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

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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 5.13: Same as Fig. 5.12 only with σse,max = 1.3. clearly passes this limit (see Fig. 5.14). 5.2.3 Comparison with experiments As mentioned in the introduction to this chapter, PIC-simulations can include aspects of the multipactor, which are difficult to analyse theoretically. As a more realistic description is possible, quantitative comparison with experiments becomes feasible. In the experimental study by Woo [63] coaxial lines made of copper were used. When taking values for the secondary electron emission properties for copper from the ESA standard [50], the lower thresholds of the PIC-simulations are not in very good agreement with the experimental data. However, the secondary emission properties can vary a great deal between different samples of the same material and contamination can reduce the first cross-over point and increase the maximum SEY. Thus by slightly lowering the first cross-over point in the PIC-simulations, very good agreement is obtained (see Fig. 5.15). In paper F an alternative method of obtaining the experimental threshold when using the secondary emission properties given in the ESA standard [50] is presented, based on a modification of the used model for the SEY [22]. However, this will not be discussed further in this summary. In the experiments an increase in the multipactor threshold for de- 88 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 1.2 1.4 1.6 1.8 V /V ω max Figure 5.14: Number of electrons after 200 rf-cycles. The vertical straight lines indicate Vω,o = v1/2 and Vω,o = v2/2. Parameters used: Ri/Ro = 0.1, f = 1.5 GHz, σse,max = 2.0, vT/vmax = 0.01, and W1 = 50 eV. log 10 (Amplitude) [V] 3.2 3 2.8 2.6 2.4 2.2 2 1.8 1.6 1.4 −1.6 −1.4 −1.2 −1 −0.8 −0.6 log (Frequency) [GHz] 10 Figure 5.15: Multipactor breakdown regions for copper electrodes. The region confined by circles (or white crosses, when inside a dark region) is from Ref. [63]. The dark regions are obtained by the PIC-code with: Ro/Ri = 2.3 (Z = 50 Ω), σse,max = 2.25 (from table A-6 in [50], W1 = 27 eV, and vT = 3 eV (vT/vmax = 0.111). 4500 4000 3500 3000 2500 2000 1500 1000 500 0 4500 4000 3500 3000 2500 2000 1500 1000 500 89
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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
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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 100 and 101: σse,max the zones become wider and
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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