than following the Fowler-Nordhiem or Richardson-Dushman relations. Explosive emitters are capable of achieving high current densities, in some cases up to 107A/cm2 [87], which outperforms the thermionic, field, and photo-cathodes. The required fields for plasma for- mation have been found to be as low as 8kV/cm in the case of the carbon fiber cathode [87]. The bulk of electron emission for explosive emitters comes from individual “hot-spots”, or emission centers [88], rather than the full cathode area [87]. Gated imaging of the cathode face shows that the electron emission illuminates approximately 50% of the total area [87, 88]. Note that the illuminated emission centers indicate an increased electron density or temperature, and emission may be present in lower intensity regions. The illumination percentage is dependent on the electric fields applied to the cathode and the diode geometry. In the case of DARHT-I [33], it was reported that the discharge illuminates ∼80% of the cathode face for a 5-cm-diameter emitter and a diode voltage of 3.8 - 4 MV. Coleman et. al. performed experiments with the DARHT Axis-I, 5-cm-diameter velvet cathode exploring the properties of velvet emission over a 100ns pulse length. Both the emitter face and the AK-gap were imaged to determine the current density on the surface and calculate the expansion velocity of the cathode plasma. Cathode edge enhancement resulted in light intensity levels that were 3x higher on the edge of the cathode than in the 29 center. The expansion velocity, calculated through LSP simualtions, is dependent on the electron density of the generated plasma. For lower density plasmas, ne ∼ 1012 cm−3, the expansion velocity is approximately 2.38 cm/µs. This is ∼5x higher than for plasmas with ne = 1015 cm−3. This work also verified through visible spectroscopy measurements that the dominant ion species for the generated plasma is hydrogen (H+ 2 ), which corroborates work by Krasik and colleagues [89]. In addition to the velvet cathode, popular materials for explosive emission include carbon- fiber, graphite and metal-ceramic. The current density levels extracted from explosive emit- ters depends on the microprotrusions that exist on the surface. Ref. [30] found that velvet cathodes with a larger tuft density had a better performance overall when compared to vel- vet with sparse tuft spacing, as all velvet tufts participate equally in the surface flashover process. Work performed in Ref. [90] documents the emission characteristics for different graphite micro-structures, showing that graphite cathodes with larger particles and more irregular shaping had high current levels and a lower threshold for emission turn-on. Rakhee Menon and colleagues [13] tested the characteristics of graphite and velvet on the KALI-5000 experiment, where the AK-gap was varied for both materials. The polymer velvet cathode had an earlier turn-on time, resulting in peak current 20ns earlier than that for the graphite. The extracted HPM power for a 15-mm AK gap was consistently larger with the velvet cathode, which is thought to be due to both the lower turn-on delay and a more uniform electron beam. A primary disadvantage of explosive emitters is the high rate of plasma expansion. As the plasma grows, the AK gap effectively closes and the current levels increase, resulting in a time dependent current [30, 91] that is problematic for pulses > 0.2µs. Promising results 30 combating this expansion have been produced by carbon velvet cathodes with a cesium iodide coating [92, 93]. These cathodes were tested over 1-µs pulses with diode voltages of ∼250kV and currents ∼2kA. Imaging of the AK gap showed no evidence of plasma expansion or gap closure. The addition of the CsI coating decreased the beam emittance by a factor of 2 and the turn-on fields were reduced from ∼ 20kV/cm to 0.2V/cm [92]. However, using a CsI coating presents additional challenges, including ablation of the CsI during emission which can coat the inside of the diode. In general, explosive emitters are an inexpensive electron source and the materials are more tolerant to vacuum pressures > 10−7 Torr than thermionic and photo-emitters. They are also capable of producing stable current with pulse lengths on the order of 100-200ns. These characteristics, combined with the high extracted current, make these cathodes desir- able. However, as mentioned above, the pulse quality is degraded by the formation of the cathode plasma. This is explained in detail in Ch. 5 - 7. 2.5 Electron scattering physics Once electrons are transported through a diode it is common to diagnose the beam distri- bution. This can be done in various ways. A common way to measure the beam profile or current density is to implement a diagnostic screen such as a scintillator [89, 94] or Cherenkov emitter [95, 96, 97, 98]. As electrons travel through a given diagnostic material, energy is lost to several interactions including: multiple scattering of the source electrons, knock-on production of secondary electrons, Compton scattering, and the production and absorption of Bremsstrahlung and characteristic X-rays [99]. The energy lost as a function of the distance traveled defines the stopping power of the electrons within a given material 31 [99, 100, 101, 102]. Figure 2.8: Electron range versus energy for three materials: aluminum (Z = 13, ρ = 2.7g/cm3), copper (Z = 29, ρ = 8.96g/cm3), silicon dioxide (ρ = 2.2g/cm3), and aluminum oxide (ρ = 3.95g/cm3). Material ranges extracted from [102]. The electron range in a material decreases as the material density, ρ, increases. The stopping power is dependent on the material density and atomic number (Z). Fig. 2.8 demonstrates the electron range as a function of energy for four materials: aluminum, copper, aluminum oxide, and silicon dioxide. With an increase in atomic number and density, the maximum electron range at a given energy is decreased. The angular distribution of an electron beam within a given material is influenced by the Moli´ere model of multiple scattering [103, 104]. This is summarized well in the context of 500keV electrons by Ref. [97]. The average quadratic angle of diffusion (or average scattering angle) for electrons in matter is given by (cid:69) (cid:68) Θ2 W = Θ2 dln (cid:32) 1 1.167 (cid:18) Θd ΘM (cid:19)2(cid:33) , (2.25) 32 Figure 2.9: The average scattering angle, (cid:10)Θ2 for 250keV electrons as a function of W material thickness for four materials: aluminum, copper, silica, and alumina. The atomic numbers listed for the dielectrics are an averaged Z. Note that the scattering angle for SiO2 and Al2O3 lie closely on top of one another. (cid:11)1/2 where Θd, the characteristic angle, is defined by Θ2 d = 4πna (∆z) Z (Z + 1) (cid:18) re γβ2 (cid:19)2 , (2.26) ∆z is depth of the collision, re the classical radius of an electron, Z is the atomic number, na is the atomic density, and β is the ratio of the electron velocity to the speed of light. ΘM refers to the Moli´ere screening angle defined as: (cid:32) (cid:118) (cid:117) (cid:117) (cid:116)θ2 0 ΘM = 1.13 + 3.76 (cid:19)2(cid:33) , (cid:18) αz β (2.27) 33 where α is the fine structure constant (α ∼ 0.007297) and θ0 is the screening effect of the Coulomb potential defined as: θ0 = αZ0.33 0.885γβ . (2.28) Fig. 2.9 shows the average scattering angle, (cid:10)Θ2 W (cid:11) for 250keV electrons as a function of material thickness for aluminum, copper, silica, and alumina. 2.6 Cherenkov emission Cherenkov radiation, an additional way to measure the current density of an electron beam, is generated when the electron velocity passing through the material exceeds the phase velocity in that material, ve− > vp [95, 96]. The angle between the source electron beam and the produced Cherenkov photons is given by: cos(θC ) = 1 β ˜n , (2.29) where ˜n is the index of refraction of the material. The energy threshold for Cherenkov emission can be solved once ve− = vp. Then β = 1/˜n. The relationship between β and the Lorentz factor is used to define the Cherenkov energy threshold: Eth = me (cid:32) 1 (cid:112)1 − 1/˜n2 (cid:33) − 1 . (2.30) Snell’s law and trigonometry place a fundamental limit on the maximum Cherenkov angle 34 Figure 2.10: Cherenkov angle and exit angle for three dielectric materials: Silica (˜n = 1.46), Kapton polymide (˜n= 1.50) and Alumina ( ˜n= 1.77). The solid lines represent the Cherenkov angle while the dashed lines represent the exit angle, defined through Snell’s law, as a function of energy for each material. Table 2.2: Thresholds for Cherenkov emission and total internal reflection (TIR) for various indices of refraction, ˜n. The thresholds were calculated following Eq. 2.29. Material Index ˜n Cherenkov Threshold [kV] TIR Threshold [kV] SiO2 Kapton Willow® Glass Nylon Bicron PEEK Al2O3 1.46 1.50 1.51 1.53 1.58 1.67 1.77 190.34 174.58 170.99 164.17 149.02 127.03 108.31 987.44 631.63 581.41 502.46 376.21 258.49 190.15 achievable in each material, which is defined by the index of refraction: θL = arcsin (1/˜n) . (2.31) 35 Once the photons generated in the material approach and exceed this angle, the exit angle (θ2) becomes parallel to the material surface and total internal reflection is reached. The energy threshold for total internal reflection can be derived from Eq. 2.29. Fig. 2.10 shows evolution of the Cherenkov angle (solid line) and the corresponding exit angle (dotted line) as a function of energy for silicon dioxide, Kapton polymide film, and aluminum oxide. See Tab. 2.2 for a list of the Cherenkov and total internal reflection thresholds for various materials. It is shown that with an increase in index ˜n, the energy threshold for Cherenkov emission and TIR are decreased. 36 Chapter 3. Experimental Design and Diagnos- tic Methods 3.1 The cathode test stand 3.1.1 Diode vacuum vessel The concept of the cathode test stand was introduced in Ch. 1. The purpose of the test bed is to document the emission characteristics of velvet cathodes for pulse lengths on the range of 0.3µs - 2.2µs and over the energy range γ = 1.2 - 1.5, β =0.5 - 0.75. The cathode and anode shrouds are composed of polished stainless steel and the gap spacing is adjustable. The AK gap is fixed to 22-mm and the velvet emission surface is recessed an additional 3-mm into the cathode shroud for all experiments described in this thesis. As mentioned in Ch. 1, the emitter diameter is variable and data has been collected with 7.5-mm, 15-mm, and 25-mm diameter cathodes. The diode and insulator are designed to withstand fields < 200kV/cm for 2.2µs. During operations, the diode is kept under vacuum levels on the order of 10−6 - 10−7 Torr. Fig. 3.1 shows a left side view of the cathode test stand with relevant components and diagnostics labeled. Each diagnostic shown will be explained in detail throughout this chapter. E-dots and B-dots are used to measure the diode voltage and the extracted current levels. The Diamond Radiation Detectors (DRDs) are an additional tool for monitoring the excess electron emission. Two separate imaging paths are implemented to monitor cathode emission and plasma growth. Additional imaging is performed to monitor the distribution on the current density diagnostic shown in Fig. 3.1. 37 Figure 3.1: Left side view of the cathode test stand with labeled diagnostics in the compen- sation can (comp. can) and diode. 3.1.2 PFN Marx The diode shown above is driven by a 4-stage, 400kV PFN Marx [42, 43, 44, 45] that produces a ∼2.2µs-long voltage pulse with a maximum amplitude of 300kV. The PFN in composed of 4 “sub-PFNs”, or stages, of equal capacitance that are stacked in a Marx configuration [43], as shown in Fig. 3.2a. Each stage is charged in parallel. After the spark gaps are triggered, the 4 stages combine in series, quadrupling the voltage in the first stage. Each capacitor has a capacitance of 0.04µF and are rated at 100kV. Each stage is a 7-section type E PFN [44], meaning that the inductors are continuous providing magnetic coupling between cells. The average impendance over all stages is 20Ω [42]. In addition to the capacitor location, Fig. 3.2a points to the locations of other important components such as the spark gap switches, the inductors, and the 4:1 trigger transformer. The rise-time of the PFN voltage pulse depends on the load; in this case it is ∼90ns and specified as the time needed to rise 38 from 10% to 90% of the maximum voltage value. Figure 3.2: (a) PFN with spark gap switches, capacitors, inductors, and the Rogowski coil labeled. (b) PFN current measured with a Rogowski coil (Shot 8075). 3.1.2.1 PFN Rogowski The PFN current is measured using a Rogowski coil, a current transformer typically used to measure alternating current (AC) or high-speed pulses (pulsed power applications). In the simplest form, this current detector is a helical coil of N turns where one end is returned to the starting point through the central axis of the wound coil such that both leads are in the same location [105, 106, 107]. The coil is wrapped around a current carrying conductor. When the current passes through the conductor, a voltage is induced in the Rogowski coil. This voltage is proportional to the rate of change of the current in the conductor following the relationship V = L dI dt , (3.1) where V is the induced voltage, L is the inductance of the coil, and dI dt is the rate of change of the current. The Rogowski coil’s output signal is dI dt which is integrated with an external 39 hardware integrator to output the current signal in Amps (A). Fig. 3.2b shows a processed current waveform extracted from the Rogowski coil in the PFN where the pulse is crowbared at t ≃ 700ns. Table 3.1: Tabulated list of common PFN charges and the corresponding diode voltage and approximate current levels for each cathode. The 7.5-mm data is compiled from the 231109 data set, the 15-mm data primarily the 221201 data, and the 25-mm data from 240724 data. PFN Charge [kV] Vmax [kV] 7.5-mm Current [A] 15-mm Current [A] 25-mm Current [A] 45 50 55 60 65 70 75 160 180 200 215 240 255 275 17 22 31 37 47 56 64 30 60 70 85 100 110 125 42 66 106 136 163 187 209 The measured diode voltage and current are dependent on the charge of the PFN, which ranges from 40kV - 75kV depending on cathode size. Tab. 3.1 lists various PFN charges and the resulting diode voltage and current for three different cathode sizes. At the lowest set-point, the maximum diode voltage is ∼160kV. The highest set-point of 75kV corresponds to a diode voltage of 275kV. Note that the current levels increase with both an increase in cathode diameter and with the PFN charge. The maximum head current measured is ∼209A for a 75kV PFN charge with the 25-mm-diameter cathode. 40 3.1.2.2 Compensation can and associated diagnostics Before the voltage pulse reaches the cathode stalk, it passes through an oil filled compensation can, or comp can, through a coaxial transmission line connected to the crowbar. The comp. can, shown in Fig. 3.3a, primarily consists of a ballast resistor connected to ground. The 206Ω ballast resistance compensates for the sever impedance mismatch from the 20Ω PFN Marx to the ∼2kΩ class diode impedance and helps maximize the voltage on the diode. Note that the resistive divider shown in Fig. 3.3b is a high inductance diagnostic that produces a delayed signal and is subject to RF interference. As such, it is utilized only as a backup voltage diagnostic. The E-dot labeled in Fig. 3.3a will be explained below. Figure 3.3: (a.) The cathode test stand with labeled pulsed power components. (b.) The resistive divider inside the compensation can (comp. can). 41 3.1.3 Crowbar and associated diagnostics The length of the voltage pulse is determined by a spark gap triggered crowbar capable of reducing the voltage pulse to 0.3µs. An image of the inside of the crowbar with the high voltage input and output, the spark gap, the current monitor, and other relevant diagnostics pointed out is shown in Fig. 3.4a. The current in the crowbar is measured with a Pearson model 110A 20:1 transformer [108]. This current transformer consists of a hollow iron core, called the primary winding, and wire wrapped around the core, referred to as the secondary winding. The conductor carrying the current passes through the center of the iron core, initiating a magnetic field in the primary winding. This field then generates a current in the secondary winding, proportional to the current in the conductor. Unlike the Rogowski, the current transformer’s output signal does not require processing from an external hardware integrator. The extracted current waveform for the crowbar is shown in Fig. 3.4b. At t ∼ 700ns, the crowbar breaks down resulting in the immediate rise in current. Once the crowbar breaks down, the voltage pulse no longer passes through the crowbar and into the diode. The crowbar breakdown delay determines the length of the voltage pulse that passes to the diode, thus controlling the current pulse length. A comparison of the PFN current for two different crowbar breakdown times is shown in Fig. 3.5. The crowbar delay, digitizers, and delay generators are all controlled and monitored using the Data Acquisition, Archival, Analysis, and Control (DAAAC) package from Voss Scientific. This software is also used to monitor the output signals from all diagnostics and perform signal processing (such as numerical integration) in real time. 42 Figure 3.4: (a) Image of the crowbar with labeled diagnostics (b) Crowbar current collected with a Pearson transformer (Shot 8075) where the pulse is crowbared at t ≃ 700ns. Figure 3.5: The PFN current at a 40kV charge with crowbar breakdown at ∼1400ns (shot 9768) and with crowbar breakdown at ∼ 400ns (shot 9770). 43 3.2 Current and voltage diagnostics 3.2.1 B-dots The beam current is measured with inductive diagnostics called B-dots [109, 110, 111]. The B-dots work similarly to the Rogowski coil described above and are used to monitor the extracted current. A schematic of the process is outlined in Fig. 3.6a. The electron beam current generates an azimuthal magnetic field (Bθ), which in turn induces a voltage in the B-dot that is proportional to the rate of change in current, following the relationship in Eq. 3.1. The B-dots used on the test stand, pictured in Fig. 3.6b, utilize a balanced loop design chosen to limit the background signal resulting from electron impact [109]. The loop is made of two pieces of a semi-rigid coaxial cable, and the center conductors are soldered to one another midway through the loop. Figure 3.6: (a) B-dot measurement method. (b) Differential B-dot. Each B-dot detector produces two output signals. The first represents the positive rate 44 of change in the magnetic flux in addition to any common modes that arise including direct electron impact [109]. The second signal represents the negative change in flux plus the common modes. Subtracting the two signals gives twice the change in flux and cancels out the common modes. The initial output signal for the B-dot detectors has units of Volts. The signal, like the Rogowski coil, must be integrated either numerically or with an external hardware integrator. The scaled current for each B-dot is derived from a calibration on a transmission line. 3.2.1.1 Diode B-dots As indicated in Fig. 3.1, the B-dots are deployed in two separate locations. The first set is a singular differential B-dot in the diode positioned along the +Y axis, referred to as the diode B-dot. The raw unprocessed signals for Diode B-dot 1 and diode B-dot 2 are shown in Fig. 3.7. Diode B-dot 1 must be numerically integrated and scaled by the calibration constant to be properly processed. Diode B-dot 2 passes through a hardware integrator; this signal must be scaled by the integrator’s time constant and a calibration constant. Note that the signal to noise ratio is approximately 70% lower for diode B-dot 2. Figure 3.7: Raw Diode B-dot1 (a) and Diode B-dot2 (b) waveforms. 45 3.2.1.2 Downstream B-dots and BPM array The Beam Position Monitor (BPM) is an array containing four differential B-dots all located 12cm downstream of the cathode shroud. The location of the BPM and the installation ports are shown in Fig. 3.8. The B-dots are located along +x, -x, +y, and -y axes. Taking the difference of the detectors on the x-axis and y-axis and then averaging the two resulting waveforms results in the position of the beam as a function of time [109]. Averaging the 8 signals produces the average current and takes into account the position dependence. Figure 3.8: (a) The axial location of the B-dot Array (or Beam Position Monitor (BPM)) is shown with the +/-y B-dots labeled. (b) The BPM housing is shown with the -x B-dot location labeled. A comparison between the diode B-dot and BPM array measurements is shown in Fig. 3.9. A notable difference between the two signals is the slight “pre-pulse” in the Diode B-dot. This is likely current induced on the stalk or shroud during the rise of the voltage pulse. This induced current is not extracted through the diode and therefore not detected with the BPM B-dots. The diode diagnostic is cross calibrated to the +y B-dot in the BPM such 46 that the head currents fall within ∼10%. Note that Diode B-dot 2 is a hardware integrated signal which decreases the signal to noise ratio, particularly noticeable at the head of the pulse. The pulses begin to diverge throughout the pulse, and by the end of the pulses shown in Fig. 3.9, the difference in the signals is ∼ 17%. Figure 3.9: Overlay of Diode B-dot 1 and the BPM array average (Shot 8075). 3.2.2 E-dots Capacitive pickups called E-dots are used to passively monitor the differential voltage ( dV dt ) on a nearby electrode [111, 112]. The diagnostic function can be derived from: E = (cid:82) V dt RAeq 1 ϵ0 , (3.2) where R is the resistance, Aeq is the area of the detection surface, and ϵ0 is the constant. The E-dot measures dV/dt which must be integrated and calibrated to determine the voltage. For all E-dot measurements shown, the integration was performed numerically. Fig. 3.10 shows a raw E-dot waveform (a) and the numerically integrated signal (b). The maximum 47 voltage amplitude is reached at 150ns with a 15% overshoot. The voltage then decreases before stabilizing at t ∼ 300ns. Note that the rise time for the voltage pulse is ∼80-90 ns. Figure 3.10: The (a) raw and (b) processed signal from the comp can E-dot (Shot 8075). Figure 3.11: (a) Images of the E-dot. (b) The E-dot and the reference electrode used to measure the voltage in the comp. can. An image of an E-dot is shown in Fig. 3.11a. There are two deployed E-dots on the diode test stand, as referenced in Fig. 3.1. The first E-dot is located in the comp. can and monitors the differential voltage on the reference electrode, shown in Fig. 3.11b, which is electrically connected to the cathode stalk and ballast resistor. The second measurement is taken in the diode such that the E-dot is aligned with the edge of the cathode shroud. 48 Without emission, the E-dots agree within 2% and were both calibrated over a wide range of voltages with a known load [46]. This is shown in Fig. 3.12a for a maximum voltage of ∼105kV. During emission, the signals begin to diverge after ∼500ns, as demonstrated in Fig. 3.12b for Vmax ∼ 275kV. The E-dot located in the diode is subject to charge collection that compounds throughout the pulse. However, the E-dot located in the comp can is not subject to external fields and does not exhibit charge collection. As a result, the difference in signal increases throughout the voltage pulse with a percent difference of approximately 6% at the end of the pulse. The difference between the two diagnostics worsens with an increase in pulse length and PFN charge. Figure 3.12: Overlay of the processed waveforms for both E-dots (a) without electron emis- sion (Shot 8023) and (b) with electron emission (Shot 8075). 3.3 Current density and emission diagnostics 3.3.1 ICCD imaging There are three distinct imaging paths on the cathode test stand: one imaging the cathode, one for AK gap imaging, and one to image the current density diagnostic. Imaging is per- 49 formed with PI-MAX4 Intensified Charge-Coupled Devices (ICCD) [113]. In the simplest terms, an ICCD converts photons into to an electronic signal and produces an image. An image intensifier consists of a photocathode and a microchannel plate (MCP). When a pho- ton impacts the photocathode of the image intensifier with an energy in excess of the work function of the photocathode material electrons are produced These electrons multiply while they are accelerated down the micropores of the MCP by the bias voltage on the MCP. These electrons are then accelerated to the phosphor which subsequently produces the image cap- tured by the CCD. Each PI-MAX4 camera has a 1024×1024 pixel array with 12.8×12.8µm pixels. The camera has a frame rate of 32MHz and a 16-bit digitization, producing high resolution images with gate widths as low as 3ns. 3.3.1.1 Cathode imaging The ICCD focused on the cathode measures any light emitted in the cathode geometry. In the case of this dissertation with a velvet cathode we measure light emission from the ionized monolayers of water vapor, Hα [33]. These are also referred to as the emission centers by Ref. [87]. The distribution of these emission centers can be used to infer the current density on the cathode. The camera is mounted at a 33-degree-angle and utilizes an external turning mirror and the polished surface of the anode shroud as reflecting surfaces (imaging path shaded in red on Fig. 3.13). A raw image with reference dimensions for a 15-mm-diameter cathode is shown in Fig. 3.14a. Due to the mounting angle, the cathode images are post-processed and scaled by a factor of 1.8 in the x-direction. The calibrated experimental images, like that shown in Fig. 3.14b, are cropped such that only the velvet surface is visible. The light shown on the experimental images is a result of the emitted Hα light (men- 50 Figure 3.13: Cathode imaging path. Figure 3.14: (a) Raw spatial image with imaging area in dotted red rectangle. (b) Calibrated experimental image 7247. 51 tioned above) on the cathode surface [33]. Images show various emission centers, typically concentrated on the outer edge of the emission surface. Details on these experiments are presented in Ch. 5. 3.3.1.2 AK gap imaging The AK gap imaging path, shown in Fig. 3.15, utilizes an external turning mirror to measure the growth of the cathode plasma throughout the current pulse. The ICCD is typically paired with a 105-mm Nikon lens with additional spacers inserted in order to shorten the overall working distance and improve the magnification. The camera configuration changes between operation days to suit experimental needs. The gate width is typically set to 200ns due to the lack of light intensity and expansion of the plasma in the axial direction. Figure 3.15: AK gap imaging path. A raw image with reference dimensions is shown in Fig. 3.16a where the full AK gap is 52 visible. The anode shroud is on the left and cathode shroud on the right. In post processing, the image is flipped 180-degrees horizontally and cropped to the red rectangle, producing an image like Fig. 3.16b. This experimental image was taken at 164kV with a current of 182A. The increased intensity represents the plasma plume, which is approximately 3-mm-wide. Details on the AK gap imaging results and the extracted expansion velocity are presented in Ch. 7. Figure 3.16: (a) Raw spatial image with imaging area in dotted red rectangle. (b) Calibrated experimental image 9096. 3.3.1.3 The current density diagnostic A popular way to measure the current density of an electron beam is to implement an inva- sive screen diagnostic such as fluorescent or scintillation screens [89, 94], optical transition radiation (OTR) [114, 115, 116], and Cherenkov emitters [95, 96, 97, 98]. The choice of diag- nostic method is largely based on the beam energy and experimental needs. The experiments described throughout this thesis focus on current density measurements taken with either 53 scintillation screens or Cherenkov emitters. Scintillation occurs when a charged particle or high energy photon collides with a material called a scintillator and emits either ultra-violet or visible light. Cherenkov emission physics was detailed in Ch. 2. Current density measurements for electron beams produced with these methods are highly affected by the electron-material interactions outlined in Ch. 2. These interactions can confuse the measured distribution on the diagnostic, particularly for sub-relativistic particle beams. In order to quantify the effects of both electron scatter and Cherenkov emission and optimize the current density measurement, two primary diagnostic configurations are utilized. A critical element to both designs is an effective path to ground to terminate the electron beam and avoid charging the chosen dielectric. Both diagnostic configurations are placed in the diagnostic mount shown in Fig. 3.17a with external grounding hardware along the outer diameter. The pictured conductive mesh is not present for all experimental configurations. The mount shown holds a 4.5” diameter screen with a viewing diameter of 108-mm. There is also a separate mount with a reduced diameter of 3.7” and an 87.6-mm viewing diameter. The Cherenkov configuration (see Fig. 3.17b) pairs a Cherenkov emitter with a fine copper mesh, like that shown in Fig. 3.17a, providing a path to ground without prematurely ranging out the electron beam. This diagnostic method was shown to produce consistent beam profile measurements in the context of Ref. [98], which measured the current density of a 500keV, 30kA electron beam with a 1-mm-thick fused silica disk. Various Cherenkov materials were tested in the context of this dissertation, with varying material properties: index of refraction (˜n), atomic density, and atomic number. Selected materials are listed in Tab. 2.2. An ideal material has thresholds for Cherenkov emission and total internal 54 Figure 3.17: (a.) An image of the current density diagnostic mount with a conductive screen (fine copper mesh) and additional grounding hardware. (b.) The Cherenkov configurations (c.) The X-ray scintillation configuration. reflection that compliment the energy range of the experiment. Various configurations and Cherenkov materials will be discussed in Ch. 8. The X-ray scintillation method, Fig. 3.17c, utilizes a metal foil that is placed upstream of a scintillation screen [89, 94]. Upon impact with the metal target, the electrons scatter and range out producing a pulse of Bremsstrahlung X-rays that mimic the profile of the electron beam. The fluorescence generated by the X-ray pulse is then imaged with an ICCD. The measured X-ray induced scintillation pattern is strongly influenced by the stopping power physics described in Ch. 2, material thickness, Z, and material density [99, 100, 101, 102]. Two primary configurations will be discussed in Ch. 8: the “Aluminum Pie” and a 200-µm- thick copper foil. In both cases the foil is paired with a BC-400 [117] polyvinyltoluene-based plastic scintillator, chosen for its high light output, fast response time of 0.9ns, and decay rate of 2.4ns. See Ref. [117] for a full list of the scintillator properties. The current density diagnostic, in all configurations, is imaged with an additional PI- 55 Figure 3.18: Current density diagnostic Pi-MAX4 imaging path. Figure 3.19: (a) Raw image for Pi-MAX4 with imaging area in dotted red rectangle. (b) Calibrated experimental image 7247. MAX4 ICCD following the imaging path shown in Fig. 3.18. The raw image is pictured in Fig. 3.19a, which is cropped down to produce experimental images such as 3.19b. Note that a background subtraction is performed to eliminate any reflections seen in the diagnostic 56 mount. In addition to the PI-MAX4, the current density diagnostic is imaged with a fast framed CCD composed of 8 distinct ICCDs each capable of taking 2 images. This camera, the Simacon, follows a similar imaging path to that shown in Fig. 3.18a, except that before the second turning mirror a beam splitter is used which projects the image vertically to another pair of turning mirrors. In total, the Simacon produces 16 images of the diagnostic throughout a single current pulse. The inter-frame delay is programmable, and images have a 12-bit digitization. Due to the 300ns delay of the camera phosphor, only the first 8 images produce trustworthy data. Fig. 3.20 shows the first 8 images produced with the Simacon for a 3.7”-diameter alumina diagnostic with individual image gates of 100ns and a 0ns inter-frame delay. The images span the first 900ns of a single pulse. Figure 3.20: Simacon image for shot 7140. Each image is 100ns in width with no inter-frame delay. Images span the first 900s of the current pulse. Gain levels need to change to between experiments, particularly for the current density diagnostic camera as some materials had larger light outputs than others. To ensure consis- tency, a gain study was performed to determined the relationship between gain and image 57 Figure 3.21: (a) Images of the current density diagnostic with differing gain. All images were taken over 30ns with t = 510-540ns with a voltage of 220.1 ± 2.8kV and a current of 197.4 ± 5.1A. Shot numbers and gain are listed. (b) Intensity line-outs for each image. (c) The linear relationship between the maximum integrated intensity level and the gain. Fit is included on graph. intensity. Utilizing the current density diagnostic with a 1-mm thick silica disk paired with a fine copper mesh, images were taken with gains ranging from 10-50. The results are shown in Fig. 3.21. All images were taken over t = 510-540ns with a voltage of 220.1 ± 2.8kV and a current of 197.4 ± 5.1A. The image intensity and the programmed gain have a linear relationship at a given voltage, allowing for easy comparisons between different data sets. Note that though the temporal location is identical between images, the distributions on the current density diagnostic are not identical. These results are explained in detail in Ch. 8. 58 3.3.2 Diamond Radiation Detectors (DRDs) The DRDs are implemented throughout the test stand to monitor the excess emission and scatter. These detectors are traditionally used for soft X-ray detection. However, any radia- tion capable of producing a free carrier within the diamond will be detected [118, 119]. Any photons with energies greater than diamond’s bandgap, 5.5eV, will be detected including X- rays, gamma rays, and ultraviolet radiation. These devices can also be used to detect high energy particles such as neutrons, α particles, pions, or electrons [120, 121]. The mechanism for detection is independent of radiation or particle type. The diamond is placed between two metal electrodes where an external voltage is applied, producing an electric field across the detector. When the radiation is absorbed by the diamond, free electrons are created that then travel through the material and conduct current [118, 119]. The signal is proportional to the photon or particle flux. When considering a DRD for radiation detection, it is crucial to examine the absorption rates for diamond [122, 123]. Fig. 3.22a demonstrates the percentage of photons that are absorbed by 1-mm-thick diamond as a function of photon energy in keV. The absorption rate is greater than 70% when Eγ <∼ 7keV . As the photon energy increases, the absorption rate decreases. For Eγ > 30keV , the absorption rate is less than 5%. The higher energy photons not absorbed will pass through the diamond rather than creating an electron-hole pair and no signal will be detected. High energy electrons are capable of generating the necessary free carriers within the diamond. To isolate the electrons from possible low-energy X-rays, range thick covers or foils are placed over the detection surface. Fig. 3.22b shows the X-ray transmission for 73- 59 Figure 3.22: (a) The percentage of photons absorbed by 1-mm-thick diamond as a function of energy. (b) Electron range (red) as a function of particle energy and the percentage of X-rays transmitted in 73-µm-thick aluminum (black) as a function of photon energy. Values extracted from [102, 122, 123]. µm-thick aluminum and the electron range within an aluminum foil as a function of particle energy [102, 122, 123]. It is shown that photon energies greater than ∼ 20keV will pass through the aluminum cap and onto the diamond. The low energy photons will be absorbed by the aluminum before reaching the diamond to generate a DRD signal. When a 73-µm- thick aluminum foil was placed over the diamond surface, the signal was unchanged. To fully range out the electrons within the energy range of the experiment, foil thicknesses of over 300µm must be used. The DRDs utilized on the test bed are made in-house at LANL and the diamond collectors are 1-mm-thick and have a detection area of 2 × 3 mm2. Selected DRDs are capped with 400-µm thick aluminum while other detectors are left uncovered in order to characterize the radiation/particle type. Experiments described in Ch. 6 determined that the DRD signals are dominated by excess electron emission and electron scatter in both the diode and off 60 Figure 3.23: The test stand with DRD and B-dot locations labeled. Pictures of the DRDs are included for reference. the current density diagnostic. Detector arrays are located in the diode, in the BPM array, and in a flange downstream of the anode shroud, as pictured in Fig. 3.23. To increase signal levels on the downstream array, selected DRDs were connected to 3” vacuum cables, placing the detector in the line of the beam. The DRD configuration varies depending on experimental needs. Results and comparisons between the DRD measurements and current measurements are shown in Ch. 6. 61 Chapter 4. Numerical Simulation Tools Various tools are necessary to validate and confirm the experimental data produced on the diode test bed. The two most prominent tools are Trak and MCNP6®, which each have different applications. Trak is used to calculate the electric field ( −→ E ) and magnetic field ( −→ B ) geometries within the diode. Additionally, the code is utilized to optimize the electron beam by examining the diode geometry and to estimate beam characteristics including the beam envelope, extracted current, and beam emittance. MCNP6® is used as a tool for better understanding the physics processes in the current density diagnostic (Ch. 8). Throughout this chapter, I will briefly discuss how each code operates and the applications relevant to the experiment. Explanations for each code are derived from their respective manuals (Trak: [48], MCNP6®: [49]). 4.1 Trak The beam dynamics in a diode cannot be accurately predicted through analytical methods such as the envelope equation described in Eq. 2.20. As such, computational methods are necessary to explore the beam characteristics as it travels through the diode [124]. In this work, calculations concerning the beam dynamics and beam characteristics for a given diode geometry were performed using Trak. Trak [47, 48] is a finite element code used to calculate the orbits for charged particles. The code is versatile, handling design applications such as ion sources, accelerators, and vacuum tubes [47]. The program is particularly useful for modeling the emission and transport of high-current, space charge limited, relativistic electron beams [125, 126, 127, 128]. There are several components to the Trak package including Mesh, EStat, and Trak. 62 Figure 4.1: (a) A portion of the .MIN Mesh input file defining the cylindrical geometry of the cathode shroud. (b) A simplified version of the diode drawn in Mesh. The individual diode elements are labeled. The AK gap is set to 22-mm, the recess at 3-mm, and the emitter is 25-mm in diameter. 4.1.1 Mesh The first step in simulating the diode dynamics is defining the two-dimensional geometry in Mesh. This is completed by either using the interactive Mesh drawing editor or by creating a .MIN input text file. The code then creates elements with triangular cross- sections: called the conformal triangular mesh. The size of the triangular elements can be defined and adjusted within the .MIN file to improve the resolution along certain regions of the geometry. Selecting an appropriate element size is critical for plotting the geometry and properly calculating the electric fields and particle orbits. If the mesh size is too large or too small, certain components of the geometry may be drawn incorrectly and non-physical fields may be produced. After defining the mesh size in the vertical and horizontal plane, the user defines various 63 regions and the corresponding geometry. Note that the geometry and mesh size may be defined using either planar rectangular (x-y) geometry or cylindrical (r-z) geometry. Fig. 4.1a shows a portion of the input text file where the cathode region is being defined. The cathode is composed of various lines and arc segments and the full region can be shifted along the horizontal axis using the XSHIFT command. After the file is processed, it can be plotted in Mesh, as shown in Fig. 4.1b for the cathode test stand geometry. Note that the simulation utilizes a cylindrical coordinate system. The different regions are the cathode shroud, anode shroud, cathode plug, emission surface, diode wall, and the vacuum. 4.1.2 EStat EStat utilizes the region defined in the .MIN file and the nodes from the .MOU file to calculate the electrostatic potential lines and electrostatic fields with no beam present. In the EStat input file demonstrated in Fig. 4.2a, the user defines the potential on the electrodes. Dielectric insulators can be defined as well. For the example shown, the potential is set to 250kV on the cathode, cathode plug, and emitter regions. No potential is applied to the anode or diode wall. The electrostatic potential is defined through Poisson’s equation, which for ideal di- electrics is written as: ∇ ∗ εr∇ϕ = − ρ ϵ0 , (4.1) where εr is the relative dielectric constant and ρ is defined as the volume charge density. The electric field can be related to the potential by E = −∇ϕ. 64 (4.2) Figure 4.2: (a) A simplified example of a .EIN EStat input file. A potential of -250kV is placed on the cathode shroud, cathode plug, and emitter. (b) The absolute electric field with no beam present for the diode plotted in EStat. (c) The potential lines with no beam present calculated for the diode plotted in EStat. This analytical method is used to calculate and model the electric field on each node defined in the Mesh .MOU output file. The calculated electric field and potential lines for the diode configuration are shown in Fig. 4.2b and c. The average electric field applied to the emitter face, calculated through EStat, is ∼60kV/cm. 4.1.3 Trak Finally, Trak calculates the space charge limited emission from the emission surface defined in the input file. It also calculates the particle orbits and the self induced electric fields based on the EStat solution. The Trak .TLS output file lists the space-charge limited current for each iteration, the emittance, beam divergence, the current density at a given axial location 65 Figure 4.3: (a) An example .TIN Trak input file for the diode. (b) The particle trajec- tory/orbits and potential surfaces calculated and plotted in Trak. as a function of the radial location r, and radius at a z-location defined in the Trak input file. The orbits and beam loaded potential lines for the simplified diode example are shown in Fig. 4.3. Note that the electric fields and potential lines calculated in Trak will differ from the EStat calculations due to fields generated by the electron beam that affect the fields within the diode. Trak calculates the particle orbits by solving the relativistic equations of motion listed in Ref. [47]. Trak can operate in various modes defined in the input file: Field, Track, SCharge, RelBeam, FEmit, or Plasma [48]. Simulations concerning the cathode test stand are performed in RelBeam mode, defined with the PARTICLES RELBEAM command in Fig. 4.3a. This tracking mode takes into account the beam-generated magnetic fields on 66 the electric field mesh when γ > 1 [126]. The emission off the cathode, defined with the EMIT command, operates in the space charge limited regime and the current density is calculated following the Child-Langmuir law discussed in Ch. 2. For additional details on the RelBeam tracking mode, the emission definitions, and other operation modes in Trak, see Ref. [48, 126]. The particle orbits plotted in Fig. 4.3b demonstrate interesting beam dynamics. After the beam is generated off the emission surface, the beam slightly converges. This is a result of the radial electric fields in the diode. After passing through the anode, the beam begins to diverge. This divergence is a result of the space charge effects in the beam. The beam size is dependent on the emitter diameter, the diode voltage, and the cathode recess. It is important to note that the rays shown in Fig. 4.3b do not carry equal current and therefore the density of the rays does not represent the current density [127]. 4.1.4 Optimizing the experimental geometry Trak simulations are used to optimize several components of the diode geometry such as the AK-gap, cathode diameter, and the cathode recess. This optimization process includes measuring the extracted current levels, the electric fields on the cathode face, and the current density profile at a given z-location. To explain details on the optimization process, let us look at the cathode and how changing the geometry alters the beam characteristics. The current density profile is highly dependent on the geometry and field shaping of both the cathode shroud and emitter surface. In the context of this dissertation, the current density is higher at the cathode edge due to the reduced electric field at the center of the cathode. This reduced field is a result of space charge effects. A simple way to mitigate 67 Figure 4.4: Mesh simulations for the diode showing a cathode plug recessed (a) 0-mm (flush with the cathode shroud) and (b) 3-mm. this effect is to recess the cathode into the cathode shroud, demonstrated through Trak simulations modeling the DARHT Axis-I in Ref. [127] and work in Ref. [34] discussed below. A simulation of the diode test bed with a flush cathode and a cathode with a 3-mm- recess is shown in Fig. 4.4. The corresponding extracted current density over the emission surface face is plotted in Fig. 4.5a. For the flush cathode, or no recess case, the current density on the edge of the emission surface is ∼ 118A/cm2. This is over a factor of 2 times greater than at the cathode’s center. This effect is often referred to as “edge emission” [127]. As the cathode is recessed, the edge emission effect is decreased significantly, as the potential and field on the cathode emitter face has decreased. The electric field plots for the flush and 3-mm cases are shown in Fig. 4.5b. For the flush case, there is an obvious increase where r = 1cm that does not appear for the recessed cathode. The extracted current drops from 347A in the flush case to 147A for a 3-mm-recess. Additionally, the average electric field across the cathode drops over 50% at r = 1cm. Note that the electric fields continue to drop as the recess is increased leading to a limit in the recess amount, as a certain electric field 68 Figure 4.5: (a) The current density on the cathode emitter face, calculated through Trak, for no-recess (in red) and a 3-mm recess (in green). The black vertical line represents the edge of the cathode. (b) The absolute electric field across the emission surface for each cathode recess. must be reached to initiate emission. In the case of the test bed, the electric field threshold is ∼40kV/cm. More details on emission thresholds are discussed in Ch. 5. Ref. [34] quantified the relationship between cathode recess and extracted current levels for the EPURE Axis-I diode. The injector uses a velvet cathode to produce a 2kA, 80ns elec- tron beam with a diode voltage of 3.8MeV. Simulations were performed with the relativistic 3D LSP code, and show that the current levels decrease with an increased recess. The cur- rent evolution for the injector described as a function of cathode recess can be modeled with a fourth order polynomial: I = 3408.08 − 491.40(recess) + 47.76(recess)2 − 3.07(recess)3 + 0.08(recess)4. Additionally, simulations show that increasing the cathode recess reduces the electric field at the cathode edge and reduces the hollowness of the current density profile, which agrees with Ref. [127] and Fig. 4.5. Trak is also used to quantify differences in the emission for different emitter diameters. These details will be described in Ch. 5. Other uses of this program include determining the electric field thresholds for emission (Ch. 5), calculating the plasma expansion velocity 69 (Ch. 7), verifying the expected current density levels on the current density diagnostic (Ch. 8), and calculating the expected beam emittance. 4.2 MCNP6® MCNP6®, or Monte-Carlo N-Particle, is a Monte-Carlo code developed and distributed by Oak Ridge National Laboratory and Los Alamos National Laboratory for radiation transport calculations [49]. The code uses the Monte-Carlo process, which represents the random walk of a particle as it interacts with other particles and materials. A single particle’s history is made up of several events with a certain probability. The probability of each event is determined sequentially, but Monte-Carlo computational methods can simulate several particles simultaneously. These codes then calculate the average of some aspect of the particle’s behavior specified by the user called output tallies. MCNP6® tracks over 37 different particle types, including electrons and photons. The code tracks various aspects of the particle behavior including: current, particle flux, energy deposition, particle creation methods, etc.. The particle flux is tallied on a mesh defined in the input deck. Each tally has an associated statistical error found in the output file. The output file also contains a tally fluctuation chart, with ten pass/fail conditions to aid the user in determining the validity of the results. The structure of the MCNP6® input deck is complex. The basic components of the file are listed in Fig. 4.6. First, the user must define the geometry of the problem by defining the cells and surface. The cells are defined by the intersections and boundaries of the surfaces. In the cell card, the user defines each cell by specifying the cell number, the material number, the material density, and a list of the surfaces that bound the cell. A simple MCNP6® 70 Figure 4.6: The different components of an MCNP input deck listed in order of location in the input script. Figure 4.7: A simple input geometry shown in the MCNP6® plotter: a 600-µm-thick alu- minum disk is placed in front of a 700-µm-thick plastic scintillator, each 1-mm in diameter. The cells and surfaces are labeled for reference. Note that the numbers assigned to each cell and surface are arbitrary. 71 geometry is shown in Fig. 4.7, where a 600-µm-thick aluminum cylinder has been placed in front of a 700-µm-thick plastic scintillator. Note that the numbers assigned to each cell and surface are arbitrary. The Al foil (the magenta rectangle) and the plastic scintillator (the blue rectangle) are two individual cells. The particle importance is also defined in the cell card. If the importance is set to 0, the particle history will no longer be calculated once entering that region. The surface card defines the boundaries of the cells, as shown in Fig. 4.7. There are various types of surface geometries that can be used in MCNP6®, which are defined in the user manual [49]. Following the surface card is the data card, which holds various definitions. First, the mode definition signifies what particles the user is concerned with throughout the problem. In the context of this dissertation, mode p e (photons and electrons) will always be used. MCNP6® allows the user to define different aspects of the particle source without changing the general structure of the input deck. After defining the particles of interest, the user can identify what scattering and production processes should or should not be enabled. Let us look closer at the electron input, or the PHYS:E card. There are 15 total inputs, one of which being an unused placeholder. The different inputs, in order, are: 1. emax : This refers to the upper limit on the electron energy. 2. ides: This input controls the production of electrons by photons. If the value is 0, this production method is turned on. If ides = 1, the production of electrons by photons is turned off. This secondary electron production method is enabled for electron scatter simulations. 3. iphot: This controls photon production through electron interactions. If iphot = 0, 72 the production method is enabled. If the value is equal to 1, photon production by electrons is disabled. For electron scatter problems, iphot = 0. For simulations focusing on Cherenkov production, iphot = 1. 4. ibad : This value controls the bremsstrahlung angular distribution. If ibad = 0, the full bremsstrahlung tabular angular distribution is used. If ibad = 0, the simple angular distribution approximation is used. The default value is 0. 5. istrg : This value controls electron straggling. If istrg = 0, the sampled value straggling method is used to compute energy loss at each collision. When istrg = 1, the expected value method is used at each collision. The default value, 0, is used for the simulations described in this thesis. 6. bnum: The bnum value controls the creation of bremsstrahlung photons. When bnum = 0, bremsstrahlung photons are not produced. When bnum is greater than 0, the code will produce bnum times the analog number of bremsstrahlung photons. For electron scatter problems, bnum = 1, which is the default value in MCNP6®. 7. xnum: This controls the electron-induced x-rays produced on each electron sub-step. When xnum = 0, these photons will not be produced. If xnum > 0, the code produces xnum times the number of electron induced X-rays. 8. rnok : This controls the creation of knock-on electrons. Knock-on electrons will not be produced when rnok = 0. If rnok > 0, rnok times the analog number of knock-ons will be produced. For problems concerning electron scatter, knock-on production is enabled with rnok = 1. 73 9. enum: This represents the generation of photon-induced secondary electrons. This secondary electron production method is disabled if enum = 0. If enum > 0, enum times the analog number will be produced. The default value of enum = 1 is typically used throughout this thesis. 10. numb: This controls bremsstrahlung production on each substep of the problem. Analog production is used when numb = 0. If numb > 0, bremsstrahlung is produced on each substep. For electron scatter problems, numb = 1. 11. i mcs model : This represents the choice of Coulomb scattering model. Angular deflection is used when the value = -1. If i mcs model = 0, the standard Goudsmit- Sanderson angular deflection method is used. This is the default value for MCNP6® and throughout this thesis. 12. mode electron elastic: This controls the electron elastic cross section for single event transport. Large angle scattering is used if the value is set to 0. Total elastic cross section is used if the value is set to 2. The default value of 0 will always be used. 13. J : This is an unused placeholder that must be included in the input definition. 14. efac: This controls the stopping power spacing. The default value of 0.917 is always used. 15. electron method boundary : This represents the energy (in MeV) in which the code begins to transport electrons by a condensed history algorithm. Below this value, single event transport is used. This value will vary based on the problem. 74 16. ckvum: This is the value used to scale the Cherenkov production. This value will vary based on the simulation, but is typically set to 0.001. The maximum value is 1. For more information on source definitions and implemented scattering methods, see Ref. [49]. The different processes can be enabled or disabled depending on the desired information. After the PHYS:E definition, the source energy and particle number are defined. Finally, the user defines the tallies of interest mentioned previously. MCNP6® is used throughout the dissertation to replicate and analyze the processes discussed in the later sections of Ch. 2. The simulations performed are used to validate and further understand measurements made on the current density diagnostic. The simulation geometry is kept simple: a pencil electron beam interacts with a given material (either a metal foil, a scintillator, or a Cherenkov emitter). When running simulations, there are two primary setting configurations concerning the scattering and particle production processes. For each, the pencil beam is composed of a certain number of electrons with a defined energy. However, in one set of simulations, used for the X-ray scintillation experiments, all secondary processes listed above are enabled. To understand Cherenkov effects, all secondary processes other than Cherenkov photon production are turned off. This is to focus on the Cherenkov production as a function of electron beam energy. Without the interference from other particle creation methods, we can confirm Snell’s law and verify the Cherenkov and total internal reflection thresholds. 75 Chapter 5. Emission Characterization Different methods were used to characterize various aspects of the electron emission off a vel- vet surface on long time scales, including: cathode conditioning details, how the morphology of the velvet evolves throughout shot lifetime, the electric fields necessary to initiate emis- sion, and the total emission area. Several emission details are dependent on the total area of the emission surface: the extracted current, measured current density, and the emission threshold. The emission details for a given cathode size evolve throughout the cathode’s lifetime, thought to be partially due to changes in the diode vacuum pressure. These details are presented below. Some of the data presented here is an extension of the physics observed and published in Ref. [46]. 5.1 Conditioning New velvet cathodes must be conditioned before rigorous operations. Conditioning, as de- fined in Ref. [30], is the process of removing surface contaminants from the sample. The conditioning process depends on the overall field strength and maximum current levels. On the cathode test stand, new velvet samples may not emit until the maximum PFN charge (75 - 80kV) is reached, though this is dependent on the geometry. Additionally, it may take several shots at a given voltage for the emission delay, rise-time, and head current levels to stabilize. For the cathode test bed, the velvet is conditioned at the beginning of every operation day by taking several shots at a low voltage. The PFN charge voltage is then slowly increased until the rise time of the current pulse and the head current are stabilized. This stabilization typically occurs for a PFN charge of 50 - 55kV, which corresponds to a maximum diode 76 voltage of 170 - 200kV and electric fields of ∼50-60kV/cm. In this section, we will first introduce the overall electric field thresholds for electron emission. We then discuss the differences in emission delay and how this evolves as the diode voltage increases. Finally, we discuss the effects of vacuum pressure on the emission and the morphological changes of the velvet sample as the shot number increases. 5.1.1 Electric field thresholds The emission threshold, Ethresh, is defined as the electric field on the cathode face that must be reached or exceeded for electron emission to be initiated. Field thresholds are dependent on diode voltage and cathode size and may vary slightly between shot days. To discuss Ethresh in detail, we first discuss the definition of emission delay relative to voltage application and how the field thresholds are calculated. Fig. 5.1 shows the diode voltage and extracted current as a function of time for seven different PFN charges. Data was produced with a 15-mm-diameter cathode and the vacuum pressure was 4.7 × 10−7 Torr before the first shot. Note that with an increase in voltage, the current increases and the delay in emission is reduced. The decrease in emission delay as a function of diode voltage is highlighted in Fig. 5.1c and d, where the waveforms are cropped to the first 300ns of the voltage pulse. In general, an increase in voltage results in earlier emission. The emission turn-on is the temporal location in which the current reaches approximately 10% of the head current value, relative to the start of the voltage pulse. The emission delay is noted on Fig. 5.1c with solid data points to highlight the change in delay as a function of diode voltage. The difference in the temporal location where the voltage reaches 10% of the peak value and the emission turn-on is referred to as the emission delay. 77 Figure 5.1: The (a,c) voltage and (b,d) extracted current waveforms generated by a 15-mm- diameter cathode at various PFN setpoints. The solid data points in (c) denote the temporal location of the beginning of the current pulse. All data extracted from 221201 operations. Ethresh is calculated by taking the diode voltage value at the start of emission and eval- uating EStat or Trak simulations with the appropriate geometry for the given voltage. The average field on the cathode face is then extracted from EStat. Fig. 5.2a shows the corre- lation between the emission delay and the PFN charge and Fig. 5.2b shows the correlation between the emission delay and Ethresh for a 15-mm-diameter cathode. The measured diode vacuum pressure was 7.12 × 10−7 Torr during operations. The emission delay decreases lin- early from 35kV to 65kV, as shown in Fig. 5.2a. The delay begins to level out at the higher voltages. The highest error in the emission delay appears for the 35kV set-point and the 78 55kV set-points. Figure 5.2: The emission delay plotted for the 15-mm cathode for 230426 operations. The thresholds and other emission details for the same cathode on 221201 can be found in Ref. [46]. The relationship between the emission threshold, Ethresh, and the emission delay is not a linear relationship, as demonstrated in Fig. 5.2b. Let us examine Fig. 5.1c. Note that the voltage waveforms reach Vmax at differing temporal locations and that each pulse has an inflection point approximately 100ns after the beginning of the pulse. The variation in the emission threshold and non-linearity in the correlation with emission delay is due to the 90ns voltage rise-time and the profile of the rise of the voltage pulse. It is important to note that the trend varies slightly between operation days, and the error is increased at lower diode voltages. Emission details for the 15-mm-diameter cathode on a different operation day can be found in Ref. [46]. The trend is similar, but the thresholds are increased and the error in the emission delay is increased. 79 5.1.2 Current rise time The emission threshold and PFN charge voltage also play a role in the rise-time of the current waveform. The current rise-time is defined similarly to the voltage rise-time: the difference in the temporal location between where the waveform reaches 90% and 10% of the head value. An interesting feature in the data produced on the cathode test stand is that the shape of the current rise changes with the charge voltage. To explore this, we direct our attention to Fig. 5.3, which demonstrates the rise of the voltage and current pulses for three charge voltages: (a) 35kV (Vmax ≃ 125kV ), (b) 50kV (Vmax ≃ 180kV ), and (c) 75kV, (Vmax ≃ 275kV ). Note that the maximum spread in the voltage waveforms from the earliest to latest shot ranges from 2.5 - 12.5ns. Additionally, the general shape of the voltage pulse is unchanged. The spread in the profile of the current rise has a clear dependence on the charge voltage and emission voltage. At the lowest charge voltage, Fig. 5.3a, the current has a mean rise time of 27.7 ± 10.9ns, as noted with the shaded region in both the current and voltage waveforms. Note that emission begins after the voltage overshoot. The rise-time decreases between charge voltages of 45 -50kV. Fig. 5.3b demonstrates the 50kV case, showing an average rise-time of 10.6ns ± 0.8ns. The cathode begins emitting ∼20ns before Vmax, which results in a monotonic current rise-time. As the charge voltage increases, emission begins earlier in the voltage pulse. At the highest set-point, shown in Fig. 5.3c, the rise-time increases to 61.25ns ± 2.1ns. Rather than a linear increase, the current waveforms at high voltage have a fast initial increase, a slight inflection where the current is approximately half of its head value, and 80 Figure 5.3: The voltage (top) and current (bottom) waveforms over the first 300ns of the voltage pulse at three different PFN charge voltages: (a) 35kV, Vmax ≃ 125kV (b) 50kV, Vmax ≃ 180kV (c) 75kV, Vmax ≃ 275kV . All data was compiled from the 230426 and generated with a 15-mm-diameter cathode. The shaded region represents the current rise- time. then increase again before reaching the head current of ∼150A at 173ns. This trend of a slower rise time is witnessed for charge voltages ≥ 60kV, as shown in Fig. 5.1d. This is due to the inflection in the voltage waveform where t ∼ 100ns. At these charge voltages, emission begins when V < Vmax, as shown in Fig. 5.1c, and the continuous increase in V results in a non-monotonic current rise, as demonstrated in the shaded regions of Fig. 5.3c. The changes in rise-time as a function of emission and charge voltage result in the corre- lation plots shown in Fig. 5.4. Note the increase in the y-axis error bars in Fig. 5.4a after the charge voltage exceeds 50kV. This is a result of the inflection in the voltage waveform and the resulting change in the shape of the current waveform described above. For low charge voltages, the emission delay and current rise-time vary between shot days 81 Figure 5.4: The current rise time as a function of (a) PFN charge and (b) the emission threshold. Data compiled from the 230426 data set and generated with a 15-mm-diameter cathode. and, in some cases, between shots during the same operation period (witnessed in Fig. 5.3a). This trend and large spread in emission delay is due to the cathode conditioning process. On the diode test bed, the cathode must be conditioned at a low voltage at the beginning of operations. For the lowest charge voltages, the cathode is still conditioning and the emission is unstable, resulting in large error similar to that shown in Fig. 5.4 for the 35kV PFN charge. The shape of the cathode rise is also dependent on the cathode size and the amount of shots taken with a given sample, known as the shot lifetime. 5.1.3 Vacuum pressure effects Vacuum pressures within the diode are P < 1.5 × 10−6 Torr. The pressure during operations depends on several factors: external temperature, new diagnostics, the amount of time the system has been under vacuum, and the material chosen for the current density diagnostic. We evaluated the correlation between the diode vacuum pressure and changes in the emission characteristics. Six operation days are listed in Tab. 5.1, all utilizing the 25-mm-diameter 82 cathode, are with the lowest emission threshold, the emission delay for a 75kV PFN charge, and the current rise-time for a 75kV PFN charge. The corresponding waveforms are shown in Fig. 5.5. Note that the crowbar breakdown delay is intentionally varied between shot days and the decreased pulse lengths for 07/24/24 and 09/03/24 are not a result of the vacuum pressure. Table 5.1: The vacuum pressure on a given shot day and the emission threshold, emission delay, and rise-time for the 25-mm diameter cathode. Vacuum pressures listed were taken before the first shot and varied slightly throughout operations. The emission delay and current rise-time are averaged for the 75kV PFN set-point (Vmax ≃ 275kV ). The listed emission threshold is the minimum value for that shot day. Date Vacuum Pressure [Torr] Ethresh [kV/cm] Emission delay [ns] Current Rise Time [ns] 04/04/2024 7.04 × 10−7 41.05 ± 0.61 55.09 ± 2.05 48.13 ± 2.01 05/10/2024 4.72 × 10−7 40.78 ± 0.33 55.75 ± 1.62 48.13 ± 2.90 05/28/2024 8.19 × 10−7 45.93 ± 0.55 67.50 ± 1.82 36.88 ± 2.12 06/13/2024 7.20 × 10−7 40.94 ± 0.43 58.88 ± 1.20 46.13 ± 1.36 07/24/2024 9.01 × 10−7 47.13 ± 0.68 61.00 ± 3.63 41.38 ± 2.91 09/03/2024 1.01 × 10−6 41.00 ± 1.62 50.83 ± 3.55 50.83 ± 0.36 Ave ± σ 7.71 × 10−7 ± 1.86 × 10−7 42.81 ± 2.80 58.46 ± 5.46 45.06 ± 5.05 The deviation in average pressure across the six shot days listed is 24.1%. The average Ethresh across all shot days is 42.81 ± 2.80kV/cm, which is a 6.5% deviation from the mean. This small deviation shows there is little to no impact on the emission threshold over the change in vacuum pressures listed. The overall deviation from the mean for the emission delay at a 75kV PFN set-point is 9.3% and is 11.2% for the average rise-time. Again, this 83 Figure 5.5: (a) Voltage and (b) current waveforms corresponding to data presented in Table 5.1. Note that the programmed pulse length was not constant for all data sets shown. shows that there is no clear correlation between the diode pressure at the beginning of operations and the emission characteristics at this charge voltage. 5.1.4 Velvet tuft tip evolution It has been documented that the emission characteristics and morphology of explosive emit- ters changes throughout shot lifetime. Comprehensive analysis has been performed on car- bon fiber cathodes using a Scanning Electron Microscope (SEM). Ref. [129] shows that after 1.6 million pulses with 4.5ns duration and voltage amplitudes ranging from 250-260kV, the height of a carbon fiber decreases by 0.6mm and the structure of each fiber is dramatically altered due to the ablation of the individual fibers. Ref. [130] tested three different car- bon fiber cathodes: bare unimodal, bare bimodal, and CsI-coated bimodal. The CsI on the tip of the coated fibers ablated after the first few pulses in the conditioning stage. After 10000 pulses with a 100ns pulse length and voltages of 250kV, the bare unimodal and the CsI-coated bimodal saw a decrease in cathode performance, i.e. a decrease in extracted current, increase in turn-on time or emission delay, and increase in field threshold for explo- 84 sive electron emission. However, the bare bimodal cathode saw an improvement in electron emission. Studies from [87] show that for an AK gap of 30mm, emission area of 100cm2, and voltages of 200kV, carbon fiber cathodes saw a 9% reduction in measured current from 100 to 10000 pulses. Though cathodes composed of carbon fibers and carbon fabric did not show dramatic differences, velvet cathodes showed increase in emission delay as the shot number increased. The degradation of velvet, along with materials such as corduroy, are likely due to the melting of fibers due to surface flashover. Similar patterns were witnessed with the cathode test stand. A 15-mm-diameter velvet cathode was utilized for over a year of operations, producing over 1300 emission shots with over 500 shots at diode voltages above 250kV. The dominant pulse length for these shots was 0.5µs, with a significant number of 1µs pulses and 1.5µs pulses. One particular shot, taken after nearly 500 high voltage pulses, demonstrated extreme excess emission in the current waveform and large amount of beam loading in the diode voltage. Following this pulse, the emission patterns began to degrade and the extracted current at the head of the pulse decreased by 43%. These pulses are shown in Fig. 5.6. Note that Shot 7745 is considered normal emission for this cathode size: the cathode was fully conditioned and the emission for that operation day was within reasonable error. The emission centers measured on the cathode ICCD also captured changes after 500 high voltage shots were exceeded, as demonstrated in Fig. 5.7. Both shots were taken at t = 258ns with a gate width of 10ns and gain of 30. Shot 8344 has a decreased illumination area and the emission centers are exclusively toward the +y portion of the emitter. This trend continued for all following shots at all operation set-points until the cathode removal 85 shortly after. Figure 5.6: (a) The voltage waveforms and (c) the current waveforms for a 15-mm cathode at different moments throughout shot lifetime. Figure 5.7: Cathode images before (Shot 7745) and after (Shot 8344) the 15-mm cathode had reduced performance. Both images were taken at t = 258ns with a gate width of 10ns and a gain of 30. To explore the possible causes of the emission changes, Scanning Electron Microscope (SEM) images were taken with a Thermo FEI Quattro SEM [131] to document the morphol- ogy of various velvet samples. Images of a new black velvet sample, considered the baseline 86 for all measurements, for magnifications ranging from 50× - 1500× are shown in Fig. 5.8. The average tuft size is 20µm and the tuft density is ∼220 tufts/mm2. All imaging was completed with a low vacuum detector, a 30kV accelerating voltage, and a current of 0.78pA in 1.5 Torr of water. Imaging resolution is 3072×2048 and the magnification ranges from 50× to 2500×. Figure 5.8: SEM images of a new velvet sample at (a) 50× (b) 250× and (c) 1500× magni- fication. Three different samples were tested with the SEM to document the morphological changes throughout shot lifetime: a fresh sample, a sample used to produce 10 shots at high voltage, and the sample used to produce 500 high voltage shots described above. In all cases, a thorough scan of the velvet was performed to determine if the blunting of the tufts is spatially dependent. Fig. 5.9 shows the various SEM images for each case with a magnification of 1500×. Each image was taken at similar spatial location: approximately halfway between the center and edge of the emission surface. For the fresh sample, shown in Fig. 5.8 and Fig. 5.9a, the majority of tufts appear freshly cut with minimal blunting. After analyzing the produced images, it was observed that 32% of the tufts had some type of deformity, defined as any blunting, rounding, splitting, or fraying of the tuft. This likely results from the production process for velvet and the transport of the sample. 87 Figure 5.9: Three SEM images at different points in a cathode’s conditioning process: (a) new sample (b) sample after generating 10 high voltage shots during 230620 operations (c) sample after over 500 high voltage shots. The magnification for all images is 1500×. Each image was taken at a similar spatial location: halfway between the center and edge of the emission surface. A 7.5-mm-diameter velvet cathode was briefly placed in the diode test bed and produced 10 high voltage shots before its removal. The sample had not been fully conditioned and the minimum field threshold was 81.9kV/cm ± 1.5kV/cm. The average start of emission was 163.4 ± 19.3ns. SEM imaging, Fig. 5.9b, shows a deformity percentage of 41%. Though blunting is demonstrated, the percentage is too low for the cathode to be deemed fully conditioned. Fig. 5.10 shows a comparison between the waveforms for the unconditioned and fully conditioned 7.5-mm cathode. The fully conditioned cathode, which had produced approximately 50 emission shots and 20 high voltage shots, begins emission 20ns earlier than the unconditioned cathode and has a well defined current head that is 7% greater. The final image, 5.9c, shows the 15-mm-diameter cathode that produced 500 high voltage shots and demonstrated significant emission changes. SEM imaging of this sample shows that approximately 79% of the tufts are deformed. When approaching this level of deformity, it is in the best interest of the experiment or accelerator to remove the sample as the performance degrades. The excess current and extreme beam loading can be catastrophic to the diode and damage diagnostics downstream. 88 Figure 5.10: The (a) voltage and (b) extracted current waveforms for the 7.5-mm cathode before the conditioning process was complete and after the cathode was deemed fully condi- tioned. The charge voltage was set to 75kV for both cases. The under-conditioned data is a 4-shot average from 230620 operations and the conditioned data is a 5-shot average from the 230712 data-set. 5.2 Cathode light emission Imaging the cathode face provides information on various emission details, including an approximate current density at the emission surface. The intensity of the images is dependent on current, voltage, temporal location, and the diameter of the emitter. The captured cathode light is an indication of the ionized monolayers on the cathode’s surface [4, 33] and the emission centers indicate increased temperature and electron density. Cathode imaging shows several hot-spots, or emission centers, that are most concentrated on the outer edge of the velvet [87]. This is shown in Fig. 5.11a, which shows 5 images gated from t = 500 - 530ns at a 75kV charge voltage. Data is generated with a 25-mm- diameter cathode. The general emission pattern is consistent, though the location and intensity of the individual emission centers may vary, as shown with the intensity profiles in Fig. 5.11b. Large, high-intensity emission centers are shown on the +x side of the cathode 89 Figure 5.11: (a) Cathode images taken at a 75kV charge voltage. For each image, the camera is gated from 500 - 530ns. The average current is 249.8 ± 10.2A and the average voltage is 232.4 ± 0.96kV. (b) The intensity profile projected onto the x-axis for each shot. (c) The average current and voltage waveforms overlaid with the maximum integrated intensity across each cathode image. All data is generated with a 25-mm-diameter cathode and compiled from the 240613 data set. across all images. In some cases, such as shot 9871, there exist certain emission centers with dramatically higher intensity levels than the rest of the emission surface. The average current and voltage for this data set are shown in 5.11c along with the integrated intensity for each image. The average current over this temporal location is 249.8 ± 10.2A and the diode voltage is 232.4 ± 0.96kV. The variation in integrated intensity is 13%, with an average of 2.69 × 106. This points to the stochastic nature of the emission centers. However, the location of the emission centers and slight change in intensity does not alter the measured current, as the variation in average extracted current corresponding to the images shown is <5%. 90 The cathode light emission levels generally increase as a function of applied electric field, as shown in Fig. 5.12a. Additionally, an increase in the applied field results in an overall increase in the uniformity of the emission centers. Each image was taken approximately 200ns after the emission delay and the camera gates for each shot are shown in Fig. 5.12b. When V = 152kV, the emission centers are concentrated on the outer edge and the overall integrated image intensity is 9.6×104. This value increases to 1.3×105 when V = 199kV and when V = 229kV, the measured integrated intensity is 1.6 × 105. This increase is dependent on both the current and measured voltage. The enclosed emission area and the measured current density at the emitter increase with voltage as well. At the lowest voltage setting shown, the overall emission area, or the enclosed area divided by the full area of the emitter, is 49.6%, corresponding to a current density of J = 41.9 A/cm2. At the highest set-point: the illumination percentage is 52.9% with J = 78.1 A/cm2. Additionally, the image intensity increases as a function of time for any given voltage pulse. The temporal dependence is investigated by adjusting the ICCD camera gate between shots. As emission is initiated, the light intensity is decreased. The intensity values peak at the end of the current and voltage pulses. Various images at different temporal locations are shown in Fig. 5.13a. All images were taken for a PFN set-point of 60kV with a 25-mm- diameter cathode. The number of emission centers increases as time progresses. Early in time, the primary emission centers are located on the outer edge of the velvet surface. As time increases, these centers begin to fill in the full cathode area. Fig. 5.13b shows the integrated cathode image intensity plotted as a function of time. Each data point corresponds to a different shot. For reference, the data points are overlaid with the current and voltage from a single shot. Note that for each cathode image the diode 91 Figure 5.12: (a) Cathode imaging at different voltage set-points. (b)-(d) the current and voltage waveforms for each image and the corresponding camera gate. For each image, the camera gate was set to be approximately 200ns after the emission delay. All data was compiled from the 240404 data set and generated with a 25-mm-diameter cathode. voltage set-point remained constant. However, early images are gated during the 15% voltage overshoot. The overall intensity increases by 205% from 165ns to 405ns and the intensity increase as a function of time is linear, following the trend: cathode intensity ∼ 295.9 ∗ t where R2 = 0.90 . The total illumination percentage and measured current density also increases as the pulse progresses. Fig. 5.13c shows the illumination area plotted as a function of time. The increase in emission area is in part due to the continuous charge accumulation on the velvet surface and results in an increase in the extracted current. The correlation between emission area and time, after removing obvious outliers, follows the logarithmic fit: Emission Area = 254.4 ∗ ln(t) − 1481.2 with an R2 value of 0.72. 92 Figure 5.13: (a) Cathode images taken at different temporal locations. Times listed are in ref- erence to the voltage pulse.(b) The integrated cathode light intensity for the 25-mm-diameter cathode plotted as a function of time overlaid with the current and voltage waveforms for shot 9370. The PFN charge was set to 60kV for all captured images. The imaging data was compiled from 240404 and 240510 data-sets. (c) The enclosed emission area divided by the total cathode area, known as the illumination percentage, as a function of time overlaid with the current and voltage waveforms. 5.3 Cathode plasma lifetime The cathode ICCD is used to calculate the decay constant of the hydrogen plasma formed on the cathode surface. Lifetime studies include gating the cathode camera both during and after the voltage pulse. The temporal location of the camera gates in comparison to the extracted current and measured diode voltage is shown in Fig. 5.14. All data for this study was generated with a 15-mm-diameter cathode, a vacuum pressure of 3.6 × 10−7 Torr, 93 and the maximum diode voltage was kept constant at 250kV. Crowbar breakdown was set to occur at t ≃ 710ns, resulting in a 500-600ns long current pulse with an average emission delay of t = 105.9 ± 10.4ns. All cathode images were taken over a 10ns gate with a gain of 30. In total, over 21 images at distinct temporal locations were taken to fully document the progression of the cathode plasma. Note that each image corresponds to a different emission shot. Figure 5.14: Current and voltage waveforms for shot 7702 with all camera gates (shown in red) from Fig. 5.15 plotted as a function of time. The cathode image progression is shown in Fig. 5.15. Shots where t > 710ns represent the cathode plasma after the voltage pulse is terminated. However, there is an increased cathode light intensity where t = 800ns. This is due to the slight reflection in voltage and resulting current extracted at the same temporal location. After this slight reflection, the intensity once again decreases. Intensity levels are not negligible until t = 2700ns, signifying that the cathode plasma does not fully decay until > 1000ns after the end of the current/voltage reflection. The decay constant of the cathode plasma was calculated by taking the integrated inten- 94 Figure 5.15: Cathode images taken during and after the end of the current pulse. The camera timing is listed for each individual shot. Data generated with a 15-mm cathode on 12/08/2022 shot day. The maximum voltage was 250kV (PFN charge of 70kV). Figure 5.16: Current and voltage waveforms for shot 7702 plotted along with the integrated cathode image intensity for all images taken after the end of the current pulse. The decay constant for the lower trend is τ = 0.5µs and τ = 1.0µs for the upper trend. sity of each captured cathode image. The integrated intensity value was plotted against time and an exponential fit was applied to the images taken after t ∼ 710ns, as shown in Fig. 5.16. Cathode emission is stochastic, leading to a relatively large spread in measured intensity. To take this into account, two separate fits were applied: one for the upper intensities and one 95 for the lower intensity data. The trend for the lower intensity data follows Int ∼ e−0.002x and the upper trend follows Int ∼ e−0.001x. The decay constant, τ , is calculated by taking the inverse of the exponent for each trend. The two trends give bounds for the cathode plasma decay: 0.5µs ≤ τ ≤ 1.0µs . 5.4 Varying emitter diameter Several beam characteristics are altered with an increase in the total area of the emitter. In this section, focus will be on the correlation between cathode diameter, extracted current, current density at the cathode face, and the emission electric field thresholds. Discussion on the effect of cathode size on excess emission and plasma expansion will be discussed below in Ch. 6 and Ch. 7. 5.4.1 Extracted current and current density An increase in the cathode diameter leads to an obvious increase in the extracted current measured within both the diode and BPM array. Fig. 5.17 shows the voltage and current waveforms for the three diameters. Each waveform is a 5-shot average from a given operation day. Note that the voltage waveforms are unchanged and the maximum diode voltage is 275kV. The head current increases by ∼245% from the 7.5-mm-diameter cathode to the 25-mm-diameter cathode. The current increases by 200% between the 7.5-mm and 15-mm cathode. An important feature to discuss is the shape of the current rise between each cathode. The smaller cathodes, particularly the 7.5-mm-diameter cathode, has a slow rise when compared to the 25-mm-diameter cathode. At this operation set-point, the larger cathode has a well defined head-current which drops by 5% before a steady increase at t = 295ns, mimicking 96 the shape of the voltage pulse. This is not typical for the smaller cathode sizes, which do not have a well defined current head and the current levels increase throughout the full pulse length due to the growth of the cathode plasma. Figure 5.17: (a) Voltage and (b) extracted current graphs for the three cathode diameters. The 7.5-mm data is a 5-shot average from 7/12/23 operations, the 15-mm data a 5-shot average from 12/01/22 operations, and the 25-mm data a 5-shot average from 4/4/24. All waveforms were taken with a 75kV PFN charge that corresponds to Vmax ∼ 275kV . To highlight the changes in the current density we first discuss the cathode illumination, pictured in Fig. 5.18 which shows a typical cathode image for each size. The temporal location of the camera gate varies slightly between the images, causing a discrepancy in the measured voltage value. However, all images were gated after the head of the current pulse. It should also be noted that the 7.5-mm and 25-mm cathode have a gate width of 30ns and a gain of 10 while the 15-mm-diameter cathode image has a gate of 10ns and a gain of 30. The distribution of the emission centers evolves with cathode size. For the largest cath- ode, there are multiple emission centers over the full face of the cathode, with a total illumi- nation area of 298.0mm2, 61% of the total area. The smallest cathode has larger emission centers concentrated on the outer edge of the velvet. The enclosed emission area is 26.2mm2 97 which illuminates 59% of the total cathode area. The 15-mm cathode also showcases large emission centers along the outer edge of the emission surface with a total enclosed emission area of 107mm2, 61% of the velvet surface. Figure 5.18: Cathode images for the (a) 7.5-mm-diameter cathode, (b) the 15-mm-diameter cathode, and (c) the 25-mm-diameter cathode. Images were taken at the head of the current pulse (camera timing varies slightly) and at the same PFN charge (75kV, Vmax ≃ 275kV ). Note the change in scale between images. Shot 8768 and 9686 has a camera gate width of 30ns and a gain of 10, and Shot 7573 has a gate width on 10ns and a gain of 30. Table 5.2: Current densities, emission area, and electron density for the different cathode sizes. All data was collected for Vmax = 275kV . Calculations were performed using the images in Fig. 5.18: shots 8768, 7573, and 9686. Cathode Diameter [mm] Voltage [kV] Emission Area [mm2] Measured J(x,y) [A/cm2] Beam Density [cm−3] 7.5 15 25 255.3 243.0 260.5 26.2 (59%) 107.0 (61%) 298.0 (61%) 270.6 142.45 69.9 7.55 × 1010 4.03 × 1010 1.94 × 1010 The emission area is tabulated in Tab. 5.2 along with the measured current density and estimated electron density of the beam. Both values see a general decrease as the cathode size increases. This is partially due to enhanced edge emission, which is most apparent in 98 the smaller cathode cases. This edge emission is in part due to the design of the cathode plug. For the smaller cathodes, the cathode plug is designed such that there is an exposed ring of aluminum around the velvet surface. This creates a triple point, a location where a metal, dielectric, and vacuum intersect. This triple point results in an electron avalanche on the outer edge, thus producing excess edge emission noticeable in the imaging. This effect contributes to a larger extracted current than that predicted in Trak. Com- parisons to Trak models and further explanation on the discrepancy between the simulations and experiment will be described in Ch. 7. 5.4.2 Emission thresholds Figure 5.19: The emission delay plotted as a function of the emission threshold for the 7.5- mm, 15-mm, and 25-mm cathodes. The operation dates are listed for reference. Finally, we discuss the difference in the electric field thresholds as a function of cathode size. Fig. 5.19 shows the emission delay as a function of emission threshold for each cathode. Generally, larger emission delays and higher field thresholds are seen with the 7.5-mm- cathode, with the 25-mm cathode close behind. The fastest emission occurs for the 15-mm- 99 diameter cathode, which also demonstrates the lowest Ethresh. The spread in the emission threshold is increased for charge voltages above 60kV, most noticeable for the 7.5-mm and 25-mm-diameter cathodes. 5.5 Conclusions Important details concerning the electron emission from a velvet surface include the field thresholds, emission delay, and the current density measured on the cathode face. It has been shown that these characteristics are dependent on the diode voltage and the cathode diameter. On the cathode test stand, the lowest emission threshold was observed to be 36kV/cm with the 15-mm cathode. For all cathode sizes, these trends vary between op- erational set-points but are generally consistent when comparing identical set-points from different operational days. There are observable changes in both the current rise-time and emission delay during conditioning. As the velvet material ages and the morphology of the velvet fibers changes the emission can begin to degrade. Monitoring the cathode light emission with an ICCD allows for monitoring of the current density at the emission surface. The measured current density decreases with an increase in cathode size. However, the cathode uniformity is improved for the larger cathodes. The cathode plasma has a measured decay rate in the range 0.5 - 1.0 µs. 100 Chapter 6. Characterizing Excess Emission Velvet cathodes show evidence of plasma growth [33, 34, 46, 91], excess emission [29, 46, 87], impedance collapse [4, 87, 132], and an increase in the measured gun perveance [4, 88, 89]. Excess electron emission is noticeable in the measured current and presents large transients, thought to be an arc on the velvet surface that results from large charge accumulation throughout the pulse [46]. Ref. [87] measured a similar effect with a carbon fabric cathode, collimated detectors, and a 180kV, 2kA beam extracted for > 400ns. Similar patterns are observed in Ref. [29] and the fluctuations are thought to be a result of the nature and non-uniformity of explosive emission. The excess emission, or arcing, is evident for other diagnostic measurements taken on the diode test bed and is witnessed in the voltage measurements in the form of beam loading [133]. For excess emission to begin, a given charge threshold must be exceeded, found to be 8µm/cm2 [46]. Note that this threshold has error bars as it is a stochastic phenomena. As the cathode lifetime increases emission may degrade after exceeding this threshold as seen with some data in Ch. 5. In this chapter, we characterize the charge thresholds and corresponding excess emission delay for each cathode size and discuss the statistical variation. Various methods are used to fully characterize the excess emission: including DRDs and ICCD imaging of the cathode face. Note that evaluating the excess emission with a gated camera presents statistical challenges and cannot be used as a standalone measurement. It is shown through several diagnostic methods that the appearance of excess emission and the percent increase in the intensity of the current transients is increased for the smaller cathode areas. We also discuss 101 the temporal evolution of the measured current, the calculated perveance, and the current transients for pulse durations exceeding 300ns. Results presented in Ref. [46] and this dissertation are the first detailed documentation of the temporal dynamics and statistics of the excess emission. 6.1 Long pulse emission measurements Measured pulse lengths on the cathode test stand vary from 300ns - 1500ns. As the pulse progresses, a steady increase in the current is observed as a result of the expansion of the cathode plasma [4, 34, 46, 91]. Fig. 6.1 shows the (a) voltage and the (b) extracted current generated with a 25-mm-diameter cathode and a diode voltage of 215kV as a function of time for three different pulse lengths: 300ns, 600ns, and 1100ns. Note that this pulse length is in reference to the temporal length of the current pulse. The 300ns current pulse, shown in red, does not have a significant current increase and the slope is negligible. Additionally, there is no evidence of arcing measured within the BPM array. The 600ns and 1100ns current pulses show obvious and steady current increases and dramatic excess emission, particularly evident in the 1100ns pulse shown in blue. The current transients are exacerbated later in time, exceeding 300A, and result in intense beam loading, or a fast decrease in the measured voltage. This temporal dependence will be discussed in a later section. The Child-Langmuir Law, derived in Ch. 2 (Eq. 2.5), is used to predict the extracted current density for a given diode voltage. The space charge limited current is dependent on the measured diode voltage, the emitter diameter, and the AK gap. As the gap separation 102 Figure 6.1: The (a) voltage and (b) extracted current waveforms for a 25-mm-diameter cathode with a diode voltage of ∼215kV at three different pulse lengths: 300, 600, and 1100ns. is time-dependent, we rewrite the one-dimensional Child-Langmuir Law as: J(t) = 4ϵ0 9 (cid:114) 2q me 3/2 0 V (d(t))2 , (6.1) where we consider the evolution of the gap distance, d, throughout time. The consequences of the AK-gap closure and resulting current increase observed in this experiment are detailed in Ch. 7. The relationship between the beam current and diode voltage is represented as: I = KgunV ∗ . (6.2) Rather than using the standard V 3/2 relationship defined in Child’s Law, the power is expressed as * as the beam approaches the relativistic regime [4]. For this experiment, the power relationship evolves throughout the current pulse, as 103 demonstrated in Fig. 6.2a. Three different I-V curves, or perveance curves, are shown: one for measured current and voltage 50ns after initial emission, one with values taken 100ns after initial emission, and one representing the one-dimensional Child-Langmuir law where I ∼ V 3/2. Note that the times listed are in reference to the beginning of the current pulse and the temporal location with respect to the voltage pulse will vary at each operating voltage, as demonstrated in Figs. 6.2b and c, which show the current and voltage at two different charge voltages. The values for t1 = 50ns are noted with the circular marker and the t2 = 100ns are noted with the square marker on all waveforms. The current values predicted by Child’s law utilize the diode voltage taken 50ns after initial emission. Figure 6.2: (a) The perveance curve generated for a 15-mm-diameter cathode at two different temporal locations: 50ns after emission begins and 100ns after emission begins. The 1- D Child Langmuir prediction is included for reference. At t = 50ns, the current-voltage relationship is: I ∼ V1.56. At t = 100ns, I ∼ V1.62. (b) The diode voltage and measured current for a 45kV charge voltage. (c) The diode voltage and measured current for a 75kV charge voltage. For reference, the current and voltage 50ns after emission are shown with circular markers and the values 100ns after emission are shown with square markers. The extracted current and diode voltage are collected over a wide range of charge voltages 104 and the relationship is calculated by fitting a power series model to the data. In each case, there is a clear deviation from Child’s law at both temporal locations. The measured current is 20 - 30% greater than the predicted current 50ns after emission. The current is 40 - 50% greater 100ns into the current pulse. The I-V curve evolves throughout time as well. After 50ns, shown in maroon, the relationship follows I ∼ V 1.56. The power value continues to increase as the pulse progress, and after 100ns (shown in blue) the relationship follows I ∼ V 1.62. The variation and increase in the power value is in part due to the cathode plasma expansion velocity and the subsequent AK-gap closure. 6.2 Excess emission As mentioned previously, the transients in the current waveforms are a result of excess emission and signify an arc on the velvet surface due to an accumulation of charge [46]. These transients are stochastic both in amplitude and temporal location. Excess emission in the current waveforms is generally 30% larger than the current at the head of the pulse [46]. Fig. 6.3 shows three current waveforms for each cathode diameter: (a) 7.5-mm (b) 15-mm and (c) 25-mm-diameter cathode. In each case, the diode voltage was 275kV and the measured pulse length ∼ 500ns. When comparing the data between the three emitter sizes, it is clear that the transients have increased intensity and appear more frequently for the smaller cathodes. Data generated with the 25-mm-diameter cathode generally presents low-amplitude transients, shown in Fig. 6.3c, where the largest shown transient has an amplitude 50% greater than the 210A head current. The largest transient shown for the 15-mm-cathode in Fig. 6.3b is 170% greater than the 120A head current. This difference is most dramatic for the 7.5-mm-diameter case, Fig. 6.3a, with an increase of over 200% for 105 the largest shown transient. Figure 6.3: The extracted current for a (a) 7.5-mm-diameter cathode, (b) 15-mm-diameter cathode, and (c) a 25-mm-diameter cathode. In each case, the diode voltage is 275kV and the measured length of the current pulse is ∼500ns. As demonstrated in Fig. 6.3, current transients are observed for all cathode sizes and excess emission is evident for all diode voltages. In each case, there is a general delay between the head of the current pulse and the first instance of excess emission, coined the Excess Emission delay (EE delay), shown in Fig. 6.4a. The first instance of excess emission is defined as the first prominent current transient that corresponds to a change in slope within the calculated charge waveform, as demonstrated in Fig. 6.5. The charge is calculated by integrating the current measured in the BPM array with respect to time. The larger cathode demonstrates a consistently larger avergae EE delay, at least 10% greater than the other cathode sizes at any given voltage, and the average delay ranges from 223ns to 362ns. Note that the stochastic nature of the transients leads to a rather large error at all diode voltages for each cathode size. The 25-mm-diameter cathode has an overall 27% decrease in the EE delay from a diode voltage of 160kV to 275kV. The average EE delay for the 15-mm-diameter cathode ranges from 147ns at 275kV to 236ns at a 160kV 106 diode voltage. This cathode generally produces the lowest EE delay. The 7.5-mm-diameter cathode EE delay ranges from 191ns at a 190kV diode voltage and peaks at a diode voltage of 240kV with an average emission delay of 255ns. Figure 6.4: (a) The excess emission delay as a function of diode voltage, (b) the charge threshold for each diode voltage, and (c) the surface charge density threshold at each diode voltage assuming that the emission area is 80% of the total cathode area. Note the difference in scale. Results are shown for each cathode size. 7.5-mm-data extracted from 231109, 15- mm data extracted from 221201, and 25-mm data extracted from 240404. Figure 6.5: The extracted current overlaid with the calculated charge for (a) a 45kV charge voltage and (b) a 75kV charge voltage. Both shots generated with a 7.5-mm-diameter cath- ode. The EE delay is a direct consequence of the charge threshold, shown in Fig. 6.4b. The 107 charge threshold is defined as the calculated charge at the same temporal location as the first observed current transient. As mentioned briefly above, the slope of the charge waveform increases in tandem with the appearance of a current transient. This is most obvious for high intensity transients, such as when t = 400ns and t = 600ns in Fig. 6.5a. The 25- mm-diameter cathode has a charge threshold at least 40% larger than the smaller cathodes across all operation settings, with a minimum of 24µC at 180kV. This corresponds to a charge density of 6.0 ± 1.8µC/cm2 as shown in Fig. 6.4c. This charge density was calculated following Ref. [46], and assumes that the emission area is 80% of the total cathode area. Using a general 80% emission area accounts for variation between shots and the changes resulting from an increased diode voltage. The charge threshold is minimized for the 7.5-mm-diameter cathode with an average value of ∼6µC at the lowest charge voltage. Values for the 15-mm-diameter cathode are within a similar range with a minimum threshold of ∼11µC. The largest measured charge density is shown for the 7.5-mm-diameter cathode, with values above 17µC/cm2. The average charge density for both the 15-mm and 25-mm-diameter cathodes ranges from 6µC/cm2 to 14µC/cm2 with large error bars. The large difference in EE delay and charge thresholds across cathode sizes results in the differences between the amount of excess emission instances and the amplitude of the current transients as presented in Fig. 6.3. The charge density for the 7.5-mm-diameter cathode is over 3 times larger than the 15-mm and 25-mm cathodes for a diode voltage of 275kV. This difference is thought to be a result of the cathode plug design discussed in the later sections of Ch. 5 and increased levels of edge emission. 108 6.2.1 Beam loading and impedance collapse An additional indicator of excess emission levels is the beam loading observed in the voltage waveforms, which presents a reduction in the voltage amplitude that is nearly in sync with the observed current transients. The large beam current produced in this experiment is capable of loading down the voltage from the PFN and causing a decrease in the measured diode voltage, which is described in Ref. [46]. Each measured instance of beam loading maps to a notable current transient, as shown in Fig. 6.6a for a 7.5-mm-diameter cathode. At t = 530ns, the voltage decreases by 4%. At the same approximate temporal location, the current rapidly exceeds 230A. The beam loading precedes the current transient by ∼10ns, a result of the time needed for the PFN to charge the current path [46]. The rapid increase in current and decrease in the diode voltage results in an effective impedance collapse (Fig. 6.6b), an effect frequently observed in high current diodes [4, 87, 132]. The beam impedance, Z(t), is calculated through: Z(t) = V (t) I(t) , (6.3) which follows Refs. [4] and [134]. The 15% voltage decrease at the head of the pulse combined with the increase in current results in the initial impedance drop, where Z(t) decreases from ∼ 5kΩ to 2kΩ. When t ≥ 500ns significant excess emission is witnessed in the extracted current and the impedance shows a rapid decrease to 1kΩ. Excess emission is further demonstrated through calculating the time dependent gun 109 perveance: KGun(t) = I(t) V (t)3/2 . (6.4) The above equation is derived from Child Langmuir law defined in Ch. 2 and follows calcula- tions in Ref. [4]. Kgun(t), shown in Fig. 6.6b, demonstrates a steady increase throughout the head of the current pulse and then rapidly increases by a factor of two with the appearance of the current transient and beam loading (t ∼ 540ns). Increases in perveance are observed in Ref. [88] which notes a increase by a factor of 3 over a pulse duration of approximately 1.5µs. This effect is also witnessed in Ref. [89] for current densities above 50A/cm2, with a total perveance increase of 60% throughout a 300ns pulse. However, neither case observed rapid transients like what is demonstrated in Fig. 6.6b. Fig. 6.6c further demonstrates the evidence of beam loading within the voltage waveforms by comparing the loaded voltage case from Fig. 6.6a with an unloaded case for the same diode voltage (275kV). The unloaded, or open circuit, case is acquired when emission is not achieved. The loading in the voltage waveform is evident and the pattern is nearly identical temporally to the transients observed in the current waveform, impedance, and perveance. The difference in the two waveforms is shown in magenta in Fig. 6.6d. A linear fit is applied to the unloaded case from t = 410ns - 690ns, resulting in the fit: V (t) = −226.5 − 0.03t. To investigate the beam loading effect further, the difference between the loaded and unloaded voltage and the difference between the loaded voltage and the calculated fit are shown in Fig. 6.6d. The two calculations agree within 5%, well within reasonable error. The maximum loaded voltage is over 13kV, approximately 6% of the total measured voltage at this time. 110 Figure 6.6: (a) Current and voltage waveforms produced with a 7.5-mm-diameter cathode at a voltage of 275kV (shot 8956). (b) The impedance and gun perveance (KGun) as a function of time. (c) A loaded (shot 8956) and an unloaded (shot 8482) voltage waveform. (d) The difference in the unloaded and loaded waveforms (pink) and the difference in the loaded waveform and unloaded linear fit (blue). Note the difference is scales. 6.2.2 DRD measurements The DRDs introduced in Ch. 3 are used to further characterize and monitor the excess emission levels. These detectors, all utilizing a 2mm wide x 3mm long x 1mm thick diamond collector, show transient patterns similar to those shown in the current waveforms. There are three sets of DRDs located along the test stand: one set within an angular port in the diode, one set within in the BPM array at z = 12.3cm, and finally a set downstream of the 111 current density diagnostic within a 6-cm-long angular port at z = 21cm. (see Fig. 3.23 in Ch. 3). The correlations between the measured current, measured diode voltage, and the DRDs along the test stand are shown in Fig. 6.7 for a single shot. The maximum diode voltage is 250kV and the beam was generated with a 15-mm-diameter cathode. Note the difference in the diode current and the BPM current in Fig. 6.7a. The current slope is increased for the diode measurement and the current transient at t = 660ns is 1.5× greater than the current measured in the BPM array. The diode B-dot is more susceptible to scattered electron current in the diode as it has a direct line of sight to the cathode shroud and can measure all current produced in the top portion of the diode. All DRDs shown in Fig. 6.7b have a signal just above the background levels when electron emission is initiated (t ∼ 100ns). The signal is largest for the DRDs within the BPM array. This is due to the location of the DRDs: upstream of the current density diagnostic where the electron beam is terminated. The first current transient is observed where t = 260ns, and a small transient is observed for the BPM DRD at this location. The BPM DRD has a nearly identical pattern to the current measurements, aside from a significant transient at t = 580ns that is not as pronounced in the current or voltage measurements. The diode DRD signal also mimics the pattern of the current waveform closely, with significant transients at 510ns and 660ns. The downstream DRD does not demonstrate this pattern as clearly, and has a decreased signal-to-noise ratio because it is downstream of the current density diagnostic, as discussed in Fig. 3.23. For the data set presented in Fig. 6.7, the chosen current density diagnostic was a 500-µm-thick plastic scintillator with 200-µm-thick copper foil placed upstream. To verify that the increased signal and fluctuations in all diagnostics was a result of 112 Figure 6.7: (a) Current and voltage measurements taken on the test stand for a diode voltage of 250kV. Data was generated with a 15-mm-diameter cathode. (b) Corresponding DRD signals measured in the diode, BPM array, and in the downstream flange. (Shot 7691) See Ch. 3 for more information on the DRD axial locations. excess electron emission, a filtering study was performed with the DRDs, shown in Fig. 6.8. In Ch. 2 we introduce electron ranging and in Ch. 3 we discuss how range thick aluminum is paired with DRDs in order to isolate the electron signal from possible X-ray signals. It is shown through Fig. 3.22 that 73-µm-thick aluminum will absorb X-rays with energies less than 20keV. Experiments were performed where this thickness of aluminum was placed over the diamond surface to filter out the low energy X-rays. Results show no change in the DRD signal, confirming that any measurement made with the DRDs was a result of electron detection. To prove this further, an additional filtering study was performed to confirm that the measured signal was a result of excess electron emission. This study utilized 400-µm-thick aluminum covers placed over the diamond collection surface. Fig. 6.8a shows the overlay between the diode B-dot signal and a DRD located in the diode. This DRD did not utilize an aluminum filter and is considered ‘open’. Note that the general trend in the transients between both signals is nearly identical, with notable 113 Figure 6.8: DRD signals taken throughout the diode overlaid with the corresponding current measurement: (a) the diode B-dot and an open diode DRD, (b) the BPM current overlaid with both DRDs in the BPM array, and (c) the BPM current overlaid with the signal for a DRD ∼8.5cm off center-line (solid line) and the signal for a DRD in a tube ∼17cm off center-line (dotted line). Both downstream DRDs are at z = 21cm. All data was generated with a 15-mm-diameter cathode and a diode voltage of 275kV (shot 8075). transients where t = 480ns, 545ns, and 595ns. Fig. 6.8b shows the current and DRD measurements taken within the BPM array. The DRD located on the +x side of the BPM array is open while the DRD on the -x side has a 400-µm-thick filter, or cap, over the diamond sensor. 400-µm-thick aluminum will range out electrons with energies less than ∼300keV. The DRD +X signal closely resembles the 114 current measured with the BPM array and the transients appear at the same location in both waveforms. Additionally, the “double peak” profile at t = 595ns is demonstrated in both measurements. However, the DRD on -x with the aluminum cap shows no discernible signal, signifying that the electrons were ranged out within the aluminum cap and could not be detected by the diamond. This further solidifies that the transients and fluctuations in the diagnostic waveforms are a result of excess electron emission from the velvet cathode. Finally, Fig. 6.8c shows the comparison between the BPM current and two DRDs located downstream of the current density diagnostic. Note that the current density diagnostic was fully removed for this shot set and the beam was not terminated before reaching the downstream DRDs. One DRD is placed ∼8.5cm off center-line (solid line) and is in the path of the beam while the other DRD is in a tube ∼17cm off center-line (dotted line). Both DRDs are open. This signal is 4× greater for the DRD in the path of the beam and shows intense signal fluctuations from 300ns - 450ns. A final feature to note is shape of both downstream DRD waveforms from t = 100 - 270ns. The head is well defined and has a ∼15% decrease in signal, similar to the voltage waveforms. This is thought to be due to the beam dynamics after passing through the diode, though this feature has not been fully diagnosed. 6.2.3 Optical diagnostics Evidence of excess electron emission is also demonstrated with ICCD cathode imaging. Fig. 6.9a shows a comparison between cathode images taken with a 15-mm-diameter cathode and maximum diode voltage of 250kV. The second image, shot 7691, captured an instance of excess emission from t = 648 -658ns. The corresponding voltage, current, and DRD waveforms for this shot are shown in Fig. 6.7. The distribution of emission centers on the 115 cathode surface is altered for shot 7691, with larger emission centers and increased intensity levels near the +x cathode edge. Figure 6.9: (a) ICCD images for two shots with a temporal gate location of t = 648-658ns. The measured voltage and current are listed for each shot. (b) The extracted current as a function of time and the corresponding cathode camera gate location. (c) Full image intensity projections onto the x-axis for shots 7689 and 7691. Data generated with a 15-mm-diameter cathode at a charge voltage of 70kV. The current within this time-frame is ∼200A above the current prior to the excess emis- sion, as pictured in Fig. 6.9b. The time averaged current is 89% larger for the excess emission case and the voltage is decreased by almost 16kV due to beam loading. The measured image intensity is 2.7× greater for the excess emission case, as shown in Fig. 6.9c. The imaging and extracted intensity level corroborate the claims made in the previous section: that the excess emission witnessed in the various diagnostic measurements is a result of intense and rapid electron emission. 116 Observing and diagnosing the excess emission through optical methods alone is statis- tically challenging. Due to the stochastic nature of the arcs, featured in Fig. 6.3 for each cathode size, one can not guarantee that the camera gate will capture the excess emission instance and the timing of the arc cannot be predicted accurately. 6.2.4 Time dependence As discussed in an earlier subsection, the current transients and observed arcing increase in intensity and number as the pulse progresses, a consequence of the continuous charge accumulation on the velvet cathode. As such, longer current pulse lengths result in increased excess emission levels that can be catastrophic on the system. The ∼1000ns-long current pulses generated with a 15-mm-diameter cathode shown in Fig. 6.10 demonstrate this idea, with a transient reaching almost 800A in shot 7400. However, some pulses on this time- scale may not present any arcing of this magnitude, as witnessed with shot 7380, though low intensity transients are still noticeable throughout the pulse. Statistical analysis is performed investigating this temporal dependence further and to determine limitations on the duration of the current pulse. For consistency, a general threshold is defined to calculate the number of current tran- sients and the corresponding intensity for various shots. This threshold, shown in magenta in Fig. 6.10a, must take into account the slope of the current waveform and thus the plasma expansion velocity. A linear fit is applied to an average of 28 BPM current waveforms gen- erated with a 15-mm-diameter cathode with identical operation settings (diode voltage of 250kV). The average current slope is: I(t) = 114.6 + 0.08t, shown in blue on Fig. 6.10a. A transient, or arc, is then considered relevant if the amplitude is 3σ above this fit as shown 117 in magenta. Figure 6.10: (a) Shots 7380 and 7400 from 221012 operations, generated with a 15-mm- diameter cathode with a diode voltage of 250kV (PFN = 70kV). The current fit, represented by the blue line, is I(t) = 114.6 + 0.08t. The excess emission is considered relevant if the current exceeds 3σ of the calculated fit at a given temporal location, shown in magenta. (b) Number of measured excess emission instances within 50ns windows. (c) The current amplitude for each excess emission instance as a function of time. The upper fit is I = 18.4 e(0.003t) and the lower fit is I = 0.081t + 139.59. The histogram shown in Fig. 6.10b demonstrates the number of transients within 50ns windows for a suite of 28 current pulses with durations of 1000ns. The distribution of the 118 number of transients observed is complex and points to the randomness of this phenomena. Excess emission levels above the defined threshold do not occur until after t = 300ns, ap- proximately 170ns after emission is initiated for this particular data set. The peak amplitude of the transients as a function of time is shown in Fig. 6.10c and demonstrates two distinct trends. The first, an exponential fit to the upper intensity data following: I = 18.4 e(0.003t). The second trend is a linear fit for the lower intensity data: I = 0.081t + 139.59. Together, these trends suggest that though lower intensity arcs will appear regardless of pulse length, the likelihood of a high intensity transient occurring increases exponentially with time. 6.3 Results and discussion Excess emission is a result of continuous charge accumulation on the velvet and results in intense transients in the current waveforms. The increased emission loads down the voltage pulse from the PFN producing obvious beam loading in the diode voltage. The combined effects result in impedance collapse and an increase in the time dependent gun perveance. As the excess emission effect is stochastic, several diagnostic methods are used simultaneously to characterize the emission including DRD measurements. ICCD imaging of the cathode face can also be used, but is statistically challenging. Together, these diagnostics verify that the increased current levels result from charge accumulation on the velvet. The charge density threshold is ∼6 - 8µC/cm2 for the 15-mm-diameter and 25-mm- diameter cathodes. The threshold is ∼ 2× greater for the 7.5-mm-diameter cathode, with larger error bars due to the stochastic nature of excess emission. The 7.5-mm-diameter cathode shows the lowest threshold of 6µC, which results in increased excess emission levels. Additionally, the current transients appear more frequently than what is observed for the 119 remaining cathode sizes. For all cathode sizes, the number of excess emission instances is statistically random. Generally, transients appearing later in time are increased in amplitude. It is shown with the 15-mm-diameter cathode that there is an exponential increase in the amplitude of current transients as a function of time. Increasing the current pulse beyond ∼1000ns results in large current fluctuations that can be detrimental to the system. It is expected, based off the correlation between charge threshold and cathode size, that likelihood of high intensity current transients is increased further as the size of the cathode decreases. 120 Chapter 7. Evaluating AK gap closure rates As described in previous chapters, the measured beam current extracted from a velvet emitter on the cathode test stand has a steady, linear increase throughout the pulse. This is a result of the expansion of the cathode plasma and subsequent AK-gap closure and is commonly observed for explosive emission cathodes [4, 29, 30, 34, 91, 132, 134, 135]. AK-gap closure specific to velvet cathodes has been detailed in the context of the EPURE Axis-I injector and accompanying Mi2 test bed [34, 91]. In Ref. [91], work on the Mi2 dual-pulse test stand was presented that demonstrates an effective AK-gap closure and expansion of the hydrogen plasma. The experiment utilized a 5-cm-diameter velvet cathode to produce two 700keV, 80ns, 2kA electron beams with pulse spacing ranging from 0.1 - 3µs. A higher current is observed on the second pulse and exceeds the current predicted through numerical methods when not accounting for expansion of the emission surface. The discrepancy increased with an increase in pulse spacing and it was determined that the current increase was a result of plasma expansion and an effective decrease of the cathode recess. Throughout this chapter, we discuss the observed current increase, plasma expansion velocity, and effective gap closure in the context of the cathode test stand. The expansion is estimated through two methods. One, through Trak simulations that estimate the overall emission offset necessary to produce the measured current at a given diode voltage. This method is based on work presented in Refs. [34, 91], described above. The second method utilizes ICCD imaging of the axial plasma expansion in the AK-gap, described in Ch. 3. It is shown in Ch. 5 and 6 that several emission characteristics for velvet cathodes are dependent on total emitter area: the emission delay, extracted current, measured current 121 density, and the severity of excess emission. Additionally, the diode geometry and emitter area are directly correlated to the rate of plasma growth. Throughout this chapter it is shown through both methods that the rate of expansion increases for decreased emitter area, with expansion rates exceeding 20mm/µs for the 7.5-mm-diameter cathode (calculated through Trak simulations). To conclude, we discuss the discrepancy between the two methods and possible sources of error. 7.1 Expansion velocity calculations Trak is utilized to estimate the overall decrease in the AK-gap based off the measured current increase and diode voltage. The measured diode voltage at a given temporal location is programmed into the EStat input file and Trak supplies the predicted current for a given geometry. Figure 7.1a demonstrates the nominal case for the 7.5-mm-diameter cathode at a diode voltage of 215kV. At this voltage level and cathode geometry, the extracted current is I = 25.8A. Then, the definition of the emission surface is moved off the cathode plug, effectively decreasing the cathode recess, as shown in Fig. 7.1b for a 2-mm emission offset. Changing the emission definition results in an extracted current of I = 42.4A, a 64% increase from the nominal case. The emission offset is altered until the current levels match what is measured with the BPM array. As the voltage increases, the required offset increases. Fig. 7.1c shows the extracted cur- rent for the 7.5-mm-diameter cathode as a function of diode voltage calculated through Trak for various emission offsets. Experimental data for a wide range of voltage set-points is indi- cated with the blue (values taken 50ns after emission) and purple (values taken 100ns after emission) scatter plots, compiled from 231109 operations. At all voltages, the experimental 122 current exceeds the “no offset” prediction shown in red. For V > 180kV, the measured cur- rent for both cases exceeds the 1-mm-offset prediction. The calculated expansion or offset increases throughout the current pulse, with a larger plasma growth or emission offset later in time. At the highest voltage set-point, the estimated expansion is ∼ 3-mm after 100ns, approximately 2× greater than at 50ns. Figure 7.1: Trak simulations showing the extracted beam for (a) no offset and (b) a 2-mm emission offset. In both cases, simulations were performed for the 7.5-mm-diameter cathode and a diode voltage of 215kV. (c) The Trak predicted current as a function of diode voltage over a wide range of emission offsets. Experimental data collected over a wide range of voltages is included for reference. Values were taken either 50ns or 100ns after the emission delay and are compiled from the 231109 data set. The method described above is used to calculate the expansion velocity, νexp, of the 123 cathode plasma. To estimate the expansion rate at a given diode voltage set-point, the current and voltage are averaged over 20-30ns for a given pulse. The values are collected over the first ∼200ns of the current pulse. Trak is used to calculate the expected offset based off the time averaged current and voltage levels. Note that the expansion velocity is only calculated using numerical methods over the first 200ns of the current pulse. As explained in Ch. 6, excess emission is measured approximately 200ns after emission is initiated. These extreme current levels cannot be accurately simulated through Trak. Fig. 7.2a shows current pulses generated with a 7.5-mm-diameter cathode and maximum diode voltage of 215kV (60kV charge voltage) overlaid with the current predicted in Trak. Trak 1 represents the predicted current assuming a negligible expansion of the cathode plasma. Note that there is a visible decrease in the predicted current. This is a result of the 15% voltage drop from ∼150 - 300ns described in Ch. 5. Trak 2 is calculated by adjusting the emission offset in order to match the current measured with the BPM array. Corresponding Trak simulations are shown for a diode voltage of 182kV in Fig. 7.1c (nominal, no offset case) and Fig. 7.1d (5.4-mm offset case). The current levels and change in emission offset from Trak simulations indicate that the plasma expansion velocity for the 7.5-mm cathode at 215kV is vexp = 27mm/µs. At t = 340ns, the measured current is approximately 68A for a diode voltage of 182kV, corresponding to an overall offset of 5.4-mm, as shown in Fig. 7.1d and a 22% decrease in the effective AK-gap. It is important to note that the decrease in the gap spacing and increase in extracted current alters the radius of the beam, shown in Fig. 7.1b where V = 182kV. The expected beam radius at z = 60mm for the extreme, 5.4-mm offset case is 21.5-mm. This is ∼2× greater than the nominal case, where the predicted beam radius is 10.9-mm. 124 Figure 7.2: (a) Extracted current waveforms for the 7.5-mm-diameter cathode with the predicted Trak current with no emission offset (Trak 1) and the Trak current calculated through changing the emission offset (Trak 2). The maximum diode voltage is 215kV (60kV charge voltage). (b) The corresponding beam radius for V = 182kV predicted through Trak for the nominal case, 2-mm-offset case, and 5.4-mm-offset case. (c) Trak simulation for the nominal case where V = 182kV. (d) Trak simulation for the 5.4-mm-offset case where V = 182kV. Data extracted from 231219 operations. 7.1.1 Dependence on emitter size In Ch. 6, we discussed the dependence on cathode size with respect to the excess emission details. Altering the cathode size also results in changes to the measured current slope and AK-gap closure rates. As demonstrated in the extracted current waveforms shown 125 throughout Ch. 6, the slope of the extracted current increases as the cathode area decreases at all charge voltages. This is a direct consequence of the relationship between expansion velocity and cathode size. Note that this is additionally related to the increasing charge density, discussed in Ref. [46]. Figure 7.3: (a) Extracted current waveforms for the 25-mm-diameter cathode with corre- sponding Trak calculations. Trak 1 represents the predicted current for the nominal case and Trak 2 represents the matched current calculated through changing the emission offset definition. The maximum diode voltage is 215kV (60kV charge voltage). (b) The corre- sponding beam radius at V = 184kV for the nominal case and a 1.76-mm emission offset. (c) Trak simulation where V = 184kV with no emission offset. (d) Trak simulation for the 25-mm-diameter cathode for V = 184kV, I = 155.5A, and an emission offset of 1.7mm. Data extracted from 240718 data set. Fig. 7.3a shows extracted current waveforms for a 60kV charge voltage and predicted 126 Trak currents for the 25-mm-diameter cathode. Trak 1 represents the nominal case and Trak 2 represents the predicted current calculated by changing the emission offset to match the experimentally measured current. For V = 184kV the Trak predicted current for no emission offset is I = 93.0A, as shown in Fig. 7.3c. However, at t = 340ns, the measured current within the BPM array is 155.5A. To match this current, the required Trak emission offset is 1.7-mm, as shown in Fig. 7.3d. This is a 6.8% reduction in the effective AK-gap. The change in beam radius as a function of z-location is shown in Fig. 7.3b for V = 184kV. When z = 60mm, the expected beam radius for the 1.7-mm expansion case is 24.5-mm, ∼53% greater than the nominal case. Table 7.1: Tabulated list of the charge voltage, calculated expansion velocity, and the esti- mated emission offset at t = 340ns for each cathode size. The expansion rate was calculated over t = 180 - 340ns. Data for the 7.5-mm-diameter cathode extracted from 231219. Data for the 15-mm-diameter cathode extracted from 221201. Data for the 25-mm-diameter cathode extracted from 240718 and 240724. Diode Voltage (cid:10)vexp,7.5mm (cid:11) Final Offset (cid:10)vexp,15mm (cid:11) Final Offset (cid:10)vexp,25mm (cid:11) Final Offset [kV] [mm/µs] [mm] [mm/µs] [mm] [mm/µs] [mm] 180 215 250 275 21.2 27.0 21.9 26.7 3.90 5.4 5.1 6.1 13.6 13.6 13.3 16.7 2.6 2.97 3.35 3.60 10.3 5.7 3.2 3.3 1.34 1.70 1.50 1.55 The resulting expansion velocity for the 25-mm-diameter cathode at a maximum diode voltage of 215kV is vexp = 5.7mm/µs. This value is over 4× less than that measured for the 7.5-mm-diameter cathode for the same voltage operation setting. The overall emission offset 127 where t = 340ns is reduced by over 3-mm for the 25-mm-diameter cathode. Additionally, the increase in beam radius as a function of time is decreased for the larger cathode. The trends shown between Figs. 7.2 and 7.3 continue for all charge voltages. Table 7.1 lists the expansion velocities and estimated offset where t = 340ns, calculated through Trak, for all three cathode diameters at four different voltage set-points (corresponds to 50kV, 60kV, 70kV, and 75kV charge voltages). In each case, the expansion velocity was calculated over t = 180 - 340ns. In general, the 25-mm-diameter cathode has the lowest measured expansion velocity, with rates > 3× less than the smallest cathode. Additionally, this cathode has the smallest overall offset at each diode voltage. The measured expansion velocity for the 15-mm-diameter cathode consistently falls between νexp for the 7.5-mm and 25-mm-diameter cathodes. 7.2 AK gap imaging AK-gap imaging was performed following the configuration detailed in Ch. 3. This mea- surement compliments the method described above. To measure the plasma growth through ICCD imaging, we consider the visible extent of the imaged plasma plume, like that shown in Fig. 7.4a. The intensity over the full image is projected onto the z-axis and results in the intensity profile shown in Fig. 7.4b. The intensity profile can be modeled with an expo- nential function, shown with the dashed line, and the corresponding decay rate is taken as the measured plume extent. This is referred to as a “1/e” fit. For shot 9049 shown in Fig. 7.4, which was generated with a 7.5-mm-diameter cathode at a charge voltage of 60kV, the calculated plume extent is 1.09mm, noted with the solid red line on both the image and the intensity profile. 128 Figure 7.4: (a) Shot 9049 with the calculated plume extents for three different methods: a 1/e fit, the FWHM of the intensity profile, and the extent where the intensity is 10% of the maximum value. (b) The intensity profile with the exponential fit and the calculated extent for each method. Note that the 1/e and FWHM values lie closely on top of one another. Exact values for the calculated extent for each method are tabulated in Table 7.2. There are additional metrics for calculating the plume extent, though less reliable than the method described above. One of these methods is calculating the full width half max (FWHM) of the intensity profile. For shot 9049, the FWHM plume extent is 1.10mm, noted with the solid green line in Fig. 7.4. Note that this lies close to the measured 1/e plume extent. A third way of calculating the plume extent is to locate the z-position in which the intensity is 10% of the maximum intensity. This value is typically larger than the 1/e and FWHM calculations and is 1.55mm for shot 9049, shown with the purple solid lines in Fig. 7.4. The resulting plume extents for each measurement method are listed in Table 7.2 for shot 9049. All plume extents calculated throughout this dissertation utilize the 1/e method. Calculating the plume extent for various images across the current pulse is used to cal- 129 culate the expansion velocity. Note that due to the recess of the emission surface, the total expansion must exceed 3-mm in order to measure the plasma plume with the ICCD. Results are shown for the 7.5-mm and 25-mm-diameter cathodes. Table 7.2: The plume extent calculated for shot 9049 using three different methods: a 1/e fit, the FWHM of the intensity profile, and the extent where the intensity is 10% of the maximum value. Image was taken at a 60kV charge voltage, generated with a 7.5-mm- diameter cathode. and the ICCD was gated from 520-730ns. The image and corresponding intensity profile is shown in Fig. 7.4. Corresponding current and voltage waveforms are shown in Fig. 7.5. 1/e Fit FWHM 10% Max Intensity 1.09 mm 1.10 mm 1.55 mm 7.2.1 Statistical variation Due to the low light intensity, the camera gates for the AK-gap ICCD are extended to ∼200ns. Keep in mind the AK gap imaging is dependent on both the cathode plasma expansion and the excess emission; the latter is highly stochastic as shown in Ch. 6. As a result, there is a variation between each shot, particularly those gated toward the end of the pulse. Fig. 7.5a shows 4 images taken with identical camera settings at the same voltage set-point: 60kV charge voltage, 210ns gate width, and gated from 520-730ns. The log-transformed images are shown for reference in order to enhance the distribution. The measured plume extents are listed and the corresponding intensity line-outs is shown in Fig. 7.5b. The temporal location of the camera gate relative to the current and voltage waveforms are shown with the shaded rectangle in Figs. 7.5c and d. The measured voltage within this gate is 180.1 ± 3.4kV. The current measured with the BPM array is 83.7 ± 9.5A. Note that at this time, 130 several pulses show intense excess emission (see Fig. 7.5d). Figure 7.5: (a) Four images (linear intensity on top, log intensity on bottom) gated from 520-730ns with a charge voltage of 60kV for the 7.5-mm-diameter cathode. The plume extent for each shot is listed. (b) The intensity line-outs for each shot. (c) The voltage waveforms and (d) extracted current waveforms for the shown data set. The shaded area corresponds to the temporal location at which imaging occurred. Data extracted from 231219 data set. The measured AK-gap image intensity for each shot is shown in Fig. 7.5b. Despite the low deviation in the diode voltage and 11.35% variation in the average extracted current, the measured maximum intensity varies by 47% relative to the average of 659.3. The large variation in measured light intensity is likely a result of the excess emission levels and should be kept in mind moving forward. However, the average plume extent is 1.06 ± 0.17mm, and has approximately a 16% variation from the mean. This deviation falls within a similar 131 range as the deviation in extracted current. 7.2.2 Voltage dependence Figure 7.6: (a) Single shot images for the 7.5-mm-diameter cathode as a function of diode voltage with the measured plume width listed. Charge voltages, in order, are 50kV, 60kV, 70kV, and 75kV. (b) Normalized intensity line-outs for each image. (c) The voltage wave- forms and (d) extracted current waveforms for the shown data set. The shaded area cor- responds to the temporal location at which imaging occurred. Data extracted from 231219 operations. As described in section 7.1, Trak predicts a greater offset at higher voltage, as demon- strated in Fig. 7.1c. This is demonstrated with AK-gap imaging, as shown in Fig. 7.6a, which shows images of the plasma plume generated with a 7.5-mm-diameter cathode for increasing voltages. Plume extents are listed and the corresponding normalized image inten- sity is shown in Fig. 7.6b. Each image has a gate width of 200ns and is gated at the end of 132 the current pulse, as represented by the shaded rectangles in Fig 7.6c and d. In general, an increase in voltage leads to an increase in the measured plume and emission offset. However, there are certain exceptions to this trend. The measured plume at a 50kV charge voltage, or 180kV, is slightly greater than that at a 60kV charge voltage (215kV). This is considered a result of excess emission levels. In Fig. 7.6d, it is shown that a cur- rent transient fell within the AK-gap camera gate for shot 9019 that exceeds 100A. Excess emission increases the overall plume width and measured light output. At the highest voltage operation setting of 75kV (shot 9080 in purple), the measured plume extent is 1.36-mm, resulting in an overall expansion of 4.36-mm after taking the cathode recess into account. This is ∼1.6× higher than the 70kV case demonstrated with shot 9065. This general trend is observed with the 25-mm-diameter cathode as well and is confirmed with Trak simulations. 7.2.3 Temporal evolution We now discuss the imaged temporal evolution of the plasma plume and compare the two cathode cases. All experimental measurements shown in this section are taken with a diode voltage of 215kV and the camera gate widths for each case are ∼200ns. Fig. 7.7a shows the evolution of the plasma plume generated with a 7.5-mm-diameter cathode throughout the current pulse. Single images are used and the shot numbers are listed for reference. Corresponding intensity line-outs for each shot are shown in Fig. 7.7b and the voltage waveforms are shown in Fig. 7.7c. Note that the difference in pulse length is intentional and does not alter imaging results, as the shorter pulses correspond to the images gated within 160-560ns. 133 Figure 7.7: (a) Temporal evolution of the AK-gap imaging for the 7.5-mm-diameter cathode at a 215kV voltage set-point. The linear intensity images are shown on the left and the (b) log-transformed images are shown on the right. Shot numbers listed for reference. The corresponding normalized intensity line-outs. (c) The voltage waveforms for the shown data set. (d) Corresponding extracted current waveforms overlaid with the measured plume width. Note the differences in pulse length between shots is intentional. Data extracted from 231219 operations. Over the first 200ns of the current pulse, the image intensity on a linear and log scale is negligible. Note that Trak simulations suggest an emission offset of ∼2.7mm where t = 360ns. However, as this is less than the 3mm cathode recess, the expansion early in time cannot be detected with the ICCD. The plume extent increases in the next 200ns, most noticeable in the log-transformed images, and is approximately 1-mm, which results in an overall expansion of 4-mm after accounting for the 3-mm cathode recess. Towards the end of the current pulse, the average plume extent is 5-mm. The offset is overlaid with the average current in Fig. 7.7d. After applying a linear fit to the measured plume widths, vexp = 2.3mm/µs. There is a significant error for 970-1220ns, which can be contributed to large 134 current transients late in time. Figure 7.8: (a) Comparison for the 7.5-mm-diameter cathode and 25-mm-diameter cathode. All images are 5-shot averages. The maximum diode voltage is 215kV (60kV charge voltage). (b) Average extracted current and the plume extent for each cathode. The linear fit for the 7.5-mm cathode is 0.0023t + 2.57 (data extracted from 231219 operations). The linear fit for the 25-mm cathode is 0.0017t + 2.86 (data extracted from 240718 operations). Comparisons of the cathode plasma expansion between the 7.5-mm and 25-mm-diameter cathode are shown in Fig. 7.8. Note that the images were averaged over 5 shots for each cathode at all temporal locations. Imaging, Fig. 7.8a, shows that the intensity levels are comparable for the two cathodes but the plume extent is larger for the smaller cathode. The calculated expansion rate for the 25-mm-diameter cathode is νexp = 1.7mm/µs, as demonstrated in Fig. 7.8b, 26% less than νexp for the smaller cathode case. Though νexp for each cathode calculated through imaging varies significantly from the expansion rate calculated via Trak, the claim that smaller cathodes exhibit larger expansion rates holds. The increase in expansion rate with a decrease in cathode size results from an increased current density and a higher electron density. 135 7.2.4 Comparison to cathode imaging AK gap images for the 25-mm-diameter cathode, like those shown in Fig. 7.8, show various “hot spots” not witnessed in the 7.5-mm-diameter cathode data. These “hot spots” corre- spond to the emission centers in the cathode images described in Ch. 5. A comparison of the cathode images and AK gap images for the 25-mm-diameter cathode at a PFN charge of 60kV is shown in Fig. 7.9. All images were gated at 970ns. The gate width for the cathode imaging was is 30ns with a gain of 10 and the gate width for AK gap imaging is 200ns with a gain of 30. Areas with high intensity in the cathode images generally map to high intensity areas in the AK gap imaging and an increased plume extent at a similar y-location. Areas with more emission centers also map to increased plume extent. For example, shot 9934 shows an emission center at y = ∼0mm where the image intensity is ∼ 2× greater than the remaining emission centers. At the same approximate y-location, the AK gap imaging shows slightly increased intensity levels. Additionally, the plasma extent is increased where y = 0mm, with an overall plume extent approximately 1-mm larger than what is observed across the remainder of the cathode area. This correlation is observed across all data generated with the 25-mm-diameter cathode. This correlation is not witnessed in the imaging for the 7.5- mm-diameter cathode data, as the emission centers are typically larger and not distributed across the cathode face, as described in Ch. 5. 136 Figure 7.9: (a) Cathode and (b) AK gap images for a 25-mm-diameter cathode (compiled from 240718 shot day). All shots were taken at a set-point of 60kV and gated at 970ns. Cathode images have gate width of 30ns and a gain of 10 while AK gap images have a gate width of 200ns and a gain of 30. 7.3 Results and discussion The measured expansion velocity is heavily dependent on the diode voltage and the total emission area. Dramatic levels of plasma expansion are witnessed with the smaller cathode, with a total estimated offset exceeding 5-mm in extreme cases and expansion rates exceeding 20mm/µs. These values are greatly reduced for the largest cathode. Trak simulations suggest 137 that the expansion velocity for the 25-mm-diameter cathode at a similar diode voltage is 5.7mm/µs. AK-gap imaging confirms that the expansion rate is decreased for the larger cathode. Imaging was not performed for the 15-mm-diameter cathode. However, based on the information presented in Tab. 7.1 and the observed changes in current slope, the visible expansion rate will fall between νexp for the 7.5-mm and 25-mm-diameter cathodes. Differences are observed in the calculated expansion rates for the two methods. For example, the total emission offset observed through AK-gap imaging for shot 9047, shown in Fig. 7.6a, is 1.25mm and the resulting measured current is ∼140A. However, at this offset the Trak predicted current is <60A. There is a clear deviation between the two methods for all measurements which results in significant differences in νexp. These differences are due to several factors and assumed error for each method. The sources of possible error are as follows: • Trak assumes uniform emission at a single defined z-location. However, this is not accurate as there is some depth to the plasma sheath from which the electrons are extracted. This is not taken into account within the simulations. • We know from AK-gap imaging that the expansion is not uniform along the vertical axis. Trak may not accurately represent this radial distribution. • Low light intensity at the outer edge of the plasma plume cannot be not detected by the ICCD, despite the increase in camera gate width. The overall expansion and AK-gap closure is likely greater than what is measured through imaging. • The gate width for the AK-gap ICCD is increased due to the low light intensity. How- ever, this does not allow for accurate measurements of the plasma growth. Additionally, 138 the images are altered towards the end of the pulse due to the increased amount of excess emission. • Excess emission throughout the pulse alters the expansion velocity calculation for both methods. For Trak calculations, the emission offset is dramatically increased during the current transient. For imaging, the light output is increased, as demonstrated in Fig. 7.5. Obtaining accurate νexp calculations will be helpful for future work performed on the cathode test bed. However, in the context of this dissertation, the observation of the change in the effective AK-gap and the resulting changes in measured beam radius confirm that the velvet cathode is not suitable for long-pulse applications. 139 Chapter 8. Optimizing Current Density Mea- surements Current density measurements for electron beams produced with diagnostic screens are highly affected by electron-material interactions, as described in the later sections of Ch. 2. Collisions within the material produce secondary electrons and photons, which contribute to the stopping power of the primary electrons [99, 100, 101, 102]. Multiple scattering models and analytical diffusion angle calculations have been widely documented and must be taken into account when utilizing screen diagnostics for current density measurements [103, 104, 136, 137, 138, 139, 140]. X-ray scintillation, defined in Ch. 3, is a common method for electron beam current density measurements. Work in Ref. [89] used a 125-µm-thick tantalum foil placed upstream of a 2-mm-thick plastic scintillator in order to monitor the current density distribution. The produced low-energy electrons were completely ranged out within the metal foil and did not interact with the plastic. Instead, the electrons generated a Bremsstrahlung X-ray pulse within the Ta, which was subsequently measured on the scintillation screen through fast X-ray imaging. Similar methods are shown in Ref. [94]. The experiment utilized a 100- µm-thick YAG:Ce scintillator crystal partnered with a 25.4-µm-thick stainless steel foil to measure the beam profile distribution of an elliptical electron beam with V = 20kV and I = 1.5A. The foil was implemented to prevent damage to the YAG:Ce and to measure the current density through the X-ray scintillation method described above. Cherenkov emitters are an alternative current density diagnostic method and thought to be preferable as these materials are typically free of fluorescence [96]. The effectiveness 140 of a Cherenkov diagnostic is dependent on the index of refraction of the material and the electron beam parameters, as Cherenkov radiation is not initiated until a threshold dependent on the refractive index is exceeded. The Relativistic Klystron Amplifier [97, 98] produces a 500keV, 100ns FWHM electron beam with a current of 30kA using an explosive emitter. The beam collides with a 1-mm-thick fused silica Cherenkov emitter and the produced photons are imaged with a high-speed gated camera and a streak camera. This diagnostic method produced consistent beam profile measurements [98]. The electron beam generated on the cathode test stand is non-relativistic with β = 0.5 - 0.75. In this chapter, we present results from various configurations in order to quantify the effects of electron scatter and Cherenkov limits on the resulting current density dis- tribution. The diagnostic configurations and imaging paths are discussed in detail in Ch. 3. Experiments have been performed that diagnose the physical processes that complicate the measured distribution. These experiments have been validated through MCNP6® [49] simulations. Finally, we discuss the optimal measurement configuration. 8.1 Electron ranging studies X-ray scintillation experiments, following the configuration in Fig. 3.17c., test the effect of atomic number, material density, and foil thickness on the measured current density. The chosen scintillation screen is a BC-400 plastic scintillator due to the high light output and fast decay rate of 2.4ns [117]. Two separate experiments are described below. The first pairs the scintillator with various thicknesses of aluminum foil. The second pairs the BC-400 with a 200-µm-thick copper foil. The electron range for both metals as a function of energy and the scattering angle as a function of foil thickness can be extracted from Figs. 2.8 and 2.9. 141 The “Aluminum Pie” was constructed to test the effect of foil thickness on the measured distribution while holding the atomic number, Z, constant. The foil, shown in Fig. 8.1a, consists of four different quadrants with various thicknesses of Al (Z = 13): 200-µm, 300-µm, 400-µm, and 600-µm. Emax, the maximum energy at which the electrons will range out, varies in each quadrant and is listed in Fig. 8.1. Quadrant 1, the 200-µm-thick quadrant, will range out electrons with E < 191keV. The thickest quadrant, ∆z = 600µm, will stop electrons with E < 395keV, exceeding the maximum achievable energy of the experiment. The average scattering angles for each thickness of aluminum are tabulated for 250keV electrons in Tab. 8.1. The aluminum pie is placed upstream of a 700-µm-thick plastic scintillator with a viewing diameter of 88-mm. The diagnostic is located ∼140mm from the cathode shroud. Data was generated with a 15-mm-diameter cathode. Figure 8.1: (a) The Al pie configuration. Each quadrant is a different thickness of Al, listed on the image. The listed Emax refers to the largest electron energy that will be fully ranged out in the foil. (b) Electron range within aluminum as a function of energy [102]. The data points correspond to the thicknesses of each quadrant. 142 Table 8.1: Scattering angle for each thickness of aluminum included on the Al pie, calculated through Eq. 2.25. Energy is set to 250keV. Thickness [µm] Average Scattering Angle, (cid:10)Θ2 W (cid:11)1/2 [o] 200 300 400 600 84.6 106.7 125.7 158.1 Imaging was performed over the first 400ns of the voltage pulse, covering voltages over the range 200kV - 257kV. Fig. 8.1a shows a subset of the images taken during this study. It is immediately apparent that there is a difference in both the distribution and intensity particularly with the thinnest Al sample. The images corresponding to V = 257kV and V = 245kV show large contributions from electron scatter within the 200-µm-thick quadrant. This effect is mitigated as the energy decreases. The thicker quadrants have little to no visible scatter, as the majority of the beam is ranged out within the foil. Fig. 8.1b shows the measured voltage and current from the experiment overlaid with the maximum integrated intensity from the images in Fig. 8.1a. The integrated intensity was calculated by averaging the intensity levels over each quadrant and then integrating with respect to the x-axis. The intensity levels for the 200-µm quadrant have a peak that coincides with the maximum level of the voltage pulse; as the voltage drops, the intensity drops within the same range as the remaining quadrants. The increased intensity in this region demonstrates energy sensitivity, but it is convoluted by several species interactions within the BC-400 including electron 143 Figure 8.2: (a) Measured beam distributions from the aluminum pie configuration. Images are shown for a subset of four measured diode voltages over the range 222kV - 257kV. The camera gate times are indicated. (b) The diode voltage and the extracted current from the 15-mm-diameter cathode overlaid with the integrated intensity from a larger set of images. scintillation, secondary electron creation, and X-ray scintillation. Intensity levels for all quadrants fall to comparable levels for t > 250ns. Distributions measured for the 200-µm-thick quadrant at high energy result from the electrons scattering within the aluminum foil and losing energy before a fraction diffuse into the plastic scintillator. Secondary electron production further alters the distribution. The electron energy of the primary beam exceeds the 191keV ranging threshold by 35%, and a fraction of the primary and secondary electrons pass through the Al and scatter in the 144 scintillator. Simulations confirm that for a 250keV electron beam colliding with a 200µm- thick Al disk, roughly 6% of the electrons, including the generated secondaries, escape the metal foil. The secondary electron yield for this simulation primarily consists of knock-on electrons, with a small percentage of generated secondaries being auger electrons and photo- electric electrons. As the energy drops towards 191keV, more electrons are ranged out within the foil resulting in a more uniform distribution with decreasing intensity levels. This follows for the 300-µm-thick quadrant as well, as Emax = 248keV is just below the maximum energy measured. Fig. 8.3 shows the remaining primary beam energy as a function of distance traveled within aluminum, assuming an initial energy of 250keV. The dashed lines refer to the different foil thickness in the aluminum pie. At 200µm, the primary beam has lost approximately half of the initial energy. At 300µm, over 92% of the initial beam energy has been deposited in the foil. As the beam energy has dramatically decreased after the electrons have traveled through the foil, it is expected that there are little to no contributions from electron scatter in the measured distribution on the scintillator. Note that the primary electron beam has been fully ranged out at 304µm. The electron trajectory for each quadrant of the aluminum pie simulated using MCNP6® is shown in Fig. 8.4. The thickness of aluminum used in the experiment is placed upstream of a 700-µm-thick BC-400 scintillator. The source is a pencil electron beam with an energy of 250keV and 104 source particles. Note that simulations performed with Trak estimate an RMS divergence angle of ∼10o for V = 250kV and I = 110A. It is expected that the initial divergence of the primary electron beam will have little contribution to the electron scattering patterns on the diagnostic and thus, modeling the experiment with a pencil electron beam 145 Figure 8.3: The remaining energy as an electron beam with an initial energy of 250keV passes through aluminum [102]. The dashed lines represent the different foil thicknesses used on the Al pie. is a valid way of investigating the electron-material interactions and measured distributions. The following scattering and particle production mechanisms are enabled in the MCNP6® simulations: production of electrons by photons, Bremsstrahlung photon production, knock- on electron production, generation of photon-induced secondary electrons, and Cherenkov photon production. The simulations represent a median between the images shown in Fig. 8.1a where V = 257kV and V = 245kV. The 200-µm-thick aluminum simulation is the only model in which the scattered electrons escape the aluminum and scatter within the plastic scintillator, resulting in a non-uniform trajectory. Quadrants 3 and 4, 400-µm and 600-µm, show no evidence of electron scatter and have constant intensity levels throughout the head of the current pulse. The maximum electron energy in order for the particles to pass through the foil and scatter within the diagnostic 146 Figure 8.4: The simulated electron trajectory and scatter for each quadrant of the aluminum pie (see Fig. 8.2) using MCNP6®. screen exceeds that of the experiment. Thus, the images are free of electron scatter within the plastic, and the imaged distribution is a result of the produced Bremsstrahlung X-ray pulse. This is confirmed further with the simulations shown in Fig. 8.4. Copper (Z = 29) is capable of ranging out higher electron energies than aluminum for the same ∆z, though the average scattering angle within the foil is much greater (see Fig. 2.9). To observe the effects of high Z materials, a 200-µm-thick Cu foil was placed upstream of the 700-µm-thick plastic scintillator with a viewing diameter of 88-mm. The diagnostic is placed ∼140-mm from the cathode shroud. The maximum energy at which electrons will range out in 200-µm-thick Cu foil is 395keV. Distributions produced with the Cu-foil configuration and a 15-mm-diameter cathode show a fairly uniform current density, as seen in Fig. 8.5a. The image shown was taken over a 10ns gate where V = 229kV and I = 139A. At this energy the electrons are fully ranged out within the copper, producing a uniform distribution on the scintillation screen. The intensity projection over both the x and y axis further establishes a uniform distribution. 147 Figure 8.5: (a) Measured distribution and intensity projections for a 700-µm-thick BC- 400 diagnostic with 200-µm-thick Cu foil placed upstream. The image was taken from t = 258 - 268ns where V = 229kV and I = 139A (Shot 7798). (b) MNCP6® simulations showing the electron scatter trajectory within a 200µm-thick copper foil. (c) Simulations showing the electron scatter trajectory within 200µm-thick aluminum. Both simulations use a pencil electron beam with energy of 250keV and 104 source particles. The foils are 1-mm in diameter. All electron scattering mechanisms are enabled. 148 MCNP6® is utilized to explore the Z dependence further. Figs. 8.5b and c show sim- ulations for 200-µm-thick copper and aluminum interacting with a 250keV pencil electron beam with 104 source particles. For both materials, all electron scattering mechanisms were enabled. In the aluminum, the electrons scatter within the metal and then escape the foil, similar to the measured distributions shown in Fig. 8.2a. In the copper, all electrons are either back-scattered, or fall below the energy cut-off, which depicts the electrons fully rang- ing out within the material. The extent of the electrons within the copper foil is ∼90µm. The simulations quantify a significant difference in electron trajectories between the two materials; the measurement with a Cu foil upstream is not confounded by forward scattered lower energy electrons as is shown with aluminum. As the beam profile measured with the Cu foil configuration in Fig. 8.5a is not affected by forward scatter and the distribution is fairly uniform, it is possible to measure the current density. By considering the intensity profiles shown in Fig. 8.5a, we obtain a FWHM measurement with respect to the x-axis and y-axis, resulting in the measured diameter of the beam. Along the horizontal axis, the measured diameter is 67.0mm and is 65.6mm along the vertical axis. As the measured current is 139A, the average measured current density is: J = 3.99 A/cm2. The current density profile along each axis is shown in Fig. 8.6a. To confirm the consistency of the measured distribution, we consider 5 images taken with identical settings: 70kV charge voltage, gain of 10, and gated from 258-268ns. The average current density is 3.91 ± 0.05A/cm2 in x and 4.01 ± 0.20A/cm2 in y. This shows fairly good consistency, particularly when compared to the Al pie distributions shown above. Finally, we compare these distributions to the predictions made via Trak. For V = 229kV and I = 139A, Trak suggests an emission offset of ∼2.6mm. The predicted beam radius for 149 Figure 8.6: (a) Measured current density for shot 7798 (see Fig. 8.5a for image and intensity profile). (b) Maximum beam radius measured through Trak for the no-offset and 2.6-mm emission offset cases. The voltage is set to 229kV for each case. The blue data point represents the average measured beam radius for the copper foil configuration at t = 258ns and 70kV charge voltage. Data extracted from 230109 operations: shots 7798 and 7800-7803. (c) The current density profile calculated via Trak for each offset case where V = 229kV. the nominal case and the 2.6-mm offset case as a function of z-location is shown in Fig. 8.6b. The average measured beam radius at z = 140mm for 5-shots, 32.82 ± 0.50mm, falls along the trend for the no offset case rather than the predicted expansion. The beam radius extracted via Trak is the maximum radius from the horizontal axis, which will present a larger value than that measured on the diagnostic. The current density for each case at a z-location of 140mm is shown in Fig. 8.6c. In each case, we see a hollow current density distribution, with a higher maximum value for the no offset case. The maximum current 150 density for the nominal case is 2.74 A/cm2 at r = 33.5mm. For the 2.6-mm offset case the maximum current density is J = 2.4 A/cm2 at r = 17.5mm. The current density decreases from 40 - 50mm, with a final peak of J = 2.07 A/cm2 at r = 53.5mm. Note that this exceeds the radius of the diagnostic. Table 8.2: Tabulated list of the simulated and measured beam radius at z = 140mm for a diode voltage of V = 229kV. Experimental measurements were taken with the Cu foil configuration described in Fig. 8.5a. Experimental data compiled from 230109 operations and is averaged for shots 7798 and 7800-7803. Current [A] Max. Radius [mm] RMS Width [mm] FWHM [mm] Trak: No offset 78.6 Trak: 2.6-mm offset 138.9 Exp. Data 134.0 ± 7.2 34.0 55.1 44 34.5 54.0 N/A N/A 49.1 ± 1.1 65.6 ± 1.0 Tab. 8.2 shows the current, maximum radius, and the RMS width for each Trak case. The experimental data and radius measured by considering the FWHM of the intensity profile is included for reference. Note that the experimental RMS width value falls between the RMS width for the Trak simulations. The FWHM for the experimental distribution is 65.6 ± 1.0mm, corresponding to a measured beam radius of 32.8mm, which falls closely to the maximum radius for the no-offset Trak simulation. The discrepancy between the experimental case and the 2.6-mm predicted offset simulation is in part due to the behavior of the cathode plasma and space charge effects not accounted for in Trak. 151 8.2 Cherenkov emitter studies The effectiveness of a given Cherenkov emitter as a current density diagnostic is dependent on the material properties including the index of refraction (˜n), atomic density, and atomic number. Experiments were performed for a variety of materials with varying ˜n and the energy dependence was documented. For all experiments described below, a fine copper mesh was placed upstream of the material, following the configuration described in Fig. 3.17b. The “Cherenkov Pie” is designed to evaluate the Cherenkov yield of various materials simultaneously. The materials are as follows: 127-µm-thick Kapton Polymide, 50-µm-thick Nylon, 101-µm-thick Willow® Glass [141], and 76-µm-thick PEEK. Thin material substrates were chosen to help minimize electron scatter within the material. The indices of refraction range from 1.5 - 1.67. The refractive index and corresponding thresholds for each material are listed in Table 2.2. Table 8.3 lists the atomic density, atomic number, and the measured 1/e decay rate for each material and the experimental configuration is shown in Fig. 8.7a. The materials are adhered to the fine copper mesh with carbon tape. Teflon tape is used on the downstream side to further secure the materials to one another. In quadrant 3, the Willow® Glass quadrant, there is a triangular subsection in which there exists no Cherenkov emitter, thus producing “dead space” in the imaging. This cannot be detected on the spatial calibration image, but is noticeable in the experimental results. The results were generated with a 25-mm-diameter cathode with a current pulse length of 200 - 300ns; the lowest and highest operating points are shown in Fig. 8.7b and c. At the lowest set-point, the voltage ranges from 135kV - 165kV and the maximum current is 152 Figure 8.7: (a) Spatial calibration image for the Cherenkov Pie with labeled quadrants. The materials are directly adhered to a fine copper mesh with carbon and Teflon tape. (b) The current and voltage waveforms for the lowest experimental operation settings. (c) The current and voltage waveforms for the highest operation settings. For all data collected with the Cherenkov pie configuration, the 25-mm-diameter cathode was utilized to produce a 200 - 300ns current pulse. approximately 81A. At the highest setting, the voltage ranges from 230kV - 270kV and the maximum current is 208A. For Kapton, Nylon, and the glass: data is collected both above and below the Cherenkov threshold, resulting in an experimental separation of the contri- butions from electron scatter, fluorescence, and Cherenkov emission. For PEEK, images were taken above the Cherenkov threshold (127keV) and above the total internal reflection threshold (258keV). Fig. 8.8a shows the measured distribution over a subset of energies for the Cherenkov pie configuration. When Vave = 153kV , only the PEEK emits Cherenkov radiation. The intensity levels are 4x higher than the Kapton, and there is a slight non-uniformity in the imaged distribution. In images 2 and 3, all four materials are above the Cherenkov threshold 153 and below the total internal reflection threshold. The intensity levels for PEEK are 2-3 times greater than all other materials. In the final image, where Vave = 265kV , the electron energy exceeds the total internal reflection threshold for PEEK. The intensity levels within this quadrant increase by a factor of 1.5 and the measured distribution covers the full material area. The intensity levels in the other materials are slightly increased, and the glass indicates a depression near the center. Table 8.3: Material properties for each quadrant of the Cherenkov pie. The Cherenkov thresholds and total internal reflection thresholds are listed in Table 2.2. Material Index ˜n Atomic Density [g/cm3] Average Z 1/e decay time [ns] Kapton Nylon 1.50 1.53 Willow® Glass 1.51 PEEK 1.67 1.42 1.14 2.56 1.32 5.0 3.3 5.8 4.4 142.9 136.9 1014.8 254.8 The Cherenkov threshold for Kapton is reached at 175keV. However, images taken at E < 175keV indicate a measurable signal in the top left quadrant. MCNP6® simulations confirm that Cherenkov photons are not produced where V < 175kV. The distribution in the Kapton quadrant in this energy range is a result of fluorescence. Nylon performs as an ideal Cherenkov emitter; signal levels are near the noise floor for E < 164keV, the Cherenkov threshold. At V = 192kV, Nylon has intensity levels comparable to Kapton. A similar trend is witnessed for the glass. PEEK has the highest intensity for all shown images (generally ∼1.5-3x higher than 154 Figure 8.8: (a) Measured beam distributions for the Cherenkov pie configuration. Imaging shown over a subset of diode voltages over the range 153 - 265kV. All images were taken at the head of the current pulse (times listed are relative to the voltage pulse and do not account for the difference in emission delay). (b) MCNP6® simulations for each material in the Cherenkov pie for a beam energy of 227keV. 155 the remaining materials). In the final image, the electron energy exceeds PEEK’s energy threshold for total internal reflection. The measured pattern is scattered and diffused making the distribution difficult to interpret. This measurement is a result of total internal reflection within the material, and is not an accurate depiction of the beam profile. Fig. 8.8b shows the MCNP6® simulations for each material. The beam energy is 227keV, which corresponds to the third image in Fig. 8.8a. All electron-material interactions were disabled other than Cherenkov production. PEEK demonstrates the highest exit angle of ∼70o, as this energy is close to the total internal reflection threshold. The exit angles for all materials match analytical calculations. The normalized integrated image intensity as a function of voltage is plotted for each material in Fig. 8.9. All materials show an exponential relationship between the integrated intensity of the image and the corresponding diode voltage. Nylon, shown in Fig. 8.9b., has the highest deviation from the fit, with an error of approximately 15%. The remaining three quadrants have an error of less than 10%. Kapton (˜n = 1.50) and the Willow Glass (˜n = 1.51) have the strongest correlation with voltage and the imaged distribution is fairly uniform. Measurements made with materials with a similar index or lower are optimal within the desired energy range. Silica has a similar measurable energy range, with an index of refraction of ˜n = 1.46 and a Cherenkov threshold of 190keV. Data was collected with a 1-mm-thick silica disk paired with a fine copper mesh. The axial location of the diagnostic is unchanged from the Cherenkov pie configuration. The material thickness was chosen such that the electrons will fully range out within the silica. As data can be collected below the Cherenkov threshold, the effects of electron scatter can be monitored closely. 156 Figure 8.9: The normalized integrated intensity of each imaged quadrant as a function of voltage. The data for each material has been individually fitted to an exponential curve, shown with the black dotted line. The solid vertical lines represent the Cherenkov threshold for each material. For PEEK, the total internal reflection threshold is represented by the dashed vertical line. 157 Figure 8.10: A subset of the results from the silica configurations over the voltage range 156 - 225kV. The images were taken at the same temporal location relative to the current pulse: immediately after the rise in the current waveform. Figure 8.11: The normalized integrated intensity for silica over a wide voltage range. Data generated with a 25-mm-diameter cathode. The Cherenkov threshold is denoted with the solid vertical line and the exponential fit is represented by the black dotted line. 158 Fig. 8.10 shows the imaging results for the SiO2 diagnostic configuration, where the beam was generated with a 25-mm-diameter cathode. The first image was taken at V = 156kV, below the Cherenkov threshold for SiO2. The second image was taken near the Cherenkov threshold, and the third above with V = 225kV. The image produced for V = 156kV has a non-zero intensity and a nonuniform distribution indicative of electron scatter. From Eq. 2.25, we know that the scattering angle for 1-mm-thick SiO2 at 156keV is ∼ 140o. The distribution becomes more central as the voltage increases. As with the materials described previously, the image intensity increases exponentially with beam energy, shown in Fig. 8.11. The percent error for the fit listed on the intensity plot is approximately 8%. The strong voltage correlation within the desired energy range coupled with uniform, repeatable beam distribution, makes SiO2 an ideal current density diagnostic for electron beams with E > 190keV, β > 0.685. 8.3 Discussion on optimal configuration The distribution measured using the 200-µm thick Cu configuration shows a uniform current density, which is quantified through the corresponding MCNP6® simulations. The average measured current density falls within a reasonable range of that predicted through Trak. The measured beam radius with this configuration is repeatable, with a 1.5% variation from the mean. However, the experiments utilizing Al foil of a similar thickness to measure beams with comparable energies show irregular patterns indicative of electron scatter within the BC-400 diagnostic. This results from the thickness of the foil being less than the calculated electron range. The ranging limits were further confirmed with the aluminum pie experiment, which shows regular distributions in the 300 to 600-µm quadrants. Therefore, it is shown 159 that X-ray scintillation is optimized for materials with high Z and density, assuming the material thickness is greater than the tabulated range [102]. The Cherenkov pie tested various materials with differing material properties simultane- ously. PEEK has the highest refractive index of the shown materials, allowing for measure- ments both above and below the Cherenkov threshold. It was found that when V > 258kV, the intensity levels increase by a factor of ∼1.5 and the distribution is non-uniform. This is not shown for the remaining materials at the same diode voltage, further demonstrating the effect of total internal reflection on the measured distribution. For all the Cherenkov emitters shown, the integrated intensity increases exponentially with the diode voltage. This relationship is strongest for the 1-mm-thick silica diagnos- tic. For silica, Kapton, and the Willow® Glass, this increase begins shortly before the Cherenkov threshold. Nylon performs as an ideal Cherenkov diagnostic as the intensity levels are negligible until the Cherenkov threshold is surpassed. 160 Chapter 9. Conclusions A cathode test stand has been developed to fully explore the emission characteristics of various cold cathodes and photocathodes. Present work is concentrated on the study of velvet emitters for pulse durations in the range 300 - 1500ns. Throughout this dissertation, we have presented various diagnostic methods and techniques for characterizing the emission. Throughout this work we have documented the necessary electric fields to initiate electron emission, the temporal behavior of the extracted current, the visible emission on the cathode, and have measured the current density profile. Velvet cathodes are commonly used as high-current electron sources for pulse lengths less than 200ns. However, these cathodes are not suitable for accelerator applications requiring pulse durations greater than 200ns. Contributing factors to the overall limit of the current pulse duration include excess emission and high plasma expansion rates. Excess emission presents as intense current transients and noticeable beam loading in the measured diode voltage. Additional diagnostics are deployed to further monitor this effect: including DRDs and an ICCD focused on the face of the cathode. Excess emission worsens over time with current transients exceeding 700A approximately 800ns after the emission delay. The extracted current shows a steady linear increase which results from the AK-gap closure and plasma expansion rates >3mm/µs, calculated via Trak. The plasma growth is additionally monitored with an ICCD focused on the AK-gap. We show that both the expansion velocity and excess emission are heavily dependent on the total area of the emitter. The 7.5-mm-diameter cathode generally shows a reduced charge threshold for excess emission and an increased AK-gap closure rate. This is a result of the 161 exposed aluminum on the cathode plug surrounding the velvet emission surface. The width of the aluminum ring decreases as the emitter area increases and there exists no exposed aluminum for the 25-mm-diameter cathode. The 7.5-mm-diameter cathode plug has the largest amount of exposed aluminum, which creates a triple point and results in high amounts of edge emission. This complicates several measurements, including the current density. The high edge emission combined with space charge effects complicates the measurement for all diagnostic configurations. All experimental measurements were made with non-relativistic electrons (γ = 1.2 - 1.5, β = 0.5 - 0.75), creating a myriad of challenges in measuring current density on a diag- nostic screen. Electron scatter, Cherenkov radiation, and total internal reflection confuse the measured current density profile on screen diagnostics. The effects from beam-material interactions have been tested experimentally and the results were verified through computa- tional methods. MCNP6® simulations show that for electron scattering patterns, materials with high Z and density effectively range out the electron beam for thicknesses greater than the tabulated range [102]. It is shown that X-ray scintillation is a promising measurement method within this regime. Placing a 200µm-thick copper foil upstream of a plastic scintillator results in a uniform and repeatable current density measurement. Thin Al foil allows for forward scatter within the plastic diagnostic, confusing the measurement. Additionally, Cherenkov emitters prove to be a reliable diagnostic for measuring the current density of low-beta electron beams. The index of refraction must be chosen properly for the energy range of interest. The relationship between diode voltage and measured integrated image intensity has a strong exponential correlation. 162 9.1 Recommendations for future work Additional simulations should be performed to investigate the behavior of the cathode plasma as a function of time. The combination of Trak simulations, cathode imaging, and AK-gap imaging provides useful information on the plasma’s characteristics. However, these methods make several assumptions that introduce significant error into calculations concerning esti- mated current density and plasma expansion rates. Ref. [135] uses computational methods to model various aspects of the cathode plasma generated by a velvet cathode: ionization thresholds, the electron density, and the temporal evolution of the mean electron energy. Simulations assume an initial atomic density of 1018 cm−3 and an initial electron density of 1012 cm−3. The monolayer areal density is 3 × 1015 cm−2 and there are roughly 20 total desorbed monolayers, which gives the total number of desorbed atoms as < 6 × 1018. Work in Ref. [33], utilizes visible spectroscopy, cathode imaging, AK gap imaging, and LSP PIC simulations to explore the behavior of the hydrogen plasma generated by the DARHT Axis-I velvet cathode. It is shown that the initial ion temperature is 3.2eV and the surface aver- aged plasma density is 1014 cm−3. It is also demonstrated that lower density plasmas have a higher rate of plasma expansion. Similar computational methods can be implemented in the context of this dissertation to explore the temporal of the evolution of the cathode plasma. The assumptions and observations made in Refs. [33, 135] concerning initial beam density, initial ion temperature, monolayer densities, and initial electron densities can be applied. Obtaining additional information on the cathode plasma’s behavior specific to the cathode test stand will help guide future experiments and will be useful for comparing the reliability of various cold cathode materials. 163 Though uncoated velvet cathodes are not suitable for long pulse durations, other cold cathode materials may be ideal for this application. Work in [93] shows a stable extracted current with negligible AK-gap closure over 1µs for velvet cathodes coated with CsI. It is shown that the cathodes have an increased lifetime and the emission is not altered after 1- million pulses. The drawbacks of this cathode include desorption and ablation of the coating during operations, which can coat the inside of the diode. Graphite cathodes are an additional popular emitter choice as they generate large current densities and have a low threshold for plasma formation. Ref. [142] states that graphite cathodes are superior to the velvet cathode in terms of durability and shot-to-shot variation. However, work in [13] demonstrates that the plasma expansion velocity is comparable to that measured with the velvet cathode for 100ns pulse lengths. This increased expansion velocity may make graphite a poor candidate for long pulse emission studies. Carbon fiber cathodes have an improved lifetime when compared to the velvet cathode and show a fast emission turn-on [87]. Ref. [132] demonstrates that the carbon fiber cathode generates a current density over 2× that of the polymer velvet cathode. Additionally, the measured initial emission area was 100%, much larger than other cathodes tested. However, the measured expansion rate exceeds that of both velvet and graphite for a 100ns pulse length. Other possible candidates for this application include stainless steel, metal-ceramic cathodes, and CsI coated carbon fabric [87, 132]. Emittance measurements are crucial when determining whether an emitter is suitable for high brightness applications. As a follow-on to this dissertation, a pepperpot should be installed on the diode test bed. A pepperpot is a common emittance diagnostic and consists of an aperture plate coupled with a screen diagnostic, such as a scintillator or 164 Cherenkov emitter. After the beam collides with the screen, particles pass through the aperture with some angular spread [143]. 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