MSU RETURNING MATERIALS: PIace in book drop to remove this checkout from LIBRARIES .—:_—. your record. FINES WI” be charged if book is returned after the date stamped below. 'JULI 5 ‘1“ 23 cog ENERGY DISTRIBUTION AND TRANSFER IN FLOWING HYDROGEN MICROWAVE PLASMAS BY Randall Chapman A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemical Engineering 1986 ABSTRACT ENERGY DISTRIBUTION AND TRANSFER IN FLOWING HYDROGEN MICROWAVE PLASMAS By Randall Chapman This thesis is an experimental investigation of the physical and chemical properties of a hydrogen discharge in a flowing microwave plasma system. The plasma system is the mechanism utilized in an electrothermal propulsion concept to convert electromagnetic energy into the kinetic energy of flowing hydrogen gas. The plasmas are generated inside a 20 cm ID resonant cavity at a driving frequency of 2.45 GHz. The flowing gas is contained in a coaxially positioned 22 mm ID quartz discharge tube. The physical and chemical properties are examined for absorbed powers of 20 - 100 W, pressures of 0.5 - lO_torr, and flow rates of 0 - 10,000 p-moles/sec. A calorimetry system enclosing the plasma system to accurately measure the energy inputs and outputs has been developed. The rate of energy that is transferred to the hydrogen gas as it flows through the plasma system is determined as a function of absorbed power, pressure, and flow rate to i 1.8 W from an energy balance around the system. The percentage of power that is transferred to the gas is found to increase with increasing flow rate, decrease with increasing pressure, and to be independent of absorbed power. An energy transfer efficiency of 50 % has been reached for the described apparatus at a flow rate of 8,900 p-moles/sec and a pressure of 7.4 torr, and for a absorbed power range of 20 - 80 W. An optical spectroscopy system to measure the line intensities and widths of the plasma emission has been developed. The electron density, plasma frequency, percent ionization, atomic electronic temperature, and molecular rotational and vibrational temperatures of the plasma are determined as functions of absorbed power, pressure, and flow rate. The electron densities are found 12 13 to range from 10 - 5 x 10 cc-1. The percent ionization is found to range from 0.001 - 0.1 %. The atomic electronic temperature is found to range from 3500 - 6500 °K. The molecular rotational temperature is found to range from 225 - 850 °K. The molecular vibrational temperature is found to range from 4000 - 17,000 °K. A simplistic heat transfer model that characterizes the energy transfer of the plasma-wall interactions utilizing the calorimetry and spectroscopy results has been developed to lend some insight to the dominant processes involved. TABLE OF CONTENTS List of Tables . List of Figures Nomenclature . Introduction . Experimental I. Plasma Cavity . II. Flow System . III. Microwave System IV. Calorimetry System V. Spectroscopy System . VI. Experimental Conditions Calorimetric Measurements Spectroscopic Measurements I. Emission Spectroscopy . II. Characteristic Temperatures . III. Electron Density Heat Transfer Model Conclusion . List of References . ii . iii iv xiii 10 15 17 21 23 25 40 49 123 178 194 199 LIST OF TABLES Experimental Conditions Transition Probabilities and Wavelengths of the Atomic Transitions Energies and Degeneracies of the Atomic Electronic Levels . Wavelengths of the Molecular Transitions Energies of the Molecular Rotational Levels Franck - Condon Factors and Frequencies of the Vibrational Transitions . Energies of the Molecular Vibrational Levels . Deconvolution Functions Constants for the Electron Density Calculation . iii 24 53 54 79 81 105 106 127 129 10. 11. 12. 13. 14. 15. 16. 17. LIST OF FIGURES Performance gap Electrothermal propulsion concept Plasma cavity TE* d 111 mo e . TM011 mode . Hydrogen flow system . Microwave system . Calorimetry system . Cooling water system . Cooling air system . Spectroscopy system Energy inputs and outputs * % P for the TE gas % P as a function of flow rate gas at various pressures . % P as a function of pressure gas at various flow rates % P as a function of flow rate water at various pressures . o ressure % Pwater as a function f p at various flow rates iv 111 and TM011 modes . 11 12 13 16 18 19 20 22 26 31 32 33 35 36 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. % Pair as a function of flow rate at various pressures . % Pa as a function of pressure ir at various flow rates Potential energy curves for hydrogen . T as a function of flow rate elecl at various pressures . Te1ec2 at various pressures . as a function of flow rate Telec3 as a function of flow rate at various pressures . T elecl at various flow rates T e1ec2 at various flow rates as a function of pressure as a function of pressure Telec3 as a function of pressure at various flow rates Electronic temperatures as of flow rate at 0.7 torr . Electronic temperatures as of flow rate at 1.3 torr . Electronic temperatures as of flow rate at 1.7 torr . Electronic temperatures as of flow rate at 2.3 torr . Electronic temperatures as of flow rate at 4.8 torr . Electronic temperatures as of flow rate at 7.4 torr . functions functions functions functions functions functions 37 38 51 56 57 58 59 60 61 62 63 64 65 66 67 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. Electronic temperatures as functions of pressure at 0 p-moles/sec . Electronic temperatures as functions of pressure at 150 p-moles/sec . Electronic temperatures as functions of pressure at 450 p-moles/sec . Electronic temperatures as functions of pressure at 750 p-moles/sec . Electronic temperatures as functions of pressure at 1300 p-moles/sec Electronic temperatures as functions of pressure at 4800 p-moles/sec Electronic temperatures as functions of pressure at 8900 p-moles/sec Electronic temperatures as functions of absorbed power at 150 p-moles/sec and 0.7 torr Electronic temperatures as functions of absorbed power at 150 p-moles/sec and 7.4 torr Average rotational power as a function of flow rate at various pressures Trotl as a function of flow rate at various pressures . T as a function of flow rate rot2 at various pressures . T as a function of flow rate rot3 at various pressures . Trot4 as a function of flow rate at various pressures . Average rotational temperature as a function of pressure at various flow rates vi 68 69 70 71 72 73 74 75 76 83 84 85 86 87 88 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. T as a function of pressure rotl at various flow rates . . . . . . . . . . . . . 89 Trot2 as a function of pressure at various flow rates . . . . . . . . . . . . . 90 Trot3 as a function of pressure at various flow rates . . . . . . . . . . . . . 91 Trot4 as a function of pressure at various flow rates . . . . . . . . . . . . . 92 Rotational temperatures as functions of flow rate at 0.7 torr . . . . . . . . . . . . 93 Rotational temperatures as functions of flow rate at 1.3 torr . . . . . . . . . . . . 94 Rotational temperatures as functions of flow rate at 1.7 torr . . . . . . . . . . . . 95 Rotational temperatures as functions of flow rate at 2.3 torr . . . . . . . . . . . . 96 Rotational temperatures as functions of flow rate at 4.8 torr . . . . . . . . . . . . 97 Rotational temperatures as functions of flow rate at 7.4 torr . . . . . . . . . . . . 98 Rotational temperatures as functions of pressure at 150 p-moles/sec . . . . . . . . . 99 Rotational temperatures as functions of absorbed power at 150 p-moles/sec and 0.7 torr . . . . . 100 Rotational temperatures as functions of absorbed power at 150 p-moles/sec and 7.4 torr . . . . . 101 Rotational temperatures as functions of absorbed power at 8900 p-moles/sec and 7.4 torr . . . . . 102 Tvibl as a function of flow rate at various pressures . . . . . . . . . . . . . . 107 vii 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. v at various pressures . T ib2 as a function of flow rate Tvibl as a function of pressure at various flow rates Tvib2 as a function of pressure at various flow rates Vibrational temperatures as functions of flow rate at 0.7 torr . Vibrational temperatures as functions of flow rate at 1.3 torr . Vibrational temperatures as functions of flow rate at 1.7 torr . Vibrational temperatures as functions of flow rate at 2.3 torr . Vibrational temperatures as functions of flow rate at 4.8 torr . Vibrational temperatures as functions of flow rate at 7.4 torr . Vibrational temperatures as functions of pressure at 150 p-moes/sec Vibrational temperatures power at 150 p-moles/sec Vibrational temperatures power at 150 p-moles/sec Vibrational temperatures as functions of absorbed and 0.7 torr as functions of absorbed and 7.4 torr as functions of absorbed power at 8900 p-moles/sec and 7.4 torr . n e1 at various pressures . n e2 at various pressures . as a function of flow rate as a function of flow rate viii 108 109 110 111 112 113 114 115 116 117 118 119 120 131 132 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. ne3 as a function of flow rate at various pressures . nea as a function of flow rate at various pressures . nel as a function of pressure at various flow rates n82 as a function of pressure at various flow rates ne3 as a function of pressure at various flow rates nea as a function of pressure at various flow rates Electron densities as functions of flow rate at 0.7 torr . Electron densities as functions of flow rate at 1.3 torr . Electron densities as functions of flow rate at 1.7 torr . Electron densities as functions of flow rate at 2.3 torr . Electron densities as functions of flow rate at 4.8 torr . Electron densities as functions of flow rate at 7.4 torr . Electron densities as functions of pressure at 150 p-moles/sec . Electron densities as functions of absorbed power at 150 p-moles/sec and 0.7 torr Electron densities as functions of absorbed power at 150 p-moles/sec and 7.4 torr ix 133 134 135 136 137 138 139 140 141 142 143 . 144 145 146 147 93. 94. 95. 96. 97. 98. 99. 100. 101. 102. 103. 104. 105. (wpl/w)2 as a function of flow rate at various pressures . (wpz/w)2 as a function of flow rate at various pressures . (wp3/w)2 as a function of flow rate at various pressures . (”pa/”)2 as a function of flow rate at various pressures . (wPI/w)2 as a function of pressure at various flow rates (wpz/w)2 as a function of pressure at various flow rates (wpa/w)2 as a function of pressure at various flow rates (cope/w)2 as a function of pressure at various flow rates Normalized plasma frequencies squared as functions of absorbed power at 150 u-moles/sec and 0.7 torr Normalized plasma frequencies squared as functions of absorbed power at 150 p-moles/sec and 7.4 torr PIl as a function of flow rate at various pressures . P12 as a function of flow rate at various pressures . P13 as a function of flow rate at various pressures . . 149 150 . 151 . 152 . 153 . 154 . 155 . 156 . 157 . 158 . 160 . 161 162 106. 107. 108. 109. 110. 111. 112. 113. 114. 115. 116. 117. 118. 119. 120. 121. PIA as a function of flow rate at various pressures . P11 as a function of pressure at various flow rates P12 as a function of pressure at various flow rates P13 as a function of pressure at various flow rates PIA as a function of pressure at various flow rates Percent of flow Percent of flow Percent of flow Percent of flow Percent of flow Percent of flow Percent ionizations rate at 0.7 ionizations rate at 1.3 ionizations rate at 1.7 ionizations rate at 2.3 ionizations rate at 4.8 ionizations rate at 7.4 ionizations as functions torr . as functions torr . as functions torr . as functions torr . as functions torr . as functions torr . as functions of pressure at 150 p-moles/sec . Percent ionizations as functions power at 150 u-moles/sec and 0:7 Percent ionizations as functions power at 150 p-moles/sec and 7.4 U as a function of flow rate max at various pressures . U as a function of pressure max at various flow rates xi of absorbed torr of absorbed torr 163 164 165 166 167 168 169 170 . 171 172 173 174 175 176 182 183 122. 123. 124. 125. 126. 127. 128. Urot as a function of flow rate at various pressures . U as a function of pressure rot at various flow rates Urot as a function of absorbed power at 150 u-moles/sec and various pressures . T as a function of flow rate wall at various pressures . Twall as a function of pressure at various flow rates T and T as functions of flow rate max wall at various pressures . Trota and Twall at various pressures . as functions of flow rate xii 185 . 186 187 189 190 191 192 NOMENCLATURE velocity of light charge of an electron gravitational constant degeneracy of the nth level Planck constant Boltzmann constant lower or final level propellant mass flow rate mass of an electron upper or initial level electron density Franck-Condon factor vch vibrational level plasma-wall interaction area transition probability constant for electron density calculation discharge tube diameter energy of the nth level force xiii F(J) GF G°(V) n.5,... meas I 5P Pabs air gas rad Pwater PI Re energy of the Jth rotational level Gaussian fraction th energy of the v vibrational level Balmer series lines measured emission line intensity specific impulse Jth rotational level Lorentzian fraction Lyman series lines atomic mass population of Nth level power absorbed by the microwave system power absorbed by the cooling air power absorbed by the gas as it flows through the system power contained in the electromagnetic radiation that escapes the system power aborbed by the cooling water percent ionization partition function Reynolds number spectral response function theoretical line strength temperature xiv air Telec gas max rot vib wall TE (3 rot max cooling air temperature electron temperature atomic electronic temperature gas temperature maximum possible gas temperature rotational temperature vibrational temperature discharge tube wall temperature electromagnetic resonant mode electromagnetic resonant mode heat transfer coefficient heat transfer coefficient based on Trot heat transfer coefficient based on Tmax propellant exit velocity permitivity of free space _ wavelength mean free path wavelength of the transition from level n to level frquency collision frequency frequency of the transition from level n to level m XV AT AA AA AA AA AA 1/N % Pair gas % Pwater frequency of the vibrational transition from level v' to level v" angular frequency plasma frequency initial or upper level final or lower level solid angle temperature difference doppler line width instumental line width stark line width total measured line width l/N fractional height line width percent of the power absorbed by the microwave plasma system that is absorbed by the cooling air percent of the power absorbed by the microwave plasma system that is absorbed by the gas as it flows through the system percent of the power absorbed by the microwave plasma system that is absorbed by the cooling water xvi INTRODUCTION The placement of a satellite or similar object into a useful orbit about the earth usually occurs in two steps. The object is first lifted from the ground to low earth orbit (LEO), then it is raised to geosynchronous earth orbit (GEO). There are currently two different types of propulsion technologies developed, chemical thrusters and electrostatic thrusters. The chemical thrusters characteristically have a high thrust density at a low specific impulse. Whereas the electrostatic thrusters have a low thrust density at a high specific impulse. A chemical thruster must be used to get an object off the ground and into LEO due to the high thrust density required to reach escape velocity. Either thruster may be used to raise the object from LEO to CEO. However, since the first part of the mission is the most expensive of the steps, it is desirable to look at the inherent efficiencies of the two thrusters in getting an object from LEO to CEO. This efficiency is measured in terms of the total mass of fuel and payload that is required in LED to raise that payload into GEO divided by the resultant 2 payload mass in GEO. This ratio as a function of specific impulse is given in Figure 1. Specific impulse is given as where F - force m - propellant mass flow rate 5 - gravitational constant Ve - propellant exit velocity The electrostatic thruster has a much lower ratio than the chemical thruster. However, the time it would take for the electrostatic thruster is two orders of magnitude greater than that for the chemical thruster. Figure 1 also shows that there exists a performance gap between these two propulsion technologies. 63 A schematic for a proposed electrothermal propulsion concept 19’ 21 This propulsion concept is is given in Figure 2. actually a hybrid of the electrostatic and chemical thruster technologies and theoretically has the capability to fill the existing gap. An additional advantage that MASS REQUIRED IN LEO PAYLOAD MASS IN GEO CHEMICAL THRUSTER /(1doy) I I ELECTROSTATIC THRUSTER l (100 days) a I I * aoo 1600 2400 3200 4000 Isp (sec) Figure 1. Performance gap Solar Panel Microwave Oscillator Hydrogen Tank J #- * L_ --- Nozzle Plasma Cavity Thermalization Chamber Figure 2. Electrothermal propulsion concept 5 this concept has is that there are no metallic electrodes or surfaces in contact with the plasma. The electrothermal propulsion concept utilizes a microwave-sustained plasma system as the mechanism to convert electromagnetic energy into kinetic energy of a gas as it flows through the system. Electricity generated by solar cells runs the microwave power generator. The microwave radiation is coupled to a resonant cavity setting up electromagnetic fields. Hydrogen from a storage tank is fed through a quartz discharge tube coaxially positioned in the resonant cavity where the plasma is formed. The electrons in the plasma are accelerated by the electromagnetic fields thereby increasing their kinetic energy. The electrons impart their energy to the other species of the plasma through collisions. The kinetic energy of the hot gas is then maximized as the gas relaxes to thermodynamic equilibrium in the thermalization chamber. The gas is then expanded through the nozzle to produce thrust. This study focuses on the energy exchange between the electromagnetic radiation and the gas kinetic energy. A calorimetry system enclosing the microwave plasma system has been designed and built to accurately measure the energy inputs and outputs of the plasma system. 20. 24' 25' 101’ 102 A calorimetric measurement technique has been developed to determine the distribution of energy 6 within the microwave plasma system. The power that is ultimately transferred to the hydrogen gas as it flows through the microwave plasma system is measured as a function of absorbed power, pressure, and flow rate. An optical spectroscopy system has been developed to determine the physical properties of the plasma. 18’ 22 Electron density, percent ionization, plasma frequency, atomic electronic temperature, molecular rotational and vibrational temperatures are determined from emission line intensity and width measurements as functions of absorbed power, pressure, and flow rate. A simplistic heat transfer model utilizing the results of the calorimetric and spectroscopic measurement techniques has been developed to lend some insight as to the dominant energy transfer mechanisms. 20' 24' 25’ 101’ 102 Heat transfer coefficients that characterizes the energy transfer processes involved in the plasma-wall interactions are calculated as functions of absorbed power, pressure, and flow rate. For the experimental conditions involved in this investigation, the following regimes are established: 1) The Reynolds number is on the order of 50 so that the velocity profile of the hydrogen plasma may be regarded as laminar. 12 7 2) The ratio of the discharge tube diameter to the molecular mean free path is on the order of 100 so that the hydrogen plasma may be regarded as a continuum. 12 3) The plasma parameter is on the order of 0.05 so that the hydrogen plasma may be regarded as an ideal 86 gas. EXPERIMENTAL 1. Plasma Cavity The device used to generate the plasma is a resonant cavity. Details of the plasma cavity are given in Figure 3. The water cooled cylindrical resonant cavity has a fixed diameter of 20 cm ID, a continuously variable length of 6 - 40 cm, and is fabricated from brass. The screened window alIows for visual observation and spectroscopic measurements. The water cooling is required for constant boundary conditions and to prevent damage to the cavity. The cavity is capable of supporting several resonant modes which represent eigen values of the solution to Maxwell's equations involving the experimental 94' 120 For all of the experimental data, the parameters. probe depth and sliding short length are adjusted to obtain a match (minimum reflected power) between the magnetron output and the loaded resonant plasma cavity. Since the driving frequency and cavity diameter are fixed, the different operating modes are obtained by changing the cavity length. The simplest description of a plasma is MICROWAVE COUPLING PORT O SCREENED VIEWING WINDOW SLIDING SHORT Figure 3. Plasma cavity 10 the cold plasma model with the important plasma characteristic being the electron density. The cold plasma model is sufficient for the level of treatment involved in this investigation. The presence of a plasma only slightly perturbs the empty cavity modes since the diameter of the plasma is much smaller than the diameter of the cavity. Figures 4 and 5 show the electric field lines and , * plasma formation pOSitions for the TE111 and TM011 modes, respectively. The TM mode is used for this study 011 because the plasma forms away from the wall keeping the plasma-wall interactions to a minimum. As can be seen, the plasma is not homogeneous and in addition the plasma looks slightly different for the different experimental conditions. It grows in size and becomes brighter with increasing power and shrinks in size becomes dimmer with increasing pressure and flow rate. 11. Flow System A schematic of the hydrogen flow system is given in Figure 6. A regulated stream of 99.9999 % hydrogen is fed through 1/4 in. stainless steel tubing to a stainless needle valve that controls the flow rate which is measured by a mass flow meter, which is calibrated for hydrogen gas and has a range of 0 - 8,900 p-moles/sec (0 - 12,000 sccm 11 \\,II// . //\\\ PIosmo Discharge Cavity Tube WoII ' / WoII FHH I \ I ~ 605 .__ éfifi +Flow l I l ® — Plosmo Region e - Electric Field Lines ’ 5* de Figure 4. T 111 mo Discharge Covity Tube Well A / Woll 77M}: _ :01 18:; —"' l \ ""‘"‘ +_Gos [ _m_ _ _ Flow __ _ \\ // __ __ / .— \'i |,/ iiitilii ® - PIosmo Region 4 - Electric Field Lines Figure 5. TMOll mode 13 umpuouom mmHQDOUOELocellinu uDO xcme ucumz chOLU»: II. mcwaoou xumpcouom Sum>mu manage o>~m> fil CH scum: mcmfioou xcmb caucupxm was? o>am> anaconda / \. / “ ._ _. ilf/ 9.5m Esau?» 091V? %rl» wmsmu Easum>i\\\ cu Lm< mcmHoou L uao Lm< ocmHoou sopuouom scum: 3o~m mmmz moamu wcsmmotm Hydrogen flow system Figure 6. 14 or 0 - 20 mg/sec). The pressure upstream of the needle valve is measured by a Bourdon tube type pressure gauge and is maintained at 1100 torr. The pressure drop across the needle valve is large so that fluctuations upstream of the valve will not effect the flow rate or downstream pressure. The hydrogen gas is then fed through 1/4 in. teflon tubing to the discharge tube. The discharge tube is 22 mm ID, has a 30 mm 0D air cooling jacket, and is fabricated form quartz. The plasma is formed in the discharge tube which is positioned in the plasma cavity. The hydrogen gas is then fed through 25 mm ID pyrex tubing to the vacuum pump. The pressure of the plasma is measured immediately downstream of the plasma cavity by a capacitance type pressure gauge which has a range of 10.3 - 103 torr. The pressure of the plasma for a given hydrogen flow rate is adjusted by introducing 99.95 % hydrogen downstream of the plasma. The air cooling of the discharge tube is required for constant boundary conditions, to maintain a constant atom recombination rate, and to prevent damage to the discharge tube. The cooling air flows counter current to the hydrogen flow. Previous to installation, the discharge tube was cleaned with KOH and rinsed with HP. The discharge tube is kept at a vacuum when not in use to 15 prevent contamination. The leak rate for the entire system was less than 2 p/min. The maximum flow rate possible for pressures of 0.7, 1.3, 1.7, 2.3, 4.8, 7.4 torr are 150, 450, 750, 1300, 4800, 8900 p-moles/sec, respectively. 111. Microwave System A schematic of the microwave power delivery system is given in Figure 7. Electromagnetic radiation is produced by a microwave generator which has an output range of 0 - 500 W at a fixed frequency of 2.447 GHz. The radiation is directed through rectangular waveguide to the water cooled circulator which protects the magnetron from reflected power. The radiation is then through waveguide and coaxially cable to the directional couplers. The radiation in then critically coupled to the resonant cavity with a variable depth 7/8 in. coaxial excitation probe. Power meters and 10 dB directional couplers measure the incident and reflected power levels. Recorders are connected to the power meter to give time histories of the experimental runs. The power meters and directional couplers are calibrated with an accurately known power level at 2.447 GHz which is produced by a variable frequency sweep oscillator and amplified to about 3 W by a traveling wave tube. Hatched Lo, l6 -————-Microwave Power Generator Matched Load > Circulator I Recorder \ .' I Directional CI _I 1.1.1.... \ ‘ 5L Power Meters \ ~\7‘-Excitation Probe Plasma Cavity Figure 7. Microwave system 17 1V. Calorimetry System A diagram of the calorimetry system is given in figure 8. The cooling air and water are delivered to the calorimetry system at a constant flow rate and temperature. Copper-constantan thermocouple measure the temperatures of the coolant streams. The thermocouples are connected to reference junctions which are maintained at 0 °C in a constant temperature ice bath. Solid copper wires are run from the reference junctions to the recorders that measure the thermocouple voltages and give time histories of the experimental runs. The thermocouples are calibrated with a calorimetric thermometer which has a resolution of i 0.001 ’C. Diagrams of the water and air cooling systems are given in Figures 9 and 10, respectively. These systems are individually calibrated by utilizing a dummy load. Microwave radiation is fed into an insulated matched load which is cooled by one of the coolant streams. The flow rates of the coolant streams are measured by calibrated flow meters and kept constant. The inlet temperature of the water cooling stream is also kept constant. It is not as critical to keep the inlet temperature of the air cooling stream constant. The typical temperature rise measured for the water cooling stream is 0.2 - 1.3 °C and for the air cooling stream it is 3 - 25 °C. For an 18 cosumasmcu beams mc-00U oHQDOUOELm:P.IJ §\\\» [.3982ng \\ d Emmuum .lllliig moo cmmoprz _I madsouoeboce ocoem mciemsm . mmmmg \\w . wHQDOUOEuch L \_ .1 ODOhm * LL< ccmfioou mo>m>oLumz Calorimetry system Figure 8. 19 1' Surge Tank Constant ///////’ Temperature Filter / Bath / D Constant Temperature Bath I Flow Meter i l—I—‘ f l | I J " Recorder Reference V Valve Junctions Fill Tank Plasma Cavity D— The rmocoup les Figure 9. Cooling water system 20 / RegUlator Air Compressor Filter Constant Temperature Flow Meter Bath ‘ Recorder ‘ | Valve -———- I 1.3,? a Reference Junctions Exhaust I -o-—— | a——Hydrogen Gas _J Stream Discharge Tube D ..... Thermocouples Figure 10. Cooling air system 21 absorbed power range of 0 - 100 W, the microwave power absorbed by the matched load is measured by the calibrated power meters and directional couplers. An effective heat capacity in then calculated for each coolant system. The overall calorimetry system is then double checked under zero flow rate plasma conditions. V. Spectroscopy System A diagram of the spectroscopic diagnostic system is given in Figure 11. A detailed description of the operation of the spectroscopy system has been given previously and will not be repeated here. 18 The emission from the plasma is monitored by a 0.5 m spectrometer. Two diffraction gratings are used. The molecular spectra and line width measurements are taken with the 2400 G/mm grating which has a range of 1050 - 5000 A. The atomic spectra was taken with the 1200 G/mm grating which has a range of 1050 - 10000 A. The optimum slit widths are found by trial and error. They are 35 p for the entrance slit and 40 p for the exit slit. The spectrometer is placed as close to the plasma as possible and is about 50 cm. An upper limit of z 10 torr for the plasma - pressure is realizable since as the pressure increases the emission intensity decreases and above 10 torr the emission is too weak to take useful spectra. An optical mwOmOUmm 22 mmah mom>m:> omzmmmUm >4nEDW mw>>Om O O Spectroscopy system Figure 11. 23 lens system is not used. Since the spectroscopic results are to be used in conjunction with calorimetry results, spatially averaged measurements were desired. The spectrometer is positioned to observe the brightest portion of the plasma. A high sensitivity PMT is used to measure the plasma emission. The spectroscopic system has a resolution of better than 0.5 A. The PMT is operated at 900 V from a high voltage dc power supply. The PMT output is monitored by an fast response electrometer which was connected to a recorder to provide the spectras. The response of the spectroscopic system is calibrated with a quartz halogen tungsten coil lamp. V1. Experimental Conditions Table 1 give the ranges of the experimental parameters in this investigation. II 24 Table 1. Gas Flow Rate Pressure Reynolds Number (Re) Mean Free Path (A) Tube Diameter (D) D/A Rotational Temperature (Tr0 t) Vibrational Temperature (Tvib) ) Electronic Temperature (T elec Electromagnetic Mode Absorbed Power (Pabs) Driving Frequency (3;) Collision Frequency (um) um/w Electron Density (ne) Electron Temperature (Te) Plasma Frequency (up) wp/w 2 w w ( p/ ) Percent Ionization Debye Length Plasma Parameter Experimental Conditions H2 0 - 10,000 p-moles/sec l - 10 torr 0 - 60 0.023 2.2 cm 100 225 - 850 °R 4,000 - 17,000 °K 3,500 - 6,500 °x TM011 o - 100 w 2.45 GHz - 5 x 109 sec.1 2 x 109 0.1 - 3.5 ll 13 -l 8 x 10 - 3 x 10 cc 5 x 10 - 10 °K 10 ll -1 5 x 10 - 3 x 10 sec 3 - 20 10 - 350 0.001 - 0.1 % 9 x 10'5 - a x 10'“ cm 0.03 - 0.08 CALORIMETRIC MEASUREMENTS A calorimetric diagnostic system has been developed to determine the energy distribution in a microwave plasma system and in particularly the energy content of the hydrogen gas as it exits the microwave plasma 20’ 24' 25' 101’ 102 A literature review revealed system. that no similar techniques have been utilized. Previous calorimetric measurement techniques have involved the use of probe type calorimeters actually in the plasma itself to determine the degree of dissociation in hydrogen and oxygen plasmas. The energy inputs and outputs of the microwave plasma system are show in figure 12. The energy input is the power delivered to the plasma cavity from the microwave generator. The energy outputs are the power absorbed by the air cooling of the discharge tube, the water cooling of the plasma cavity, the energy contained in the emission radiation that escapes the system, and the energy transferred to the gas as it flows through the microwave plasma system. An energy balance around the system can be written as 25 Microwave Power In Cooling Air In Cooling Air Out II t . Hydrogen Gas I ) - _ — — —_ _ ___.... Stream — — — — -- - Cooling Water In Cooling Water Our Figure 12. Energy inputs and outputs abs gas air + water Prad Pabs is the power absorbed by the microwave plasma system and is measured by power meters and directional couplers. Pair is the power absorbed by the air cooling of the discharge tube and is measured by the air flow rate and its temperature rise. P is the power absorbed by water the water cooling of the plasma cavity and is measured by the water flow rate and its temperature rise. Prad is the power absorbed by the emission radiation as it escapes the system. For the purpose of this study, P is neglected rad since the system is almost entirely enclosed. Pgas is the power absorbed by the hydrogen gas as it flows through the microwave plasma system and is determined from the difference A detailed error analysis of the calorimetry system and the technique leads to the following error estimates: -+ APabs _ 0.8 W AP - i 0 5 W air AP - i 0 5 W 28 Resulting in an error estimate for Pgas of AP - i 1.8 W gas The results are presented in terms of percentages. The percentage of the power absorbed by the microwave system that is absorbed by the hydrogen gas as it flows through the system is denoted % Pgas' s9 -100x—3§ gas Pabs Since Pgas is the energy in the gas that is available for thrust, % Pgas is regarded as the efficiency with which the microwave plasma system converts electromagnetic energy into gas kinetic energy. Likewise, the percentage of the power absorbed by the microwave system that is absorbed by the cooling air and water is denoted % Pa ir and % Pwater’ respectively. P . s9 -100x—m air P abs P 100 x water water Pabs 29 Consequentially, for the 20 - 80 W range of this investigation, the errors are A % P - 2 - 9 % gas A % Pair - 1 - 2.5 % A % P - 1 - 2.5 % water A % Pabs - 1 - 4 % Though this approach is simplistic, it provides very useful information. This technique measures the energy flux to the gas which is exactly the quantity desired. It does not call upon the definition of a characteristic temperature. A characteristic temperature only has meaning for a system in thermodynamic equilibrium which is definitely not the case for the plasmas in this study. The measurement of Pga also includes the energy 3 contained in the gas in the the form of atomic and molecular excited states. Most of this additional energy tied up in excited states can also be converted to thrust by allowing the hot gas to first reach thermodynamic equilibrium before expanding it through a nozzle. This technique is not specific to any one gas. It can has also been used to study the effects of different gases and their properties. 24 This technique also forms the basis from which the study of energy transfer 30 mechanisms involved in the plasma-wall interactions can be expanded. Finally, this technique demonstrates the feasibility of the electrothermal propulsion concept. Figure 13 shows % Pgas as a function flow rate for * the TE111 and TM011 modes. These results show that the TM011 mode yields a larger value of % Pgas than the TE:11 mode at the higher flow rates. Figures 14 and 15 show % Pgas as a function of flow rate and pressure, respectively. % Pgas is found to increase with increasing flow rate, decrease with increasing pressure, and to be independent of absorbed power. In this study a maximum of 50 % for % Pgas has been reached. Since the relative error for % Pgas is up to 10 %, the graphs represent smoothed data averaged over 10 - 12 experimental points. The data is reproducible well within the experimental error. Since the quartz discharge tube and the cooling air are transparent to microwave radiation, the plasma first absorbs all the power absorbed by the microwave plasma system except for the power dissipated in the water cooling of the plasma cavity walls through electromagnetic currents and losses, (P ). The plasma then loses some water of its energy through interactions with the air cooled Wop gas 31 OH 111 P=1.7torr Pobs = 20 -100 W/ L 500 1000 Flow Rate (p-moles/sec) Figure 13. % Pgas for the TE:11 and TM011 modes 32 (mg/sec) 140 20 50- 7.4 40— torr °/° Pgos 4.8 30— 17 1.3' 2-3 20 5000 10000 Flow Rate (b—moles/sec) Figure 14. % Pgas as a function of flow rate at various pressures Pobs = 20 -100 w 50— 08900 p-moleslsec ‘40- CVQ>FDEJCJES 3o— \ 4800 20— \ 4EK) 1300 10‘ 750 ~150 5 1C) Pressure (torr) Figure 15. % Pgas as a function of pressure at various flow rates 34 discharge tube wall, (Pair)' The plasma also loses additional energy through emission radiation. The uv radiation is subsequentially absorbed by the discharge tube wall and the visible and ir radiation is absorbed by the plasma cavity wall. The quantity of energy that is lost from the plasma and then reabsorbed by the walls is not known but assumed to be negligible. Figures 16 and 17 show % P as functions of flow water rate and pressure, respectively. % P is found to be water independent of absorbed power and to be relatively independent of flow rate and pressure. Consequentially, the effects of flow rate and pressure on % Pgas are due to their effects on % P . . air Figures 18 and 19 show % Pair as functions of flow rate and pressure, respectively. % Pair is found to decrease with increasing flow rate, increase with increasing pressure, and to be independent of absorbed power. Since % Pwa is relatively constant at about ter 17.5 %, than 82.5 % of the absorbed power is intially absorbed by the plasma. This is the maximum possible value for % P a 'obtainable with this experimental g s apparatus and is reduced by interactions of the plasma with the discharge tube wall. The problem then becomes one of keeping the energy in the flowing gas. This °I 35 30-: 0.7 torr \ 1.3 20- — i 7 7 4 °/°P """"'"" f water W8 10,- Pabs = 20-100W I 5000 10000 Flow Rate (iJ-moles/sec) Figure 16. % Pwater as a function of flow rate at various pressures 30 20 °/° Pwater 10 36 All Flow Rates Pubs = 20 -1oo w 5 10 Pressure (torr) Figure 17. % P as a function of pressure water at various flow rates 37 90 Pubs = 20-100 w 80 70‘ °/°Pair 60 50 40 7.4 30- torr 20 I 5000 10000 Flow Rate (p-moles/sec) Figure 18. % Pair as a function of flow rate at various pressures 38 90 80- 150 70- 750 450 1300 °/° Pair 60- ’////’4800 50- 40— , 8900 (p-moles/sec) 30— 20 ' 5 10 Pressure (torr) Figure 19. % Pair as a function of pressure at various flow rates 39 problem illustrates the importance of the plasma-wall interactions and the need to understand them better. As can be seen from figures 14 and 15, an upper limit for % P has not been found. % P could be further gas gas increased by increasing the flow rate, using larger diameter tubes to increase the volume/surface area ratio to decrease th plasma-wall interactions, increasing the pumping speed to be able to reach lower pressures at a given flow rate. It is interesting to note that % Pgas is independent of power. Therefore, % Pgas can not be increased by increasing the input power. SPECTROSCOPIC MEASUREMENTS 1. Emission Spectroscopy A spectroscopic diagnostic system has been developed to determine the chemical and physical properties of a 18’ 22 The use flowing hydrogen microwave plasma system. of emission spectroscopic techniques to study plasmas have several distinct advantages. The measurement techniques in no way interfere with the plasma. The techniques simply involve monitoring the naturally occurring emission of the plasma. There are generally three different types of measurements made in emission spectroscopy; continuum intensities, line intensities, and line shapes. The presence of electrons is what makes a plasma unique and interesting. For most plasmas and certainly the plasmas considered in this study, the electrons are the driving force of a plasma. Therefore, the physical state of a plasma is most often characterized by the electron density and temperature. Consequentially, a great deal of effort has been spent in developing various diagnostic techniques to measure these 40 41 quantities. 5, 15, 28, 54, 56, 73, 92, 93, 95, 121, 137, 153 Since the electrons are the driving force of the plasma, they are usually at a higher temperature than the rest of the species in the plasma. Plasma emission that is due directly to the free electrons in the plasma is from bremsstrahlung and electron-ion recombination processes. These processes give rise to continuum radiation. Therefore emission diagnostic techniques involving continuum measurements give the best estimates of the electron temperature. Experimental measurements of the electron temperature utilizing the line-continuum 27, 104 intensity ratio , continuum intensity ratios 28, 61’ 78 methods have been made. However. continuum slope techniques involving the continuum radiation suffer from two major drawbacks. First, these techniques require that the population of the various ionic species are known along with their contribution to the continuum radiation. Second, these techniques assume that the electron velocity distribution is Maxwellian. Since self-consistent field models have shown that the electron distribution is not Maxwellian and the ionic specie populations are not known, these techniques are not applicable to the plasmas in this study. A technique has also been developed to determine the electron temperature of a non-equilibrium plasma based on 42 the intensity ratio of the Balmer series lines 108, however this technique is simply a correction factor for the atomic electronic temperature which will be discussed later. Micro electric fields produced by the ions and free electrons in the plasma influence the shape of the emission line through the Stark effect. The Stark broadening of emission lines in plasmas has been studied extensively. 5, 15, 28, 54, 56, 73, 92, 93, 95, 121, 137, 153 Stark broadening is pressure broadening caused by charged perturbers and tends to be important for lines originating from allowed electric dipole transitions. The first line profiles were calculated with the classical 50 The electron produced fields were path approximation. calculated using an impact approximation. The ion produced fields were calculated using a quasi-static approximation. Local thermal equilibrium is assumed exist, however this assumption is not critical to the results. Electron shielding and ion-ion correlations are also included. The impact approximation assumes that the duration of the perturbations is short so only that the net change caused by a collision matters. The quasi- static approximation assumes that the motion of the perturbers can be neglected. These approximation represent the extreme limits. 43 Improvements to the theory have included the effects of the Stark broadening of the upper and lower levels of the transition 4’ 51’ 52’ 52’ 53, interference from cross terms and quadrapole interactions 84, incompleted collisions 71, and ion dynamics. 65 The theory has also been extended to lower electron densities. 134 The majority of the work has been done on the Hfi line. The balance of the work has been mostly on the other Balmer series lines, with some work being done on the Lyman series lines. The Hp line has a dip in the center for electron densities z 1017 cc'l. This dip is not observed in this study as the electron densities are much lower. The impact approximation is useful at the line center and the quasi-static approximation is useful at the wings. There is some degree overlap for these approximations, however to get the total line profile a transition between the approximations must be performed. General relaxation theories have been developed that describes this transition 29, 49, 127, 128, 133, 134, 143, 144 The region. relaxation theory treats the radiators after their initial excitation as trying to equilibrate with a heat bath consisting of the perturbers. Other theories include 124 model microfield methods which do not assume that 44 Te - Tgas and account for the line center dip, and exact one electron solutions. 90 A great deal of effort has been spent to experimentally verify these calculated line profiles. Most of this work has been done with a wall-stabilized dc are which typically has an electron density of z 1017 cc-1. 39, 64, 68, 69, 70, 71, 82, 83, 117, 118, 148, 149, 150' 151 Some work has been done with an electromagnetically driven T-type shock tube which typically has an electron density of z 1016 cc'l, 9. 96 Work at electron densities of z 1015 cc.1 was done with a 42 1 10 plasma jet and z 10 4 with a large Z-discharge. All the theories deviate from the experimental results, however they are all within 5 % for the “3 line and 10 % for the other lines. Recently, Stark broadening has been used to measure the electron density in the arc of a duoplasmatron ion 1 79 source , in inductively coupled plasmas , in high density Z-pinch plasmas 98, and in high voltage sparks. 123 Stark broadening has also been used to measure the electric field intensities in turbulent plasmas 154, and 45 the electric field profiles in low pressure dc discharges. 45 Emission line radiation is due to transitions within the atoms, molecules, and ions of the plasma. Radiation in the uv-visible region is the result of electronic transitions. The original intent of this investigation was to experimentally determine the absolute population and level distributions of all the species in the plasma. However, an extensive literature survey revealed that efforts to experimentally measure these quantities has not been successful. All techniques to measure absolute populations found in the literature have utilized some sort of theoretical prediction model to obtain the results. While relative excited level populations of an electronic state of a specie can be readily obtained, absolute values are neither easily obtainable nor accurate. The best estimate that can possibly be obtained will still have an error of greater than 50 %. In addition, emission spectroscopy suffers from the inherent drawback that the information obtained is for the upper or initial state of the transition only. Thus emission spectroscopy can not yield any information about the ground state of a specie which is the most populated state . The chemical and physical pr0perties of a plasma in 40, 76 thermal equilibrium have been calculated. The 46 concentration of all the various species for a hydrogen plasma in thermal equilibrium as a function of temperature have been calculated. 110 The populations of excited hydrogen atoms in a plasma consisting of hydrogen atoms, hydrogen ions, and free electrons having a Maxwellian distribution have been calculated, along with the power radiated by those excited atoms. 8 Density ratios of hydrogen ions and atoms in a non-thermal plasma have been calculated using an ionization equilibrium. 135’ 136 Population densities of hydrogen atom and ion levels have been calculated for plasmas of interest to thermonuclear research. 33-38 The distribution of population densities among the energy states of hydrogen ions and the recombination rate coefficients for electrons and ions in a non thermal plasma have been calculated using collision- 5: 7. 74' 97 The vibrational level radiative models. population distribution for hydrogen molecules and relative concentrations of negative ions has been calculated. 72 The degree of dissociation and ionization has been calculated for an electrodeless hydrogen discharge. 47 Cross-sections for the dissociation of hydrogen by electron impact have been calculated. 85 The effect of flow on the chemical and physical properties of 14 a hydrogen plasma has been investigated. Calculations 47 of the chemical and physical properties of low pressure, weakly ionized, hydrogen plasmas have been made using a self-consistent field approach. 91’ 99’ 106' 107 The density of H- in low pressure plasmas has been measured by Langmuir probes and mass spectroscopy as a function of pressure and electron temperature 3 and as a function of wall temperature and material. 48 Relative populations of the hydrogen atom levels have been determined from Balmer series line intensity measurements. 46 Absolute populations of the excited hydrogen atoms have been calculated from Balmer series line intensity measurements and the degree reabsorption. 126 This technique was unique to the particular experimental apparatus and can not be utilized in this investigation. The concentration of neutral atoms in a hydrogen plasma was calculated from absolute Balmer series line intensity measurements and a model involving the electron density and temperature. 88 Neutral atom density profiles were obtained from measured electron densities and temperatures and a fluid model. 87 The velocity and electronic state distributions of excited hydrogen atoms formed by the dissociation of hydrocarbons due to electron impact have been determined by Balmer 48 113, 114 series line intensity measurements. Cross- 81, 103 0 and Ly-a emission from 8 5 the dissociation of hydrogen molecules due to electron sections for Ha and H impact have been measured. Cross-sections for molecular transitions in the uv and visible regions due to electron impact have been measured. 2’ 146 Hydrogen plasma ion temperatures have been measured from the doppler 129 broadening of the Ha line. Absolute vibrational level populations of a low pressure hydrogen plasma have been measured using CARS. 111 This investigation is interested in the effects of flow, pressure, and absorbed power on the chemical and physical properties of a hydrogen plasma. For the purpose of this investigation, emission spectroscopy results are desired that do not rely on the incorporation of theoretical prediction models. This is a very important requirement since these results will be used to verify modeling efforts. 100 Emission line intensity measurements are made to determine the atomic electronic temperature and the molecular vibrational and rotational temperatures of the plasmas. Emission line width measurements are made to determine the electron density of the plasmas. The plasmas are assumed to be optically thin. This assumption is valid for emission in the visible region and 50 A detailed theoretical development of atomic and molecular spectroscopy and the procedure to obtain the characteristic temperatures has been given and will not be repeated here. Potential energy curves for hydrogen 125 are given in figure 20. Characteristic temperatures are determined from relative emission line intensities. The measured intensity of an emission line is given by where -En/kT Nhu gA Ran " nm e 1l' nm n A Q 4 N - total population of atoms or molecules. h - Plank's constant ynm - frequency of the transition gn - degeneracy of the initial state of the transition Anm - transition probability Q - partition function RA - spectral response function an . 4« solid angle En - energy of the initial state of the transition k - Boltzmann‘s constant T - characteristic temperature POTENTIAL ENERGY (eV) 51 30- 20- H’+H(1s) H(IS)+H(2p) I 20 TI 2 ‘2‘ IOP p u H(15) + H09 1512; I I I V1 2 3 4 INTERNUCLEAR DISTANCE (A) Figure 20, Potential energy curves for hydrogen 52 n - initial or upper state of the transition m - final or lower state of the transition. The transition probabilities and wavelengths of the atomic lines of interest in this investigation are given in table 2. 152 For an atomic electronic transition the equation for the measured line intensity can be written as Imeas Anm En ln -——————— - Const. - RA gn Anm k Telec where I - measured emission line intensity meas Anm - wavelength of the transition En - energy of the initial electronic state of the atomic transition T - atomic electronic temperature. elec The energies and degeneracies of the atomic electronic levels are given in table 3. The atomic spectra was taken with a calibrated 1200 G/mm grating. Table 2 . of the Atomic Transitions. Line A (sea- nm 53 1) 0.4410 0.8419 0.2530 0.9732 X X X X 10 10 10 10 Transition Probabilities and Wavelengths A (A) nm 6562.80 4861.32 4340.46- 4101.73 Table 3. Energies and Degeneracies of the Atomic Electronic Levels. Level 54 En (eV) 0 0.66122 0.96727 1.13353 18 32 50 72 55 The electronic temperature that is determined from The electronic the Ha and H lines is denoted T 6 elecl' temperature that is determined from the Ha’ Hfl’ and H7 lines is denoted T The electronic temperature that ele02' is determined from the Ho’ Hfi’ H7, and H6 lines is denoted T Figures 21, 21, and 23 show T elec3' elecl’ Telec2’ T respectively, as functions of flow rate at various elec3’ pressures. Figures 24, 25, and 26 show Telecl’ Telec2’ and Telec3’ respectively, as functions of pressure at various flow rates. Figures 27, 28, 29, 30, 31, and 32 show the electronic temperatures as functions of flow rate at a pressure of 0.7, 1.3, 1.7, 2.3, 4.8, and 7.4 torr, respectively. Figures 33, 34, 35, 36, 37, 38, and 39 show the electronic temperatures as functions of pressure at a flow rate of 0, 150, 450, 750, 1300, 4800, and 8900 p-moles/sec, respectively. Figures 40 and 41 show the electronic temperatures as functions of absorbed power at 150 p-moles/sec, and 0.7 and 7.4 torr, respectively. The electronic temperatures are found to range from 3500 - 6500 °K. The result that Telecl > T T elecZ > e1ec3 for each data point indicates that the lower atomic levels are overpopulated and can not be described by an equilibrium distribution. The error in the analysis of these results is generally i 2 - 10 °K increasing to 56 mnzcmaorh uwm\mm..ozi= mpg. 30.: N: 3 m o b m m e m N g o _ p _ _ _ _ _ _ _ i comm .2 a. .. ... x... ooow .1 braille \ .\DW 1--.]...1-.. .AA\ 5.. 83 I'll!!! Isllllllttv...‘ I F. -J?-i- \\\\ x u. Ixi , \\ {a 88 .1 a .. mach ¢.b PIJD « comm mach o.v mile m5: TN aria. mach ~2— 9.10 5:: m; m.--m .. ooom «mo» e.o «Ila «omgmh «PE: om manhcmmszH ouzombou4m T as a function of flow rate elecl at various pressures F—hJZO—lLJOCCEF-DMIU K Figure 21. 57 mozmmnozh uwm\mm..o:i: Ema 30...... N: mm m m N. m m e. m N w o _ _ b _ _ _ _ _ _ _ ttikllol \...\ ---/ 8mm \i$\\\i|\s\\| all/l/lt/IIIIIIIO \blt $\I|\ Illa/k... I s N- .JI/l # come ’ «\u / .\. .. 3... ... at ... come .\3 a r comm F 5:: v;- o-io comm mach m.v o:lo mac... m.N le mam-p p; ?-.¢ mac» m.~ m:im i comm «map 5.0 «Fig Numqub mhpcz om wmzhczwmzuh owzczhowmw as a function of flow rate elecZ at various pressures T Figure 22_ bmzmmmchamw x oum\mm.5zi: whcx .84... N: 58 oo¢~ Dowfi coca com com oov CON 0 _ _ p _ — _ _ _ Iiiiuii.unuiisissTiinuuni iiiiiii 11-: iiiiiiiii Jenni--- wit-Iiii--- 7!- 8mm II,,”',, “"“*‘“‘\“‘ Ifaqinllllll‘ll \ a. 82. i Dowv I 000m mach ¢.b DIED T comm amok m.v OIIO MED... m.N Tit mac... h.~ 92.-0 amok m.~ Elia i Doom mach h.o dllfl mum-E» 9:1: om umzpcmwmzuh ouzomhuuqu as a function of flow rate elec3 at various pressures T Figure 23, l—UJZILLIJIZCI—DOCLIJ a: mac... mmammwmm N: 59 elecl at various flow rates s m m e. m N a e _ F _ _ _ _ e m - comm w r/ .... III, M .11, - Docs m I] u III ll .1 mfiilauuiaaai.aiaiaa-oa x a . lllllmlllll “ z\-- - some m m7IIIIIEIJHHUHUUIIFHI:II.IIiIiII. D Pilittt .—. T. - a scam W n ._ m ummxmmsoz-= some .::o 9. - m .w omm\mmso=-= some u::» e some a m . umm\mmso=-= some can» omm\mmso=-: amp «:2« umwxwmsoz-s ems ¢::¢ owm\mw.._oz..= om: misam .- Doom omm\mmso=-= o «liq flow-U.— wphcz om mash-camera» 223:0qu 60 mach uncommon N: b c m o. m N _ _ _ _ _ — I C"- I -Sm'- I -C'I-I|'I---'- II- 0- 0 II .. a .. am; I, 0" ’ ' I, ’0 m0. ’ I I . I, l! I, I II \ a / x x i I, \ II \ I \ [I [Ax omm\mm4czio coco omm\mmoczio coov omm\mw4o=ic com“ omm\mm4czio omb omm\mu4czio omv omm\mw4ozic om“ omm\mm4ozio o NQMAMP mhbcz co mm:»¢mwmzm~ ouzozwomqu comm coo? oomv ooom comm ooom h-mzmwczcri-corm a: Telec2 as a function of pressure Figure 25. at various flow rates ”UNI—Uh Web-hm: Cm UKDF EMMA—Emu... Uh ZDKFUUJU 61 amok mmommmmm N: """" '8. ’I' .‘..'...p ' l ’1' 'Il omm\mm4ozic ooow omm\mmoo:io ccmu omm\mm4c:ic omh omm\mm4czio omv ommxmmoczio cmd omm\mm4ozi= c o--.» 0.lo «it 9:4 m---m I momqm» mhhcz co mochczmmzmh o~zcmhomqm comm ooow oom¢ .ooom comm coco P—UJZQ-UJKGZI—Dnfiw I as a function of pressure elec3 T Figure 26. at various flow rates 62 com oo~ cow oe— om" omm\mm4ozic whom zocm N2 _ _ _ _ _ _ oo~ co co co momomh Nomouh domJMP mhhcz co mach h.o mochoxmmzm» o_zomhomom comm ooo¢ oom¢ ocom comm coco I—UJSLUJOCGI—DIZM K Electronic temperatures as functions of flow rate at 0.7 torr 27. Figure 63 com omm\mmoozi: whom zoom N: omv ooe omm com omN cow om— oo— om _ _ _ _ _ _ _ _ _ Illa-“"‘IO‘I‘IIIUIIQ‘ Qiillilini iiiiii “-“"‘m“ a-‘-“ J moan—uh 0.2.0 Nomouh mlim “om-Eh I mhhoz co «mop m.~ machczmmzu» o—zozbomom comm ooov comv coom comm coom l—UJZLLUOCCII—DMUJ K Electronic temperatures as functions of flow rate at 1.3 torr 28. Figure 64 com com com _ _ omm\mm4ozic whom zoom N: oom ooe com lb _ _ com co“ o mom-m: Vie Nommm» m:;m ~omome «Ila mhhcz co «mop h.~ mochcmmmzmp o—zomhomom comm as come coom comm coom i—uJZfl-Lumch-me K Electronic temperatures as functions of flow rate at 1.7 torr Figure 29. 65 omm\mmoc=i= mhmz zoom N: oc¢— ccuw coco com com _ _ _ . — _ momom: silo NomoMH m:;m “coomm «Ila mbboz cc «mob m.~ mxohommm:MF oozozhomom comm coov comv coom comm coom I—LIJ:D_I.IJMCI-:DMU K Electronic temperatures as functions of flow rate at 2.3 torr 30. Figure 66 ommxmuoczi c whom zoom N: coom cooc coom och coca c m ........ k comm ----------------- m 83 come - coom comm mom-om... ell-O Nam-om? ml-m coom «coom? dlld mpwcz cc mach o.¢ m¢=Pc¢MszP ouzczpomom Hum—.obCKM-LZUb Um ZCQFCE .hm 67 o— mozzmoozh o _ c _ omm\mmoo:ic who: zoom N: h _ c m ¢ m _ _ _ ._ momomh Nomomh oomomw 0.10 mic qqu mhhoz co mac» «.5 machczmmZMP ouzozpomou comm occc comv coom comm coco I—UJZLUJMCZI—DIZLIJ K Electronic temperatures as functions of flow rate at 7.4 torr 32. Figure UKUFQKULEWh Uh ZCEhL-u .i... 68 zoom mmcmmmzm N: b m m v m momomh .Ylo Nomom» aim oomomh aria mhhcz co omm\mmoo:io o machcmumzmh o—zompomom comm ocoe come coom comm coom FUELUJIK¢i—DCKUJ K Electronic temperatures as functions of pressure at 0 p-moles/sec Figure 33. 69 mach mmcmmmmm N: c m m c m N _ _ _ _ _ _ mom-m: clue Nomomp mtzm «om-owe «Ila mbpcz co omm\mmoo:io cmo mmopcxmmzmm o—zcmhomom comm ooov come coom comm coom l—LLJZILLLIQCCEI—DKUJ K Electronic temperatures as functions of pressure at 150 p-moles/sec Figure 34. 70 zoom mxcmmmxm N: h m m e m N _ _ _ — _ _ 9!, !17/ MPH: momom» 91.-.6 Nowom» Elam domoMP «Ila mhhcz cc omm\mmoc:ic omv machcmmmzmh cozomhouom comm ooov come coom comm coom I—UZLUKGII—DOSLU K Electronic temperatures as functions of pressure at 450 p-moles/sec Figure 35. 71 «not mzsmmmma N: w l. m momomh Nomomh domomh mpmcz om omm\mmoo:ic cmh macmcmumzm» o—zczhcmom comm coce ccmv coom comm coco hmzmmmchcmm : Electronic temperatures as functions of pressure at 750 p-moles/sec Figure 36. 72 mcch mmcmmmmm N: L. m w s m _ _ _ _ _ QIIFI IIIIII lli‘lll IIIIII 'nllll lil. IIIIIII .6 D..- IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII IIIIIIIIIIIIIIIIII m .- Ib- momth 9.1.0 Nomth mlzm ammoMF «IIQ mhhcz cm ommxmmoctic com— mmcbczmmzmh oozczpomom comm cccv come coom comm coom PUZQUZEPDZU K atures as functions of pressure at 1300 p-moles/sec Electronic temper Figure 37- 73 mac» mxcmmwxm N: h c m c m _ _ _ — P h- mT- B- I.-- B- E- I'---‘ " -' " " lam Nomomh Tim. «coom» «Ila mhbcz co ommxmmoczic ooov m:cpcmum:mm cczczhomom comm ooc¢ oom¢ coom comm coco r-qumancazi—cnrm X Electronic temperatures as functions of pressure at 4800 p-moles/sec Figure 38, 74 mach mccmmmcm N: m v m _ _ _ Ncmom... ailm— «omomp «Ila mppcz om omm\mmoc:ic comm machczmmtmh oczoxpomom comm coco come coom comm coom F—LUZLUJmCi-DZU X Figure 39. Electronic temperatures as functions of pressure at 8900 p-moles/sec 75 mhpcz mmzcm cmcccmcc co cm or cm cm cv om cN co _ _ _ _ _ _ _ _ _ 0].]- \.\.\-.¢ [Ill/I ililillollli lI-l. D.- III’II \|\D monomm. Tie Nomomh m::m i «coom» «Ila mach >.c cmm\mmoc:ic cm~ N: muchcmmm:MF cuzcmhomom comm ccce ccmv coom comm coom PUZLMKGHDMU x Electronic temperatures as functions of absorbed power at 150 p-moles/sec and 0.7 torr Figure 40 . 76 mhhcz :mzcm cmcmomcc 2: 8 8 2. 8 S S 8 cm 2 o _ _ _ _ _ .Ifldflklllllhlllllklllll! oll-lI-l-l-l-IIIl-I- l‘ll\lI\II|II‘II\II\II|lm Dita. IIIIIIIIIIIIIIIIIII NONI—Uh. mlltm I. wcmomh cI.Q mach v.5 omm\mmoc:rc cm" N: machczmmzu~ o—zczmcmom comm cccv ccmv coom comm coom l—UZLUJOCOII—DOCLLJ : Electronic temperatures as functions of absorbed power at 150 u-moles/sec and 7.4 torr Figure 41. 77 150 i °K for the higher flow rates and pressures. The electronic temperatures are found to decrease with increasing pressure and to relatively independent of flow rate. It is interesting to note that as the pressure increases the scatter in the electronic temperatures decreases, indicating that the increased number of collisions due to the increased pressure brings the atomic levels closer to equilibrium. The electronic temperatures are found to increase with increasing absorbed power. Figure 40 shows a decrease in the electronic temperatures as the power is increased from 60 to 80 W. In the region from 20 to 60 W at 0.7 torr, the plasma has a different appearance than for the rest of the investigation. This is due to a mode change and is not observed in figure 41 at the higher pressure of 7.4 torr. Thus the plasmas at 150 p-moles/sec and 0.7 torr for absorbed powers from 20 - 60 W will have different characteristics than the plasmas in the rest of the investigation. In addition, 80 W is the maximum absorbed power level that can be reached for plasmas at 150 p-moles/sec and 0.7 torr, i.e.,the plasma is saturated. These graphs represent data averaged for experimental points. The reproduciblity of these results is i 800 - 1000 °K for T + 400 - 500 °K for T elecl’ - elec2’ and i 100 - 200 °K for T . For the higher flow rates elec3 and pressures, T could not be determined since the H e1e03 6 line could not be measured. 78 Recombination rates for atomic hydrogen have been 115, 147 140 calculated and measured. The energy imparted to the atoms through dissociation processes is greater than the recombination energy. 99’ 125 The populations of the lower excited states of the hydrogen atoms in a 36, 43, 44, 104 recombining plasma have been studied. The states are found to be overpopulated and out of equilibrium. These findings are illustrated in the spectroscopic results. The atomic electronic temperature is found to be greater than the gas temperature (assuming that gas temperature is approximately equal to the molecular rotational temperature which is presented later). In addition, the atomic electronic temperature decreases as higher level transitions are included in the calculation. The wavelengths of the molecular lines of interest in this investigation are given in table 4. 119 For a molecular rotational transition, the equation for the measured line intensity can be written as I i 1 1n :eas - Const. FkJT h J rot where S - theoretical line strength J Table 4. (0 - 0) B JLJA). 0 4627.98 1 4631.45 2 4643.03 3 4634.59 4 4631.85 5 4625.31 6 4618.30 (0-0) 9 4.1.5). 1 4579.45 2 4579.99 3 4578.01 4 4572.71 5 4563.72 4550.98 79 B I70 0 “NH .I.‘ 4195. 4199. 4205. 4210. 4212. 4212. 4209. 4177. 4177. 4175. 4171. 4165. 4156. Wavelengths of the Molecular Transitions. 67 78 10 13 50 03 17 72 12 16 29 19 62 80 F(J) - energy of the initial rotational state of the molecular electronic transition c - velocity of light Trot - molecular rotational temperature. The energies of the molecular rotational levels are given in table 5. 32 The theoretical line strengths of the molecular transitions are calculated by. 67 R .- - SJ - J + 1 - J SQ zJ"+; 23'+1 J" a ' z. The rotational temperature determined from the R-branch of the (0-0) and (1-0) vibrational bands of the G 12; - B 12: molecular electronic transition is denoted T and T respectively. The rotational temperature rotl rot2’ determined from the Q-branch of the (0-0) and (1-0) vibrational bands of the I 1"g - B 12: molecular electronic transition is denoted Trot3 and Trot4’ respectively. The average of the rotational temperature measurements is denoted T . rota 81 Table 5. Energies of the Molecular Rotational Levels. F(J) (cm- ) 12+-B g l V - 0 v - l 0 0 1 -7.52 -13.80 2 15.15 1.70 3 80.44 48.92 4 192.86 135.59 5 357.38 273.92 6 574.86 463.48 1H8 - B l v - 0 _X_:_l 0 0 2 74.70 80.73 3 199.18 206.98 4 376.21 380.83 5 606.19 602.96 6 888.30 873.16 82 Figures 42, 43, 44, 45, and 46 show Trota’ Trotl’ 3, and T respectively, as functions of Trot2’ Trot rot4’ flow rate at various pressures. Figures 47, 48, 49, 50, and 51 show T T T T rota’ rotl’ rot2’ and T rot3’ rot4’ respectively, as functions of pressure at various flow rates. Figures 52, 53, 54, 55, 56, and 57 show the rotational temperatures as functions of flow rate at a pressure of 0.7, 1.3, 1.7, 2.3, 4.8, and 7.4 torr, respectively. Figure 58 shows the rotational temperatures as functions of pressure at a flow rate of 150 p-moles/sec. Figures 59 and 60 show the rotational temperatures as functions of absorbed power at 150 p-moles/sec, and 0.7 and 7.4 torr, respectively. Figure 61 shows the rotational temperatures as functions of absorbed power at 8900 u-moles/sec and 7.4 torr. The rotational temperatures are found to range from 225 - 850 “K. The error in the analysis of these results is generally i 2 - 10 °K increasing to i 30 °K for the higher flow rates and pressures. These results yield that T T There is a > T rot2' r0t3 > Trota > Trotl > rot4 i 150 °K scatter in the rotational temperature results which is larger than the experimental error. Trot3 and T , which are determined from the I 1H - B 12+ rot4 g u transition, are within 50 - 70 °K of each other and consistently 200 °K greater than Trotl and Trot2’ which 83 mczcmcozm cmm\mmoczlc whcm zoom N: co m c b m m e m N o —I _ p F _ _ — _ com s-I-ii--- 9 m 2: iii::IttiI¢uiI?Hl/ll// {II-”I9 {I}! li//. (ls ell..- III/ll com .JJ» . x . o8 MK\ «:2 To wile mach m.¢ ollo com «com m.N {it mac.— c.— 9...... «cc.— mJ mil-m. mhhcz cm machcmmmzm: oczcchchc: mocmm>c hUtLUMCI—DMN Z Average rotational power as a function of flow rate at various pressures Figure 42. 84 mczcmcozb cmm\mmoc:ic who: zoom N: c_ c c c m m c m c _ _ _ _ _ _ _ o AVI/I/ .i lllllllllllllllll / °I - lllllllll Ivylll // ‘Il‘ldlm /lIo/lol ////‘|\‘ I [I 4% Jr .s. K. - r: crop ¢.b oil» as: a... ole .. can: m.N «it 5:: 5.: sale 5:: m; m---m «cob b.o «Ila . chomp mphcz cc mzchcmmmzmh oczcc .Epc: com ccv~ com com com com F-LLJZLLLJZCL'F-DKLLJ it as a function of flow rate Trotl Figure 43 . at various pressures 85 mozzmzczb umw\wm._o=..: “:3. 36....— N: as m a p w m c m N _ o _ _ _ _ _ _ r _ _ _ 4 D. O// QVQ. Dom llllllllllllllllllllllll lballlw/ il/le‘s a/JV/ ‘\ .lco/ -/./;/ 2:. o/I’I/ ‘ o/ / . oo \‘L y, 1 com 1 com 5:: v4. 9....» . 5:: a; oio I 2:. ago.— m.~ «.uk 5:: ~2— @110 5:: m._ m---m_ 55.— h o I .. com whey: whhcz cm washczmmzuh aczo:¢.—om T as a function of flow rate rot2 at various pressures Figure 44. h—thkUQfiCF-Dxm Z 86 mozcwzozh umw\mu4o:|: ”:5. 3:4... N: o— m c h m m ¢ m N — o _ _ _ _ _ _ _ _ _ 1 com r 2:. an 9,. com watt! Oil] {l1.£( It'll!!! llllll 0’! I'll-III]!!! /{\ I--J?/ {IA 8m ll, ..,/,, 5:: I. p--.» // \x r 2; ago.— O.v Gila ,XI 5 5:: m.N «.Ik I/u.\ amok 5.. 9:39 5:: m; m---m_ mach b.o «Ila I saw 2.3: whhcz Do uxzpcmuazuh $52.52; Trot3 as a function of flow rate at various pressures buzmuzcrt—aorm : Figure 45. 87 mozcmaozh uwm\wmgczln whcx 95...”. N: o— m m P m m v m N — _ _ _ _ _ _ _ _ _ 9100/ lilac/Idl/II// ‘/‘ no iii/II xv - //n.//. 0 «La .l/tH/IIIO Ex: Th 57..» ’. ZZOH Gov QIIO u mac.— m.N .Tlts I . mask 5." @239 ... .. zzoh m.~ aria ’ .\ man: P.c Gila ... \. kw :3: apps: on mzahcmumzmh gaze—pcboz com 2:. com com com. com FUZLUMCi—Dzw Z Troth as a function of flow rate 46. Figure at various pressures 88 amp: umawmwzn. N: b o m ¢ m N ~ _ _ — - P — — 4.x omw\mu..oz|: comm I oumxmmsoza: 82 p--.» 838402.... com“ mule omwxmmoozu: own «it ougwmfiozsa omv 9..-... omewmsozn: ow“ main 383.625 o I mfg: om mmzhczmmzmp Jazozchom woczu>c com 09. com com can can h—hJEQ-lflflfiCEl—DMLU X Average rotational temperature as a function of pressure at various flow rates' Figure 47. 89 mach umamwumm N: w v m _ _ _ .uwm\musoz|: uum\muqozlo ouw\mmqozls oww\mu4oz|: umm\mm;o:I= oum\mmJOzn: oum\wmgozv: come some can— own omv om~ a--.» 0:8 «:i ?..o min. upozp mbpcz om mxzpcmmmzmb gaze—pcbom com 00¢ com com can con bLUZQ-LUZCh—me z: as a function of pressure Trotl Figure 43, at various flow rates 90 «mo» umzmwuzm N: umm\mu4ozs: owm\muJO:I= umw\mu4oz:= umm\wu40233 uwm\wmgo:|= owm\muJD:I: uwm\mmgo:n: comm Dome oom— omh om¢ om— 01.0 «ii ?-.¢ m---m whack mhbcz om mxapcmumzuh qzzoflpchom com 00¢ com com 035 Dow h—kJZD—LLJKGZb-DZUJ X as a function of pressure Trot2 Figure 49, at various flow rates 91 mach wzammwzm N: Qmm\mugozu: comm coov com— own one cm— 0 uwm\mu40:|= umw\mw4oz|= oum\mu4oz:: ouw\muqozx: oww\mwgczn: umw\mu4ozlz m e m r F _ I >5.» o.lo «3i. ?-.¢ aim oqu whoxp mhbmz om umapcmumzm~ szoubchom com Dav com now car com F-uJZLUKGZb-DZLU a: Trot3 as a function of pressure Figure 50- at various flow rates com 02. 95 Figure 51 . 93 owm\wm._oza.: mp5. 30.: N: cow cog owe Dew om« cod om om oe ON C _ _ _ _ _ _ _ _ a ............................................................ a Arllllllllr Till-loll!!! 9"!!!1 l'll'llllllla'lll'll'olllul’ -l..l..l..l.-l.i $ll'll' """"" chomp Diju :3: 0.1.0 who”: 9.2.9 «pomp miim «hemp «Flo 97E: cm 5:: b5 wzahczumxmh. Jazouhchom com oov com com 02. com PMZtNOfiCl—me :6 Rotational temperatures as functions of flow rate at 0.7 torr- Figure 52. umw\mm._oz..= wt; :9.“— N: 94 --.----. ........... ---mv .................. .---- n7}--- ................. a: com «I a. cow Dlllllllllll llllllllll ID. !!!!!! ...l o..-.!I-l-l-l-l-l.i.-l-l -l.l.i.-l-l-.¢:l cow Qllll llllll I lllllll ll. IIIII lllllll iv-:-:::::::::: com chomp p:Jb 1 cos :9: o....o 9.9: 9230 32: min. «pomp «Ila 1 com 9:5. oo 55» m.“ uxahcmmmzut .Echapoz Rotational temperatures as functions of flow rate at 1.3 torr P-Lthmquci-DOCLU a: Figure 53. 95 com com _ com _ omm\mw...oz|: ”:5. 98.: N: cow ooq com cow on: o p _ _ r _ Ellis... IIIIIIIIIII MUIII‘ IIIIII ii “ “ “ "'----‘---'|-‘-¢ " if? I ?.!..:..I..... I -I-I-I-I-I-1Y..I-I..... ..... I ..... I-.¢.I-I-I.I!W ollllllul‘ltcllulllun? lllllllllllllllll ¢\Il\ll..|ll.\a| 1| Quiilltttl... chozh Dal I *hom: 0.5-.0 whom.— 01...... who”: Elia whom... I I «Em: cm can; b." maP—czumzuh .Ezof—Eoz can one com com can so» F-th:Q-hJO:GCF-ZDOEHJ 3: Rotational temperatures as functions of flow rate at 1.7 torr 54. Figure owm\ww4oz:= whom zoom N: 96 coo; coma ooo— ooo ooo oov oow o _ _ _ _ _ F _ \h. oom m..-:...-:.......- ....... ... ...... ....-..-.-............m.... ......... ---..N.\ a; u in oow oow oom «hook w:lo f ooh :2: 0.1.0 who”: 0...... «box.— Giza «to: ow mach 9N mmohczmmzuh chouhchoz Rotational temperatures as functions of flow rate at 2.3 torr Figure 55. r—UELUKGHDKU K 97 oumxmmgoz\: Mpom 3o...» N: coom 83 coom 88 83 o of: 8m ................... o3 wl ................ ... llllllllll e IIIIIIIII o8 «HHHH ..... ... ......... xi-.. ....... uuuuuuuuuuuuuuuu l (-31-). 8o uuuuuuuuuuuuuu I. IIIIIII .pI. SS: v.1» ,. 2:. «be: 0:30 whom.— 0......0 NEE. m}.-m 98 mozcmnozh oum\mugozlz whom zoom N: ou m o b m w v u c! _ _ p _ _ . -..-..........-....-......: ........ ...-..--.u. chozh ¢ho¢h «bomb whoop ”bomb pl...» 0.1.0 9:19 min. ooe oow oow ooh I oow whhcz o0 mmohcmumzuh «moh.e.h Aczouhchoz h—LUZQUKOII—DMU x Rotational temperatures as functions of flow rate at 7.4 torr 57. Figure 53... mzomouzm N: 99 F O w v m. N w .\‘mu \Q\ r 8.. com I 60* 1\|\\| \\ I \\\\ ‘t‘s Dom \‘Ll‘l \\\‘ \‘I\\\\.\| II|‘|‘|\I*\ \\‘o D\l\t |l0|tlll\\ssllu \ \\.\\? \onx 1 8m t‘t‘t‘s .||\.I“¢\\ °\\\.\\ ‘|||u\lsn°|¢|o|.|ls||tll\ 0| whom: Ollé whom: 9..-... Nhozh Elia :2: I . 8o 3.5: om omw\ww4ozno om: wzohczumzuh oczomhchox as functions moles/sec Rotational temperatures of pressure at 150 p- h-qu:a.UJn:C:h-::aguJ 3; Figure 58. 100 oo~ 9:5. muzom owozomoc om cm or cm an ac om ON cu F _ c _ _ _ _ _ _ \|\|lIOImIIII|IIII8III|ImCIIlllllll\llllm U232... \.\.\.\o blill|IIIII!|!|LT|ll!||i|||lllJ?\ttu ntllll\l. 91-..}... -l.\....ot-|.\ l..l.n¢1..\..\. \o I\\|.0llll...l|lll.o.\\\\\ @\I\!l\ they: bllb whom.— 9!..6 whey: Datum. uhomh I zoo... b.o omm\omqozlo om“ N: washommmzuh chouhchoz oom oov oom . ooo ooh ooo a—mzmmozan—oozm a: Rotational temperatures as functions of absorbed power at 150 p-moles/sec and 0.7 torr Figure 59. 101 oofi mhhoz mmzom ommzowoc om cm or oo om ov om ow oa _ _ _ _ _ L _ _ _ chomp o115 rho”: 0.1.0 -m whoop 02.10 .----. whom» main -...... Coy: To. .--. l I! . [ma «mo.— vé. omw\ou.._oz1o om— N: wmohozmmzmb chouhchoz oom oov oom ooo ooh ooo HUILUO‘CF—DKM :1: Rotational temperatures as functions of absorbed power at 150 p-moles/sec and 7.4 torr Figure-60. 102 oou 95¢: muzom owmmomoc oo oo ob oo om ov om ow o" _ _ o _ _ _ _ _ _ R.\\ \\o||\o\1|\\o\ 0.111.. 0 chow: bzlw :9: 0.1m. whom... 01-16 NEE. main Coy: I zoo.— vé omw\om._oz1: oooo N: 55.23353» omzou .2: oz oom oov oom oom ooh ooo hwzmuoccrh-oozm Z Rotational temperatures as functions of absorbed power at 8900 u-moles/sec and 7.4 torr Figure 61. 103 l l are determined from the G 2: transition and also E+-B 8 within 50 - 70 °K of each other. The rotational temperatures are found to decrease with increasing flow rates after an initial increase, to increase with increasing pressures, and to increase with increasing absorbed power. The regression coefficients and chi2 values of the linear least square fit of the line intensities are generally very good indicating that the rotational levels of the molecular electronic and vibrational states can be described by an equilibrium distribution. However, the different rotational temperatures indicate that each of the vibrational levels of the electronic states are not in equilibrium at the same temperature. For a vibrational transition, the equation for the measured line intensity can be written as Imeas Go(v') h c ln —_ - Const. - R V 4 k Tvib A qv'v" v'v" where qv'v" - Franck-Condon factor v , - frequency of the molecular v'v' vibrational transition 104 Go - energy of the initial vibrational state of the molecular electronic transition Tvib - molecular vibrational temperature. The Franck-Condon factors for the vibrational 130, 131, 132 transitions are given in table 6. The frequency of the vibrational transitions are the calculated band origns. 67 The energy of the vibrational 130, 131, 132 levels are given in table 7. The vibrational 1 1 + temperatures determined from the G 2; - B Eu and I 1Hg - B 12: molecular electronic transitions is denoted Tvibl and Tvib2’ respectively. Figures 62 and 63 show Tvibl and Tvib2’ respectively as functions of flow rate at various pressures. Figures 64 and 65 show Tvibl and Tvib2’ respectively, as functions of pressure at various flow rates. Figures 66, 67, 68, 69, 70, and 71 show the vibrational temperatures as functions of flow rate at a pressure of 0.7, 1.3, 1.7, 2.3, 4.8, and 7.4 torr, respectively. Figure 72 shows the vibrational temperatures as functions of pressure at a flow rate of 150 p-moles/sec. Figures 73 and 74 show the vibrational temperatures as functions of absorbed power at 150 p-moles/sec, and 0.7 and 7.4 torr, respectively. Table 6 . 105 Franck - Condon Factors and Frequencies of the Vibrational Transitions. c 12+ - g qv'v'“ 0.5327 0.3498 v'v" 0.4663 0.3902 8 12+ u 1 v0 (sec- ) 6.46116 x 1014 7.12956 x 101“ u (sec‘l) o 6.54066 x 1014 7.17108 x 1014 106 Table 7. Energies of the Molecular Vibrational Levels. G 12* - B 12* g u v' - v" G0 (cm-1) o - 0 o 1 - o 2230 I 1n - B 12* g U V’ - v" G0 (cm'l) o - o o l — 0 2108.26 107 ouw\wm4oz1o whom :oJm N: wozcmaozh ofi o o b m m c m a o _ _ _ _ _ _ _ _ _ Dill-Ill] --l-.-l.--J9 w. / .:. o/... .5. //. I .. /7 _ ,. ./. mare // _ / a. . _ w.» ._ \ _ 1 k .. _ __ “ .._ mach ¢.b DEED _”. 1 $2 a; 216 x o... 5:: m.w «.1... I. a. 5:: p; 6.16 . a » amok m; m.--m_ / .. 1 «MOP Foo I op. \s x\ ~o~>h mhhcz.oo washomumzwh Aczomhcmo~> ooom oomm oovm ooom hmzmwmch-oazm 2c Tvibl as a function of flow rate Figure 62, at various pressures 108 mozcwoozh omwxmuooz1o whom zoom N: om m m p m m e m on..- _ _ _ _ _ _ 51-11-1101,. .1111]: 0 // x/ xx xx mach e.b 6:10 mach o.¢ 0:10 5:: Wu «it amok b; 0.16 5:: m; m.--m mock b.o aria No~>h mhhmz oo umohcmmmzuh 4ozo~homo~> mozcmoor: FUELUOCGIF-DMLU :C Tvib2 as a function of flow rate Figure 63. at various pressures 109 amok umommmmm N: w v m owm\mw4o:1= oww\mm4o:1o omw\mm4oz1o uwm\mmmoz1o omw\mm4oz1o oum\mm4ozIo ouw\mmooz1o oomo ooo¢ oomfi ooh omv ow“ ~o~>h whhmz oo umohomumzm~ choopcmo~> ooov oomv ooom oomw oooo 1—1uzo.u.1cza:1—:a:u.1 K Tvibl as a function of pressure Figure 64. at various flow rates 110 mmo» mmomwmmm N: \- m m s. m N a a _ _ _ r _ _ b o 6:1-..- 8883212 88 .1... 1-17- 00033025 89. 6-16 .71/ 880592-: 82 6.16 .. m {.19 QUW\mm.5:1D own. {11.1 P 888.52-: cm.- 116 // 000332-: 2: 01-0 // 388.52-: o I 0, // r S 7’ II. I / .. II // 0.1-.111-6/41111111 /// clot "llll'llllldlv' 1. N.— Ildllilllllllclll 11.1-10 - I .. m: No;.— 9753 oo mmohozumzuh 4¢zo2¢xou> mozcwoozh FUELUZCPDMU Z Tvibz as a function of pressure 65. Figure at various flow rates lll ooN owm\wmoozlo whom zoom N: 2: 2: o: 8“ 2: 8 .8 o... 8 o _ _ _ _ _ _ _ m m r m . 1 m .- m r S m. - 2 m r I m 8:: 0.10 m ~o~>h 411d M . S whhzz oo amok h.o wmohozumzwh omzomhcmo~> mozzmoozh l—LUZLIJJCKCZF-Dflfim a: Vibrational temperatures as functions of flow rate at 0.7 torr Figure 66. ll2 oom oww\mwoo:1: whom zoom N: owe ooe omm oom omN ooN omw . ooo on o _ _ _ _ _ _ m _ _ v 1 o 1 o 1 oo nH0000.........0 - 2 --.........m./ .. I mg: 0.101.}... 3:: I .- oo mphoz oo zoo» m.o 3.3%”..sz ooze-Ego; mozomoozp h-qumuJozch—oaclo Z Vibrational temperatures as functions of flow rate at 1.3 torr Figure 67, 113 oum\wmooz1o who: zoom N: ooo ooh ooo oom oo¢ oom ooN ooo o #1 _ r F _ _ p e .- o 1 o 1 oo .2 .- mo 3.1111111111113311 \s T : Nou>._. min. {111... .x. :23 I ll”... 1 m: mppmz oo mmo... Q; wxohcmmmzu~ ooze-Eco; mozcooov: p-qumchrcn-oocm x Vibrational temperatures as functions of flow rate at 1.7 torr Figure 53. 114 omm\wmoo:1: who: zoom N: so.“ 0000 coco com com ca. 000 o _ _ _ _ _ _ _ _ w r m - m 1 .oo .. “No m1--.--------------..--------m.--.--.--.- .----mr-.--- -.-.-m.,. r. ..o Nmu>b minim— III smoco,c_ «1.... my: mphcz oo «mob m.N mmohcmmmzwh oczo-c¢o~> mozcmoozh I—UILILJmGZU—DMLU X Vibrational temperatures as functions of flow rate at 2.3 torr Figure 69. 115 omm\wmoo:1o who: zoom N: ooom ooov ooom oooN ooo~ o _ r _ _ r «r. 1i‘tr a. ,- m r 0 U‘0" .. S .. 2 .. .. I Nm~>h @111m .u ufl~>h fillfl m u. .. m: mphcz om amok o.v mmopczumzuh oczouhzmo~> mozomoozh Vibrational temperatures as functions of flow rate at 6.8 torr HUtLUOfiCflF—DMU it Figure 70. 116 mozomoo:h ouw\wwoo:1o who: zoom N: m 0 p o m s. m N _ r r I; _ _ P _ _ _ '1'! m @‘-'l’ '0'-.. 0'0 "-"""" I"! 1111@ ‘ O ’ I t ' o- l I. v \ --------------»--------------‘a No~>b «o~>h 0.10 I whhcz oo «mop ¢.b mzohcmmmzmp oczomhozo~> o: N— v— mo mozcmoozh I—lUZO-UQCCZI—DMLIJ Z Vibrational temperatures as functions of flow rate at 7.4 torr Figure 71 . 117 mac» mmzmmmmm NI - m m V m N a _ _ _ _ _ _ t a. I ||TII||TITIIQ «\\\\!w -. m r m P. -. S III/fl .s\ I Nd litmu|010||0000ltllll "a --:----m r I «2: min 8:: «In ,. ... ,m. r 2 mphcz om omm\wmqo=|: ow~ mmapcmum=MH 4¢zo~hczmm> wozmmaozh HUZLMKGIF—DCKU K Vibrational temperatures as functions of pressure at 150 p-moes/sec Figure 72. 118 on: 2.25 mwzom owmmommm cm on or om cm or on ow as o _ _ _ _ _ b _ L _ q 1 m u m ....-..----m -m---- ,- s‘ststttt oov 1- o." m--- x, - 2 ,6 .- 3 NS: aim 82$ I 1 mg mach >.o oumxmuuozna ow" N: mozmwzozh mm?— cmwmzmh .520 H .533 _ > h—LUZLLUOCCEF-DOCLLJ Z Vibrational temperatures as functions of absorbed power at 150 p-moles/sec and 0.7 torr Figure 73. 119 mp hm: muzom oummommc 2: cm cm on om om av om cm 3 o _ L _ u _ _ _ _ _ v :- - m ---..-.-m I m n...--- -. S I N“ I 3 we: m.--m_ «a: I I 2 5:: v.5 umm\wu..oz|: cm: «I mxapcmwmzwp Aczoupcmm; wozmmaozp hMEO-LIJZCEi—DOCU Z Vibrational temperatures as functions of absorbed power at 150 p-moles/sec and 7.4 torr Figure 7a, 4 TORR VIBRRTIONQL TEMPERRTURE H2 8900 U-HDLES/SEC 7- THOUSHNDS 120 60 70 80 90 100 50 RBSDRBED POWER HHTTS ._ O CO v-‘N can: o—u—o _, D >> N I—I— I‘P _. o : v-a E! I I I I I I I O 16 14 Figure 75. 12 10 8 6 4 HUZQLIJOCCI—DCKLU x Vibrational temperatures as functions of absorbed power at 8900 u-moles/sec and 7.4 torr 121 Figure 75 shows the vibrational temperatures as functions of absorbed power at 8900 p-moles/sec and 7.4 torr- The vibrational temperatures are found range from 4000 to 5600 °K and from 6000 to 17000 °K for Tvibl and Tvib2’ respectively. The error in the analysis of these results is i 150 - 500 °K and i 1000 - 5000 °K for Tvibl and Tvib2' respectively. Tvibl which determined from the G 12+ - B 12: transition is consistently much lower than 8 which is determined from the I 1II - B 12+ Tvib2 g u transition. This trend is consistent with the rotational ’ and T temperature results. Trot3 rot4 are greater than Trotl and Trot2’ therefore Tvib2 should be greater than Tvibl' In addition, the result that Tvib2 is so much higher than T . is consistent with the result that T v1bl rota is greater than T while T is less than T rot3’ rot2 rotl“ Tvibl is found to decrease somewhat with increasing flow rates, to increase with increasing pressures, and to be relatively independent of absorbed powers. T is found vib2 to decrease with increasing flow rates and pressures, and to increase with increasing absorbed powers for high pressures. The difference between the vibrational temperatures is found to decrease as the pressure is increased indicating that the vibrational levels are 122 brought closer into equilibrium due to increased collisions. For low flow rates, Tvib2 and its error are very large indicating that the lower vibrational levels are quite overpopulated. It is interesting to note that the I 1Hg state and its transition are known much better 1 + . than the G 28 state and its transition. The molecular spectra is taken with a calibrated 2400 G/mm grating. Relaxation times for rotational and vibrational to translational relaxations have been calculated. 109 Electron thermalization in diatomic gases has been studied. 138 The results show that the major contributions to electron thermalization are due to vibrational and rotational excitations with relaxation times also being important. This indicates that the vibrational and rotational temperatures will be greater than the gas temperature. This is illustrated in the spectroscopy results as the vibrational temperature is quite high. Measured rotational and doppler temperatures have been shown to deviate from the kinetic temperature. 77 Non-equilibrium energy distributions over the vibrational states has been investigated.105 123 III. Electron Density Electron densities are determined from the half- height and quarter-height widths of the Hfl emission line and the half-height widths of the H6 emission line. H3 is the most studied line and has the most accurate theory developed. H6 is useful at lower electron densities than the other Balmer series lines. There are three sources of line broadening present in this investigation; instrumental broadening (AAI), doppler broadening (AAD), and stark broadening (AAS). The total measured line widths (AAT) are the resultant of all three of these mechanisms. AAT - f( AAI, AXD, AA 3 ) The instrumental broadening has been found by measuring the argon line at 4200 A. This line has negligible stark broadening. The full width at half (FWHH) and quarter (FWQH) height are measured and assumed to be the instrumental half (Axljz) and quarter (Axlja) widths. The instrumental widths are also assumed to have a Lorentzian shape and to be constant for the entire investigation. The instrumental widths are 0.266 A and 124 0.388 A for the half- and quarter-height widths, respectively, of the H line; and 0.268 A for the fi half-height width of the H6 line. The half-height widths have a 2.5 % error and the quarter-height widths have a 1.8 % error. The doppler broadening is due to the thermal motion of the radiators and has a Gaussian shape. The doppler width is given by AAD - A ( 2—351 )1/2 M c where A - wavelength of the emission line T - gas temperature M - mass of the emitting particle. The FWHH due to doppler broadening for hydrogen atoms is then - 2 (1:12)”2 AA D A"1/2 D _7 - 7.16221 x 10 x (T )1/2 gas Likewise, the FWQH is then 125 AA 4 - 2 (1:14)“2 AA 1/ D -8 - 1.01289 x 10 A (T )1/2 gas The factor in the expression for FWHH and FWQH are found from the line shapes. The equation for a Gaussian line shape is At a fractional height, y - l/N. Rearranging, x - (lnN)1/2 where x is the displacement from line center at the fractional height. 80 the full width at the fractional height is AA N - 2 (lnN)l/2 AA 1/ The doppler widths are calculated for each experimental condition from the measured rotational 126 temperature which is assumed to be equal to the gas temperature. The stark broadening has a Lorentzian shape. After calculating the doppler width which is the Gaussian fraction (GF) of the total width, the instrumental and stark widths which comprise the Lorentzian fraction (LP) of the total width are found by deconvolution. 31’ 92 LF - f(GF) AA + AA where LF - “—l——-—J§ AAT U CF - H The function f for the deconvolution is found through a curve fit and is given in table 8. The curve fit is good to i 0.0001 for the half heights and i 0.0007 for the quarter heights. This error is negligible since the error involved in the measurement reading is 1.6 % for the half heights and 1.2 % for the quarter heights. The stark width is then found by difference AA - (AAT x LF) - AA 8 I Table 8. 127 Deconvolution Functions. LF - 2 an x (CF)n FWHH .999917 .003388 .103956 .071501 .029284 1.000642 -0.027469 -0.933408 -0.575569 0.017293 128 The electron density (ne) is then calculated 56 n _ 1014 s 3/2 e (AAl/N) 2 CNm(Te) (log(AA S m l/N” S where Axl/N - l/N fractional height emission line stark width C - constants Nm ne - electron density The constants CNm for these lines are given in table 9. They have been calculated from line profile tables 56 which were found using an improved impact approximation and are functions of electron temperature. Since the electron temperature is not known and the results for the atomic electronic temperature which is sometimes assumed to be equal to the electron temperature do not reveal any pronounced trends, the electron temperature used in the electron density calculations is assumed to be 5,000 °K. This assumption only introduces a 2 % error for the electron temperature range of 5,000 - 20,000 °K since the theory is not critically dependent on the electron temperature as discussed earlier. The electron density determined from the half-height and quarter-height widths of the H line is denoted nel fl 129 Table 9. Constants for the Electron Density Calculations. Te (°x) 5 3 103 104 2 x 10“ H FWHH _fi__ 020 3.68052 3.59237 3.53937 c21 -0.25916 -0.29319 -0.37050 022 0.04187 -0.03098 -0.01051 8 FW H _fl___8__ 040 2.08306 2.06096 2.06304 041 -0.19433 -O.17889 0.17359 042 -0.00900 -0.05253 -0.07317 H FWHH _5___ 020 - 1.22145 1.23042 1.23908 c21 -0.18777 -o.22175 -0.25701 0 0.03557 0.02165 0.05560 22 130 and ne2’ respectively. The electron density determined from the half-height width of the H6 line is denoted n83. nea denotes the average electron density. Figures 76, 77, 78, and 79 show nel’ n82, ne3, and nea’ respectively, as functions of flow rate at various pressures. Figures 80, 81, 82, and 83 show nel’ n82, n63, and ne respectively, a’ as functions of pressure at various flow rates. Figures 84, 85, 86, 87, 88, and 89 show the electron densities as functions of flow rate at a pressure of 0.7, 1.3, 1.7, 2.3, 4.8, and 7.4 torr, respectively. Figure 90 shows the electron densities as functions of pressure at a flow rate of 150 p-moles/sec. Figures 91 and 92 show the electron densities as functions of absorbed power at 150 p-moles/sec, and 0.7 and 7.4 torr, respectively. The electron densities are found to range from 1012 - l3 5 x 10 cc'l, with ne1 > n > n The scatter in the e2 e3' electron density measurements are greater than the theoretical error. ne1 and ne2 are found to decrease slightly with increasing flow rates and and to increase with increasing pressures. ne3 is found to be independent of flow rate and pressure. The electron densities are found to increase with increasing absorbed power. A mode change is observed as the absorbed power is increased from 60 to 80 W at 150 p-moles/sec and 0.7 torr as is observed 131 wozcwaozh uuw\mm-._oz.-: whcm 201.“. N: n: O Q b O m e. m N a O — _ — _ . _ _ p _ _ INK: PI fl :II/I mVaIIIIII // toll // I {I- .// A - - III/II . s A III/- III-I‘l-IIIIIIIIR/AW: . ll/Dlt‘\tl\ill 1. 2.: «ZOE Voh. DIIID my. ZMOH Dafi GIIIO : mac.— m.N «II-a. . mac... x...“ 0236 ”ED-P m..— Winn. mac.— b.o I 3.: 95¢: no >:mzmc zomhomdu UJJUJUi-ZDZ DUZUDHi-)- \QQ ne1 as a function of flow rate 76. Figure at various pressures 132 mozcmaozh uwm\mw._oz.-= PE: :04... N: S m o a. o m a m N a o _ _ _ _ _ _ _ _ _ Iuaoa \s s 9i?!:I.-I--I---I--.wq.H-HH-III-Hll-II&P 2‘ 151-:1“ o 24 o— z.» 2 much «.5 >23» a. much m.v oIIo 5:: m.~ «it 5:: 5.; 95¢ amok m.fl m::m 5:: to «In Nuz mhbcz om >:mzmo zomhomd— n82 as a function of flow rate at various pressures 77. Figure mqmoI—acoz DUZUDHi—>- \QQ 133 umw\mm._oz..= mpg. :04... N: Dov“ oouu Good com com Doc DON o ’I'l’ IIIIIII’I III/ at... DIIIIIIIIIIIIIIIII IIIIIIIII IDIIIIIIIIIIIIIIV IIIIII OlilIIlfilIIIIJOK\6 Inflow £105. *6“. #355 5:: a... 6.16 amok m.N {II.{ 5:: 2 9:6 5:: m; min 5.8 to «In mmz whpc: om >H~mzwo zozhomgw MANGO—0:02 DUZUDHt->- \QU ne3 as a function of flow rate Figure 78. at various pressures uwm\muaozla uhcm IQJL NI oovu cow“ oco— com com oov cam o _ _ _ _ _ _ _ 134 o— IN“ mach amok mac» can» «map much 0 cava.-00h~wzmo zomFQMAu as a function of flow rate ea at various pressures n Figure 79, hJ.JhJLJF-D:CDIE CDUJIEUthF->- ‘xCJCJ 135 5:: mmammmmm N: h . w w v m N w _ _ _ _ _ _ _ oww\mm.._cz.-D comm I owm\wu..o:I= oomc DEED IN" owm\mm.._o=.u: Dom“ Ollo 33332:: cm:- «II-a uuw\mm4ozI: omv elio owm\mugozuz om" mzim omm\mwaozlz o «lld O \b \I.\\\\.\\0 \\I\\ \\I\.\..\.\.\.\. . \\\\- IIIIIIII.‘ In“ 52 9:5. 00 >Zmzmo 22.-roman o— o~ U-thQl—Ofioz DUZUDHH? \00 Figure 30, ne1 as a function of pressure at various flow rates 136 — — mac.— wzsmmwmm NI omm\mmgozI: owm\mmmoznn umm\mmgozln oum\ww492I: omm\mm;ozla oum\mwgozI: omm\mwmozla comm I come 9...» com“ 0.6 own fl... owv 9....0 of win IN" Imfi Nuz whhcz om >Zmzun zomhoumw n: @— MJUQI—OCDZ DUZUJHi—>- \UQ ne2 as a function of pressure Figure 81. at various flow rates 137 — — .mmat mmamwuma N: w v m N a _ _ _ _ _ umw\wmmozI: 00mg owm\mw4o=la own omw\mmqozla omv omm\wm4ozla om— oum\mm40zla o Ii??? 8646 l muz whpcz om >p~mzmo zoxhumqu m a Du UJLUQF-ZOZ DLIJZUDHF->' \UQ ne3 as a function of pressure 82. Figure at various flow rates 138 much mmswwmmm N: m V m _ _ _ uum\mu;ozla com" ouw\wu4ozna own omm\mm4ozla owe umw\wwmozI: owu owm\mm402I: o o.|o fie 95¢ mi-m I In" cuz mppcz om >h~wzwo zozhow4m cu ow UJUUFZOZ DMZO‘JHO—fi \00 as a function of pressure a at various flow rates n e Figure 83. uwm\mu..oz.-= u-Em 39.: N: 139 ooN cod cm: of. ON" on: 00 cm oe ON 0 — _ _ _ _ _ _ _ _ INN o.-.\..\. mwunuununnnuuuununuunnuuuuuunu IIIIIIIIII 2 cmz onlo mmz 92:6 32 min 52 «Ila «PE: on «map To rhumzuo zozhouqu a: es as functions 0.7 torr Electron densiti of flow rate at Figure 84. 140 com uwm\mm.._oz.u= PEN 3cm... N: am; Dov omm com omN CON ow— 2: cm _ _ _ _ _ _ r _ _ I‘IIIIIIIOI 'II lllllll III-ll /I ‘8“||l““\|llu|l /I 9.1.1.... /, /’ /’ /r/z / oIII IIIIIIIIII I IIIIIIIIIIIIIIIIII .07: ”In IIIIIIIIIIIII .- IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII II cmz 0.1-o mmz @539 Nmz fizz-m. uuz «Ila IN" whhcz cm 55.— m." >.:wzuo zozhomgu o— UJUJQF-ZDZ DUZCDHO—)- \00 Electron densities as functions of flow rate at 1.3 torr Figure 85 , 141 com umw\mm4c:I= whcm zoqm N: com com cam oov com QON co“ 0 _ _ _ P. _ _ _ INuofi .xt \\\\\\ whhmz cm was» 5.“ >humzmo zozhuwgu uJ_JhJQ)P'0:CDZE CDNJIBUDFfiF->- ‘~£)£) Electron densities as functions of flow rate at 1.7 torr Figure 86. 142 owm\mm4ozla mpg. 39.: N: ooeg ooNu coo“ . cow cam Doe com o _ r _ _ _ _ _ ’8’0’ 1-1.!!! I N" cuz 9:0 mmz 91:9 Nwz m--m_ 52 I mppcz on mac.— m.N rzmzwo zozbommu o— ld—lLIJUI—GDZ DUZCDHF->- \00 Electron densities as functions of flow rate at 2.3 torr‘ Figure 87 . 143 coom oooe uwmxmwgozIa uhcm :ogu N: coom _ QOON _ ooo— cmz mwz Nwz «uz IN—ou mhpcz rhum om mach m.¢ zwo zombowgu as functions 8 torr Electron densities of flow rate at 4. Figure 83- 144 cu moz:m=o:» m _ m p omm\quo:I: whcm :94: N: b o m ¢ m N _ _ _ _ _ _ a"-"' ..... "-""".-’ mm: mm: Nuz duz “TIA. .Y-Lv main. \ l.’“" {-a IN— mhhcz on much ¢.> >humzwo zomhomqu o: eunuch-:02 DUZIDHl—>- \00 Electron densities as fundtions of flow rate at 7.4 torr Figure 39. 145 5:: uaamwumn— N: h m w v m N a _ — _ _ _ _ _ cwz Giza mmz 0:4 IN: Nuz Win 52 I b .2. .\- / .N / \.\ x x ./ OIII. \\I\ d / title,- \\\ : I’ll!!! I\i / II".\ \\\\‘A In— m.—.—:: a: umm\wm._o:.-: Dwu rhumzmo 23:0qu o: n: UJLLJUl-OCOZ DUZUDHO—>- \00 Electron densities as functions Figure 90. of pressure at 150 u-moles/sec 146 9:5. muzom OuOmOmOm OO: Om OO Ob OO Ow O¢ OM ON _ _ _ F _ _ _ _ sz O-Io «NZ 9...... Nuz alim— «uz I Electron densities as functions of absorbed power at 150 p-moles/sec and 0.7 torr Figure 91. uJJhJUi—MOZ DUJZUDHF->- \QU ago... b.O omm\wuqozIO O3 >:msz 29:09.3 ELECTRON DENSITY 150 U-HOLES/SEC 7.4 TORR 147 O O F. -O m _D O -O h w .— .— ._ C3 C: m z m m x _O O m N O m O -O m V O O O c _D m dec m -D mwuu N 2222 I??? _O :" “ 0.140 O l m N F‘ c-n O D v-l c-n U-lLIJQl—MDZ 011.12th)- \00 Figure 92. Electron densities as functions of absorbed power at 150 p-moles/sec and 7.4 torr 148 in the atomic electronic temperature results. ne3 could not be obtained for high flow rates and pressures since the H6 line widths could not be measured. The ratio (wp/w)2, normalized plasma frequency squared, is calculated from the electron density. where wp - plasma frequency w - driving frequency. wp is defined as 82 w _ ( me 6 )1/2 p e o where e - charge of the electron me - mass of the electron co - permitivity of free space. The plasma frequencies calculated from nel’ ne2’ n63, and nea are denoted mp1, wp2’ wp3, and wpa’ respectively. 2 2 Figures 93, 94, 95, and 96 show (upl/w) , (wPZ/w) , (wa/w)2, and (wpa/w)2, respectively, as functions of flow 149 wozmm:o:~ uww\mw40:IO upmm 304m N: S m o N o . m 4 N N a o m _ _ _ _ _ p _ _ _ N PI: all M Il/lll // om :m lent/Ira m I... N 7...; I. 2: a zip-I... “ o2 N M1 3 m4 \ 8N N . a N... z 8 SN m. mach Voh Full} or mm=vh mw.¢ mTIlo 5.: N; 9.-.. as x .- . I own «m: mhhcz OO Nszm: at various pressures 150 wOZOOOOE. omm\mw402.-O mpg. 30._.._ N: S m o a. m m a. m N a o I cm #3:. OI. Am» \ IIIIIIIIIIIIIlIJIIIIIlIIII‘IOHIIIIII IK\\ W s Dad I’ll!!! I'll r ~ Ialoaanlullclks [p.11 .2 . r” ,I cm: 4.... fl 8N r. OmN 5.3 e;- b--.» mach O.v oIIo ago.— m.N «.Ik .- oom 5.2. h; 93.9 mama N... .- «ILq I omm .Nmz 2:5: OO N:\Nn_: (wpz/w)2 as a function of flow rate at various pressures ZLN\ZN Figure 94. 151 umm\mu-.O£IO PE: ~64... N: coed OONN OOON OOO OOO OO¢ OON _ _ r _ _ _ _ «IIIIIIIIIIIIIIIIII .-. I‘ll-ll!!! UIIIIHIIIIIHMV\|I."V|\.I. » ------- l --------------- .o-II-It-UIaIII-Ihu-UB- ¢I.I-l-I-l-6\-\ I OO— I cm: I OON I omN mac» v.> >:ib OOOP O.¢ eilo amok m.N «- I oom 5.2 b; 0.10 5:: m; mT-m 5:: TO I I own mm: 9:5. OO N:\Nm: ZO—N\3N (wP3/w)2 as a function of flow rate Figure 95, at various pressures umw\muI_OtI= upca .54... N: 152 pa at various pressures a 8: 82 83 com 8m 8. :8 o H _ _ _ _ _ _ _ m f O m aIIIIIIIIIIIIIIIIIIIt/ cm a III-5 I c IIIIIIIIIIIII o;.I/ n DIIIIIIIIIIII /o:W/l \ .m /.I \ OII/I/Hozllll \\\\ OH: H IIthMWt:2:- ------ m // 2a Iffldl/ M - . of II n /w\ \ 8N N 6. m 9 z m r N. SN m 5:: e4. o-Iw «E: «4 oia aaO._. m.N «1...... I com 5:: 2.; T1. 5:: m; aim aaOp b.O «Ila I 86 am: 95:: OO Nszmz 153 aaOp waOOOwam N: b O O v O N a _ _ g P a. NNmNmmaoz-a owe ¢II6 ‘ "‘ llllflh‘1ifif \ / ‘l‘"l“ “ |\ ‘ ‘ \ \ \ “ o I 0‘ ‘I‘ 8‘ o / a \ ‘ k\ x. omm\wuao=-= comm .\ QumNmm4o=I= come 62:» .x umw\wm4o=-= coma cane .. ummxmmS—TO OON- flk OOO\Om-_O:IO OON m-Im. OOO\ON4O:IO O «Ila E: 2.5.: OO Nz\Nn_z OO OON OO— OON OON OOO OOO ZLN\2N («cpl/w)2 as a function of pressure Figure 97. at various flow rates 154 much wmawwmmm N: b m m e m N a _ _ _ F _ L _ a... 1111111 ...............:... nnnnnn ...:........:......... a ‘ ‘\ . "I‘.-‘|‘--".‘|b ““ bwuun--u|- . ‘-\ ouw\wmuo:-= 83832-: 82 v.-.» 83342-: 82 oio 8883:-.. 8“. «it 05333.: S.‘ 9:... 8933?: am: aim $3382-: a I Nmz mbhc: om Nz\Nmz om cod owa DON owN can own ZLN\2N (pr/w)2 as a function of pressure Figure 93. at various flow rates 155 much mmamwwmm N: umw\ww40zla coma omw\mUJo:n: omb omm\wwqoz|3 omv omm\wUAo:|= oww omw\quo=|= o mm: wbpcz om Nz\Nmz om cod omd OON owN com own ZLN\ZN (wa/w)2 as a function of pressure Figure 99. at various flow rates 156 mach wmammwmm N: 7-..-..1..-..-..------HHHHHMWW£/ 1 8 \‘i‘i‘u‘l‘ Its a. l h I oo— 1 cm" D I CON 1 omN ouw\wwqozt: com“ ollo 39832-: :2. fl ,. 8m 8933:... cm: ?..o 8833...: o2 @é ouwxmuuozu: 0 aria : omm mm: abbcz om N:\Nmz 30-N\ZN (cope/w)2 as a function of pressure 100. Figure at various flow rates 157 9:1: xuzom ommzawmc oo— am am or om cm O? on ON 0" _ _ _ _ _ h b _ _ \$\\|\¢llll lllllll Io \|\II\Q\\.\I||\ ¢\t\.\ cm: 0.1.0 mm: 0:19 Nm: mam. E: «Ila 5:: To uwm\mm._o:n= emu Nszmz om an: om“ DON omN Dom omm 30.N\2N Normalized plasma frequencies squared as functions of absorbed power at 150 p-moles/sec and 0.7 torr Figure 101. HPZ/HZ 150 U-HOLES/SEC 7.4 TORR 158 5"‘ HP! 1 I l I l l l D D D D c: D O u: D u: D to D U: a) 0) cu cu .. -‘ ZLN\2N 20 30 40 50 60 70 80 90 100 HBSORBED POHER HHTTS 10 Figure 102. Normalized plasma frequencies squared as functions of absorbed power at 150 p-moles/sec and 7.4 torr 159 rate at various pressures. Figures 97, 98, 99, and 100 show ((0 A.)2 (w m)2 (w A.)2 and (w A.)2 p1 ’ 92 ’ p3 ’ pa ’ respectively, as functions of pressure at various flow rates. Figures 101 and 102 show the frequency ratios as functions of absorbed power at 150 p-moles/sec, and 0.7 and 7.4 torr, respectively. The frequency ratios are found to range 10 - 350. The % ionization of the plasma is calculated from the electron density and pressure. The % ionization calculated from n and nea are denoted P11, el’ ne2’ ne3’ P12, P13, and PIA, respectively. Figures 103, 104, 105, and 106 show P11, P12, P13, and PIA as functions of flow rate at various pressures. Figures 107, 108, 109, and 110 show P11, P12, P13, and PIA as functions of pressure at various flow rates. Figures 111, 112, 113, 114, 115, and 116 show the % ionizations as functions of flow rate at 0.7, 1.3, 1.7, 2.3, 4.8, and 7.4 torr, respectively. Figure 117 shows the % ionizations as functions of pressure at a flow rate of 150 p-moles/sec. Figures 118 and 119 show the % ionizations as functions of absorbed power at 150 p-moles/sec, and 0.7 and 7.4 torr, respectively. The % ionizations are found to range 0.0001 - 0.1 %, with P11 > P12 > P13. P11 and P12 are found to decrease with increasing flow rates and pressures. P13 is found to be independent of flow rate and pressure. 160 mozcmaozh uwm\wm._ozaa PIE .8...“— N: o— m o b o w v m N a o c _ _ _ _ _ _ _ t r Dnunliainccnlusul... 0'31: 0 ...1.---I---+-I-..Uuufli£flv.“.“.nmuu1y, ”x... ,. V No. 0’. c. .m. ., .z. f 3. a .. mo. amok ¢.b >23» 5:: m4 o.|o 5:: m.N «it we. 5:: b; 9.20 5:: m; aim 58.— b.o «Ila. ~.o :n. 3:22. 00 ou-zo~ hzuommn. P11 as a function of flow rate at various pressures Figure 103. mmmumzv— HDZHNUO 161 wozcmzozh uww\muqo:|= ubcm :oqk N: S m m p o m e m u o _ _ . _ _ _ L _ _ Pill!IIIIIulIllltllI-ulll'ltlllltll lllllOII-lll dull. [IMHHHHHHHHMHW/ a, . 1x , t : r .0 ’o ,. r 1 as. mach mach «no» «map much much wabwoaré DF‘F‘NV’I‘ Nam wbhcz om ow-zo~ bzuomum No. vo. ma. me. —.D HOZHNUD LUMUUZF— P12 as a function of flow rate at various pressures Figure 104. 162 uum\mm.az|: mhcm 30...“. N: coed ooN— coo“ com com oov ooN _ _ _ _ _ — _ .3 5.52.1111.linfnnnHuHHHHHHaInMw. mu. ?-I-I.I-I.IO\..\-\.\. 5:: v4. v-3.» 5:: a; oulo man: m.N 1.1.... «an: n; 9.10 5:: m; m.--m mach b.o «Ila 2m mfg: om amaze hzuomwm No. we. mo. mo. «.0 HDZHNUD (LquUZI— P13 as a function of flow rate at various pressures Figure 105, 163 umw\wu._ozuz whim :9: N: cow“ QON~ oooN com com oov OON o _ _ a _ _ _ _ .r o p............ ............... iffy.-. «1 IIIIIIIIIIIIIII 11!? -I---I.-.l [III] ll\o”.V\-.\hnll\|{fl. ’0’! I"\\\. .| ND. [0,0410] a--.-..l.u..u}uu- a .8. 5:: Yb p-39 mach m.v o:lo mm?— m.N fit 1 mo. 5:: ~2— 9...» 53.— m.— m.--m «mo» >.o «Ila ~.o En. mhpcz om HUN—zo— pzmomwm LUZQUZP HOZHNUD PIA as a function of flow rate at various pressures Figure 106. 164 much mmammmmm N: b m w v m a _ flw _ _ _ lb _ II..\..|I..0I.I..\IID .......mv---.--nunuuuuuuuuuunnuuuu .ummxwuso=-= comm .II. omm\mmsoz-= com. »:au ouw\mmso=-= coma ozuo ommaflozé :2. fl. umm\musoz-= owe ¢:a¢ ouw\mwso=-: om“ m:;m omm\mm4oz-= o 4:14 dam mhhcz om ouu~zo~ hzuommm “No. ivo. “we. .wo. ~.n. HOZHNUJD LUKUUZH PIl as a function of pressure at various flow rates Figure 107. 165 much wmzmwmmm N: m c m z _ _ umm\wmqo=-3 comm omm\mmqozsz come umw\mu402|= Dom" omw\mmqoz|: own uwm\mmgozu: omv umw\mmqoz|= om~ owm\wm40z|= o '1 I---'m ......... ".".l".l.|"."‘d.l' \‘.I‘\\‘\‘-I.I --" / Num mhpmz om omNuon pzmommm No. #Q. mo. mo. HDZHNUJD LLIJOZULLJZt- P12 as a function of pressure at various flow rates Figure 108, 166 exec “mamwuma N: m a m uww\mw492|3 comd owm\mu4oz|: omb omm\mw4ozla om¢ owm\wu40213 ow“ omw\mu40:|3 o mum whpcz om ou-zo~ pzuomum No. ¢o. we. we. ~.o HOZHNLIJD LUMUUJZF- P13 as a function of pressure at various flow rates Figure 109, 167 5:: wmawmumm N: b m w v m N _ — _ _ _ _ “nuflflflunufiufl [hull-It'll- ciulislua cccccccc tutlclfluuumuflflut WW}? {2.231. fi fizz .. / omm\wul_o:|: oom~ o.|o uuw\mw._o=..= 02. 13.... oww\mw._oz|= om? 0.2.0 umw\wwn.oz..: 0m: m.--m owm\mw4o=..: c I Sm ”Cc: cm 3.522 hzuozwm No. we. we. me. To HOZHNUD LUZUUZI— PIA as a function of pressure at various flow rates Figure 110. 168 NH». vhu. mzu. mam. izations as functions e at 0.7 torr nt ion ow rat Perce of f1 HQZWNUQ Figure 111- Q-th:LJhJ==F- 169 uww\wu4ozla upcz :oqu N: com owv oov 0mm com owN OON ow— 00— cm _ h p _ . _ L _ _ _ ?-l-l-l-l-l:....l-l ..... l-l-l.l-l-.or.l.l.l ounugnxnnni nnnnnnnn Ilunlliunnnuno/ «N030: BEE: I??? an. mhpmz om mach m." ouNHZDH hzuomwm No. to. co. co. u.o HOZHNUD LUKUUZU— Percent ionizations as functions of flow rate at 1.3 torr Figure 112. 170 oww\ww4ozla PE: 39.: N: new car com com QO¢ com OON oo— o _ _ p _ _ _ _ F .+_ o No. we. co. m: Pie .. . m: 7.30 we «I m.--m gum «Fla ".0 wtmz cm can: b." amazon hzwumwm Percent ionizations as functions of flow rate at 1.7 torr Figure 113. LUZUUZO— HDZHNUD uum\wm._o:t: PE: 30...... N: 171 oov— ooN“ can: com com cow ooN o _ P a No. v «o. 1 co. 5.. 03$ 1 co. mum 0......0 NE min Zn. I ~.o 9:5. co «:2. m.N emu—22 bzwozmm Percent ionizations as functions of flow rate at 2.3 torr Figure 114. LUKUUZI— HDZHNUO 172 coom n, ‘ ~0ch Hindi-OH o.n.o.o. ooov _ m'-"--"---"-"- ...... I??? d1$¢s uuwxmusozr: uccm zone a: neon QODN _ _ 'III- IIIIIIII U n- ...... "-'-'-"-II' ,1 i--- -‘ll ‘ll'll‘l [—D wpbmz on each c.¢ ou-zo~ hzwozmm No. V0. mo. mo. —.6 HOZHNUD LUZUUZO— Percent ionizations as functions of flow rate at 4.8 torr Figure 115. whhfix DD KZDh V.N. OUN—ZDH bZUUKUL 173 mozcmaozh umm\wu.._ozlz PE: 30...". N: S m o a. m m s m N _ o _ _ r P _ _ . _ o unlollllccltdldflllrll No. 1 co. 1 mo. c: 0.!9 .. mo. mum 0!:6 N: m.--m uhm «Fla «.o ”:1: on 5:: Th amaze hzmomum Percent ionizations as functions of flow rate at 7.4 torr Figure ' 116, LUKUUZI— HOZHNUD 174 can: waawwmmn— N: w v m h L N ,.I ""."III pl '- I- a: 0.1.9 m: 9230 NT. Win In. I Ill- II'IQIIIIII-I-IIII-Il|"l no. 119‘-..) I 97E: on ummhflqozlz ow— ouN a 2n: pzmumwm No. we. co. co. LUZUHJZI— HOZHNUD Percent ionizations as functions of pressure at 150 p-moles/sec Figure 117_ PERCENT IONIZED 150 U-flOLES/SEC 0.7 TORR H2 175 0.1 D D 0‘ de¢ 0 o—u—u—au—o O7 (Lama 0 D \ O \ \ \ \\ o I" \‘ tn \ F- ~ I— b O c: \ ‘° 3 | O'.’ \ uJ ‘ 3 \ o c: | LO Q- \‘ c: \ uJ ‘ ID )7, o n: 1' D I (D I an i C: ' D ' V) I l I .1. o N D .II I I l T D 03 (D 1' N D D O O O O O O LUMUMJZI— HDZHNUD Figure 118. Percent ionizations as functions of absorbed power at 150 u-moles/sec and 0.7 torr‘ PERCENT IONIZED 150 U-HULES/SEC 7.4 TORR H2 176 OJ O D C-i ._O cu uch HHHH a.n.n.n. :Iif‘?‘? wk) 00 .— 5— C: I or, DJ. 3 O Q. Q U a: O: D (D m ¢ ._0 CI‘ 1 I r I C3 0 (D V' N D D O D O LUMUUZF— HDZHNUD Figure 119. Percent ionizations as functions of absorbed power at 150 p-moles/sec and 7.4 torr 177 The % ionizations are found to increase with increasing absorbed power. A mode change is again observed as the absorbed power is increased from 60 - 80 W at 150 p-moles/sec and 0.7 torr due to the observed mode change in the electron density results. HEAT TRANSFER MODEL As was shown earlier, the percent of the power that is absorbed by the water cooling of the plasma cavity (% P ) is relatively constant and is about 17.5 % for water all flow rates, pressures, and absorbed powers. This ~yields a theoretical upper limit of 82.5 % for the percent of the power that is absorbed by the gas as it flows through the system (% Pgas)’ Since the discharge tube and cooling air are transparent to microwaves, then 82.5 % of the power absorbed by the microwave plasma system is initially absorbed by the plasma. This assumes that the power contained in the visible and ir radiation that is subsequentially absorbed by the plasma cavity walls is negligible. The plasma then loses some of its energy through interactions with the discharge tube wall. It has also been shown that the percentage of power lost through the plasma-wall interactions (% Pair) is independent of absorbed power and dependent on flow rate and pressure. Thus the plasma-wall energy transfer mechanisms are functions of flow rate and pressure. Since it is 178 179 desirable to maximize % Pgas’ the problem becomes one of keeping the energy in the gas. A literature survey revealed that no work has been done on the energy transfer processes for plasma-wall interactions. Transport properties of dissociated hydrogen atoms in a plasma have been studied, however that was for the gas phase and did not include boundaries. 16’ 141 A heat transfer model has been developed to gain some insight into the energy transfer processes. The plasma-wall interactions involved in the energy transfer processes are electron-ion recombination, atom-atom recombination, elastic and inelastic atomic, ionic, and molecular collisions, and uv radiation. Preliminary calculations have shown that atomic recombination in some cases could account for up to 25 t of the energy transferred to the wall. 25 In order to calculate the contributions from each of these individual plasma-wall interactions to the total energy transfer, knowledge of the concentrations and temperatures of the various species in the plasma, along with the plasma-wall interaction reaction rates, are required. Unfortunately with the present experimental apparatus, this information can not be experimentally determined. Therefore, a simplistic approach is taken. 180 The focus of the present study is to calculate heat transfer coefficients from experimentally determined quantities to lend some insight as to the dominant energy transfer mechanisms. Heat transfer coefficients that characterize the energy transfer processes involved in the plasma-wall interactions are calculated as functions of flow rates, pressure, and absorbed power. Heat transfer coefficients, U, are defined by P - U A AT gas where U - heat transfer coefficient A - plasma-wall interaction area AT - temperature difference between the regions of energy transfer of the driving force of the heat transfer. Heat transfer coefficients are standard engineering calculations generally used to characterize convective- type heat transfer mechanisms. This approach treats the plasma as homogeneous and the discharge tube wall and cooling air temperatures as spatially averaged quantities. The drawback to this approach is that it only deals with the summation of all the individual energy transfer plasma-wall interactions. Consequentially, the purpose of these calculations is to identify trends in the heat 181 transfer coefficients that can be attributed to the individual energy transfer mechanisms. The first heat transfer coefficient, Umax’ is calculated by defining AT as AT - T - T max air where Tmax - maximum possible temperature for the gas. It is the temperature that the gas would attain if the gas were heated as molecular hydrogen with all the Pgas T - temperature of the cooling air. air Figures 120 and 121 show Umax as a function of flow rate and pressure, respectively. Umax is found to be independent of absorbed power. It is interesting to note that this treatment crudely accounts for all the power that is contained is the gas and that the heat transfer coefficient is independent of absorbed power; i.e., Pgas can not be increased by simply increasing the absorbed power, the rates with which the plasma absorbs and loses power is not effected by the power input. The region in which Umax increases with increasing flow rate and pressure is indicative of convective-type energy transfer °K cm 15 58C 182 (mg /sec) 10 20 I 1.7 50100 10000 Flow Rate (p-moles/sec) Figure 120. U as a function of flow rate max at various pressures 183 4800 15- Unmx (x104) 1300 10- -8900 col 0 2 > 750 Kcm sec 5.. 15C) ( IJ-moles/sec) 450/ l 5 10 Pressure (torr) Figure 121. Umax as a function of pressure at various flow rates 184 mechanisms. Umax is found to increase with increasing flow rates at low flows and to decrease with increasing flow rates at high flows, to increase with increasing pressures, and to be independent of absorbed power. These results indicate that convective processes are important at low flows and pressures, and that recombination processes are important at high flows. It is interesting to note that convective processes would be expected to be important at high flows and pressures. The second heat transfer coefficient, Urot’ is calculated by defining AT as AT - Trot - Tair where Trot - spectroscopically determined average rotational temperature T - temperature of the cooling air. air Figures 122, 123, and 124 show Urot as a function of flow rate, pressure, and absorbed power, respectively. This treatment obviously does not take into account the recombination processes since it is based on the rotational temperature which is about equal to the gas kinetic temperature. Urot is found to decrease with increasing flow rates at low flows and increase with ( U 20 rot — (x103) 15 cal °Kmn 2 ) sec 10 185 I3 17 / 23 448 74 Torr l 5000 1000 Flow Rate (p-nufies/sec) Figure 122. U as a function of flow rate rot at various pressures 2L) rot (x103) ’L5 ’L0 186 L \\\\\\4800 (p-moles sec) '8900 H50 13CND 75H) 5 Pressure (torr) I'OC at various flow rates 10 Figure 123. U as a function of pressure 187 0,7 20. torr rot (x103) 7.4 10" cal °K cm sec O 50 100 A bsorbed Power (VVatts) Figure 124. Urot as a function of absorbed power at 150 p-moles/sec and various pressures 188 increasing flow rates at high flows, to decrease with increasing pressures, and to increase with increasing absorbed.power. A convective heat transfer coefficient between the cooling air stream and the discharge tube wall has been estimated using a standard engineering correlation based on the thermal conductivity, viscosity of the cooling air, 12 The value is tube geometry, and Reynolds number. relatively independent of the experimental conditions since the cooling air is delivered at a constant flow rate and temperature, and is 7.8 x 10-4 cal/sec cm2 °K. An average wall temperature is then calculated using Fourier's law to determine the temperature difference between the discharge tube wall and the cooling air that gives rise to the appropriate amount of heat flux from the wall to the cooling air. 20 Figures 125 and 126 show the discharge tube wall temperature as a function of flow rate and pressure, respectively. The discharge tube wall temperature is found to range from 500 - 750 “K. The discharge tube wall temperature is found to decrease with increasing flow rates and to increase with increasing pressures. The discharge tube wall temperature is only calculated for an absorbed power of 80 W. Figures 127 and 128 show the discharge tube wall temperature along with Tmax and Tro , respectively, as ta functions of flow rate at various pressures. The result DISCHRRGE TUBE NHLL TEMPERHTURE 80 "9115 189 m / -co // f —m o I I I / be I I I y I mama: ’03 mama: 1 cocoa / h-h-h-h—h— .’ “sweet LN / uquh '9‘ / T ???W .. 1’ {:9 ii,“ '7 9 i "v’?’ «(6 I I I F I I C: c: o t: o c: o o c: o o c: o m r~ m u: v m P-hJI:D.hJO:CEh-ZDOZUJ a: Figure 125. T as a function of flow rate wall at various pressures THOUSHNDS H2 FLOH RRTE U-flULES/SEC 190 amok wmawmwam N: m w v m N _ _ _ _ _ omw\mumo:I: umm\quo:I= omm\mugoznn umm\mu40213 owm\quo:I= uum\mmgo:I: com: oomv com: omb omv om" DIIJP TI... . mhhmz om mmapcawmzmh 44:: mmzh mom¢:om_o com 00¢ com com com com HUStUOfiI‘IF—Dmm X Twall as a function of pressure Figure 126, at various flow rates 191 (mg/Sec) IO 20 l 1 Tmax 1000— ———— Twau FDCJtDES :: £3<:) \A/ T (°K) 500‘ l 5000 10000 Flow Rate (p-moles/sec) Figure 127. T and T as functions of flow rate max wall at various pressureS' 192 soo— ‘ " " Twoll rota 700 Temp 600 (°K) \ 500 74 . ' - 7.4 400- torr 300 . 5000 10000 Flow Rate (p-moles/sec) Figure 128. Trota and Twall as functions of flow rate at various pressures f1 193 that the discharge tube wall temperature can be greater than T or T indicates that convective heat transfer max rota from the discharge tube wall back into the plasma may occur. This suggests that recombination processes are important. The concentrations and temperatures of the various species have been calculated with a theoretical prediction model. Utilizing these theoretical results, the energy transfer due to plasma-wall interactions will be calculated and compared with the experimental results obtained with the calorimetric and spectroscopic measurement techniques. 100 CONCLUSION A calorimetric measurement technique has been developed to accurately determine the energy transferred to a gas as it flows through a microwave system. The percentage of power that is absorbed by the microwave plasma system that is absorbed by the hydrogen gas as it flows through the system (% Pgas) has been measured for flow rates of 0 - 10,000 u-moles/sec, pressures of 0.5 - 10 torr, and absorbed powers of 0 - 100 W. % Pgas is found to increase with increasing flow rates, to decrease with increasing pressures, and to be independent of absorbed power. A maximum of 50 % has been reached for % Pgas at 8900 p-moles/sec and 7.4 torr. It has been shown that about 82.5 % of the power absorbed by the microwave plasma system is initially absorbed by the plasma. The plasma then loses some of this energy through interactions with the discharge tube wall. Therefore, 82.5 % is the theoretical maximum for % Pgas with the present experimental apparatus. 194 195 Spectroscopic measurement techniques have been developed to determine the chemical and physical properties of the plasma. Electron density, plasma frequency, percent ionization, atomic electronic temperature, molecular rotational and vibrational temperatures have been measured for flow rates of O - 10,000 p—moles/sec, pressures of 0.5 - 10 torr, and absorbed powers of 0 - 100 W. Three independent measurements of the electron density, plasma frequency, and percent ionization have been made. Electron densities have been determined from quarter- and half-height line width measurements of the Ha emission line and from half-height line width measurements of the H6 emission line. Plasma frequencies and percent ionizations are calculated from these electron density measurements. Three similar measurements of the atomic electronic temperature have been made. Atomic electronic temperatures have been determined from relative line intensity measurements of the Ha and H emission lines; 8 the H , and H emission lines; and the H , H , H , and a 1 0197 H . fl H6 emission lines. Four independent measurements of the molecular rotational temperature have been made. Rotational temperatures have been determined from relative line intensity measurements of the rotational lines of the 196 l 1 (0-0) and (1-0) vibrational bands of the G 2; - B 2: and I 1118 - B 12: molecular electronic transitions. Two independent measurements of the molecular vibrational temperature have been made. Vibrational temperatures have been determined from relative band intensity measurements of the (0-0) and (1-0) vibrational bands of the C 12+ - B 12+ and I 1H - B 12+ molecular electronic 8 u 8 u transitions. Electron densities are found to range from 12 13 10 - 5 x 10 cc-1. Two of the electron densities decrease slightly with increasing flow rate and increase with increasing pressure. A third electron density is independent of flow rate and pressure. All three increase with increasing absorbed power. Normalized plasma frequencies squared are found to range from 10 - 350. They exhibit the same trends as the electron densities. Percent ionizations are found to range from 0.0001 - 0.1 %. Two of the percent ionizations decrease with increasing flow rate and pressure. A third percent ionization is independent of flow rate and pressure. All three increase with increasing absorbed power. Atomic electronic temperatures are found to range from 3500 - 6500 °K. They are relatively independent of flow rate, decrease with increasing pressure, and increase 197 with increasing absorbed power. Molecular rotational temperatures are found to range from 225 - 850 °K. They decrease with increasing flow rate after an initial increase at low flow rates, to increase with increasing pressure, and to increase with increasing absorbed power. Molecular vibrational temperatures are found to range from 4000 - 17,000 °K. One vibrational temperature decreases somewhat with increasing flow rate, increases with increasing pressure, and is relatively independent of absorbed power. The other vibrational temperature decreases with increasing flow rate and pressure, and increases with increasing absorbed power at high pressures. Comparison of the characteristic temperatures reveals that the plasma is not in thermodynamic equilibrium and that the lower excited atomic and molecular states are overpopulated. A heat transfer model has been developed to gain some insight into the energy transfer processes occurring at the plasma-wall boundary. Heat transfer coefficients characterizing the energy transfer of the plasma-wall interactions have been calculated for flow rates of 0 - 10,000 p-moles/sec, pressures of 0.5 - 10 torr, and absorbed powers of 0 - 100 W. The discharge tube wall temperature has been calculated for flow rates of 0 - 10,000 p-moles/sec, pressures of 0.5 - 10 torr; at an absorbed power of 80 W. 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