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

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analytical. Attempts were made to find a purely analytical implementation as well, but due to the strong non-linearities in the functions for the cross-sections, no accurate such implementation could be found. Details concerning the two implementations are presented in paper C and will not be reproduced here. As mentioned in chapter 2, when constructing the complete multipactor zones, the multipactor thresholds corresponding to impact velocities between the first and second cross-over points are determined for a specific order of resonance within the phase range from the nonreturning electron limit to the upper phase stability limit. The zone for that order of resonance is then the envelope of all these curves (cf. Fig. 2.3). However, to explore the basic effects on the multipactor phenomenon, it is sufficient to study the threshold corresponding to unity SEY. Thus, in most of the following charts, only the lower multipactor threshold will be considered. However, in keeping with the multipactor tradition, the complete zones will be presented as well. One concern that appears when making low pressure multipactor charts is the parameters which should be used on the chart axes. Classical vacuum multipactor charts use engineering units with voltage as a function of the frequency-gap size product, like in Fig. 2.3. By multiplying Eq. (3.11) by the gap size, d, to get the voltage and rearranging Eqs. (3.12), (3.13), and (3.14), these expressions can all be written as functions of two natural parameters, viz. fd and pd, i.e. the frequencygap size and the pressure-gap size products. Thus, for a given pd the multipactor zones can be constructed in the classical engineering units as shown in Fig. 3.7. Note that three different pd-values are used, one for each zone. The chosen values are close to the limit of stability of the numerical implementation for each zone. In Fig. 3.7 both the analytical (semi-analytical) and the numerical implementations are used to plot the thresholds. Very good agreement between the two implementations is found and therefore the faster analytical version is used to produce all other figures. The most striking first impression of the graphs in Fig. 3.7 is the difference in behaviour between the first and the higher order modes. The first order mode shows an increased threshold, which is a consequence of the friction force experienced by the electrons due to collisions with neutrals. This is in agreement with the model presented in paper B, which only considered the friction force. However, for higher order modes, the result is the opposite. Instead of an increased threshold as in the friction 50
Voltage [V] 10 2 Numeric stable phase Numeric unstable phase Analytic stable phase Analytic unstable phase pd=15 Pa mm 10 0 pd=7 Pa mm Frequency − Gap product [GHz⋅mm] pd=5 Pa mm Figure 3.7: Lower multipactor thresholds in low pressure argon for three different fixed pd-values, one for each zone. The dotted lines represent the multipactor zones for vacuum multipactor. Parameters used are: W1 = 23 eV , W0 = 3.68 eV, σse,max(0) = 3, ɛ0 = 0. 51
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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
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 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 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
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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
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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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