Multipactor in Low Pressure Gas and in ... - of Richard Udiljak

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σse,max the zones become wider and zones previously suppressed by the losses can appear (cf. Fig. 5.11). This behavior is very similar to that noted for the parallel plate geometry [46]. The lower (left) envelope is G 50 45 40 35 30 25 20 15 10 5 0.2 0.4 0.6 0.8 1 V /V ω max 1.2 1.4 1.6 1.8 Figure 5.10: Number of electrons after 200 rf-cycles. The vertical straight lines indicate the lower and upper theoretical envelopes according to Eq. (5.12). Parameters used: Ri/Ro = 0.7, f = 1.5 GHz, σse,max = 1.3, vT/vmax = 0.01, and W1 = 50 eV. obeyed, but the upper can be exceeded since a non-zero initial phase will yield a lower impact velocity and a concomitant higher upper threshold. In Figs. 5.10 and 5.11 the velocity spread is quite low, vT/vmax = 0.01. When increasing this ratio, a greater portion of the electrons can have a large negative initial phase, which leads to overlapping of the multipactor regions when σse,max is large (see Fig. 5.12). On the other hand, the increased velocity spread also increases the losses, which especially affects the higher order resonances, since the phase-focusing effect gets weaker with increasing mode order. If σse,max is low, the losses are not sufficiently compensated for and this leads to suppression of the higher order modes (cf. Fig. 5.13). This is a result similar to that found in the parallel plate case [46]. The corresponding behaviour is seen also for single-sided multipactor (see paper F). For single-sided multipactor it was noted that for the first order mode, the envelope of the breakdown zones Vω,o = v1/2 was not obeyed. This is confirmed by the PIC-simulations, where the first order mode 86 4500 4000 3500 3000 2500 2000 1500 1000 500
G 50 45 40 35 30 25 20 15 10 5 0.2 0.4 0.6 0.8 1 V /V ω max 1.2 1.4 1.6 1.8 Figure 5.11: Same as Fig. 5.10 only with σse,max = 2.0. G 50 45 40 35 30 25 20 15 10 5 0.2 0.4 0.6 0.8 1 V /V ω max 1.2 1.4 1.6 1.8 Figure 5.12: Number of electrons after 200 rf-cycles. The vertical straight lines indicate the lower and upper theoretical envelopes according to Eq. (5.12). Parameters used: Ri/Ro = 0.7, f = 1.5 GHz, σse,max = 2.0, vT/vmax = 0.1, and W1 = 50 eV. 4500 4000 3500 3000 2500 2000 1500 1000 500 4500 4000 3500 3000 2500 2000 1500 1000 500 87
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Thesis for the degree of Doctor of
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Multipactor in Low Pressure Gas and
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Conference contributions by the aut
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viii
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3.2.4 Key findings . . . . . . . .
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xii
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xiv
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addition, it is difficult to make c
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numerical study of the phenomenon i
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to physically damage microwave comp
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odd positive integer (N = 1,3,5...)
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σ se [−] 2.5 2 1.5 1 0.5 W 1 W m
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Voltage [V] 10 4 10 3 10 2 10 0 N=1
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even though it may be sufficient fr
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where φL and φR are the left and
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(cf. Fig. 2.7). When taking the env
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2.1.4 Methods of suppression Many o
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Noise (dBm) Power #1 (dBm) Match #1
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andom spread in emission velocities
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Figure 2.12: Multipactor experiment
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where kn is a factor determining th
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allows for another design margin, w
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Boundary function Method One of the
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carriers, because the NLSQ method r
Page 50 and 51: multipactor discharge. Using a Mont
Page 52 and 53: the assumption of a constant ratio
Page 54 and 55: Voltage (V) 10 3 10 2 10 1 10 −2
Page 56 and 57: 3.1.3 Main results The main result
Page 58 and 59: lytical model is obviously needed.
Page 60 and 61: where 〈vt 2 〉 represents the av
Page 62 and 63: these quantities in the range from
Page 64 and 65: analytical. Attempts were made to f
Page 66 and 67: only model, the inclusion of ionisa
Page 68 and 69: Normalised Voltage 1.1 1.05 1 0.95
Page 70 and 71: Voltage [V] 10 3 10 0 µ=0 µ=0.75
Page 73 and 74: Chapter 4 Multipactor in irises A c
Page 75 and 76: h l Figure 4.1: The geometry used i
Page 77 and 78: N e /N 0 [−] 3 2.5 2 1.5 1 Multip
Page 79 and 80: to compensate for electron losses i
Page 81: 4.4 Main results This analysis has
Page 84 and 85: support for the qualitative analyti
Page 86 and 87: where R(t) is the average position,
Page 88 and 89: where d stands for the gap width, V
Page 90 and 91: there are different oscillatory vel
Page 92 and 93: Phase [degrees] 60 50 40 30 20 10
Page 94 and 95: G 100 90 80 70 60 50 40 30 20 10 0
Page 96 and 97: possible for quite large Ro/Ri-valu
Page 98 and 99: upper right region of the figures,
Page 102 and 103: G 50 45 40 35 30 25 20 15 10 5 0.2
Page 104 and 105: creasing ratio Ri/Ro was observed.
Page 107 and 108: Chapter 6 Detection of multipactor
Page 109 and 110: Amplitude of acceleration [Gm/s 2 ]
Page 111 and 112: tipactor events that are short-live
Page 113 and 114: software and the time evolution of
Page 115 and 116: ditional test sample, a resonant ca
Page 117 and 118: the FFT. It was concluded that ther
Page 119 and 120: 6.2.1 Single carrier When using the
Page 121 and 122: Reference signal generator Phase co
Page 123 and 124: Amplitude [A.U.] 2.5 2 1.5 1 0.5 De
Page 125 and 126: Chapter 7 Conclusions and outlook T
Page 127 and 128: tioned there were multipactor in no
Page 129 and 130: References [1] W. Henneberg, R. Ort
Page 131 and 132: [27] A. Ruiz et al, “Ti, V, and C
Page 133 and 134: [51] D. Wolk, D. Schmitt, and T. Sc
Page 135 and 136: [75] R. Udiljak, Multipactor in low
Page 137: Included papers A-F 123
Page 141: Paper B R. Udiljak, D. Anderson, M.
Page 145: Paper D R. Udiljak, D. Anderson, M.
Page 149: Paper F V. E. Semenov, N. Zharova,
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