AN INVESTIGATION OF THE ELECTROMAGNETIC . V BEHAVIOR OF A MICROWAVE PLASMA SOURCE OVER A I WIDE RANGE OF PRESSURES ANO FLOW RATES ‘ ‘. ' . Dissertation for the Degree of Ph. D.' MICHIGAN STATE UNIVERSITY RAGHUVEER MALLAVARPU 1976 ‘ WHF‘V‘" "" ' wmnm .lllllmlllll‘lllllllllllllll I/ “a L AR 3 1293 00321 7881 Psfit‘i‘nadJ state Uni-Tic mity f ‘9‘ u'F'W‘ «rum "TLS 21-;- ==== :Zfi: _—'="—I This is to certify that the thesis entitled AN INVESTIGATION OF THE ELECTROMAGNETIC BEHAVIOR OF A MICROWAVE PLASMA SOURCE OVER A WIDE RANGE OF PRESSURES AND FLOW RATES presented by Raghuveer Mal lavarpu has been accepted towards fulfillment of the requirements for Ph.D degree in Electrical Engineering RAXVMAL Major professor Date M I 0-7639 ABSTRACT AN INVESTIGATION OF THE ELECTROMAGNETIC BEHAVIOR OF A MICROWAVE PLASMA SOURCE OVER A WIDE RANGE OF PRESSURES AND FLOW RATES By Raghuveer Mallavarpu The electromagnetic behavior of a microwave plasma source is ex- perimentally examined over a wide range of pressures and flow rates. The plasma source under study is a variable length microwave cavity partially filled with a cold, lossy, isotropic, homogeneous plasma column enclosed in a quartz tube. A small signal linear theory which neglects the flow rate of the gases, but takes into account the pressure dependence of the discharge, is used to qualitatively explain some of the observed experimental results. Three different types of experiments are conducted on the plasma- cavity to demonstrate its use as a versatile microwave plasma source. Two plasma cavities, i.e., Cavity 1 and Cavity 2 operating at incident powers of 30W and 1.2 KW respectively, are used to perform these experi- ments. Cavity 1 maintains a stable, low pressure, non-flowing plasma. It is suitable for examining the linear and non-linear behavior of the plasma and is amenable to conventional plasma diagnostics. A high pressure (over 1 atm.), flowing plasma can be maintained in Cavity 2 and is suitable for studying the absorbed power characteristics of the plasma source. Raghuveer Mallavarpu In the first of these experiments, unusual EM phenomena of the plasma source are examined using Cavity l. The presence of two plasma density operating points for a single eigenlength in the TE:11 mode is experimentally verified. This unusual behavior is explained as result- ing from the presence of a backward wave region in the w - k diagram of the TE:1 mode for non-zero losses. The coupling of EM energy to space charge waves, resulting in the formation of long plasma columns, is ex- perimentally demonstrated and this phenomena is qualitatively explained from the eigenlength vs. (mpe/w)2 and (palm) curves. Short wavelength standing waves of the TMOOp mode are also excited, as predicted by the theory. Two different types of sidebands are detected in the reflected power spectrum of the TE:11 mode, and the occurrence of one of these is qualitatively explained as being caused by a fluctuation in the average plasma density as a function of time. The second phase of the experimentation involves diagnostics on the plasma source. The average electron density, N0, and the electron temperature, Te, are measured over the pressure range 0.04 - 20 torr using the TM010 frequency shift, double floating probe and disc diagnostic techniques. A knowledge of these parameters is used in calculating the effective electric field Ee and the reduced field Ee/p in the plasma. The shape of the No’ Te, E8 and Ee/p vs. pressure curves follow the same general variation with pressure as those exhibited by other investigators in He gas. In the third type of experiments, the absorbed power characteristics of the plasma source are examined over a wide range of pressures, flow rates, and incident power levels. The absorbed power characteristics of a flowing plasma are shown to be significantly different from those of a Raghuveer Mallavarpu non-flowing plasma. The absorbed power is shown to increase directly as a function of the flow rate at low flow rates and then reach a satura- tion at high flow rates. This phenomena is qualitatively explained as being caused by the shielding effect of the high density plasma layer adjacent to the quartz tube. The variation of the absorbed power as a function of pressure is shown to be more uniform in this plasma source than in other types of plasma sources. No tuning stubs are required to provide an impedance match between the external microwave system and cavity. Plasmas can be sustained in argon gas beyond 1 atm. and the gas flow rate can be varied to as high as 14,000 cc/min. It is possible to couple more than 90% of the incident power to the plasma by optimizing the length, discharge pressure and the gas flow rate-of the plasma source. AN INVESTIGATION OF THE ELECTROMAGNETIC BEHAVIOR OF A MICROWAVE PLASMA SOURCE OVER A WIDE RANGE OF PRESSURES AND FLOW RATES By Raghuveer Mallavarpu A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Electrical Engineering and Systems Science 1976 To my parents Mr. & Mrs. M. Nageswara Rao ii ACKNOWLEDGMENTS The author wishes to express his sincere gratitude to his major professor, Dr. J. Asmussen, for his able guidance, encouragement and invaluable advice during the course of this investigation. Special thanks are also due to the other members of the guidance committee, Drs. K. M. Chen, D. P. Nyquist, M. Siegel and G. L. Pollack, for their time and interest in this work. The author also acknowledgestfluasupport of Detroit Edison Company, Kimberly-Clark Corporation, and the Division of Engineering research at Michigan State University for financing part of this research. iii Chapter LIST OF FIGIJRES O O O I O O O C C O O O O O O O 0 O I II III IV TABLE OF CONTENTS INTRODUCfI ON C O O O O O O O O O C O O O O O O O O 0 DERIVATION OF THE MODES ON A CONCENTRIC LOSSY COLD PLASMA ROD INSIDE A CYLINDRICAL METAL WAVEGUIDE. . . 2 1 Introduction. . . . . . . . . . . . . . . . . . 2 2 Basic Equations . . . . . . . . . . . . . . . . 2.3 Derivation of the Characteristic Equation . . . 2 4 w - k Diagrams. . . . . . . . . . . . . . . . . 2 5 Summary . . . . . . . . . . . . . . . . . . . . POWER ABSORBED IN A PLASMA WAVEGUIDE . . . . . . . . 3.1 Introduction. . . . . . . . . . . . . . . . . . 3. 2 Power Flow and Power Absorbed for TM Waveguide Modes . . . . . . . . . . .p. . . . . 3.2.1 TM Mode . . . . . . . . . . . . . . . . . . 00 3.2.2 TMO1 Mode . . . . . . . . . . . . . . . . . 3.3 Power Flow and Power Absorbed for TB Waveguide Modes . . . . . . . . . . . . . . 3.4 Power Flow and Power Absorbed for TEll. Waveguide Modes . . . . . . . . . . . . . . ELECTROMAGNETIC AND SPACE CHARGE MODES OF A COLD LOSSY PLASMA ROD INSIDE A CYLINDRICAL CAVITY . . . 4 1 Introduction. . . . . . . . . . . . . . . . . . 4.2 Theoretical Cavity Modes. . . . . . . . . . . . 4.2.1 Classification and Description of the Plasma- Cavity Modes. . . . . . . . . . . . . . . . . 4.2.2 Rotationally Symmetric Modes, TM 011 and TEOll O O O 0*. Q 0 O 0*. O O O O O O O 0 4.2.3 Dipole Modes: TE and TM . . . . . . . . 111 101 4.2.4 Space Charge Modes TMOOp' . . . . . . . . . . 4.3 Summary . . . . . . . . . . . . . . . . . . . EHERIMENTAL SYSTEMS O O O O O O O O O O O O O O O 0 iv 12 22 61 63 63 66 7O 73 75 80 88 88 93 93 94 95 97 99 100 Chapter VI VII 1 Introduction. . . . . . . . . . . . . . . . 2 The Two Plasma-Cavity Systems . . . . . . . .2.1 The #1 Plasma-Cavity System . . . . . . . 2 2 The External Microwave System for Cavity 1. . . . . . . . . . . . . . . . . 5 2 3 Diagnostic Circuits for Cavity 1. . . . . 5.2.4 The #2 Plasma-Cavity System . . . . . 5 2 5 The External Microwave System for Cavity 2.. . . . . . . . . . . . . 5.2.6 Diagnostic Circuits for Cavity 2. EXPERIMENTAL PERFORMANCE OF THE MICROWAVE PIOASMA S OURC E O O O O O O O C O O O O O I O O 0 Introduction. . . . . . . . . . . . . . . .1 Introduction. . . . . . . . . . . . . . 2 .Excitation of Two Resonant Plasma- Density Operating Points for a Single Resonant Length. . . . . . . . . . 6.2 3 Formation of Long Plasma Columns. . . . . 6.2.4 Excitation of Short Wavelength (A g=1cm) Standing Waves. . . . . . . . . . g. . . . 6.2.5 Detection .of Sidebands in the Reflected Spectrum. . . . . . . . . . . . . . . . . 6.3 Measurement of No, Te and Calculation of E8 in the #1 Plasma-Cavity . . . . . . . . . . 3.1 Introduction. . . . . . . . . . . . . . . 3 1.1 Use of a Microwave Cavity to Measure Electron Densities. . . . . . . . . . . 2 Floating Double Probe Method. . . . . . .3 Measurement of the D.C. Electrical ' Conductivity. . . .'. . . . . . . . . . 6.3.1.4 Evaluation of ve and Ee from No and Te . . . . . . . . . . . . . . . . 6.3.2 Experimental Results . . . . . . . . . . 6.4 Absorbed Power Characteristics of the Microwave Plasma Source . . . . . . . . . 6.4.1 Introduction. . . . . . . . . . . . . . . 6.4.2 Experimental Results. . . . . . . . . . . SUMMARY AND CONCLUSIONS. . . . . . . . . . APPENDIX A O O O‘ O I O O O O O 0 O O O O O O O 0 LIST OF REFERENCES 0 O . O O O O O O O O O C O Q 6 1 . . 6.2 Linear and Non-Linear Operation of Cavity 1 . 6 2 6 2 Page . 100 100 100 104 105 107 110 . 112 114 . 114 116 116 . 117 119 126 129 132 132 133 133 136 138 141 163 163 164 185 . 189 191 Figure 2.1 2.23 2.2b 2.3a 2.3b 2.4a 2.4b 2.4c LIST OF FIGURES An infinitely long metal waveguide with three con- centric dielectric regions. Region 1: Cold, lossy, homogeneous, isotropic plasma of radius a. Region 2: Quartz tube of outer radius b. Region 3: Air space from p = b to p = c. Region 4: The outer boundary of the metal waveguide. . . . . . . . . . w/wpe vs. B/kc for theTM00 mode. fpe I 6.0 GHz, (ripe/wc I 3.47. Waveguide dimensions: a I 0.3 cms., b I 0.3875 cms., c = 5.08 cms. . . . . . . . . . . w/OOpe vs. OL/kc for the TM00 mode. fpe = 6.0 GHz, (ope/wc I 3.47. Waveguide dimensions: a I 0.3 cms., b a 0.3875 ems. , C a 5.08 ems. O O C I I O O C C O O w/wpe vs. B/kc for the TM00 fpe I 4.5 GHz, (ope/Luc I 2.6. Waveguide dimensions: a I 0.3 cms., b I 0.3875 cms., c I 5.08 cms. . . . . mode for w/w S 0.9. pe w/wpe vs. a/kc for the TM00 mode for w/wpe S 0.9. fpe I 4.5 GHz, wpe/wc = 2.6. Waveguide dimensions: a I 0.3 cms., b I 0.3875 cms., c = 5.08 cms. . . . . w/wpe vs. B/kc for the TM00 f I 6.0 GHz, w /w I 3.47. waveguide dimensions: pe pe c mode for w/w S 0.9. pe a I 0.3 cms., b I 0.3875 cms., c I 5.08 cms. . . . . (Io/wpe vs. a/kc for the TM mode for w/wpe S 0.9. f I 6.0 GHz, w /w I 3.47. Waveguide dimensions: pe pe c a I 0.3 cms., b = 0.3875 cms., c I 5.08 cms. . . . . < (IO/wpe vs. B/kc for the TM00 mode for LII/wpe 0.1. f I 6.0 GHz, w /w I 3.47. Waveguide dimensions: pe pe c a I 0.3 cms., b I 0.3875 cms., c I 5.08 cms. . . . . vi Page 13 26 27 28 29 30 31 32 Figure 2.4d 2.5a 2.5b 2.6 2.7a 2.7b 2.8a 2.8b 2.8c 2.8d 2.8e 2.8f (IO/wpe vs. OI/kC for the TM00 f I 6.0 GHz, w /m I 3.47. Waveguide dimensions: . pe pe c a I 0.3 cms., b I 0.3875 cms., c I 5.08 cms. . . w/w vs. B/kc for the TM00 mode for (IO/wpe pe f I 10.5 GHz, f /f I 6.1. Waveguide dimensions: pe pe c mode for w/w pe < 0.1. S 0090 a I 0.3 cms., b I 0.3875 cms., c I 5.08 cms. . . w/w vs. OI/kC for the TM P9 00 fpe I 10.5 GHz, Lupe/O0c I 6.1. Waveguide dimensions: mode for w/w pe S 0.9. a I 0.3 cms., b I 0.3875 cms., c I 5.08 cms. . . Field distribution and charge perturbation for circularly symmetric surface wave on isotropic 12 plasma column. Reproduced from Trivelpiece . . Real part of plasma dielectric constant er vs. w/w and v /w . f I 6 GHz. . . . . . . e pe pe Imaginary part of plasma dielectric constant 61 vs. w/wpe and ve/wpe' pe 01 mode. fpe m [w I 6.1. Waveguide dimensions: a pe c b I 0.3875 cms., c I 5.08 cms. . . . w/wpe vs. B/kc for the TM w/wpe vs. OI/kc for the TM01 mode. fpe wpe/wc I 6.08. Waveguide dimensions: b I 0.3875 cms., c I 5.08 cms. . . . . w/wpe vs. B/kc for the TM01 f I 6.0 GHz. a mode for w/w pe 10.5 GHz, 0.3 cms., 10.5 GHz, I 0.3 cms. < 0.24. fpe I 10.5 GHz, (ope/wc I 6.L.Waveguide dimensions: a I 0.3 cms., b I 0.3875 cms., c I 5.08 cms. . . . w/wpe vs. a/kc for the TM01 f I 10.5 GHz, w /w I 6.08. Waveguide dimensions: pe pe c mode for w/w pe S 0.20. a I 0.3 cms., b I 0.3875 cms., c I 5.08 cms. . . Real part of plasma dielectric constant at vs. w/w and v /w . f I 10.5 GHz. . . . . . e pe pe Imaginary part of plasma dielectric constant 61 vs. w/w and v /w . f I 10.5 GHz. . . pe e pe pe vii 33 34 35 38 4O 41 44 45 46 47 48 49 Figure 2.9a 2.9b 2.103 2.10b 2.10c 2.10d 2.10e 2.10f 3.1 3.2 3.3 w/wpe vs. B/kc for the TM01 mode. fpe I 20 GHz, -w e[wC I 11.6. Waveguide dimensions: a I 0.3 cms., P b I 0.3875 cms., c I 5.08 cms. . . . . . . . . . . (II/mpe vs. OI/kc for the TM01 mode. fpe I 20 GHz, Lupe/wc I 11.6. Waveguide dimensions: a I 0.3 cms., b I 0.3875cms., c I 5.08 cms. . . . . . . . . . . . . . it * III/wpe vs. B/kC for TM10 and TE11 modes. fpe 5.3 GHz, cope/wc I 3.07. waveguide dimensions: a I 0.3 cms., b I 0.3875 cms., c I 5.08 cms. . . . . . . . . . . . . . * w/w vs. o/k for TM and TE* modes. f I 5.3 GHz, pe c pe 10 ll (ape/wc I 3.07. Waveguide dimensions: a I 0.3 cms., b I 0.3875 cms., c I 5.08 cms. . . . . . . . . . . * . < . w/wpe vs B/kc for the TE11 mode for (IO/OI)pe 0 35 and Ve/wpe I 0.2.fpe I 5.3 GHz. (ope/u)C I 3.07. Waveguide dimensions: a I 0.3 cms., b I 0.387 cms., c I 5.08 cms. * . < . w/wpe vs OL/kc for the TE11 mode for w/wpe 0 35 and I = = B Ngu$e 0.2. fpe 5.3 GHz, Lope/wc 3.07. Waveguide dimensions: a I 0.3 cms., b I 0.3875 cms., c I 5.08 cms. Real part of plasma dielectric constant Er vs. (IO/OIpe and V lb) 0 f = 503 GI'IZO o o o o o o o o o o o o o o o e pe - pe Imaginary part of plasma dielectric constant e vs. 1 w/w and v /w . f = 5.3 GHz. . . . . . . . pe e pe pe Arbitrarily-shaped metallic waveguide of unit length 81 and 82 are waveguide cross sections at Z I 0 and z a 1. C . O . C . . C O C 0 O C O C O O O C O O O O 0 Normalized absorbed power Pa/IAI2 vs. w/wpe and 00 a I 0.3 cms., b I 0.3875 cms., c I 5.08 cms. fpe=6 GHz . ve/wpe for the TM mode. Waveguide dimensions: Normalized absorbed power in the resistor Pa/III2 vs. w/2fl for a parallel RLC circuit driven by an ideal current source. L I IODH, C I 10 pf. . . . . . . . . . . viii SO 51 54 55 56 57 59 6O 64 71 72 Figure 3.4 3.5 3.6 4.1a 4.1b 4.2 5.1 5.2 5.3 5.4 Normalized absorbed power P [IAIZ vs. w/w and v /w a pe e pe for the TM01 mode. Waveguide dimensions: a I 0.3 cms., b I 0.3875 cms., c I 5.08 cms., fpe I 10.5 GHz. Normalized absorbed power Pa/IAI2 vs. (IO/wpe and ve/wpe for the TE01 mode. fpe I 10.5 GHz. Wave- guide dimensions: a I 0.3 cms., b I 0.3875 cms., c I 5.08 cms. . . . . . . . . . . Normalized absorbed power Pa/IAI2 vs. (IO/mpe and * ve/wpe for the TE11 mode. fpe I 5.3 GHz. Wave- guide dimensions: a I 0.3 cms., b I 0.3875 cms., c = 5.08 ems. C C O O O O C O O O O C O O O C O C Resonant length LS vs. the plasma density (mpe/w)2 * * 00p’ ”011' “101’ 3“" TE‘111' Operating frequency fixed at w/2n I 3.03 GHz. Waveguide dimensions: a I 0.3 cms.,b I 0.3875 cms., c g 5.08 ems. O O I O O O I O O O O O I O O O O O Q C for the modes TM Resonant length LS vs. (Lupe/w)2 for the cold plasma * modes, TMIO0p and TMlOp' Operating frequency w/ZN I 3.03 GHz. Waveguide dimensions: a I 0.3 cms., b I 0.3875 cms., c I 5.08 cms. . . . . . . . . . . . . Resonant length vs. plasma density (tripe/w)2 and ve/w for a cavity of radius 10.146 cm., plasma radius of 1.248 cm., and an operating frequency Of 2045 GHZ. O O O O I O O O O O O O O O O O O O 0 Cross section of the cylindrical cavity, 30 watt microwave source, and plasma diagnostic circuits . . . . Resonant frequency versus cavity size. Waveguide dimensions: c I 5.08 cms. . . . . . . . . . . . . . . . w/ZN vs. fpe and ve/w for the TM010 mode. Wave— guide dimensions: a I 0.3 cms., b I 0.3875 cms., c - 5.08 ems. O O O O O O O O O O O O O O O O O O O O O The #2 plasma-cavity system. (a) Cross section of plasma cavity (b) Isometric drawing. . . . . . . . ix 74 79 86 90 91 92 101 102 106 108 Figure 5.5 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8a The external microwave system for the #2 plasma- caV1ty. C C O O O O O C O C O O O C C O O O O O O O O 0 Comparison of the theoretical and experimental curves of the cavity resonant length LS vs. 2 * (wpe/w) for the TE111 mode. Waveguide dimen sions: a I 0.3 cms., b I 0.3875 cms., c I 5.08 ems I O O C C O O O O O O O O O C O O O O I I O O O O O 0 Plasma being ejected out of cavity as a result of efficient coupling to the space charge wave through an electromagnetic excitation of the * cavity (TE111 or TM011 mode). . . . . . . . . . . . . . Absorbed power vs. the discharge pressure for the TMOll mode, with the incident power P1 held constant. The cavity resonant length Ls I 8.6 cms. . . . . . . . . Absorbed power vs. the discharge pressure for the TM011 mode, with the incident power P1 held constant. The cavity resonant length LS I 8.1 cms. . . . . . . . . Absorbed power vs. the discharge pressure for the TE“;11 mode, with the incident power P1 held constant. The cavity resonant length Ls I 5.92 cms. . . . . . . . . Excitation of 8 half-wave resonances of the TMOOp mode for an off resonance electromagnetic excitation ofthe cavity (TE111 mode). . . . . . . . . . . . . . .. Excitation of 3 half-wave resonances of the TM00p mode: for a large off resonance electromagnetic excitationof the cavity (TE:11 mode) . . . . . . . . . . Sidebands detected on the spectrum analyzer in the TE;11 mode with the operating frequency m/2fl I 3.03 GHz. Cavity resonant length LS I 6 cms. Discharge pressureI 12 mtorr. Power absorbed I 14.2 watts. Plasma electron density (tripe/w)2 fluctuated between 2.04 - 3.16. Fre- quency scale: 0.2 MHz/cm. . . . . . . . . . . . . . . . Less 111 118 120 122 123 124 127 128 130 Figure 6.8b 6.9 6.10s 6.10b 6.10c 6.1la 6.11b 6.11c 6.11d 6.12s Sidebands detected on the spectrum analyzer in the TE;11 mode with the operating frequency w/2n I 3.03 GHz. Cavity resonant length LS I 6.02 cms. Discharge pressure I 12 mtorr. Power absorbed I 14.1 watts. Plasma electron density (wpe/w)2 I 2.95. Frequency scale: 2.0 WIZICmO O O O O O O O O O O O O O O O O C The effective collision frequency in A as a function of velocity and frequency. Reproduced from Whitmer and Hermanso. . . . . . . . . . . . . . . . Normalized electron density (Lupe/w)2 vs. dis- charge pressure Po and the absorbed power Pa using the TM010 frequency shift method. . . . . . . . . Effective electric field Ee vs. discharge pressure Po and absorbed power Pa’ from the TM010 frequency Shift method 0 O O O O O O O O O O O O O O O O O O O O 0 Reduced field Ee/Po vs. discharge pressure Po and absorbed power Pa’ from the TM010 frequency shift me thOd O O O O O O O O O O O C O O O O O O O O O O O 0 0 Typical floating double probe I-V characteristics at a discharge pressure of 86 mtorr. Absorbed power Pa 8 20 w. 0 O O O O O O O I O I O O O O O O O O 0 Typical floating double probe I-V characteristics for pressures above 1 torr. Absorbed power Pa I 20 w. 0 O O O O O O O O O O O O O O O O O O O I O O O 0 Typical floating double probe I-V characteristics at a discharge pressure of 140 mtorr and different absorbed power levels. . . . . . . . . . . . . . . . . Typical floating double probe I-V characteristics at a discharge pressure of 730 mtorr and different absorbed power levels. . . . . . . . . . . . . . . . . . Normalized electron density (wpe/w)2 vs. discharge pressure Po and absorbed power Pa’ from the floating double probe measurements. . . . . . . . . . . . . . . . xi Page 131 140 142 143 144 146 147 148 149 151 Figure Page 6.12b Electron temperature Te vs. discharge pressure PO and absorbed power Pa’ from the floating double probe measurements. . . . . . . . . . . . . . . . . . 152 6.12c Effective electric field Ee vs. discharge Po and absorbed power Pa’ from the floating double probe measurements . . . . . . . . . . . . . . . . . . . . 153 6.12d Reduced field Ee/Po vs. discharge pressure Po and absorbed power Pa’ from floating double probe mea- surements. o o o o o o o o o o o o o o o o o o o o o o o 154 6.133 Normalized electron density (Lupe/m)2 vs. discharge pressure Po and absorbed power Pa, from measurements using discs. . . . . . . . . . . . . . . . . . . . . . . 156 6.13b Electron temperature Te vs. discharge pressure Po and absorbed power Pa, from measurements using discs . . 157 6.13c Effective electric field E vs. discharge pressure Po and absorbed power Pa’ from measurements using discs. 0 O O O I O O O O I O O O O O O O O O O 0 O O O O 158 6.13d Reduced field Ee/Po vs. discharge pressure Po and absorbed power Pa’ from measurements using discs . . . . 159 6.143 Normalized electron density (Lupe/w)2 vs. discharge pressure Po and absorbed power Pa over the pressure range 40 mtorr - 20 torr, from three different di- agnostic methods. . . . . . . . . . . . . . . . . . . . 160 6.14b Electron temperature Te vs. discharge pressure Po and absorbed Pa over the pressure range 0.1 - 20 torr, from two different diagnostic methods. . . . . . . 161 6.14c Reduced field Ee/Po vs. discharge pressure Po and absorbed power Pa over the pressure range 0.04 - 20 torr, from three different diagnostic methods. . . . 162 6.15 Absorbed power Pa vs. eigenlength L8 and different discharge pressures Po’ for the TEO11 mode plasma of Cavity 2. Flow rate I 1000 cc/min., Incident power P1 8 1.2 KW. O O O O I O O O O O O O O O O O O O O 166 xii Figuge Page 6.16 Power absorbed Pa vs. eigenlength LS, and flow rate (cc/min) for the TE011 mode plasma of Cavity 2. Dis- charge pressure, PC I 10 torr. Incident power Pi I 12KW 169 2 6.17. TE011 resonant length vs. plasma density (wpe/w) and collision frequency (De/w) for Cavity 2. w/2n 2045 GHZO o o o o o o o o o o o o o o o o o o o o o o o 170 6.18 Power absorbed Pa vs. discharge pressure Po and inci- dent power Pi for the TE112 mode plasma of0 Cavity 2. Flow rate I 147 cc/min. Gas: argon. . . . . . . . . .. 173 6.19 Power absorbed Pa vs. discharge pressure Po and inci- dent power Pi for the TE112 mode plasma of oCavity 2. Flow rate I 520 cc/min. Gas: argon . . . . . . . . . . 174 6.20 Power absorbed Pa vs. discharge pressure Po and inci- dent power Pi for the TE112 mode plasma of oCavity 2. Flow rate I 955 cc/min. Gas: argon. . . . . . . . . . 175 6.21 Power absorbed Pa vs. discharge pressure Po and inci- dent power P1 for the TE112 mode plasma of0 Cavity 2. Flow rate I 1480 cc/min. Gas: argon. . . . . . . . . . 176 6.22 Power absorbed Pa vs. discharge pressure Po and inci- dent power P1 for the TE112 mode plasma of0 Cavity 2. Flow rate I 2500 cc/min. Gas: argon. . . . . . . . . . 177 6.23 Power absorbed Pa vs. discharge pressure Po and flow rate for the TE112 mode plasma of Cavity 2. Incident power?1 I 966 W. Gas: argon. .,. . . . . . . . . . . 178 6.24 Power absorbed Pa vs. discharge pressure PO and flow rate for the TE112 mode plasma of Cavity 2. Incident power P1 I 759 W. Gas: argon. . . . . . . . . . . . . 179 6.25 Percentage peak-absorbed power vs. flow rate for the * .TEll2 plasma of Cavity 2. Incident power Pi I 966 W . . 180 xiii Figure 6.26 Plot of absorbed microwave power vs. pressure for argon plasmas at various incident powers. Repro- duced from Bosisio et.al.54. . . . . . . . . . . xiv CHAPTER I INTRODUCTION Microwave discharges have been investigated for over 25 years1 and applications have been suggested in the areas of plasma chemistryz, laser dischargesB, and RF heating in thermonuclear fusion research4. Despite this interest, experimentally versatile steady-state microwave discharges at pressures greater than 1 torr have not been available until recentlys. In most investigations the microwave plasma formation is restricted by the metal coupling structure. For example, certain cou- pling structures produce plasmas that are small in comparison to the electromagnetic wavelength6’7, resulting in maximum plasma volumes of only about 50 cmZL. Also, many experiments can only operate over re- stricted pressure ranges7’8, and are able to achieve densities which are only slightly higher than the critical density NC, corresponding to plasma resonance at the exciting frequency8’9. Furthermore, most plasma coupling structures are complex and difficult to analyze electromagnet- ically6’7’8. This electromagnetic complexity makes direct measurement of the plasma characteristics, such as electron density,temperature, etc., difficult without disturbing the plasma and electromagnetic fields. Thus, from an experimental and practical point of view, there is a need for an RF plasma source which is able to provide a high variable plasma density, which is capable of maintaining a microwave discharge over large changes in background pressure and gas flow rate, which is able to be analyzed electromagnetically, and which is amenable to diagnostic measurement techniques for the quantification of microwave plasma para- meters. In addition, many industrial applications will require a plasma source having a volume much larger than 50 cm3. Recently, a large-volume microwave plasma source was developeds. By means of a slowg traveling-wave structure, microwave energy of up to 2.5 kW was coupled to a 19 mm outside diameter quartz tube obs taining plasmas exceeding 2000 cm3. This microwave plasma system was shown to possess a good match at many different incident power levels without external tuning systems for pressures of 1 torr up to 1 atm. in argon gas. Thus, this system appears to overcome the tuning prob- lems of previous microwave plasma sources while producing a large-volume plasma over a wide pressure range. In this thesis the experimental properties of still another micro- wave plasma source is describedlo. Here the plasma is part of a cylin- drical waveguiding system and either fast or slow waves are able to sustain a plasma. The waveguiding system is terminated at one end by a fixed short and at the other by a variable short, consequently, forming a plasma cavity. Microwave power is then coupled to the resonances of the plasma cavity, imposing the requirement for a physical length tuning mechanism. However, this tuning is a fast, simple adjustment that seems justified in view of the higher electric field (an important parameter in many plasma chemistry experiments) obtained at the cavity resonances. A linear, lossy, cold plasma theory is used in modeling the micro- wave plasma source and is described in Chapters II-IV. Attempts are made in Chapter Vfilto qualitatively explain the experimental results by comparing with this theory. The basic equations which will be used to mathematically describe a cold, lossy, homogeneous, isotropic plasma are introduced in Chapter II. From this set of equations a dispersion relation for the propaga- tion of electromagnetic and cold plasma modes is derived for a quartz- enclosed plasma concentrically located in an infinite metal waveguide. w - B and w - a diagrams are explained for the different modes, with the electron density and the electron-neutral collision frequency as the variable plasma parameters. Regions of forward and backward waves are identified on theta-lcdiagrams. The Poynting vector is evaluated in Chapter III for the lossy plasma modes that were discussed in Chapter II. From this Poynting vector a normalized power absorbed per unit waveguide length is derived for the modes. The power absorbed is studied as a function of the frequency with the electron density and the electron collision frequency as the variable plasma parameters. Volume and surface resonances of the plasma are identified and the power absorbed by the plasma at the resonantfrequen- cies is discussed. The characteristic equation derived in Chapter II is used in Chapter IV to obtain an eigenlength vs. plasma density and electron collision frequency plot fortfiuzvarious modes of a cylindrical plasma—cavity. The behavior of these modes at low and high values of the plasma densities and for a range of collision frequencies is discussed. Slow-wave and backwarddwave resonances are identified on the eigenlength plot. The region of intersection of EM resonances with slow wave resonances is also discussed. The experimental apparatus is presented in Chapter V. The design of two different cavities used in performing experimental work from 10 mtorr to 500 torr is discussed. The driving microwave circuits and the probe and microwave diagnostic circuits are explained. The experimental results are discussed in Chapter VI. The actual experiments are done in two different cavities. Experiments are carried out in the pressure range 10 mtorr to 20 torr and incident power levels up to 30 W with Cavity 1. In experiments on Cavity 2, the pressure range is l torr - 500 torr, flow rate is varied from 0-2500 cc/min and incident power levels up to 1.3 KW are used. Eigenlength curves of the TE*111 mode are verified and the coupling of EM and plasma modes is demonstrated. Non-linear effects in the form of sidebands intfluareflected spectrum of the TE:11 mode are observed. The reason for the occurrence of one of these sidebands is explained. For many experiments involving applications of a gas discharge, it is important to evaluate an effective electric field in the plasma. The determination of this quantity requires a knowledge of the electron density and the collisional frequency in the plasma. These plasma para- meters are measured as a function of pressure in the range 100 mtorr to 20 torr using microwave, probe and disc diagnostic techniques. The limitations of these methods and the accuracy of the results is also presented. Experiments on a flowing gas are conducted on Cavity 2, which is capable of handling incident powers of up to 1.3 KW. Power absorbed vs. cavity eigenlength are obtained for the TE011 mode with flow rate and the gas pressure as the variable parameters. Another set of experi— ments are conducted with a TE:12 mode where the absorbed power is measured as a function of the gas pressure with the incident power and the gas flow rate as the externally variable parameters. All these experiments show that the absorbed power characteristics of a flowing plasma differ significantly from those of a non-flowing plasma. Chapter VII summarizes the work presented in the thesis and suggests further investigations where required. CHAPTER II DERIVATION OF THE MODES ON A CONCENTRIC LOSSY COLD PLASMA ROD INSIDE A CYLINDRICAL METALMWAVEGUIDE 2.1 Introduction The general problem of propagating waves in a plasma waveguide has been examined by several workers. The problem can be divided into two specific cases which depend on the exact plasma volume occupying the waveguide: 1) A plasma totally filling the waveguide, and 2) A plasma partially filling the waveguide. Allis, Buschsbaum and Bersll obtained the w - k diagram for the various propagating modes in a lossy, cold plasma completely fillingra circular waveguide. Only EM waves can propagate in such a plasma- waveguide system. Surface wavesare not present because they require charge accumulation on the plasma surface. Trivelpiece12 and Gould made a quasistatic analysis to show that surface wave propagation is possible in a circular waveguide partially filled by a concentric,cold lossless plasma rod. Agdur and Eneander13 solved the complete electromagnetic problem by deriving the characteristic equation for the waveguide modes and solved for the cavity resonances for several important resonant modes; i.e., TElll’ TMOlO’ etc. Shohet14 ex- tended their results to include electron-neutral collisional losses and solved for cavity resonant frequency as a function of electron density and collisional losses. wave propagation along warm plasma columns in free space and par- tially filling circular waveguides has been examined by Diament, Granat- stein and Schlesingerls, Vandenplasl6 and Fredericksl7. They have shown that the cold plasma theory is not valid in and beyond the region where the phase velocity equals the electron thermal velocity and that a warm plasma description is more accurate. They also describe warm plasma modesls, Tonks-Dattner or temperature resonances, and demonstrate experi- mentally the coupling of EM modes to these resonances. In this chapter, solutions to the characteristic equation of a lossy plasma waveguide are studied in greater detail than in previous investi- gations. For example, the dispersion curves for a number of propagating modes in such a plasmadwaveguide are obtained for both the lossless and the lossy cases. These curves will show that in addition to forward EM and cold-plasma waves, it is also possible to have frequency regions where backward waves propagate. Using this complete electromagnetic description, the power absorbed per unit length has also been calculated and is discussed in detail in Chapter III. 2.2 Basic Equations Consider a cold, homogeneous, isotropic, lossy plasma of infinite extent. An electromagnetic analysis of such a plasma is well known and can be carried out by treating it as a material with a complex dielectric constant. The latter is easily derived from a consideration of the cold plasma fluid equations and the associated Maxwell's equations that describe the electromagnetic fields in the plasma. A set of basic fluid equations obtained from the first two velocity moments of the Boltzmann equation for both electrons and ions are shown below. In these equations the pressure termois neglected since Te - T1==CL in the cold plasma approximation. 3Ne + 3—t—+ V. (NeVe) = 0 2.1 a? __£.+ m (6 V)? = - e(E +‘V IKE) - (V V ) 2 2 Ineat: e e' e e ee me . BN 1 + a: +v. (NiVi) — o 2-3 a? ____i_+ (i? V)_\7=e(-E+-V 35-0937) 24 “‘13:; “‘1 1° 1 1" iimi ' where N = electron number density ion number density 2 I macroscopic electron velocity m<+ I <+ I macroscopic ion velocity electron mass 5 (D I m = ion mass 9. = electric field WIN I magnetic field e 8 electronic charge ' v = effective electron-neutral particle collision frequency, v 3 effective ion-neutral particle collision frequency. Equations 2.1 to 2.4 express the conservation of mass for electrons, conservation of momentum for electrons, conservation of mass for ions and conservation of momentum for ions,respectively. The electron-neutral particle collisional losses within the plasma are accounted for by a non- zero value of ve. The associated Maxwell's equations in such a plasma are: + 3% Vx E =-IJO'5? 2.5 (N 'N) V. E = e -$-—£- 2.6 E .0 + + 3?; VxH ' 8(N1Vi - NeVe) + 80 _t 2.7 v . fi = 0. 2.8 B . e‘E 2.9 O + + B t “0H . 2.10 These relations are valid under the assumption that the electrons and ions are free and are present in a free space medium, i.e., there is no bound charge present as in a dielectric. Assuming a time-variation of the form ejmt and expressing the vari- able quantities as the sum of a dc term and a perturbed ac term, the variables become: N = N + n ejwt 2.11 e oe e N = N + n ejwt 2.12 i oi i + + jwt Ve = Ve e assuming no dc electron drift 2.13 V1 =‘Vi ejmt assuming no dc ion drift 2.14 E = E ejwt assuming no static electric field 2.15 '15 , 'fi e3”t assuming no static magnetic field. 2.16 IO Noe and N01 are the unperturbed electron and ion particle densities re- spectively, and they are equal for both electrons and ions in a homo- geneous plasma, i.e., N0e 8 N01 = No' Using Equations 2.11 through 2.16, the first velocity moment equation for electrons as given by Equation 2.2 can now be reduced to, -> + -> jwV m = q E - v m V . 2.17 e e e e e e + + -> + In Equation 2.17, the (Ve x B) term and the non—linear term (Ve.V)Ve have been neglected. These approximations are justified provided we study those wave solutions for which Ve<we z z 2 32 where 9 = jwe and 2 = jwu. .32 .33 .34 .35 .36 .37 .38 .39 .40 .41 .42 .43 In each region the potential functions must also satisfy the separation relations: l6 2 2 2 w 2 Region 1. kpl + k2 - k1 — (c) 81 2.44 2 2 2 w 2 Region 2. kp2 + kz = k2 = (E) 62 2.45 Re ion 3 k2 + k2 = k2 - (252 2 46 g ° 03 z 3 c ° ’ 81 is the plasma permittivity and is given by Equation 2.24, and 82 is the permittivity of the quartz tube. The solutions to the Helmholtz equation must satisfy the following boundary conditions: 1) The tangential components of E and H must be continuous across the plasma-quartz tube interface; i.e., at p = a, Ez, Hz, E¢ and H¢ must be continuous. 2) The tangential components of E and H must be continuous across the quartz tube - free space interface; i.e., at p = b, Ez, Hz, E¢ and H45 must be continuous. 3) The tangential components of E must vanish on the outer metal boundary; i.e., at p = b, E2 = 0, E¢ = 0. In this class of problems the fields cannot be divided into pure TE or TM modes; thus, both Ez and H2 will be necessary to satisfy the boundary conditions for any given mode. This will ensure a general so- lution. Except for the case of rotionally symmetric modes, which can be thought of as pure TE or TM, the other modes are hybrid in character. Using equations 2.26 through 2.46, subject to the boundary condi- tions as given above, we arrive at the following 8 simultaneous equations 2 2 2 Pk J (k a) G k Jn (kp a) + H kp Nn (kp a) 2.47 01 “ D1 D2 2 2 2 17 2 2 A8 k J(k a)=B€ R J (k a)+C€ k N(k a) 2.48 2 p1 n pl 1 p2 n oz 1 92 n 02 kzn Ak J'(k a)+F J(k a)=Bk J' (k a)+Ck N'(k a) pl “ D1 ”“03 “ 01 p2 “ 02 p2 “ 92 kzn kzn + G J (k a) + H N (k a) 2.49 whoa n p2 wuoa n p2 kzn kzn kzn A J(k a)+FkJ'(k a)=B J(k a)+C N(k a) wela n pl pl n 01 weza n p2 weza n p2 + G R J' (k a) + H k N' (k a) 2.50 02 “ D2 p2 “ 02 c k2 J (k b) + H k2 Nn (k b) = K'kz F2 2.51 02 n 02 02 02 03 B 83 k2 Jn (k b) + C€3 k2 N (k b) = E'ezk2 F1 2.52 02 02 02 n 02 D3 kzn kzn B k J' k b + C k N' k b + G J k b + H N 02 n ( 02 ) 02 n ( 02 ) wuob n ( 02 ) wuob n (kpzb) kzn = ' ' E kp3F3 + K ‘ “mob F2 2.53 kzn kzn B---—J (k b)+C————N (k b)+Gk J' (k b)+ w€2b n 02 w€2b n 02 02 n 02 kzn ' = ' ————— + K' k 2.54 H kpan (kpzb) E ws3b F1 03 F4 where ' = - 2.55 E E/Jn (kp c) 3 18 I _ _ I K - K/Jn (RQ c) 2 3 F1 = Jn (kp b) Nn (kp C) - Jn (kp C) Nn (kp b) 2 3 3 3 3 = ' _ 0 F2 Jn (kp b) Nn (kp C) Jn (kp C) Nn (kp b) 2. 3 3 3 3 = I _ I F3 Jn(kp b) Nn(kp C) Jn(kp C) Nn (kp b) 2. 3 3 3 3 = I I _ I I - F4 Jn (kp3b) Nn (kp3c) Jn(kp3c) Nn(kp3b). 2 For a non-trivial solution to the simultaneous equations 2.47 through 2.54, the determinant of the coefficients must be identically zero. Hence, it follows that, .56 .57 58 59 .60 19 Ho. « s as 1:1 «Q c «Q An xv.z x N O Q a :3 3 ézn~ cx «a cmo 2 5% v. «Q c 0:3 3 scan « c x Q a m :3 A... in c x: An «Q c NQS S 5an c x «Q a «Q An xv.z x « « Q c Q is is 2 «saw Q c m a: CW 52'! c x: «a «u C 3 S éspu ax «Q c «Q An xv.fi x N N Q c is so 4 Min u 20 Upon simplifying the above determinant we obtain the following characteristic equation for the three dielectric boundary value problem I k 81 kp2 Jn( p1a) ( -—— e k F F - s k F F ) - (e k F F -s k F F ) e2 kpl Jn(kpla) 3 02 3 7 2 Q3 1 8. 3 oz 3 5 2 Q3 1 6 I kpz Jn(kpla) k F F -k F F > - (k F F - k F F ) kpl Jn(kpla) ( 03 2 8 02 4 7 p3 2 6 oz 4 5 2 2 (k2 4 k2 )2 =nkz pl 92 [ekkFFFF-ekzFFF2 wzu 6 82 k4 R2 3 p2 D3 2 3 7 8 3 92 3 4 7 ° 2 ‘1 D2 2 2 + Ezkpzkp3F1F4F7F8 - 62k p3F1F2F8 ] 2 2 2 k - k J' k n2k2z ( 02 93) 2 2 “( 018) k k + 2 2 2 2 2 'Ezkp FleFs + J (k a) (52 + 51) p p F1F2F5F7 w poszb kp kp kp l n 01 1 2 1- 2 3 2 2 2 2 2 J' k - - n( p a) n2R2 (kp kp )(kp kp ) _ 1 2 2 z 1 2 2 3 2 E1kp F1F2F7 + 2 4 4 2 ‘ Jn(kp a) 2 w Hoezab kp k k 1 1 92 p3 n2k2 2 2 2 z 2 2 2 2 2 2e k k k F F F F + (k - k ) (k - k ) F1F2F7 2 D1 D2 D3 1 2 9 1° wzuoab D1 02 D2 03 2.62 where, 21 F5 = J;(kp2a) Nn(kpzb) - N;(kp2a) Jn(kp2b) 2.63 F6 = J;(kp2a) N;(kpzb) - Ng(kpza) Jh(k02b) 2.64 F7 = Jn(kpza) Nn(kpzb) - Nn(kpza) Jn(kp2b) 2.65 F8 = Jn(kpza) Nn(k02b) - Nn(kpza) JA(kpzb) 2.66 F9 = J;(kp§O Nn(kpza) - N;(kpza) Jn(kpza) 2.67 F10 = Jn(kpzb) N;(k02b) — Nn(kp2b) J$(kpzb). 2.68 For rotationally symmetric modes, n = O and the right side of Equation 2.62 becomes zero. The left hand side is a product of two ex- pressions, each of which when equated to zero yields the TM and TE mode solutions, respectively. When n + 0 the entire Equation 2.62 must be used in obtaining a solution, since the modes are hybrid in nature; i.e., they havelxnfll Ez and H2 field components. If the enclosing quartz tube thickness were assumed zero, i.e. if we set b = a inISquation 2.62 and if Ve = 0, then we would obtain the two dielectric problem characteristic equation, as has been derived by otherslB. It is apparent that for finite losses within the plasma almost all the terms in the transcedental equation above are complex, including the Bessel's functions which are functions with complex arguments. Details of time numerical techniques involved in evaluating the roots of such an equation are explained in Appendix A. 22 Since the plasma under study is lossy, k2, in general, is complex, i.e., k2 = E3-’ja, where B is the propagation constant and a the attenua- tion constant in the z - direction. By solving the characteristic equa- tion for w vs. kz, with wpe and Ve specified,(u—E3andlu-11diagrams can be generated for each mode. Interesting electromagnetic properties can be obtained from such diagrams and these will be the subject of discus- sion in the following section. 2.4 ka Diagrams This section presents the w - k diagrams for the various propagating modes in the inhomogenous waveguide. This diagram gives a useful insight into the fast wave and slow wave solutions to this boundary value problem. It explains some modes that exist without a plasma and the transformation of electromagnetic modes in the presence of the plasma and also predicts the appearance of modes that do not exist in the empty waveguide. Both fast wave (V¢3>c) and slow wave (V¢‘ 0. These are rotationally symmetric modes and hence, they are pure TE or TM in nature. They are labeled the same 23 13,16,17. At as the corresponding modes in the empty circular waveguide high plasma densities, i.e., wpe>>w, and all losses these modes approach the coaxial waveguide mode that has the same index as the empty circular waveguide modelo. At high frequencies, i.e., w>>wpe, and all losses these modes approach the corresponding empty circular waveguide modes. (b) EESm-QE—Inzm: n>02 m>0. These are hybrid modes, the asterisk denoting their hybrid nature. They are labeled with respect to the TE or TM modes in a circular waveguide, into which they reduce when the plasma density goes to zero. At high plasma densities and zero losses, mode in a coaxial wave— nm+1) guide with a metallic center conductor. At high plasma densities and fi- * * the TE (TM )mode approaches the TM (TE nm nm nm * * * nite losses, however, the TE (TM >mode approaches the TE (TM ) nm nm nm nm coaxial waveguide mode. At high frequencies, and finite losses the * * TEmu (TMnm) mode approaches the empty circular waveguide TEmu (mum) mode. 2) Slow wave plasma modes: These modes do not exist in an empty waveguide and have a phase velocity smaller than the velocity of light over a wide range of plasma densities. They can be further subdivided into two classes of modes. (a) TMOO: This mode is circularly symmetric and does not exist in the empty waveguide. However, it is classified with respect to the circularly symmetric TM modes of an empty waveguide. This is also called a surface wave or a space charge wave. At large plasma densities and low losses the TM00 mode approaches the TEM mode of a coaxial waveguide with its phase velocity approaching the speed of light, whereas at large plasma densities and high losses it deviates from the TEM mode and becomes more of a slow wave. * (b) TMno' These are hybrid modes that are ¢ dependent. They are slow waves in a lossless plasma and for small losses. At high 24 plasma densities they asymptotically approach the coaxial TEn1 mode. * For finite losses, however, the TMno mode becomes degenerate with the * TEn1 mode and its asymptotic behavior at high plasma densities and high * frequencies, is same as that of the TEn1 mode. The following sub-sections deal with a detailed study of the nor- malized w - k diagrams, i.e., w/wpe vs. B/kc and 111/wpe vs. a/k: with * m /we and ve/wpe as variable parameters, for the TM 10, pe 00’ TMOl’ * . TE 11 modes. we and kC are the cutoff frequency and cutoff wave TM number,respectively,of the TE11 mode in an empty circular waveguide. These diagrams have been plotted for experimental waveguide dimensions: a - 0.3 cms., bl= 0.3875 cms., c = 5.08 cms. The experimental operating frequency §% = 3.03 GHz is also shown in these curves. For these wave- (0 ~59- = 1.73 GHz and kc = 0.362 cm‘l. guide dimensions, 2n TM00 mode. Space charge or electromechanical waves propagate in a stationary plasma of finite cross-section, due to a perturbation either of the average volume charge density or of the surface charge densitylz. Pro- pagation of slow waves in a cold plasma due to a volume charge pertur- bation is possible only in the presence of acbwzmagnetic field. Surface waves can propagate on a quartz-enclosed plasma rod, partially filling a metal waveguide, with or without a d-c magnetic field. The TM00 mode is a surface wave that propagates in the absence of a d-c magnetic field. The dispersion relation for the TMOm mode can be obtained as a special case of equation 2.62, by setting n = 0. The resulting equation is shown 0n the following page. 25 k J'(k a) k k .51 O2 0 p1 = e3 02 F3F5 ‘ E2 p3F1F6 2 69 s R J (k a) e k F F -‘e k F F ' 2 pl 0 61 3 62 3 7 2 03 1 8 where, F1, F3, F5, F6, F7 and F8 are as given in equations 2.57, 2.59, 2.63 to 2.66 with n = 0. The first root (m = O) of equation 2.69 is the solution to the TM00 mode, the second root (m = 1) that of the TM01 mode and so on. The TM00 mode has basically three field components: longitudinal and radial electric fields Ez and ED respectively, and a circular magnetic field H¢ . Ez would be predominant for those fre- quencies when the TM00 mode is a space charge wave and E2 would become zero whenever the TM00 mode approaches the TEM mode. The w - k diagram for the TM mode is obtained from equation 00 2.69, with ve/wpe and w elwC as running parameters. Several interesting P features of the plots of w/wpe vs. B/kc (figures 2.2a, 2.3a, 2.4a, 2.4c, 2.5a) and m/wpe vs. OL/kC (figures 2.2b, 2.3b, 2.4b, 2.4d, 2.5b) will now be explained. Figures 2.2a and 2.2b show the lossy TM00 waves for fpe - 6.0 GHz and ve/wpe = 0.1 over the entire frequency range. In Figure 2.23, the w - k diagram is separated into four regions. Region 1 is the slow wave portion of the curve. In region 2, the TM00 mode is a backward wave. Region 3 shows that the TM00 mode is almost cut off in this frequency range. In region 4, this mode is an EM wave which eventually becomes asymptotic to the light line. Figures 2.3a, 2.4a, 2.5a show the w/wpe vs. B/kc diagrams and figures 2.3b, 2.4b, 2.5b show the w/wpe vs. OL/kc diagrams for the different plasma densities of f e I 4.5 GHz, 6.0 CH2 and 10.5 GHz and for a range of collision frequencies. The ve/wpe s 0.03 curves in figures 2.5a, and 2.5b have the same w/wPe 10 26 ///{:ght Line / 4“ 2 =- + l l l l- l l l I l 4 8 12 16 20 24 28 32 B/kc Figure 2.2a. w/wp vs. B/kC for the TM00 mode. fpe=6.0 GHz. wpe/wcs3.47. e Waveguide dimensions: a - 0.3 cms., b = 0.3875 cms., c = 5.08 cms. 27 mm: .mao wo.m I o ..meu nnwm.o a n ..mau m.o n m "mCOHmcmev mvwswm>m3 .mq.m u o3\mQ3 .Nmo 0.0 u mam .mvoa cosh mnu you o&\d .m> 0Q3\3 .nN.~ mpswwm ox\d o«.. «T 2- E- «T 2- m- o- T «- o q 11 q _ — 1 _ a — - q I H 1 « 1 m m M d a 1 s. 1 m 28 .mEo wo.m u o ..mEo mnwm.o u n ..msu m.o n m «muowmcmawc ma mvwswm>m3 .o.~ u o3\mQ3 .Nmo m.q u mam .o.o.w ma3\3 pom oboe oozH mcu HOW ux\m .m> 3\3 .mm.~ wuswwm U x\m m/m pm . \ NED mo.m u mfl \ .-.. 6:43 “amps \ 29 .mao mo.m u u ..mEo mmwm.o u n ..mao m.o n m @mvflswmkrmz oooN " 03\mQ3 «NEG moq Il- QQN o¢oO IVI m93\3 HOW Unvoa DOE ms.“ HOW Uv~\d om> U x\6 «NI ON: QHI N~I ml «I o w _ _ _ _ _ N. II; #0 56.0 I: Q Q m \A fl 0 3 cum 3\Q> 3 o H oA m.o ll 0. New mo.m u.ww IL we umcomemEHw on 3\3 .nm.« muamwm ad m/m 3O .mao mo.m u o ..mao nnwm.o u n ..mau m.o u m «macamsmawv mnasww>m3 .~<.m u 03\wcs .smo o.c u mam .m.o.w_ma3\3 now @608 GOSH may now ux\m .m> ma3\3 .m<.N ouswwm U is «H 3 m 6 s « o a _ _ _ _ _ \\ uq.~ muawwm omm\\ . \i. a U . . 3 \\\ARRV\\\\\ mNm o “MM¢\ \ o A o Moo I .No III. III. III III I ll m m . I ma I 14 .w ESP 3%! .II I II Ir ll 1 «mo mo.m u :«\3 \ 6:3 233 \ \ w. 31 .mao wo.m u o ..mEo mmwm.o u n ..mau m.o u m "m:0fimcmsfiv . a .I mvflsmm>mz .nq.m u o3\mo3 .Nau o.o u m m .m.o v maa\3 pow oboe ooze mnu pom ox\d .m> oQ3\3 U x\8 q«1 om: 0H: «HI an «I o _ .1 _ E a _ 661?: u mum? o «no mo.m u e«\3 .1 c. ,.o m««.o m.o m«m.o m. L .nq.« whamsm adm/m .08 .07 .06 .05 3“ .04 w/ .03 .02 Figure 2.4c. 10.0 / / 32 / // light Line. / 6 /, 0 \ 5“Q . 3}, ‘ d@ ”D Q. é? Q. ;r' l g l I I I 0.2 0.3 0.4 0,5 0.6 0.7 B/k c w/wpe vs. B/kc for the TM00 mode for w/wpe < 0.1. fpe I 6.0 GHz, wpe/wc I 3.47. Waveguide dimensions: a I 0.3 cms., b I 0.3875 cms., c I 5.08 cms. 33 "‘ 2 L_ 2: PI :3 «I In '08 c5 c5 c5 c5 :5 II 3 3 \ m ? .06 F’ 8 z 3 \ 3 .04 "‘ 10 1 .02 F. 1 l 1 1 1 I o -o.2 -o.4 -0.6 -0.8 -1.0 -1.2 -1.z. -1.6 -1.8 a/kc < a 00 mode for w/wpe 0.1. fpe 6.0 GHz, Lupe/wc I 3.47. Waveguide dimensions: a I 0.3 cms., 4b I 0.3875 cms., c I 5.08 cms. Figure 2.4d. w/wpe vs. OI/kC for the TM 34 .mEo wo.m n o ..mEu mumm.o u n ..mao m.o n m «chHmcmaHv a a .I Q mcwsmm>m3 .H.@ u UM\m m .Nmo m.oH u w m .¢.o v m 3\3 wow macs co x\m 1| II...I II ..I II II \_ II .\ I. umo mo. n FN\3 . 093 «and: III! >\ o no.9 H.o m we 3+«\\H u 3\3 \\ \ mafia new“; \\ \ on :9 mnu pom ox\m .m> 3\3 .mm.N muswfim adm/m 35 .mao mo.m u u ..mso mumm.o u a ..mau m.o u m u we . on .I on owfiswm>m3 .H.o u 3\ 3 «mm n.0H u m .m.o v U 3\3 How oboe ooZH man now ox\d .m> M\d «NI ONI cal NHI _ a — _ as 86 n W... will. III. III. III. III III x+a\ mQB mQ3\m> H u.JmI H.o m.o .l umcowmamaww ma33 adm/m .nm.« muswfim 36 collisional loss as the ve/wpe = 0.052 curves in figures 2.43 and 2.4b and the ve/wpe = 0.07 curves in figures 2.3a and 2.3b. Similarly, the ve/wpe = 0.1 and Ve/wpe = 0.3 curves in figures 2.5a and 2.5b have the same collisional loss as the v /w - 0.175 and v /w = 0.525 curves e pe e pe respectively, in figures 2.4a and 2.4b. Figures 2.4c and 2.4d are enlargements of the circled areas of figures 2.4a and 2.4b, respectively. They shOw the low-frequency (In/wpe <0.l) details for fpe = 6.0 GHz. 12 (a) Lossless plasma or ve/wpe = . Trivelpiece has investigated this case extensively. The w - k diagram (figures 2.3a, 2.43, 2.4c, 2.5a) show that when Ve/wpe = 0, propagation is possible from zero fre- . r____ quency up to the slow wave resonance frequencym=wpe / v1+ke, where Re is the relative dielectric constant of the quartz tube. For ke = 1, i.e., free space or no quartz tube,co=wpeI’/—. The effect of the quartz tube is essentially to lower the frequency of the slow wave resonance. =0) is a slow wave and lies entirely to the right 00 of the light line. As w‘+ mpg/“1+ e’ both the phase velocity and the The TM mode (v /m e pe group velocity V¢ and V8 respectively, approach zero. Thus, at w =wpel/I:E;’ this mode become a non-propagating space charge oscilla- tion. However, as w+wpe//T:E;, there are limitations to the cold plasma theory. For Te ¥ 0, i.e., a warm plasma, and as B/kC approaches the thermal velocity line, warm plasma effects will alter the results and for still large B/kc's collisionless Landau damping becomes predominant. In this region, the cold plasma theory no longer holds. This mode can propagate only if the plasma partially fills the metallic waveguide since its propagation depends on surface charge accumu- lation. This would require that a dielectric region separate the plasma column and the circular waveguide. In most practical cases, the 37 separating dielectric region is a combination of free space and a di- electric tubing containing the plasma. The electric field and charge 12 distribution on such an isotropic plasma column are shown in Figure 2.6. At frequencies close to the slow wave resonance frequency wzw I pe Vl+ke, B is large. If Btzl, where t = thickness of the quartz di- electric, then the fields would be confined entirely to the dielectric and the plasmalz. The phase velocity at these frequencies is, thus, determined by the thickness of the dielectric, the value of the dielec- tric constant ke, and the properties of the plasma. At low frequencies or high plasma densities, w/wpe <aua scum couscoummm .qaaaoo mamman ongpuomw co o>m3 oommusm NH ofiuumeahm >aumasoufio now oofiumnusuuwa mwumno paw sowuanauumwv mamas .o.~ wuswwm , u TE. u . / C- 0- “Emfipm moavmu Sawunfififiavm . momam mosh 39 lossy TM00 mode is divided into three frequency regions: (w/wpe)< 0.1, 0.1<(w/wpe)<1/ Vl—lrké, and (w/wpe)>l/ /T_:7ké. The low frequency behavior, m/wpe<0.l, for a typical plasma density fpe = 6.0 GHz is shown in figures 2.4c and 2.4d. AS density increases, the lossless curve shifts towards the light line. For small losses, ve/wpe f 0.1, the difference between the lossy curve and the lossless curve is negligible. As Ve/wpe becomes greater than 0.1, the deviation of the lossy curves from the lossless curve is more significant. At low frequencies and high collisional losses (ve/wpe=0.525, 1, 10) the departure of the curves from the lossless TEM mode of operation is ap- parent (figures 2.4c and 2.4d). This is consistent with the values of the complex dielectric constant for frequencies in the region (w/wpe) f 0.1 (figures 2.7a and 2.7b)because at high collision frequen- cies the plasma properties approach that of a lossy dielectric. The attenuation curves at low frequencies are shown in figures 2.3b, 2.4d, and 2.5b. For frequencies in the range 0.10wpel Vii—g. It crosses the light line, becomes a fast wave and at very high frequencies becomes asymptotic to the light line, (see figure 2.23). The lossy curve thus, becomes a backward wave in the frequency range 1/ /T;k; f w/wpe130.9 (figures 2.3a, 2.4a and 2.5a). This backward wave region, however, is highly damped as shown by the 00/00pe vs. OI/kc curves (figures 2.3b, 2.4b, and 2.5b) and is no longer a true wave phenomenon. For example, for the following given plasma parameters: fpe=6.0 GHz, ve/wpe=0.l and 00/0)pe = 0.44, a wave of unit amplitude is attenuated in a distance of one wavelength to 0.0031. These curves also indicate that for very small losses, say Ve/wpe f 0.01, it might be possible to have a frequency range where the backward space charge waves are not altogether damped. Computation problems prevented the generation of such curves. As seen in figure 2.2b, beyond w=wpe / /l:k;, OI/kc increases with w/wpe for a given ve/wp , reaches a maximum then decreases and eventually e tends to zero at very high frequencies. At very high frequencies, w/wpéx>l, all the lossy TMO0 curves asymptotically approach the light line. Figures 2.2a and 2.2b show this behavior for fpe=6.0 GHz, and ve/wpe = 0.1. This high frequency part of the curve is consistent with the value of the complex dielectric constant of the plasma at such frequen- cies and losses, (figures 2.7a and 2.7b). For an fpe=6.0 GHz and a given (ve/wpe), er-*l and ei-*0 as w becomes very large. At these fre- quencies, the plasma waveguide becomes an empty circular waveguide and the TM00 mode behaves as a circular waveguide mode. 43 TM01 mode: This is a rotationally symmetric mode and, hence, purely trans- verse magnetic. Its characteristic equation is given by equation 2.69. Its field pattern is easily analyzed even in the presence of the plasma. It has radial and longitudinal electric fields ED and E2, respectively, and a circular magnetic field H¢. The dispersion equation is solved for w/w vs. B/k with w /w and v /w as variable parameters. pe c pe c e pe Figures 2.8a, 2.9a, 2.8b and 2.9b show w/wpe vs. B/kC and w/wpe vs. a/kc for fpe = 10.5 GHz and fpe = 20.0 GHz, respectively, and a range of losses. Figures 2.8c and 2.8d show the low frequency details of the 00/0)pe vs. B/kc and 00/0.)pe vs. a/k diagrams for fpe = 10.5 GHz. c (a) Lossless plasma or ve/w 829. As seen in figure 2.83, for P fpe=10.5 GHz, this mode is cut off below w/wpe = 0.23 or f = 2.42 GHz. An increase in the plasma density to fpe = 20.0 GHz as shown in figure 2.9a, raises the cut off frequency to w/wpe = 0.134 or f = 2.68 GHz. The TM01 coaxial mode cut off frequency for the waveguide dimensions chosen is f = 2.92 GHz. Thus, the TM cut off frequency is seen to 01 approach f = 2.92 GHz at very high plasma densities. The dispersion curves (figures 2.8a and 2.9a) are typical fast-wave electromagnetic solutions when ve/wpe=0. At high frequencies, the curves asymptotically approach the light line and become the TM empty waveguide mode. 01 (b) Lossy plasma or ve/w f . As shown in figures 2.8a and 2.9a, pe at high frequencies all the loss curves are asymptotic to the light line and deviate very little from the lossless curve. Also, the collisional damping at these frequencies is negligible, see figures 2.8b and 2.9b. As 00/0)pe approaches the region w/wpez0.23 in figure 2.8a, the deviation of the lossy curve from the ve/wpe - 0 curve is more significant. The w/wpe .40 .36 .32 .28 .24 .20 44 /Light Line ”q I 96 / 05’ / See enlarged / I?“ circle above / I l l 1 1 l 0 .4 .8 1.2 1.6 2.0 2.4 2.8 e/kc Figure 2.83. w/mpe vs. E3/kC for the TMO1 mode. fpe = 10.5 GHz, (ope/00C = 6.1. Waveguide dimensions: a a 0.3 cms., b 8 0.3875 cms., c = 5.08 cms. 45 .mso wo.m u o ..mao mhwm.o u a ..mao m.c u m u on ma Ho 0 on "macawamev mcaswm>m3 .wo.o n 3\ 3 .Nmu n.0H n w .0608 29 m:u MOM x\d .m> 3\3 .pw.m shaman o x\5 N.HI o.HI w.OI o.OI q.OI N.OI o — _ d _ 4 To In N.o I .41) o u 093\m? II. II II II III II II II n. m was 86.153 mo M w e.o m.o 0.24 —- 0.20 / 0.16 ~- 0 o. 3 st .L 3 0.12 - 10 0.1 1 0.08 "" (,1 ’/"’/’ ,// Light Line l,/ 0.04 ’l,’ ’,/ ’,I I,/ a/’ . I I I I J 0 0.1 0.2 0.3 0.4 B/kc Figure 2.8c. w/wpe vs. B/kc for the TM01 mode for 00/0)pe < 0.24. 46 10.5 GHz, (ope/00C - 6.1. Waveguide dimensions: a = 0.3 cms., b = 0.3875 cms., c = 5.08 cms. f pe w/wpe 0.20 0.18 0.16 0.14 0.12 47 0.10 0.1 0.08 0. 06 0. 04 0.02 .. -0. 4 -0. 6 .of8 -1: 0 -1.L2 -1.'4 -1.l6 -1.'8 Figure 2.8d. o/k C (II/00pe vs. OI/kc for the TM01 mode for 00/00pe S 0.20. fpe = 10.5 GHz, (ope/wc - 6.08. Waveguide dimensions: a - 0.3 cms., b 8 0.3875 cms., c - 5.08 cms. 48 -100 Figure 2.8e. Real part of plasma dielectric constant er vs. w/w and v /w . f = 10.5 GHz. e pe pe 49 -10 - -101 e. 1 -1...— \)_/wpe = 1.0 3.0 ..0 -101-— ' 10.0 0.1 -102 J l I 1L I TJ O .2 .4 .6 .8 1.0 1. w/wPe Figure 2.8f. Imaginary part of plasma dielectric constant 61 vs. w/wpe and V /w f = 10.5 GHz. e pe‘ pe 2 w/wpe .20 - .18 - .16 . .14 _ ve/wpe 03 012 I- .10 .. 008 [I Figure 2.93. 50 / / a See enlarged / 'circle above / B/k c ///light Line {(U/Zfl = 3.03 GHz w/w vs. B/k for the TM mode. f = 20 GHz, w /m pe c pe pe c 01 = 11.6. Waveguide dimensions: c = 5.08 cms. a = 0.3 cms., b = 0.3875 cms., w/wpe 51 Figure 2.9b. w/w vs. a/k for the TM pe c 01 11.6. Waveguide dimensions: c = 5.08 cms. mode. f = 20 GHz, w /w = pe pe c a = 0.3 cms., b = 0.3875 cms., 52 lossy curve has no cut off frequency. B/kc decreases with w/wpe and becomes zero when w/wpe = 0, as shown in figures 2.8c and 2.9a. The attenuation per unit wavelength for all the lossy curves for frequencies below 00/00pe = 0.21 in figure 2.8c and below 00/00pe = 0.115 in figure 2.9a is very high. For instance, for the following given plasma para- meters: fpe=10.5.GHz, Ve/wpe = 0.1 and w/wpe = 0.20, a wave of unit amplitude is attenuated in a distance of one wavelength to 7 x 10-23. The curves for small losses ve/wPe = 0.1 (figures 2.8a and 2.9a) almost coincide with the lossless curves above the cut off frequency. As ve/wpe is increased through the range 1 to 100 (figure 2.8a), the dif- ference between the lossy and lossless curves above the cut off fre- quency is more apparent. For very high losses ve/wpe = 100 (figure 2.8a), the mode appears to be practically cut off for frequencies below w 5 0.208 wpe or f = 2.2 GHz. So with the plasma densityfixed and as ve/wpé*” the cut off frequency of this mode approaches that of the TM01 circular waveguide mode. This behavior is consistent with the value of the complex dielectric at (w/wpe)~0.208 and fpe= lO.5(Hh:(figures 2.8e and 2.8f). As (ve/wpe) increases at this frequency,6r+l and €i+0' At high frequencies, i.e.,alarge w/wpe, €f+19 €1+0 (figures 2.8e and 2.8f) and this mode approaches the TM01 plasma. As w+0, Er remains finite and €{*dw. The plasma becomes a waveguide mode without a lossy conductor and the TM01 mode is, thus, highly damped at very low frequencies. * * ggll and TMlG_modes. The dispersion relation for these modes is obtained by putting n = l in equation 2.62. Because of their hybrid nature, these modes 53 have all the possible electric and magnetic field components, i.e., Ep, E¢, Ez and Hp, H¢, Hz, respectively. The dispersion equation is solved for w/wpe vs. B/kc with (ope/u)c and Ve/wpe as variable para- meters. Figures 2.10a, 2.10b, 2.10c and 2.10d show the w/wpe vs. B/kC and w/wpe vs. 0L/kC for a typical plasma density of fpe = 5.3 GHz. Several features of these curves will now be explained. * (a) Lossless plasma or V /w =0. For f =5.3 GHz, the TE mode e pe—- pe 11 has a cut off frequency at w = 0.58 wpe for the guide dimensions of a = 3 cms.,b = 0.3875 cms. c = 5.08 cms. This mode has the lowest cut off frequency in both the circular and coaxial waveguides. It is a typical fast electromagnetic wave, eventually becoming asymptotic to the light line. At very high plasma densitities, the cut off frequency of this mode approaches the TM coaxial mode cut off frequency. 11 (w/wpe= 0.68). The TM:O mode, which does not exist in the empty circular waveguide, has a cut off frequency at w = 0.33 wpe for waveguide dimensions: a=0.3 cms., b = 0.3875 cms., c = 5.08 cms. B/kC increases with w/wpe and this mode behaves like a fast wave up to B = 1.86 kc. For B>l.86 kc, this mode becomes a slow wave and eventually becomes asymptotic to the fre- quency of dipole resonance. This frequency obtained from the quasi static formula16, a 2 1 - (E9 2 a 2 1 + fig) 1 + e 2 a C - (wpe/w) l + 2 v—II— 1- (-3)2 —-—-————+e:2 1 + (-3)2 L is wzwpe‘IVB . In the formula, a = plasma radius, b = outer radius of 54 .28 mo.m u o .680 mmwmd u n :95 m.o u m "mcowmcmafip wwwswm>m3 .mo.m u o3\ma3 .Nmu m.m n mam .mmcoa flame cam CHEF How ox\m .m> oa3}... .moH.N muawwm a» an 0 E q.~ ctm 04 NA w.o «.0 o _ a _ _ _ \\ _.uS.~ 3sz 0% \I‘Ig .30 \ 2, .. so. 9/ \. e4 / m \ ads I To W \ /.0.. w )0 \ N30 mo.m u =~\3 an Ho. " Q I 0 mx: 3\3\ o u 0 30? .HHmH o o \ 0:3 EmS\ \ 55 umcowmaoEwu mufiswm>m3 0 ll 0 II .mao wo.m u o ..mao mnwm.o n n ..mEo m.o n m u on on o .ao.m 3\ 3 .Nmo m.m u u .mmsoa away new owns you x\s .m> o is 9.01 q.ol m.o1 «.01 _ a _ _ ma3\m> .one um ":0 mo.m u :~\3 ma 0 oH Ho.o mnaxm> _ 3\ > . «E. . .III .IIIAHmmmmW .III III. III. III. III. III. III a w 3\0> .meh on 3\3 om.o oc.o om.o 00.0 mo.o .noH.N mpswum adm/m 56 .mao wo.n u o..mao mmwm.o u n ..mao m.o u m "macamcmawu mvwswo>m3 9 .Ba u 0&0 3 .55 ms "use as a 3&0» Ba 26 v 323 you 88 A”: 2: 08 as; .9, 83? .03.~ 8%: o {a mm. v. mm. m. mm. N. md. fl. mo. 11 _ . . . . _ . . H. 1 S. I. N o m I m .0 a 1 mm. m 0 on o N .O H 3\ 3 57 u on .mEu wo.m u o ..mEo mmwm.o u n ..mao m.o a m "msoamcmaww mvwswm>m3 .no.m I 3\ 3 u on .Nmo m.m I mam .~.o u masxflzwcm mm.o v 0a3\3 now 0608 mee onu you x\d .m> 3\3 .poa.~ ouswwm ox\d oo .o: ow .0: or .o- oo .o: cm .0. ow .o: om .o: om .o: 3 .o: J11 . . . q . . . . 0.0 on 58 dielectric tubing, and 82 = permittivity of the dielectric. Without the quartz dielectric this mode would have been asymptotic to the line w - wpel/2—. As w approaches wpel/3—, the phase and group velocities V¢ and V8 approach zero and the space charge oscillations are highly at- tenuated (Figure 2.10s). However, as w + wpe / /3-, B/kC becomes large and the cold plasma theory is not valid in this region. Warm plasma theory considerably modifies the dispersion curve near V¢ = Vth’ where Vth - electron thermal velocity. For still larger B/kc's when the wave- length becomes the same order of magnitude as xde’ the debye length, collisionless Landau damping becomes predominant. Thus, the present * theory is not valid in that region for the lossless TM mode. 10 (b) Lossy plasma or ve/wpe ¥ 0. When Ve/wpe is non-zero, the * singularity19 of the TM 10 mode at the frequency of dipole resonance is * * removed. The TE 11 and the TM 10 the presence of losses. modes have one distinct solution in As shown in Figure 2.10a, for very small collisional losses = > . o (Ve/wpe 0.01) and for w 0 334 wpe the w/wpe vs B/kC curve closely * follows the lossless TM 10 curve up to w = 0.55 wpe. ForuP’0.55 mpe, B/kc first decreases then increases and the dispersion curve becomes * asymptotic to the lossless TE mode solution. A backward wave region 11 is, thus, seen to exist in the frequency range 0.565wpefi w 3 0.575 wpe' The behavior of this curve below the frequency w = 0.33 wpe is shown in Figure 2.10c. The lossy curve for small losses has no cut off frequency. B/kc goes to zero as 00/00pe tends to zero. At higher losses (Va/wpe = 0.2), the backward wave region is not too prominent, but the asymptotic behavior of this curve outside the fre- quency range 0.55 wpe0.60 wpe and in the range 0.55 mpe -jkzz I - ‘ . Er (Akzkpl/wel)Jo (kplr)e 3 6 -jkzz = — ' ' H¢ Akp Jo (kp r)e 3 7 1 1 2 jAk p1 'jkzz E = - ---- J (k r)e 3.8 2 wel 0 pl 67 Region 2: a S r S b m2 [ ] —ijz w - BJo(kp r) + CNo(kp r) e 3.9 2 2 kz —jkzz = — —— ' ' Er we [ka Jo(kp r) + Ckp N0 (kp r)] e 3.10 2 2 2 2 2 -jkg: = — ' I H¢ kpleJo (kp r) + CNo (kp r)] e 3.11 2 2 - 2 Jkpz -jkzz E2 = - we [BJo(kp r) + CNo(kp r)] e 3.12 2 2 2 Region 3: b S r S c m3 -jkzz w = [DJo(kp r) + ENo(kp r)] e 3.13 3 3 k2 -jkzz = _ __ I I Er we [ka Jo (kQ r) + Ekp No (kp r)] e 3.14 3 3 3 3 3 .ijZ = — ' I H¢ kp [DJo (kp r) + ENo(kp r)] e 3.15 3 3 3 . 2 Jkpa -jkzz E2 = - was [DJo(kp3r) + ENo(kpar)] e - . 3.16 The above equations involve five arbitrary constants: A, B, C, D, and E. The constants can be expressed in terms of one arbitrary con- stant, namely A, by applying the boundary conditions: continuity of E2 and H at r=a, r=b, and Ez-O at r=c. In terms of A, these constants ¢ are: B-F A, CIF A, E=F A 12 14 13 where, F11 = (kplF6/kp2F1) 3.17 and 12 13 14 #11 II '11 ll '11 ll #11 ll I11 ll '11 ll Using the Poynting vector the time-average power flow in the z = ' - (€2kp3/E3kp2) F2N0(kp2b) F3No(kp b). 68 (kplF7/kp2Fl) (k01F5F6J0(k03C)IkpaFlFB) -F13No(kp3c)/Jo(kp3c) I _ I Jo (kpza) No(kpza) Jo(kpza) No(kp2a) Jo(kp3c) No(kpab) - Jo(kp3b) No (kp3C) Jo(kpac) N;(kpab) - No (kp c) J; (kp b) 3 3 I _ I Jo (kpzb)No(kpzb) No(kp2b) Jo (kpzb) I _ I (Ezkpllelkpz) Jo(kpla) N0(k02a) .Jo(kpla) No(kp a) Jo(kp a) J;(kpla) - (ezkpllelkpz) Jo(kp a) J;(kpza) 2 2 direction Pz, can now be written as: .g* Pz=1§ReJExH-2da S 1 2 3.18 69 = %Re [ P21 + P + P ] 3-28 k k k a I I* e of Jo(kplr)Jo (kplr) r dr 3.29 k k zwlAl{-E;-E;-:* -2az [F F* b ' '* wez e 11 113 Jo(kp2r) Jo (kpzr)r dr + F F* bJ'(k ) N'*(k r) r d 11 12 o p2r o p r a 2 b * . .* + F12F11 ‘{ No(kp r)Jo (kp r) r dr 3 2 2 b + F F* N'(k r) N'*(k r) r dr] 3 30 12 12 o p 0 O . a 2 2 c 20 P - * d 23 - ErH¢ a b o k* k c 2 D O z = __3__3__. '202 * . ,* ZNIAI was e [F14F14 b4 Jo(kpar) Jo (kpar)r dr c * ' '* + F14F13 I Jo(kp r)No (kp r) r dr b 3 3 c * t 0* + F13F14 I No(kpar)Jo (kpar) r dr b 70 c * , ,* _ + F13F13 I No(kp3r) No (kpar) r dr], 3.31 b The power absorbed per unit length g1 for the TM,Op mode is: P = (P a z ) 3.32 z=0 -Pz z=l As is evident from the expressions for P21, P22, and P23, the power ab- sorbed/unit length R; is a function of the square of the amplitude of 2 the wave function in the plasma IAI , the incident frequency w, the P21’ P22, P23 are numerically integrated and plots of the normalized power electron plasma frequency wpe and the collisional frequency ve. 2 absorbed/unit length, Pa/IAI , vs. the plasma parameters (w/wpe) and (ve/wpe) for a fixed wpe are obtained for the TM00 and TM01 modes. These are explained in detail in the sections that follow. 3.2.1 'IEOO mode 2 F1 0 O = gure 3 2 shows Pa/IAI vs (w/wpe) for (Ve/wpe) 0.05, 0.1, 0.175, 0.3, 0.525, and fpe = 6 GHz for the TM00 mode. The (w/wpe) vs. (B/kc) and (w/wpe) vs. (a/kc) diagrams for these values of the electron density and the normalized collisional frequency were shown in Figures 2.4a and 2.46. It is clear from Figure 3.2 that the Pa/IAI2 curves for the TM00 mode have two resonances. One of these occurs near the frequency of slow wave resonance (w/wpe) - 1/ /I_;fk;'- 0.46 while the other re- sonance occurs at (m/wpe) = l. The resonance at (w/wpe)= 0.46 peaks only when the normalized col- lisional frequency is very small, i.e., when (ve/wpe) - 0.1, 0.05, etc. 10 10 10 10 71 v /w 0.1 e pe 0.175 L 0.05 .525 l 1 l l J 0.2 0.4 0.6 0.8 1.0 00/00pe TMCO mode. Figure 3.2. Normalized absorbed power Pa/IAI2 vs. w/w pe h and ve/wpefor t e Waveguide dimensions: a=0.3 cms., b-0.3875 cms., c-5.08 cms. f pe - 6 GHz. 72 104 __ R = 10K0 10 r- 10 r“ P R - 1000 a 2 III 101 - 100 l 1 l 106 107 108 109 w/Zw Hz. Figure 3.3. Normalized absorbed pOwer in the resistor Pa/III2 vs. w/ZH for a parallel RLC circuit driven by an ideal current source. L - lOuH, C = 10 pf. 73 This indicates that surface waves can be strongly excited when the frequency and plasma density are such that (w/wpe)=0.46 and when the collisional frequency is very small. The resonance at the plasma frequency wzwpe is a volume resonance. The expressions for P P 21, 22, P23 (Equations 3.29, 3.30, 3.31) reveal that these quantities reach a maximum in the neighborhood of w = wpe, giving rise to a peak in the absorbed power. It should be noted that these curves were computed with constant A. In practice, however, this does not occur because the coupling of the incident power varies with plasma density. ' A study of the two resonances described above shows that the losses in the plasma increase with decreasing ve/wpe. This behavior is analo- gous to the power absorbed by a resistor at resonance in a series or - parallel RLC circuit driven by an ideal voltage or current source, re- spectively. Typical curves for absorbed power in a resistor of a para- llel RLC circuit driven by an ideal current source are shown in Figure 3.3. As damping in the circuit goes to zero, i.e., as Raw, the ab- sorbed power in the resistor at resonance becomes very large. 3.2.2 “TM0l_mgd§ The power absorbed curves for this mode are shown in Figure 3.4 for the collisional losses (ve/wpe) = 0.1, 1.0, 3.0, 6.0 and 10.0. The electron plasma frequency fpe is fixed at 10.5 GHz. The (w/wpe) vs. (B/kc) and (m/wpe) vs. (a/kc) curves for the same electron plasma fre- quency were shown in Chapter II in Figures 2.8a, 2.8b, 2.8c and 2.8d. The behavior of the power absorbed curves of this mode can be understood by studying the variation of the plasma permittivity 61 with the frequency. The real and imaginary parts of e vs. (w/wpe) are l 74 10’- l— v /w -10.0 e pe 1 I 1, l l l 0 2 4 .6 .8 1 0 1 2 w/m pe Figure 3.4. Normalized absorbed powerPa/IAI2 vs. w/wfie and ve/mpe for the TM01 mode. Waveguide dimensions: a-0.3 cms., b80.3875 cms., C=5.08 cms. fpe = 10.5 GHz. 75 shown in Figures 2.8e and 2.8f. By comparing Figures 2.8e and 2.8f with Figure 3.4, it is evident that the power absorbed is a direct function of the lossiness of the plasma. This mode also has a volume resonance at w = wpe, and is prominent for small collisional losses (ve/w e = 0.1), P 3.3 Power flow and power absorbed for TEop waveguide modes Consider the cylindrical plasmadwaveguide with regions 1, 2, and jwt 3 as shown in Figure 2.1. Assuming a time variation of the form e , the TEop wave functions and the electric and magnetic field components for the three regions of Figure 2.1 are: Region 1: o < r 5 a el -jkzz W = AJo(kp r) e 3.33 1 -jkzz = I E¢ A kp Jo(kp r) e 3.34 1 1 -jk 2 H = -A k k J' (k r) e z 3.35 r p z o p _____l__ 1 NH 0 -jk 2 H = -jA k2 J (k r) e z 3.36 z p o p 1 1 mu 0 Region 2: a S r S b -jk z 082 = [BJ (k r) + CN (k r)] e z 3.37 o p 0 O 2 2 -jkzz = ' ' 3.38 E¢ kp [BJo(kp r) + CNo(kp r)] e 2 2 2 -kpzkz -jkzz 9 =-————-— ' ' 3.3 Hr mu [BJo(kp r) + CNo(kp r)] e _ O 2 2 76 -j kgz -jkzz Hz = mu [BJO(kp r) + CNo(kp r)] e 3.40 o 2 2 Region 3: bSrSc e3 -jkzz w = [DJo(kpar) + ENo(kp3r)] e 3.41 -jk z E¢ = kp [DJ6(kp r) + EN;(kp r)] e z 3.42 3 3 3 -kp3kz I I -ijz Hr = mu [DJo(kp r) + ENo(kp r)] e 3.43 o 3 3 .jkp3 -jkzz Hz = who [DJo(kp3r) + ENo(kp3r)] e . 3.44 The above equations involve five arbitrary constants: A, B, C, D, and E. All the constants can be expressed in terms of A by applying the following boundary conditions: continuity of E¢ and H2 at r - a, r = b, and E¢ = 0 at r a c. The arbitrary constants in terms of A are: B FllA, C e Fle, D = F13A, and E a F14A’ where F11 = (kp F6/kp F1) 3.45 1 2 F12 = (kp.F7/kp F1) 3.46 1 . 2 = _ I I . F13 No(kpac) F14/Jo(kp3C) 3 47 = ' . F14 (kszSJo(kp3c)Fll/kp3F8) 3 48 and 77 = I _ I F1 Jo(kp a)No(kp a) Jo(kp a)No(kp a) 3.49 2 2 2 2 3 ' _ I F2 Jo(kp c)No(kp b) Jo(kp b)No(kp c) 3.50 3 3 3 3 3 I I _ I I F3 Jo(kp c)No(kp b) Jo(kp b)No(kp c) 3.51 3 3 3 3 = ' _ 0 F5 Jo(kp b)No(kp b) No(kp b)Jo(kp b) 3.52 2 2 2 2 = ' I - 0 F6 (kp /kp ) Jo(kp a) No(kp a) Jo(kp a)No(kp a) 3.53 1 2 1 2 1 2 = I _ I F7 Jo(kp a)Jo(kp a) (kp /kp )Jo(kp a)JO(kp a) 3.54 2 1 1 2 1 2 = I _ I 7 F8 (kpalkpz)F2N°(kpzb) F3No0 )0 A” ~ g \O In C) O O Q O O 5 Eu 91 e) /m)2 = (1+k (00pe TEM 1 T v e/u) :_O-.-l-- hd 001’ Figure 4.1b. 111 100 1000 1 5 10(wpe/w)2 Resonant length LS vs. (mpe/w)2 for the cold plasma modes, * TMOOp and TMIOp' Waveguide dimensions: 5.08 cms. Operating frequency w/ZN = 3.03 GHz. 8 - 0.3 cms., b - 0.3875 cms., c = 92 1040 - 9.8 9.6 9.2 9.0 8.8 8.6 lENGYH IN CM N ‘ N O I 0 6.0- H/ * ,/ - T TM 58_ wzh w1 //// /o 5.6- / | l I 54. | YM001 l 5.2 v | / | 5.0 - | I I 48 | 1 L I l l A I ‘4 ' ""01 1.0 10 (‘11 $100 1000 10000 Figure 4.2. Resonant length vs. plasma density (Lupe/w)2 and ve/w for a cavity of radius 10.146 cm., plasma radius of 1.248 cm., and an operating frequency of 2.45 GHz. 93 4.2 Theoretical Cavitnyode 4.21. Classification and Description of the Plasma-Cavity Modes It is convenient to classify the resonant lengths of the plasma- cavity into three groupslo. 1) "Perturbed" cylindrical cavity resonances. These resonances are the empty cavity electromagnetic resonances which are "perturbed" by the presence of the plasma. Thus, the forward and backward traveling waveguide modes associated with these resonances always have a phase velocity greater than the speed of light, i.e., they are fast wave electromagnetic modes. This group of resonances can be further divided into two subclasses of modes: . > . 3) TE or TMOmp’ m 0 Omp These resonances are pure TE or TM resonances since they are0,m>0 nmp nmp These modes are hybrid resonances. They are labeled with respect to the TE or TM modes in an empty circular waveguide into which they de- generate when the plasma density equals zero. It is useful to note that * for high plasma densities and zero losses, (i.e., Ve/w-O) the TEmn * resonance (or TMnmp resonance) approaches the TMInmp resonance (or TE resonance) in a coaxial waveguide with a metallic center con- 11,111+]. ,P ductor. The TE:11 mode shown in Figure 4.1a belongs to this family of modes. However, for large values of collision frequency, the resonant length increases, decreases, and then increases again returning to the TE111 coaxial cavity resonant length. 94 * 2) Cold—plasma resonances (TM001 and TMh01’ n These resonances do not exist in the empty cavity and are affected >0) by the finite electron temperature only when the wave phase velocity V 43 is approximately equal to the thermal velocity Vth = VEET;7E;_ and w > wpe. Thus, they are called cold-plasma modes. Each of the modes classified above are now described in detail. 4.2.2 Rotationally Symmetric Modes, TM011 and_TE011 (a) Lossless Plasma. ve/ w = 0. As shown in Figure 4.1a, the TMO11 mode is comprised of a single half-wave resonance of the TM waveguide 01 mode discussed in Chapter II and has an empty cavity resonant length of L8 = 7.32 cms. With increase in plasma density (mpg/w)2, the eigenlength increases slowly at first and then increases steeply in an almost linear fashion. At very high plasma densities, when the plasma rod behaves more like a conductor, the eigenlength curve becomes horizontally asymptotic to the TMO11 coaxial cavity resonant length line. This region occurs at LS . 8 cms. for the cavity with dimensions a = b = 1.248 cms. and c = 10.146 cms., as shown in Figure 4.2. For the eigenlength curves of Figure 4.1a, the TMO11 coaxial cavity resonance occurs at LS = 19.1 cms. and is not shown in the latter figure. For the operating frequency and waveguide dimensions of Figure 4.1a, the TE011 mode is cut off. It is shown in the more general curve of Figure 4.2. It has an empty cavity resonant length of L8 - 9.02 cms. In a manner similar to the TM011 mode, the TE011 mode at high plasma densities, approaches the TE011 coaxial cavity resonance of LS - 9.55 cms. (b) Lossy plasma ve/g_i_g. As shown in Figure 4.1a, the eigen- length of the TMO11 mode at low plasma densities, (nope/00)2 - 0.1, is 95 LS = 7.32 cms. The asymptotic behavior and the general form of the curve is almost identical to the lossless curve. For a given eigen- length, however, the lossy curve operates at a higher plasma density than the lossless curve. At very high plasma densities it becomes asymptotic to the TMO11 coaxial cavity resonant length LS = 19.1 cms. The behavior of the eigenlength curves is consistent with the w - k diagrams for the TM01 mode shown in Figures 2.8a and 2.9a. The effect of the quartz tubing has been to reduce the empty cavity resonant length from LS z 7.42 cms. to L8 = 7.32 cms. For dimensions of the experimental cavity of Figure 4.13, this mode appears to have a large variation in both the resonant length and the electron density. The eigenlength curves suggest that it might be possi- ble to vary the length of the plasma column from 7.4 cms. to 18 cms. and the average plasma density from (Lupe/00)2 = 3 to at least (Lope/01)2 = 100, if the required RF input power were available. The behavior of the lossy TE mode resembles that of the TM 011 011 mode. As shown in Figure 4.2, at high plasma densities the lossy curves become asymptotic to the TE011 coaxial resonance given by L8 = 9.55 cms. * * 111 M101 ,. * (a) Lossless plasma. ‘Vefln = 0. As shown in Figure 4.1a, the TE 4.2.3 Dipole modes; TE 11 mode has an empty cavity resonant length of L8 = 5.99 cms. The lossless eigenlength curve at first rises slowly with increasing plasma density, than very steeply in the neighborhood oftnpe < /310 and eventually be- comes vertically asymptotic to the dipole resonance line given by «upe/w)2 = 3. If the effect of the quartz had been neglected, this curve would have been asymptotic to «ape/002 - 2. For densities beyond (upefin)2 = 3, this eigenlength curve would normally be horizontally 96 asymptotic to the TM coaxial mode eigenlength line17. The TM 111 111 mode, however, is cut off at the chosen experimental operating frequency, f = 3.03 GHz. The general case is shown in Figure 4.2 where the loss- * less TElll curve asymptotically approaches the TM coaxial resonance, 111 LS = 9.55 cms. at very high plasma densities. The TM*01 mode, (see 1 Figure 4.13), i.e., the first half wavelength resonance of the TM?0 mode, does not exist in the empty cavity. It is present only in the presence of a plasma and for densities wpe > V3 m. It is vertically asymptotic to the line, (cape/00)2 = 3. With increase in plasma density the eigen- length increases and the curve eventually becomes-asymptotic to L8 = 5.925 cms., the TE111 coaxial cavity resonant length. In the neighbor- hood of (cape/0.1)2 = 3, this mode is essentially a slow space charge wave as described in Chapter II. It behaves as a fast electromagnetic wave for L8 2 5.8 cms. The TMIOp modes, for p = 2, 3 ... are also vertically asymptotic to (wpe/w)2 = 3, and horizontally asymptotic to L8 = 5.96 p, p = 2, 3, etc., respectively, as shown in detail in Figure 4.1b. (b) Lossy plasma,¥ve[g_i_g. For this case the TM* mode and the 101 TE:11 mode have identical eigenlength solutions. This mode can best be studied by further subdividing the losses. 1. Small losses ve/w = 0.1. As shown in Figure 4.13, the low plasma density [(wpe/w)2 a 0.1 ] eigenlength is L8 - 5.99 cms. The eigenlength increases slowly with plasma density up to (nope/w)2 - 1.5. In the neigh- borhood of (tape/w)2 = 3, the eigenlength increases, then decreases sharply and rises again. It eventually becomes asymptotic to L8 - 5.925 cms., the TE111 coaxial cavity resonant length. The region in which the eigen- length decreases with increasing plasma density (2.8 S («ape/00)2 S 3.3) corresponds to a backward wave (see Figure 4.13). The backward wave * region for the TE11 waveguide mode was described in Chapter II. 97 It is useful to observe that for (nope/(0)2 < 3 and for (wpe/w)2 > 3, there are operating regions where it is possible to have two plasma den- sities for a fixed eigenlength. As shown in the w/wpe vs. OL/kc diagrams for this mode (Figure 2.10b) wave attenuation is high in the backward wave region. 2. High Losses ve/w = 3.0. At such high collision frequencies, the resonant length of the TE:11 mode is relatively insensitive to varia- tions in the plasma density. For small values of (cope/w)2 the plasma is essentially a lossy dielectric and the eigenlength is close to that of the TE111 empty cavity mode, L8 = 5.99 cms. As (Lupe/00)2 becomes large the plasma becomes a lossy conductor. The resonant length of this mode approaches that of the TE111 coaxial cavity mode, LS I 5.925 cms. It is clear from Figure 4.13 that the eigenlength is almost constant for density variations above (cope/w)2 > 10. This is true for all colli- sion frequencies. This region would be suitable for operating RF dis- charges with practically no tuning of the lengthlo. It would seem that a plasma with pressures varying from low to high values can be formed in this region without jumping out of resonance. This would make this mode practical for flowing and fluctuating plasmas in plasma chemistry appli- cations or as a general RF plasma sourcelo. 4.2.4 Space Charge Modes TM00p These modes do not exist in the empty cavity. In the presence of the plasma, however, they exist over a wide range of resonant lengths. Figure 4.13 shows the eigenelength curves of several modes, TMOOZ’ TMOO3, TM in the region of experimental operation i.e., LG I 5.2 cms. to 004 L8 = 8.0 cms. It is in this range of resonant length, in which these * modes intersect with two electromagnetic modes TM011 and TElll' These 98 regions of mode intersection are of special experimental importance. It will be discussed in experimental sections to follow. Small losses Ve/w = 0.1. The behavior of these modes is best studied by looking at the eigenlength curves of TM for very small 00p losses, say ve/w = 0.1. At high plasma densities the TM curves for 00p p = 1, 2, 3 etc., are horizontally asymptotic to the TEMp resonant length given by L8 = p 4.95 cm. as shown in Figure 4.1b. With a decrease in plasma density the eigenlength of these modes falls steadily at first and then drops very steeply for small decreases in plasma density. The almost vertical drop of the TMO0p eigenlength curve with decreasing plasma density continues until it approaches the region wpe > V11k; m, where ke = 3.78 is the quartz dielectric constant. In this region the curve reaches a point of zero slope, after which the eigenlength increases very sharply with 3 further decrease in the plasma density. This curve cannot approach the horizontal asymptote of an EM mode, because that mode is cut off at the operating frequency, f = 3.03 GHz, (Figures 4.13 and 4.1b). The TM002 mode is not shown in its entirety in Figure 4.13. This same type of behavior, however, is true for all losses and a typical eigenlength curve for TM , ve/w = 0.1 is shown in Figure 4.10. 002 The TM00p lossless curves for p = 1, 2 ... almost coincides with the TM00p ve/w = 0.1 curves; the difference being that the lossless curves eventually become asymptotic to the line (Lupe/w)2 I (1+ke) I 4.78, and do not rise again with a decrease in plasma density. The behavior of TM00p curves is consistent with the w - k diagrams for the TM00 modes described in Chapter II (Figures 2.2, 2.3, 2.4 and 2.5). waveguide As can be inferred from the 111/00pe vs. a/kc (Figures 2.3b, 2.4b and 2.5b) curves of Chapter II for the TM modes, only the forward space 00 99 charge region (00pe > 4.78m) with small collisional losses (Va/w = 0.1) has low damping. The backward wave region, i.e., when the eigenlength increases with decreasing plasma density, is not of significance as a wave phenomena because of heavy damping. However, it still might be possible to experimentally couple energy to the plasma in this region. 4.3 Summary The lossy cold plasma theory of Chapter II has been used here to obtain the eigenlengths of EM and space charge modes of a microwave- plasma cavity. The eigenlength curves suggest that it might be possible to operate the plasma-cavity over a wide range of electron densities, collision frequencies and in a number of different modes. The primary EM modes of operation are TMOll’ TE011 and TElll' A plasma source oper- ated in these modes has applications in plasma chemistry experiments and in pumping gas lasers. Also, the TM mode, which as electric fields 011 in the form of an axial quadropole, is capable of exerting radio fre- quency forces on 3 plasma for confinement purpose323. The backward wave region in the lossy TE:11 eigenlength curves sug- gests that it might be possible to have two plasma density operating points for a single eigenlength. Also, of interest are the regions where the eigenlength curves of the space charge modes TM00p intersect with those of the EM modes TM011 and TElll’ suggesting that it might be possi- ble to couple the EM energy to space charge waves. These observations and the usefulness of the plasma-cavity as a RF plasma source will be experimentally studied in Chapter VI. CHAPTER V EXPERIMENTAL SYSTEMS 5.1 Introduction Two microwave cavities have been used to experimentally study the linear resonances, the non-linear behavior and the absorbed power char- acteristics of the microwave plasma source. Both cavities are cylindri- cal, have a sliding short for tuning and a screened window for viewing purposes. The two cavities, however, differ in size. Cavity 1 has a radius of 5.08 cms. and operates at the available incident power of 30W while cavity 2 has a radius of 10.15 cms. and operates at incident powers of up to 1.3KW. 5.2 The Two Plasma-Cavity Systems 5.2.1 The #1 PlaSma—CavitygSystem A cross-section of Cavity 1 is shown in Figure 5.1. This variable length cavity has been designed to excite several resonances in the 2 to 4 GHz frequency range. The waveguide dimensions have been chosen so that when operating in the TE:11 cavity mode the ratio of the resonant length to radius is approximately one for a 3.03 GHz signal. A cavity radius of 5.08 cms. satisfies this design requirement. Several of the resonant modes of this cylindrical cavity are shown in Figure 5.2. In this figure, the resonant frequency is shown as a function of the cavity length. Also, shown in Figure 5.2 are a few of the coaxial cavity modes. These modes are of interest because a very dense cylindrical plasma has electrical properties similar to a metal rod inside the cavity. 100 101 . .nfisoumo omunoamgv «3339 can cannon 0.330.335 3m? om ..Egmu gnomuvcflko 08— mo com—con mnouU .H .m own—mam ooh—5m “Suzanna to? on .uEu mo .m 3.3.2 .35: 35300 33.39.33“. / on: .3539 9:33:35 pom .51.. . . 5..»er («34.3. .8" . 3. . . fiqu-oaua "QT. .. a. .m\ 0:0 9:3: K mamas» 3.356 Eugen—sonar: ousauuuagou— .3356 33 mono:— 03965 was mnflaofi _ _ _ _ _ poison—~05? imam .330 . _ ~332on «1.0309311. -3939»: . _ -ozmuno _ u . my _ .3325“; _ xumnvofl my 033.22, _ “ Hauu . ~3u>uu _ - nonunio— >um>au gasket" H38 “ _ _ .2508 .3333 _ . 02w? . Mombasa 25.3003» . £308 .3363 c2002“: 9 . .333 _ some 33 _ ~32 ooom neumzmuno _ . moo?» .3505 uoBom «c0305 9. " acunusoumu .3 .m . . . .mfiu wo.mnuo "mcowmamafin mcfinmm>m3 080 0 m1.” «H NH OH w o e N .mNHm >uw>mo msmum> hucmswmum unmaommm 102 - u q u a u D 0UOE UfiHH GOmeHH—mfimhu HNHNNOO In I. I. I. O mmvoa hairdo Hmwxmoo II III mmvoa hufi>mu Hmuwuvawamu / 2m: / / GHQ omo .N.m muswwm 2H9 ‘3 103 Cavity 1 is fitted with a mechanical device that smoothly varies the length and a micrometer that measures changes in cavity length of the order of .01 mm. This precise tuning arrangement enables the varia— tion in cavity length for any changes in plasma conditions and thus en- ables the study of the cavity eigenlength as a function of the plasma * density. This is especially useful in verification of the TE111 eigen- length curves (see Chapter VI). The cylindrical cavity is driven by the microwave system shown in Figure 5.1 by a miniature radial or loop type of probe coupling. The radial probe which excites radial electric fields in the cavity is suit- 1: able for exciting the TE111 mode. The loop type of coupling can be used for generating an efficient TMO11 plasma. The power coupled to the plasma can be adjusted by varying the depth of the probe into the cavity and in case of the loop probe, by also adjusting the orientation of the loop. At the chosen frequency of w/2n = 3.03 GHz, this cavity can be operated in the TE* TM0 and TM00p modes. The TM* * 111’ “1101’ 11 101 3"“ TMoo modes exist onlyixxthe presence of the plasma. It is important to study P the behavior of the EM modes TE:11 and TM011 over a wide range of pres- sures, because of their applications in areas such as plasma chemistry and possible applications to plasma confinement and gas discharge lasers. All the low pressure work in this thesis has been done on plasmas generated in Cavity 1. This plasma-cavity system can be pumped down to a pressure of 10 mtorr and has a tight vacuum control. Thus, this system. is ideally suited for studying warm plasma modes such as the Tonks Datt- 17 ner resonances , which occur at very low pressures and very low plasma * densities. When driven in the TE111 mode, the fields in the cavity are 104 overwhelmingly dipolar; and thus, the monopole and quadropole fields, which are excited in the usual scattering experiments when studying TD resonances, should not be present24’25. Also, non-linear phenomena arising out of strong RF-bounded plasma interactions and any hysteresis effects of the plasma can be conveniently examined. The #1 plasma- cavity is also ideally suited for generating space charge waves, as will be demonstrated in Chapter VI. 5.2.2 The External Microwaveg§ystem for Cavity l A line diagram of the experimental system is shown in Figure 5.1. The incident microwave signal at a frequency of 3.03 GHz is generated by an external cavity klystron which is connected to an oscillator syn- chronizer to form a phase-lock loop. The synchronizer locks the klystron oscillator to a harmonic of the oscillating frequency of an internal reference crystal, to produce a frequency stable microwave source. Such a frequency source is necessary, since the plasma media is dispersive and the microwave circuits are frequency sensitive. The stabilized RF power from the klystron is delivered to a variable attenuator, which controls the input power to a traveling wave tube amp- lifier (TWT). By adjusting the variable attenuator, the amplified output power from the TWT can be varied from 0 to 30 watts. An isolator protects the TWT's output helix from being damaged by reflected microwave power. Most of the experimental work on the Cavity l was done at an incident frequency of 3.03 GHz. However, 3 Variable frequency source was employed whenever a number of different frequencies were required. A pair of directional couplers were used to measure incident and reflected power from the cavity. The spectrum of the reflected power 105 could be analyzed by connecting a spectrum analyzer to the reflected signal directional coupler. 5.2.3 Diagnostic Circuits for Cavity l The #1 plasma-cavity system is provided with circuits for measuring the average plasma density and the electron temperature from a discharge pressure of 10 mtorr to 20 torr. The microwave probe circuit shown in Figure 5.1 uses the TM 0 fre- 01 26,27,28,29 quency shift technique to measure the average plasma density. This method can be used in the range 10 mtorr to 200 mtorr; the upper limit on the pressure being determined by the requirement that Vez<m3 .ovoa OHOZH mnu How 3\o> can mam .m> sN\3 .m.m ouswwm on m N.N 4w —1 — .... Ho. 55 .WIN: «é o.~ 107 data can be analyzed by the usual double-probe theory to obtain numbers for electron density and electron temperature30’40. For pressures above 1 torr the probe data is usually not reliable. The plasma number density at higher pressures is obtained from the D.C. conductivity of the plasma. This is measured by introducing discs longi- tudinally into the quartz tube so as to be barely immersed in the plasma7. Plasma diagnostics using probes and discs is further discussed in Chapter VI. The average luminosity of the plasma can be monitored by attaching a photometer to a one mm hole drilled in the side of the cavity. By cali- brating the photOmeter reading against a known density measurement of the plasma using another technique, it is possible to measure changes in the electron density by observing changes in the light intensity of the plasma. 5.2.4 The #2 Plasma-Cavity System This plasma-cavity system has been used to investigate chemical re- actions in microwave discharges, but is general enough to be useful for other applications such as a high-power light souce, an active plasma for lasers, and a source of free radicals for chemical lasers. The plasma is formed in the quartz tube (inside radius equals 1.25 cm.) which is located on the axis of the cylindrical plasma-cavity system (inside radius equals 10.15 cm.) as shown in Figure 5.4a. The outer walls of the cavity are water cooled by tubing attached to the exterior wall sur- face shown in Figure 5.4b, and the quartz tube can be forcedeair cooled when necessary. A screened viewing window provides a visual viewing port. Many small holes are cut into the exterior walls providing coaxial ports required for microwave diagnostic measurements. 108 .maasmuv uwuuoaomH Anv >ufi>mo mammaa mo coauoom mmouo Amy .amuwhm >ua>moloamoaa ~* 0:9 .q.m shaman 3V monou waHHooo seams upon wafizofir cocomuom . .AA-“ w Houmonvm .mm .nsu mamoan no swanuuonm _u.a uuumov , \..\ \-\\x . . ‘ ‘ [’4‘ \4 . uuoa used.“ umBom -noua owumoswmwv Hoaxmoo pom moaon A3 onsu mammam uuumov uuosm usficwam.hH/// mafiaaooo QOOH uo moose Hafixmoo manmumafivm.\\1 109 Depending on which cavity mode is excited, two adjustable loop or probe coupling systems located in the cavity side allow the RF energy to be introduced into the cavity. These adjustable coupling systems behave like a variable impedance transformer. Thus, by adjusting the depth of a probe (or rotating the loop or by varying the loop size), the plasma-cavity impedance can be continuously adjusted. The cavity length, which is continuously adjustable up to 35 cm., can be varied as the plasma conditions change. The inside cavity length could be determined from a centimeter scale, which was adjusted to read absolute cavity length by using the short length adjustor as a reference (see Figure 5.4). The variable cavity length allows the production of a variable high-density plasma inside the cavity operating from pressures of 1 torr to 1 atm (argon gas). This retuning can be achieved even under widely varying plasma loading conditions, and in practice, the length changes required to retune the cavity from no load to full load vary, depending on the cavity mode, from as much as l - 2 cm. to less than several millimeters. This small retuning length results from the fact that the ratio of plasma diameter to cavity diameter is much less than one. Thus, the presence of the plasma inside the cavity only slightly perturbs the cavity resonance frequency. Since the plasma fills only part of the cavity, the plasma and the external metallic cavity walls combine to form the resonant circuit. This plasma-cavity system is a high-frequency equivalent of Babat's RF plasma systemsBz. However, one cannot think of system performance in terms of lumped circuit elements, i.e., inductors and capacitors, because of the short electromagnetic wavelength of microwaves. The plasma-cavity system is a distributed parameter resonant circuit since the length of 110 the plasma can be of the same order of magnitude or larger than the free- space electromagnetic wavelength. Thus, an active RF discharge has cer- tain short sections of the plasma behaving similar to an E or an H discharge (as defined by Babat32). The fact that the plasma does not fill the entire cavity allows an RF plasma to be sustained inside the cavity with densities much greater than the critical density. If the plasma were allowed to fill the entire cavity, the plasma density would be limited to approximately the critical density or less (except in the region near the coupling ports where evanescent fields exist), since all homogenous isotropic waveguide modes are cut off at frequencies below the plasma frequencyll. 5.2.5 The external microwave system for Cavity 2 A line diagram of the external RF system is shown in Figure 5.5. The RF signal source is a fixed frequency, 2.45 GHz magnetron oscillator capable of delivering 1.3 kw of continuous wave power. As shown in Figure 5.5, the RF power from the oscillator is incident on a power divider circuit. This power divider is constructed from three 3-dB side- wall hybrid couplers, two matched dummy loads, and a tandem sliding short3l. By moving the sliding short, the power delivered to the power divider output arm can be continuously varied from zero to full magnetron output. This divider is designed so that the input port will always be matched for any sliding short position if the other three ports are matched. The power output from the divider passes through a three-port circulator, through the incident and reflected directional couplers, and is incident on the plasma-cavity system. The power that is reflected from the cavity travels back into the dummy load attached to the third 111 %uw>wonmammfla we msu you amumhm o>o3ouoHE chumuxo may .m.m ouswwm nuance m>msouofia unmam hoooovoum undue duos ofiuwoawmwv muw>mo mammaa HoumHSUHfio Hova>wv .8ng Houooumw ou House o>m3 ¢ umuaam _ _ HausuEmnnsm _ uuosm . . soumHSUHHo _ woamNHH _ mouoom _ muoaaooo _ _ Hmawwm Hmaoauooufin _ _ mu _ /\ /\ q . _ . _ _ _ All _ . Hosoa uozoa . _ vouooamou usovwoaq n“ _ an a" _ . .I'nI'l'I'jr"- vmom vmoa monouma vosouma 112 arm of the circulator. Thus, the circulator protects the magnetron from the large amounts of reflected power that may be present during certain phases of experimentation. Furthermore, it allows the magnetron to work into a matched system independent of the plasma-cavity load. The two- directional couplers monitor the power in the main waveguide arms and thereby provide a means to measure the incident, reflected, and absorbed power in the cavity. The power incident on the cavity is fed into a coaxial system, and an adjustable length, radial probe, or loop couples the power into the resonant modes of the plasma-cavity system. The cavity diameter and ex- citation frequency were chosen to allow only one cavity mode to be excited for a given cavity length. Coupling power into a given mode was accom- plished by orientation of the loop or depth of the probe. Tuning stubs which are used in some plasma-cavity experiments will not be required since adjustments in the coupling probe and cavity length will produce the impedance match necessary for all modes of operation. 5.2.6 Diagnostic circuits for Cavity 2 A diagnostic cavity mode can also be excited in addition to the driving mode to measure the average plasma density26. This circuit is also shown in Figure 5.5. The diagnostic input is coupled into the cavity through a small coaxial coupling loop inserted into an appropriate coupling hole shown in Figure 5.4b. ‘This loop is positioned to minimize the coupling of the RF sustained mode energy out of the cavity and maxi- mize the coupling of the diagnostic mode energy into the cavity. The length independent TM 010 and TM020 modes are convenient for diagnostic purposes and the average plasma density can be obtained from standard 113 26 ' perturbation formulas or from exact computer solutions of the lossy plasma-cavity model discussed in Chapter IV. CHAPTER VI EXPERIMENTAL PERFORMANCE OF THE MICROWAVE PLASMA SOURCE 6.1 Introduction In this chapter the experimental properties of the microwave plasma source are examined over a wide range of pressures, namely 10 mtorr - 500 torr. The type of experiments conducted on this source can be broadly divided into three categories: 1) Observation of any unusual electromagnetic phenomena such as the appearance of sidebands and the qualitative explanation of these phenomena using the linear theory derived in Chapters II, III, and IV. 2) Measurement of the plasma parameters No and Te’ and the calcu- lation of an effective electric field, Ee’ in the plasma. 3) Study of the absorbed power characteristics of the plasma source and its dependence on background pressure, gas flow rate, incident power and eigenlength.of the cavity. Cavity 1 has been used in the pressure range of 10 mtorr - 20 torr to examine the linear and non-linear electromagnetic properties of the plasma cavity. This is described in Section 6.2. Eigenlength curves of the TE:11 mode are verified and space charge waves are excited in the cavity. Two different types of sidebands are detected in the reflected spectrum and speculation as to the cause of these is presented. In applications of this plasma source in plasma chemistry, or gas discharge lasers, it is important to measure the effective electric field Be vs. the discharge pressure. This parameter is obtained by 114 115 measuring No and Te’ i.e. the average electron density and electron tempera- ture of the ionized gas. The low power and the efficient low pressure operation of Cavity 1 make it ideally suitable for plasma diagnostics by the conventional probe30, disc7, and frequency shift technique326’33-36. The measurement of No’ Te over the pressure range 40 mtorr - 20 torr, the calculation of Ee’ and the accuracy and limitations of these mea- surements are described in section 6.3. The absorbed power characteristics of the plasma source as a func- tion of the background pressure, gas flow rate, incident power and eigen- length of the cavity are examined in section 6.4.. Cavity 2 is used to perform these experiments, because of its operation over a broad pressure range (1-500 torr), large variation in flow rates (0-14,000 cc/min) and high incident power levels (up to 1.3 KW). These experiments are per- formed on two different modes: a) TEOll' In this mode, the eigenlength is dependent on (cope/w)2 and (ve/w). b) TE:12. The eigenlength is almost independent of (tape/w)2 and (ve/w) for critical densities beyond 10 (see Figure 4.2). The theory of Chapters EIthrough IV is used to qualitatively explain some of the experiments described in this chapter. This theory cannot fully explain all experimental phenomena because of its restriction to: 1) small signal linear phenomena, 2) ionized gases with a zero flow rate. However, the theory does take into account the collision frequency losses, i.e., the pressure dependence of the experimental phenomena. 116 6.2 Linear and Non-Linear Operation of Cavity 1 6.2.1 Introduction Cavity l is driven by a 30W, 3.03 GHz microwave source as shown in Figure 5.1. The RF plasma source is excited by a Tesla coil, and the linear resonances of the plasma-cavity are observed by monitoring the reflected power. At the fixed operating frequency of 3.03 GHz, it is possible to excite the following plasma cavity modes: dipole EM modes, TE:11 and TMIOl’ the rotationally symmetric EM mode, TMOll’ and the space charge modes TMOOp’ p = l, 2, 3 ... etc. The empty cavity resonance * of the TE111 mode occurs at L8 = 6.0 cms. and theTE coaxial cavity reson- lll ance at LS = 5.92 cms. The TM011 mode has an empty cavity resonance at LS = 7.42 cms. (see Figures 4.1 and 5.2). Based on experiments conducted in the low pressure regime, (lO mtorr- l torr) four different types of experimental results are reported here. They are: l) The presence of two resonant plasma densities for a single 7: resonant length while operating in the TE111 mode. 2) Ejection of the plasma from the ends of the cavity while oper- * ating at specific resonant lengths in the TE111 and TM011 modes and in a specific range of plasma densities and collision frequencies. 3) Formation of short wavelength standing waves (£52 1 cm.) in the plasma when the plasma cavity operates in the off resonance region * of the TE111 or TM011 4) Detection of two different types of sidebands in the reflected modes. power spectrum. Each of these experimental phenomena is explained in detail on the following pages. 117 6.2.2 Excitation of Two Resonant Plasma-Density Operating Points for a Single Resonant Length It was shown in Chapter IV that the resonant length vs. (wPe/w)2 for a low loss TE:11 mode first rises, falls and then rises again to become asymptotic to the TE111 coaxial mode. The theoretical curve for ve/w = 0.1, is shown on an expanded scale in Figure 6.1. Experimental curves at discharge pressures of 12 mtorr and 85 mtorr are also plotted on Figure 6.1. All electron density measurements in this experiment have been made using the TM010 frequency shift method. The experiment is conducted by starting the discharge at a pressure of 100 mtorr, an incident power of 30W, resonant length of 6 cms. and then tuning the resonant length to 5.92 cms. by maximizing the photometer reading. The discharge pressure is now gradually reduced to a low value say 12 mtorr. Such a low pressure is necessary to provide a suitable comparison with the low collisional loss (ve/w - 0.1) theoretical curve. At a pressure of 12 mtorr and with the maximum avaliable incident power of 26W, the resonantly-tuned operating point is at L8 = 5.90 cms. and (mpg/w)2 - 6.42. As the incident power is gradually reduced and the resonant length tuned at the same time, the dashed curve as shown in Figure 6.1 is obtained. At (lope/w)2 = 4.8 and LS - 5.85 cms., the plasma cavity abruptly jumps to the operating point of L8 = 5.85 cms. and (cope/w)2 8 1.73 (not shown in figure). This point corresponds to a low it density non-maximized resonant length operation in the TE111 mode. As the resonant length is increased so as to retune the plasma, the operating point shifts to L8 = 6.05 cms. and (wPe/w)2 = 3.26. The incident power is gradually reduced, but the operating point does not shift. However, once the incident power falls below a certain threshold, the operating point jumps abruptly to L8 - 6.05 cms. and (nope/w)2 = 1.99. lfldsexperimentally verifies the fact that for a single resonant length 118 .080 mo.m u 0 .. . .. 80 . 0 .0:0 0:08 0 0pw=w0>03 .0voa Haama 050 How A3\0Q3V .0? mac mama o u a m m o u . a a . N 0A nuws0H uomaomou muw>m0 0&0 mo 00>p=0 Hmuo0awu0ex0 mom H00w00uo050 0&0 mo somauonaou H.o 0H=wwm 0a a a N. o m w NA \ v m N _ _ 5 M q q q - Q om 1 n.m H a s 1 w.mm p. w 0 D\\ .I \ ‘ IO‘U . I a ‘0‘ ._ II|I||I| l Ol.|oq'lol..°|4nlv|‘ln|.\ / o l m / . m. .m u. .... O . s / . m II D n o o \\ \ o s w \\ 8 \ O o \o a \ I \ ..CouE mm H 00:30.3 09330va D 0 ... To .0>.uo0 suwcgcommo ZFMH. uduo0EMu0QXM .|.Il .uuou—E N— u 0.2.30.3 093:0va .0>.30 59.03030 Swag. ~3c0E~u0axum Ilull III 1 m ..w 0 10 n 3\ > .0>.~o0 59.03030 Zimmh 303000038 4 m.o L [1“ {1.5 119 * operation in the TE111 mode it is possible to have two different plasma densities. If the resonant length and the incident power are increased the operating point moves to L8 = 6.1 cms. and (wpe/w)2 = 3.12. When the incident power is once again gradually reduced below a certain thres- hold power level, the operating point jumps to L8 = 6.1 cms. and (wpe/w)2 = 2.25. At very low incident powers the plasma can be resonantly sus- tained at L8 = 6 cms. and (cope/(u)2 = 1.37. The dotted curve is drawn to fit all the experimental points. Obviously, an exact match cannot be obtained between the 12 mtorr experi- mental curve and the ve/w = 0.1 theoretical curve. However, the experi- mental curve closely follows the theoretical curve and has the same general shape. It was not possible to sustain a plasma in the region below L8 = 6 cms. and in the density range 3 f (Lupe/m)2 §_3.5, where the theoretical resonant length decreases with increasing plasma density. A similar experiment is conducted at a pressure of 85 mtorr and a curveznsshown in Figure 6.1 is obtained. The double density region in the neighborhood of (cope/w)2 = 3 does not appear to be prominent at this pressure. This experimentally verifies the theoretical eigenlength curves for collision frequencies greater than 0.1 (see Figure 4.1). 6.2.3 Formation of longgplasma columns The RF plasma in the 30W cavity is electromagnetically excited in the TE:11 or TM011 modes. The cavity length is tuned for resonance. It is found that while operating in the pressure range of 20 mtorr - 2 2 200 mtorr and an electron density range of (wpe/w) = 5 to (mpg/w) = 15, the plasma is ejected out of the cavity at either ends (see Figure 6.2). It is possible to more than double the plasma volume internal to the cavity in this mode of operation. The length of the plasma column 120 Ejected plasma Cylindrical cavity with a radius of 5.08 cms.. Quartz tube /— Sliding short SOQ miniature coaxial line Figure 6.2. Plasma being ejected out of cavity as a result of efficient coupling to the space charge wave throu h an electromagnetic excitation of the cavity (TE111 or TM011 mode). 121 ejected out of the cavity is a direct function of the power input to the cavity. As might be expected, there is an enhanced power absorption by the plasma in the region where the plasma column is ejected. This is clearly demonstrated in Figure 6.3. This figure shows an experimental plot of the absorbed power in watts vs. the discharge pressure in tort for the TMO11 mode with the resonant length'LS held constant at 8.6 cms. The curves have been obtained for different incident powers P = 25W, 1 20W and 15W. The curves clearly show two peaks in the absorbed power, one in the low pressure region (around 80 mtorr) and one in the high pressure region (around 90 torr). The low pressure peaks occur at the same time that the plasma is ejected out of the cavity, the absorbed power in this region being directly proportional to the length of the plasma column ejected out of the cavity. More than 90% of the incident power is absorbed by the plasma in this region of operation. The high pressure peak in the absorbed power curves is a result of increasing collisional losses in the TM011 plasma. At very high pressures when the plasma assumes conductor-like properties, the power absorbed gradually decreases. A similar set of curves for the TMO11 mode but, at a different length, L8 = 8.1 cms., are shown in Figure 6.4. Again, distinct peaks in the absorbed power can be noted at low and high pressures. These two set of curves for the TM011 mode, i.e., at Ls = 8.6 cms. and L8 = 8.1 cms., demonstrate that the plasma cavity when excited in this mode proves to be a useful RF plasma source that can be operated over a wide range of resonant lengths, pressures and electron densities. No tuning of the resonant length is required. 122 .mao o.w n ma numcma uamsom0u >0fi>00 05H .unmumaou am 00som 0000H0afi 0:0 sags .0vos HHozH 050 new whamm0ua 0mumsomfiw 0:0 .m> 0030a c0nuomn< ..m.o 0u=me 0H0: .HHOU CH NHmewhfl OMMmfiumHQ 02 S a TB N S W - - — I V 1 w I NH 1 o“ 1 ON 8338M u; Janod paqzosqv 0H0: 0% 00300 0c0wwoca 0:0 :003 .0008 HHo .050 H.w n 0: :0wa0H 0000c000 >00>00 0:9 .00000000 SH 0:0 you 00500009 0000:0000 0:0 .0> 00300 00:000:< .0.0 003000 HuO0 0% 00000000 0wum:00Ha 2: 2 0 0...: 0-2 m . . . \4II. o .. 0. a 30a ”NH #1 m I: L o 3 3.: I m [it w v 2 a 1 D. .d u o 38 ... m LIY00 0:9 .00000000 0 00300 00000000 0:0 :003 .0008 Hammh 0:0 000 00000000 0000:0000 0:0 .0> 00300 00:000:< .m.0 000wah 0000 00 00000000 0000:000a 2: s 0 72 92 q q q _ N: c: on 0N sizan u; Janod paqxosqv 125 A plot of the absorbed power vs. the discharge pressure has also been experimentally obtained for theTE:11 mode and this is shown in Figure 6.5. The dark curves show the effect of holding the resonant length constant at L8 8 5.92 cms. At high pressures, the usual peaks in the absorbed power are obtained as a result of collisional losses in the plasma.7n30btain an ejection of the plasma out of the cavity at low pressures, a tuning of the cavity resonant length is required. The dot- ’ted curves show enhanced power absorption as a result of resonant length tuning. The ejection of the RF plasma column out of the cavity at low pressures and the associated enhanced power absorption for both the TM011 and TE:11 modes can be explained as resulting from the coupling of EM energy to the space charge modes. This can be understood by studying * the general plot of the eigenlength vs. (cope/w)2 for the EM modes TElll’ * TMlOl’ TM011 and the space charge modes TMOOp (see Figure 4.1). It is observed from this plot that the TM space charge resonances intersect 00p the TE:11 mode resonant curves at L8 = 5.92 cms., and in the plasma den~ sity range of S : (Lupe/(0)2 : 15. They intersect the TMOll mode re- sonant curves in approximately the same density range, but over a wider range of resonant lengths. Experimental measurements of resonant length, density and pressures indicate that ejection of the plasma out of the cavity takes place in the regions where the TE:11 and TM011 mode resonances intersect with the TM00p space charge wave resonances. The plasma-cavity is electromagneti- cally excited in the TE:11 or TMO11 modes. Under the right operating conditions of density, length and pressure, the EM energy is non-linearly coupled to a space charge traveling wave. This surface wave, which is 126 radially effenescent, propagates along the plasma column and ionizes the gas as it travels. The 0 - k diagrams of Chapter II (Figures 2.3a, 2.43 and 2.5a) indi- cate that the space charge mode propagates for frequencie310 x ‘V \ 108:- \ I I p I \ i P I p 9,,“ (Ramsauer and Kollath, Vm/Po Frost and Phelps) 107 J L 1 1 L I l 1 l I 0.1 1.0 10 VELOCITY(VVOLTS). Figure 6.9. The effective collision frequency in A as a function of velocity and frequency. Reproduced from Whitmer and Hermanso. Vm(v) 3 Bfo f” 2 2 v 3v dv o [vm(V)+w] Ve = . 6.9 I” 1 v3 Bfo 2 2 -—- dv o [Um (v) + m ] BV The above equation can be integrated for different gases assuming a Maxwellian distribution for fo.‘%n(v)iscalculated from measured cross- sections, available from the data of Ramsauer and Kollath48, Frost and Phelpsag, provided electron temperature numbers are available from separate measurements. As an example, Figure 6.9 shows a plot of ve/po vs. the RMS value of the velocity, = 3kTe/me, for different values of w/po in argon gas. This curve has been reproduced from Whit- mer and Herrmann50 and is used in the next section in estimating ve. 6.3.2 Experimental Results * 111 operation of Cavity 1 over the pressure range 40 mtorr to 20 torr. Using The plasma parameters No and Te have been measured in the TE mode argon gas as outlined earlier three different measuring techniques have been used to cover this pressure range. 1) Discharge pressure 40 mtorr - 240 mtorr. The TM010 frequency shift method was found to be effective in this range. Beyond a pressure of 240 mtorr the TM010 mode was highly damped because of increasing collisional losses in the plasma. The normalized electron density vs. discharge pressure for three different absorbed powers Pa = 16W, 12W and 8W are shown in Figure 6.103, for this pressure range. As expected, the electron density steadily increases with pressure and absorbed power. At a pressure of 235 mtorr and for P8 = 16W, the value of No is 1.65 x 1012 cm3. 142 14 F— 12-— 10r- N s \ 0 D. a 8 r P a 8 w A ------ 12 w o------ 16 w 6 I—. 4 I J I 1 1 I 0 40 80 120 160 200 240 P , mtorr 0 Figure 6.10s. Normalized electron density (mpg/w)2 vs. discharge pressure Po and the absorbed power Pa using the TM frequency shift 010 method. 143 20 1— 16 ‘- z \ > ‘1‘ 12 - O .... X M” P a I---- 16 w v---- 12 w o---- 8 w 8 I.— 4 I I J 0 80 160 240 Figure 6.10b. P , mtorr 0 Effective electric field Ee vs. discharge pressure Po and absorbed power Pa, from the TM010 frequency shift method. 44 r- 144 40 - 32 " I 5. 2'. \ q. l c> 04 x o a. \ m0 ' P a V---- 12 W I---- 8 W 8 F' I 0 l l j 80 160 240 P0’ mtorr Figure 6.10c. Reduced field Ee/Po vs. discharge pressure PO and ab- sorbed power Pa, from the TM 010 frequency shift method. 145 Since the electron temperature cannot be measured using this tech- nique, a value of 90,0000K has been used for Te on the pressure range 40 mtorr - 240 mtorr. This estimate for T8 has been obtained from probe data measurements to be described later. Plots (fl? Ee and Ee/p calculated from equation 6.8 are shown in Figures 6.10b and 6.10c. respectively. Ee 3nd Ee/p decrease with in- creasing pressure 3nd electron density and appear to be almost inde~ pendent of the absorbed power. Ee varies from 2 x 104 V/M at 45 mtorr to 6.3 x 103 V/M at 235 mtorr for 3 Pa = 16W. 2) Discharge pressure 140 mtorr to 1.05 torr. The double floating probe method has been used to measure the electron density and electron temperature in this range. At very low pressures (below 100 mtorr) and in the high pressure regime (above 1 torr) the probe data did not provide reliable results. A typical double probe I-V curve at a pressure of 86 mtorr is shown in Figure 6.113. It is clear that the saturation regions are not clearly defined, thereby causing an error in the density calculation. At high pressures, the saturation current was too small as a result of the collision-dominated plasma. This is demonstrated by two I-V characteristics at pressures of 5 torr and 11 torr where the ion saturation current decreases with an increase in pressure from 5 to 11 torr, see Figure 6.11b. In the pressure range 100 mtorr to l torr, the I-V curves are more conventional, with well defined linear and sat- uration regions. A typical set of such curves is shown for different power levels and different pressures in Figures 6.llc and 6.lld. 146 .3 ON u 00 00300 00:000:< .0000E cm 00 00000000 0w0m:0000 0 00 000000000000m:0 >IH 0:000 0H:0o0 wcfiumoam H000009 .mHH 0 000w00 N'l j 0 HIII 00H0> .> 14. mm Jo we 9w 0 JNI owl 0&1 owI 0 . q 0 q . 147 0 q_ 4 o g . . ’4. ( aub— 2 ' g / 1 n ) 1 n " l l I T ” -10 -5 ,/ 5 10 U V, volts 0 O ; __ -2 P o 0 ' o -—-- 5 torr ' a -—-- 11 torr 0 -_ -4 Figure 6.11b. Typical floating double probe I-V characteristics for pressures above 1 torr. Absorbed power Pa = 20 W. ma 148 ' 20 40 / i V, volts ,d--2 P a A ---- 20 W o---- 16 w o---- 12 w Figure 6.11c. Typical floating double probe I-V characteristics at a 'discharge pressure of 140 mtorr and different absorbed power levels. 149 O 6 4&— 6' g 4 .L. . H {I a g 2 4 l J. «F : § ' ; .L > -40 -20 20 40 , V, volts 1 O uni-"4 ‘P-6 Pa 1 -8 o--—- 16 W A---- 12 W ‘P-lO V Figure 6.11d. Typical floating double probe I-V characteristics at .a discharge pressure of 730 mtorr and different ab- sorbed power levels. 150 The experimentally measured electron density and electron tempera- ture vs. discharge pressure for P8 = 20W, 16W, 12W are shown in Figures 6.12a and 6.12b. It is observed from Figure 6.12a that in the pressure range 100-400 mtorr, the electron density decreases and then rises again with pressure. As explained in section 6.2.3, the unusual behavior in this low pressure range is believed to be a result of coupling of the * TE electromagnetic energy to the TM 111 00p space charge wave. Normally, this space charge wave would propagate along the plasma column and ionize the gas as it travels (see Figure 6.2). However, in this diagnostic technique, the location of the two probes (see Figure 5.1) prevents the plasma volume from increasing longitudinally. As a result, the absorbed power per unit volume increases causing a peak in the electron density vs. pressure curve. Beyond 400 mtorr, the electron density rises steadily with pressure and appears to saturate around 1 torr. However, probe measurements beyond a pressure of 800 mtorr tend to yield lower than actual values for the electron density because at these pressures, the collisionless probe theory may not be applicable. At 800 mtorr and Pa = 20W, the value of No is 1.85 x 1012 cm3. The electron temperature (see Figure 6.12b) appears to be almost independent of the power absorbed by the plasma, but decreases steadily with pressure. At 1 torr, Te is approximately 60,0000K. The effective electric field (Figure 6.12c) and the reduced field Ee/p (Figure 6.12d) are also independent of the power absorbed, but decrease with an in- crease in electron density and pressure. The floating double-probe measurements obtained follow the same general variation with pressure as those obtained by Maksimov7 in a 151 .000080000008 00000 000000 wcaumoaw 050 5000 .00 00300 00000000 000 00 00000000 0w00£0000 .0> NA3\003v 0000000 00000000 000000800z .0NH.© 000w00 O 00005 . m coca com coo 000 com 0 q 4 \0 _ 1% .10 |.w 10H 1N." l1 .100 ..00 W (m/adm) 152 .00W0E0000008 00000 000000 w0000000 000 5000 .00 00300 00000000 000 00 00000000 0m000o000 .0> H 00000000500 000000Hm .0NH.0 000w00 0 00008. 0 0000 000 000 000 000 0 T . _ 0 . _ l 0 I111 .I ... al IL 0 x T.— 0 0., O I 0 x 3 NH ..III. 3 00 II...- 3 ON llll’ I. OH m 0 153 0.000080000006 00000 000000 w0000o00 000 8000 .00 00300 00000000 000 00 0w0000000 .0> 0 00000 00000000 030000000 .0N0.0 000m00 0 00005 . 0 0000 0000 000 com 000 000 com 000 com com 0 0 _ 0 0 _ _ 0 _ _ - 0 o //». f 3 N0 IIIID 3 00 IIIIQ 3 0m .iIIO 000 O0 00 _0Ix 3 N/A E 154 .000050000008 00000 000000 wc000000 8000 .0 0 0 0 0 00300 00000000 000 0 00000000 0w0000000 .0> 0\ 0 00000 0000000 0 00008 . 0 .000.0 000000 82 . 83 80 80 03 com o _ _ _ _ _ 0 3 S .....I 3 3 ----» 3 ON :1... m0 O 9 WWW/A ‘£_OI x a/ a 155 3.0 GHz Helium microwave discharge and by Bell55 in a 20 MHz Helium discharge. Since argon gas has been used in the plasma cavity, an absolute comparison between the results of this section with those of Maksimov and Bell is not possible. 3) Discharge pressures above 1 torr. Most of the commonly used techniques for measuring the plasma parameters (probes, frequency shift method) fail in this pressure region because of the collision-dominated plasma. However, a simple technique using discs to measure the conductivity has been found to be useful in estimating the electron density up to a pressure of 20 torr. Discs of different cross-sections were tried and a disc of almost the same cross-sectional area as that of the quartz tube of Cavity 1, gave numbers for electron density that seemed to match the results obtained by the double probe measurement at a pressure of l torr. The results of the electron density measurement from conductivity calculations are shown in Figure 6.13a. At a pressure of 20 torr, and Pa = 20W, the value of No is 7.84 x 1012/cm3. The electron temperature was estimated from the slope and the saturation current of the I-V characteristics of the discs. The results obtained by this method match those obtained by the probe measurements at l torr. The electron tempera- ture is slightly dependent on the power absorbed and reaches a uniform value as pressure increases. Plots of Ee and Ee/p vs. pressure are shown in Figures 6.13c and 6.13d, respectively. Both the effective field and the reduced field reach a steady value at a pressure of 20 torr. At this pressure Be is 2.5 x 103 V/M and is independent of the power absorbed. 156 5000 .00 00300 00000000 0m 3 N0 III: > .00000 m0000 000050000005 000 00 00000000 0w0000000 .0> ~03\0030 0000000 00000000 0000005002 0 0000 . 0 00 N0 0 0 .m00.o 003000 157 .00000 w0000 000050000005 5000 .00 00300 00000000 000 00 00000000 000000000 .0> 00 00000000500 000000Hm .0ma.o 000000 0 0000 . 0 z 2 -..--. 3 2 ----- 3 8 l.-- v Q OI X l HO ‘7_ 158 .00000 w0000 000050000005 500m .00 00300 00000000 000 00 00000000 0w0000000 .0> 0m 00000 00000000 0>0000wmm .UM0.0 003000 0000 .00 ON 00 N0 0 o _ 0 _ N W MW .11“ O 3 N0 till. 1.0 3 3 --....> an 3 8 .....i I x 0 I 0 n} E _A / "N |.o pm 159 60 F- 50 ‘- 40 " 30 _‘ O Q) 20 — P a o--—- 20 w A ---- 16 W 10 _. I‘---- 12 W J J 4 I 4 0 4 8 12 16 20 Figure 6.13d. Reduced field Ee/Po vs. discharge pressure Po and absorbed power Pa’ from measurements using discs. (wpe/w) Figure 6.14a. 160 60-— _____. ' TMOlO frequency Shlft —---— Floating Double probes ——--— Discs 0 --P = 16W a 0 ---P = 12w 50... a . 0/ /' ' 40— / ' 0 / -’ 30 I 0/ / ,0/ ° 20_ ,/ / ,0" / 10_ " I'D/ / ---O~‘ ,’ ’0’ ./ “\1V x o“‘O----O-"o o/ 0 l J l l l i I l 0.04 0 l 0 2 0 5 1 2 5 10 20 P , torr 0 Normalized electron density (cope/w)2 vs. discharge pressure Po and absorbed power Pa over the pressure range 40 mtorr - 20 torr, from three different diagnostic methods. 161 12 '- Floating Double Probes ---- Discs O-—-P =16W a 0--—P =12w a 10 ‘- 8— 3‘ Q ~3' \ l \ S \ x 6 -— \ a) \ \ E" \ \ R \ \ \ \ \ 4— \ \ \ ‘\ ,—C\ \ \ ’0’ \ \\\‘O—-” -Q ‘6 \o-——-—-'°' \ b ‘2__ o l I l I l l l 0.1 0.2 0.5 1.0 2 5 10 20 P , torr 0 Figure 6.14b. Electron temperature Te vs. discharge pressure PO and ab- sorbed Pa over the pressure range 0.1 - 20 torr, from two different diagnostic methods. 162 TMOIO frequency shift ----- Floating double probes ——-— Discs .---Pa = 16W 0---P = 12W 3 2 \ é \ E 'x \ i 104 L- b O \ E: \ (D \s [-11 5 r- .\ \ o 2 - \ 103 0 \ 5 r— \. 2 ~ \ 102 L 1 l 1 J 1 I v) .04 .1 .2 .5 1 2 5 10 20 P , torr 0 Figure 6.14c. Reduced field Ee/Po vs. discharge pressure Po and absorbed power Pa over the pressure range 0.04 - 20 torr. from three different diagnostic methods. 163 For purposes of comparison, the plasma parameters and the reduced fields obtained frrmxthethree different measurement techniques are dis- played over the entire pressure range in Figures 6.143, 6.14b, and 6.14c. 6.4 Absorbed Power Characteristics of the Microwave Plasma Source 6.4.1 Introduction The #2 plasma-cavity system has been used to study the absorbed power characteristics of the microwave plasma source. The plasma-cavity was tested in argon gas. The quartz center tube was connected to a vacuum system which could be pumped down to several microns of Hg. Once evacuated to low pressures, argon was inserted into the system and plasma initiation was achieved by 1) adjusting the pressure of the argon gas somewhere between 0.5 to 10 mm Hg., 2) applying the high microwave power. and 3) length tuning the empty cavity for resonance at the oscillator frequency of 2.450 GHz. The microwave source and a cross-section of Cavity 2 are shown in Figures 5.4 and 5.5. Gas breakdown was achieved near precalculated cavity resonant lengths. Once breakdown was accomplished, the pressure, RF power, cavity length, and cavity coupling adjustments could be varied to pro- duce the desired plasma conditions. With a little experimental experi- ence, this tuning procedure could be achieved in less than one-half minute without fear of extinguishing the plasma. By varying the input gas flow and exhaust pumping rate, a plasma could be established in the flowing gaseous environment. The flow rate could be continuously varied from zero to over 14,000 cm3/minute, the upper limit of the experimental flow measurement capability. The plasma cavity could be operated in many different cavity re- sonances simply by adjusting the cavity length and input coupling. For 164 example, the following empty cavity modes have eigenfrequencies equal to 2.450 GHz when the cavity length is varied from 6 to 20 cm.: TElll’ TM T TM011’ TE211’ TE011’ E212’ TE012’ TM112’ TE113’ etc. With the proper cavity length and RF coaxial coupling (i.e., loop 111’ TE112’ TM012’ or probe), the plasma cavity system will sustain a plasma on any of these modes. However, only the TM , and TE modes, where p = 1, 2, Olp’ TE01p or 3 were studied extensively. llp All three of these modes were able to maintain microwave plasmas in argon gas over a wide range of pressures and flowing gas conditions. The appearance of the plasma varied considerably as the pressure and power were varied. At pressures less than 5 mm Hg, the discharge could be resonantly sustainedSI’52 in a TD resonance or in a pure electro- magnetic resonance. In either case, the discharge took on a dull to bright reddish pink astimzpower was increased. 'In the pressure range of 5 to 80 mm Hg, the discharge color varied from dull pink to blue to a bluish white at high power levels (1 KW). At pressures of 80 mm Hg or more, thin intense discharge streamers appear following paths which have high displacement currents in the absence of a plasma. When ex- citing the TEOln resonance at pressures greater than 200 mm Hg hot 32,53 plasmas, similar to low-frequency induction plasmas , can be formed inside the quartz tube. 6.4.2 Experimental Results Two different types of_experiments were performed to study the ab- sorbed power characteristics of the argon plasma maintained in Cavity 2. 1) In the first of these experiments, the absorbed power of the plasma was studied as a function of the cavity length with the gas dis- charge pressure (po) and the gas flow rate as the variable parameters 165 (see Figures 6.15 and 6.16). These experiments were conducted using the TE011 mode, because of its usefulness in plasma chemistry experiments and also because of its gradual variation in eigenlength vs. electron density (see Figure 6.17). Because of equipment limitations, only the following parameters have been measured:hntheseexperiments: the gas flow rate, discharge pressure and the length of the cavity. It was not possible to make density and temperature measurements using the conventional probe and TM frequency shift diagnostic techniques. Probe measure- 010 ments on the high pressure plasma of Cavity 2 yielded erroneous results because of high electron-neutral collision frequencies. Also, the in- sertion ofa.probe into the plasma of Cavity 2, caused a significant amount of power to be coupled to the external surroundings. This was considered to be a safety hazard. The use of the TM010 frequency shift method was also limited by the high pressures employed in Cavity 2. The failure of these methods and the absence of more sophisticated techniques required that all arguments used in explaining the experimental phenom- ena be based on the above-mentioned experimental quantities and on esti- mates of the electron density and temperature. In the absence of direct measurements of the electron density, col- lision frequency, rate of ionization and other parameters involving a flowing gas, the arguments presented below are speculative. However, these explanations may provide the background on which further theoreti- cal and experimental research may be based to fully understand this problem. Figure 6.15 displays the experimental absorbed power Pa vs. the cavity eigenlength LS for the TED mode. All experimental points in 11 Figure 6.15 were measured at a constant flow rate of 1,000 cc/min. and 166 900 "' 800 _ 700 ’— 600‘- P o 500 r- 0') III 100 torr cc 3 a}: 400 '— 70 40 300 20 200 I- 100 '- . L4 ...__.. Region l___..' rfi Region 2 I I I I I I I ,J 9.0 9.05 9.10 9.15 9.20 9.25 9.30 9.35 9.40 L , cms. Figure 6.15. Absorbed power Pa vs. eigenlength LS and different discharge pressures Po’ for the TE mode plasma of Cavity 2. Flow 011 rate = 1000 cc/min,.Incidentpower Pi = 1.2 KW. 167 each curve represents the power absorbed vs. cavity length for a differ- ent pressure. Two regions of operation can be clearly distinguished in these curves. In region 1, which covers the approximate eigenlength 9.0 cms - 9.1 cms., the absorbed power increases as a function of the discharge pressure. In region 2, which includes eigenlengths from 9.2 - 9.4 cms. the absorbed power increases inverselyansthe discharge pressure. These experimental observations can be explained by studying the theoretical TEO1 absorbed power vs. (w/wpe) curve for different (ve/wpe), as described in Chapter III and shown in Figure 3.5. Note that the curve of Figure 3.5 has been plotted for a plasma density of fpe = 10.5 CH2 and for the waveguide dimensions of Cavity 1. However, the behavior of the curve is general enough, so that it can be used to qualitatively explain the variation of absorbed power and plasma density vs. pressure in Cavity 2. In region 1 of Figure 6.15 the cavity operates close to the empty . cavity resonance. The electron density in this region is small and, hence, (m/wpe) becomes large. This experimental region of operation corresponds to the right end of the theoretical TE01 absorbed power curves shown in Figure 3.5. In this region of the theoretical curves, the normalized absorbed power increases with the collision freqeuncy. (Compare curves for (ve/wpe) = 0.1 and 1.0). This type of behavior would be more apparent at still higher values of (Va/mp8). This seems to justify the experimental observations made in region 1 of Figure 6.15. In region 2 of Figure 6.15, the electron density is large and, hence, (w/mpe) is small. This region of experimental operation would lie to the left of the theoretical TE01 absorbed power curves (Figure 3.5). In 168 this part of Figure 3.5, the normalized absorbed power increases inversely with the collision freqeuncy. This theoretical behavior explains the experimental observations made in region 2 of Figure 6.15. Figure 6.16 shows the absorbed power, Pa’ vs. the cavity eigenlength, LS, with the discharge pressure held constant at 10 mm. Eachcfifthe curves of Figure 6.16 have been plotted for different gas flow rates. These curves show that for a given flow rate, the absorbed power reaches a peak at a certain eigenlength. For example, when the flow rate is zero, the peak occurs at LS = 9.15 cms. and the absorbed power is only 490W. As the flow rate increases, the absorbed power peak shifts towards higher eigenlengths and for flow rates of 250 cc/min and beyond, the absorbed power peak remains at LS = 9.35 cms. At the same time, the absorbed power also increases with the flow rate and is highest for a flow rate of 2000 cc/min. In providing a qualitative explanation for the shift in cavity eigenlength, with changes in flow rate, the eigenlength plot of the TE011 mode for Cavity 2 (Figure 6.17) will be used. Before using the curves of Figure 6.17, it must be noted that the experimental TE empty Oll cavity and coaxial resonances are lower by .05 cms. than the correspond— ing theoretical values due to the finite thickness of the plasma enclosing quartz tube, holes in the cavityiknidiagnostic purposes, wall imperfec- tions, etc. Hence, .05 cms. should be added to all TE experimental 011 eigenlengths for a direct comparison with the theoretical curves of Figure 6.17. The TEOl1 eigenlength curves have been evaluated for a zero flow rate. The applicability of these curves to a non-zero flow rate situation is not clearly understood. It is expected that a non-zero flow rate, would modify the values of electron density and the collision frequency from their zero flow rate values. However, a flowing plasma 169 1000 900 '- 800 "‘ 700 " o S 600 '- m I S 3 500 “‘ '63 0.. o o ...4 400 '- Flow rate=0 o o c 300K a o 8 \ N \ 200 " 100 *- l l l 1 l l l Alj 9 00 9 05 9 10 9 15 9.20 9 25 9 30 9 35 9 40 L ,cms. Figure 6.16. Power absorbed Pa vs. eigenlength Ls’ and flow rate (cc/min) for the TE011 mode plasma of Cavity 2. Discharge pressure, P0 = 10 torr. Incident power Pi = 1.2 KW. 170 .Nmu m¢.N u :N\3 .N hufl>mu now A3\w>v hocmskum aoamfiaaou can ~A3\wm3v huamamv mammfia .m> numama uamcommu Haoms .mH.o muawfim A3 onsv N \ ooocfi ooow cog on H m11 a _ _ 0.0 “.0 1 3. N.o % A T.- J ..A T a u 00 14 m.o mu 3 m ¢.o m.o 171 still has a discrete electron density, temperature and collision frequency, i.e. , its steady state operation can be represented as a single point on Figure 6.17. Assuming that the electron temperature may vary between 20,0000K and 90,0000K, the normalized electron neutral collision fre- quency, (VB/w), can be estimated from Figure 6.9 to vary between 1 and 3.5. This band of collision frequencies would correspond to the shaded region of operation shown in Figure 6.17. The experimental curves of Figure 6.16 can best be explained by classifying the curves of different flow rates into three different groups: 1) Flow rate = 0 cc/min. 2) Flow rate = 60 cc/min. 3) Flow rates = 100, 250, 500, 1,000, 2,000 cc/min. 1) The peak-absorbed power for a zero flow rate occurs at LSC = 9.20 cms., and the operating point lies on line A, as shown in Figure 6.17. LSC is the corrected eigenlength. 2) With an increase in the flow rate to 60 cc/min., the eigenlength of the peak of the curve shifts to LSC = 9.35 cms. The peak-absorbed power also increases as a result of the increase in the ionized gas volume. This contributes to a rise in the electron density and the operating point lies along line B (Figure 6.17). 3) A further increase in the flow rate to 100 cc/min. causes the peak absorbed power to increase from 560W to 790W. The new eigenlength of the peak of the curve occurs at LSC = 9.395 cms. This dramatic rise in absorbed power is attributed mainly to the increase in the volume of ionization because of the large flow rate. The operating point now - lies along line C (Figure 6.17). The flow rate is now increased gradually in the range 250 cc/min. to 2000 cc/min. It is observed that for this large variation in the 172 flow rate, that the eigenlength of the peak-absorbed power remains con- stant at LSC = 9.40 cms. and the peak—absorbed power varies only from 900W to 950W. A possible explanation for this strange behavior is that the substantial increase in the flow rate may not cause a proportional increase in the volume of the ionized gas. As the flow rate is varied in the range 0'to 250 cc/min, the volume of the ionized gas increases directly with the flow rate. This fact has been experimentally verified by observing that the light intensity of the gas increases with the flow rate. This implies that there must be a large increase in the absorbed power (see Figure 6.16 for flow rates 0, 60, 100, 250 Cc/min.) and, hence, an increase in the electron density. The electron density at 250 cc/min. may be sufficiently large to form a high density plasma next to the inside of the quartz tube. This plasma would prevent the penetration of the fields into the internal volume of the gas and thus, have the effect of preventing the rest of the gas from ionization. This shielding effect of the outer layer of the plasma allows a large volume of the incoming gas to bypass the ex- citation region in the cavity. Thus, a dramatic increase in the flow rate from 250 cC/min. to 2000 cc/min. has little or no effect on the peak power absorbed by the plasma. 2) In the second type of experiments the behavior of the absorbed * power of a TE112 mode plasma was studied as a function of the discharge pressure with the incident power P and the gas flow rate as the vari— i able parameters. The values used for the incident power P were 966W, 1 759W, 552W and 276W. A family of such curves was obtained by varying 'the pressure with flow rate constant. The flow rate values used were 147, 520, 955, 1480, and 2500 cc/min. 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