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

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The step-like behaviour of the increasing threshold is due to the fact that several multipactor zones are involved (f · h ≈ 11.5 GHz·mm). Starting with mode number N = 7 for ’current model a)’, the lower threshold for the parallel-plate case is found and as the h/l-ratio increases, the zone corresponding to N = 7 shrinks until, with an almost sudden voltage step, the next threshold, being determined by the N = 5 zone, is reached. Finally the last N = 3 zone determines the threshold before it also vanishes. In addition to the experimental comparison, Fig. 4.5 brings forward the importance of different parameters of the current model as well as of the used model for SEY [22]. By increasing the initial velocity (’current model b)’), the overall threshold decreases as a lower field strength will be sufficient to reach the same impact velocity (cf. Eq. (2.7)). The effect of an increased thermal spread, WT, is that the electron losses increases and the threshold starts to increase for lower h/l-values (also shown in ’current model b)’). By lowering the first cross-over point (’current model c)’), the parallel-plate threshold decreases, since an additional zone, N = 9, comes into play. However, as it shrinks away, the threshold increases in a sudden step to the same level as in case ’a)’ and then it follows ’a)’ except that the steps occur at higher h/l-values. An increased first cross-over point, case ’d)’, shows a change of behaviour opposite to ’c)’, except for the parallel-plate threshold as it is still the N = 7 zone that determines this threshold. In the current model a uniform electric field has been used. Due to the geometry of the iris, the actual electric field will tend to be curved outwards at the edges of the slot instead of being straight (cf. Fig. 4.1). Since the field amplitude is higher in the centre of the iris than at the edges, the Miller force [10], which is proportional to the negative gradient of the square of the electric field amplitude, will tend to push the electrons out of the iris. This effect is most important for the higher order resonances, where several RF-cycles are required to cross the gap. In addition to the Miller force, the curved electric field will have a component in the z-direction, which, in particular for the first order mode, will drive the electrons toward the iris edges. This means that the electron losses will be greater than in the case of a uniform field, which will lead to an even further increase of the multipactor threshold. This effect should be more pronounced for thin irises and could explain why the current model predicts the existence of a discharge beyond a certain h/l-ratio where experiments cannot detect it (cf. Fig. 4.5). 66
4.4 Main results This analysis has shown that the random electron drift along the iris length due to the initial velocity of the secondary electrons tends to significantly increase the multipactor threshold in a waveguide iris as compared to predictions based on the classical two parallel-plate model. Inherent in the presented model is the scaling parameter h/l, which makes it possible to produce useful multipactor susceptibility charts in the traditional engineering units. An increase in the h/l-ratio results in a shrinkage of each multipactor resonance zone. For each zone, the zone reduction effect is more pronounced for lower frequencies. A consequence of this is that the multipactor free region in the parallel plate model at low frequency-gap-height products grows with increasing h/l-ratio. 67
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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
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 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: to compensate for electron losses i
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
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
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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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