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

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Voltage (V) 10 3 10 2 10 1 10 −2 Threshold curves in low pressure air (fd=1GHz ⋅ mm) Multipactor in air Multipactor in vacuum Corona in air 10 −1 10 0 Pressure (Pa) Figure 3.2: Thresholds for multipactor and corona discharges in air as functions of pressure together with the multipactor vacuum threshold as a reference level. Parameters used are: σc = 6.9 × 10 −20 m 2 , W1 = 23 eV, k = 2.5, N = 1, f × d =1 GHz·mm and d = 0.1 m. 40 10 1 10 2
stability factor becomes: G = (νc ω ω (CΦ − 1) + C (Φ − 1))tan α + 1 − C νc ω νc (1 − CΦ)tan α − (CΦ + 1) (3.8) where C = (k + 1)/(k − Φ). In Fig. 3.3 the phase limits, where |G| = 1, have been plotted together with the non-returning electron limit. Both the positive and negative phase error limits tend to decrease with increasing pressure. However, the limit for non-returning electrons increases, which is a more important limit when the electron impact energy exceeds the first cross-over energy, thus reducing the width of the multipactor zone. Phase limit (degrees) 40 20 0 −20 −40 −60 −80 10 −3 −100 Postive phase error Negative phase error Non−ret. el. in vacuum (Semenov et. al.) Numerical non−returning electron limit 10 −2 Phase Limits 10 −1 Pressure (Pa) Figure 3.3: Phase limits in a low pressure gas based on the simple analytical model. The dashed line and the solid line (dashed at the end) show the upper and lower phase limits beyond which a phase error will start growing. The dash-dot line is the phase below which emitted electrons will not be able to escape from the wall of emission. The dotted line is the phase limit obtained using Eq. (2.15) and is an approximation of the dash-dot line in the vacuum case. Parameters used are: σc = 6.9 × 10 −19 m 2 , N = 1, k = 7.6, d = 0.1 m, and W1 = 23 eV. 10 0 10 1 41
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Thesis for the degree of Doctor of
Page 3: Multipactor in Low Pressure Gas and
Page 6 and 7: Conference contributions by the aut
Page 8 and 9: viii
Page 10 and 11: 3.2.4 Key findings . . . . . . . .
Page 12 and 13: xii
Page 14 and 15: xiv
Page 16 and 17: addition, it is difficult to make c
Page 18 and 19: numerical study of the phenomenon i
Page 20 and 21: to physically damage microwave comp
Page 22 and 23: odd positive integer (N = 1,3,5...)
Page 24 and 25: σ se [−] 2.5 2 1.5 1 0.5 W 1 W m
Page 26 and 27: Voltage [V] 10 4 10 3 10 2 10 0 N=1
Page 28 and 29: even though it may be sufficient fr
Page 30 and 31: where φL and φR are the left and
Page 32 and 33: (cf. Fig. 2.7). When taking the env
Page 34 and 35: 2.1.4 Methods of suppression Many o
Page 36 and 37: Noise (dBm) Power #1 (dBm) Match #1
Page 38 and 39: andom spread in emission velocities
Page 40 and 41: Figure 2.12: Multipactor experiment
Page 42 and 43: where kn is a factor determining th
Page 44 and 45: allows for another design margin, w
Page 46 and 47: Boundary function Method One of the
Page 48 and 49: 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 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 102 and 103: G 50 45 40 35 30 25 20 15 10 5 0.2
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creasing ratio Ri/Ro was observed.
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Chapter 6 Detection of multipactor
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Amplitude of acceleration [Gm/s 2 ]
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tipactor events that are short-live
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software and the time evolution of
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ditional test sample, a resonant ca
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the FFT. It was concluded that ther
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6.2.1 Single carrier When using the
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Reference signal generator Phase co
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Amplitude [A.U.] 2.5 2 1.5 1 0.5 De
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Chapter 7 Conclusions and outlook T
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tioned there were multipactor in no
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References [1] W. Henneberg, R. Ort
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[27] A. Ruiz et al, “Ti, V, and C
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[51] D. Wolk, D. Schmitt, and T. Sc
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[75] R. Udiljak, Multipactor in low
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Included papers A-F 123
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Paper B R. Udiljak, D. Anderson, M.
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Paper D R. Udiljak, D. Anderson, M.
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Paper F V. E. Semenov, N. Zharova,
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Multipactor in Low Pressure Gas and in ... - of Richard Udiljak

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