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

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σ se [−] 2.5 2 1.5 1 0.5 W 1 W max Secondary electron yield σ se =1 0 0 500 1000 1500 2000 2500 Primary electron energy [eV] Figure 2.2: Secondary electron yield as a function of the impact energy. Plotted using the formula for secondary electron yield presented in Ref. [22]. Parameters used are: Wmax = 400 eV, σse,max = 2, and Wzero = 10 eV. 10 W 2
solution or some kind of approximate solution will have to be used. In Ref. [21] an approximate formula for the non-returning electron limit is given and re-writing it for the constant v0 approach yields, � 16v0 αmin = − (2.11) 5v0 + 3vimpact Using Eqs. (2.6), (2.9), and (2.11) with v1 equal to the velocity corresponding to the unity secondary electron yield, the lower multipactor threshold can be plotted. However, multipactor breakdown is possible also for impact velocities greater than v1, in fact, for all impact velocities between the first and second (v2) cross-over points, the phenomenon can occur, i.e. for v1 < 2Vω cos α + v0 < v2 , (2.12) where Eq. (2.7) has been re-written using the oscillatory velocity Vω = eE0/mω. Thus, in order to construct the complete multipactor boundaries, the thresholds for a number of different energies between these two points should be determined and then the envelope of all the thresholds will be the complete multipactor susceptibility zone (see Fig. 2.3). Furthermore, each order of resonance, N, will have its own zone and, as shown in Fig. 2.3, the zones become narrower with increasing N. This type of chart, based on the assumption of constant initial velocity, will be referred to as a Sombrin chart, since J. Sombrin is one of the major advocates of this assumption [29]. Using the other approach, with a constant ratio between the impact and initial velocities, k = vimpact/v0, the formulas for the resonant phase, Eq. (2.9), the amplitude, Eq. (2.6), and the non-returning electron limit, Eq. (2.11), will have to be slightly re-written: tan α = 1 k − 1 E0 = e( k+1 k−1 αmin = − � kωd v1 mω 2 d − (k + 1)N π 2 Nπ cos α + 2sin α) � 16 8 + 3(k − 1) � (2.13) (2.14) (2.15) Using these formulas, multipactor charts similar to the one in Fig. 2.3 can be produced, cf. Fig. 2.4. When this is used, the charts are commonly referred to as Hatch and Williams charts, as they were the first 11
Page 1 and 2: 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 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 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
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to compensate for electron losses i
Page 81:
4.4 Main results This analysis has
Page 84 and 85:
support for the qualitative analyti
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where R(t) is the average position,
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where d stands for the gap width, V
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there are different oscillatory vel
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Phase [degrees] 60 50 40 30 20 10
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G 100 90 80 70 60 50 40 30 20 10 0
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possible for quite large Ro/Ri-valu
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upper right region of the figures,
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σse,max the zones become wider and
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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
Page 109 and 110:
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
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
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Chapter 7 Conclusions and outlook T
Page 127 and 128:
tioned there were multipactor in no
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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
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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Multipactor in Low Pressure Gas and in ... - of Richard Udiljak

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