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

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3.1.3 Main results The main result found in paper B is that a higher microwave power is required to initiate breakdown in a low pressure gas, since the collisions tend to slow down the electrons. By combining the low pressure multipactor graph with the corona threshold curve, it was concluded that with increasing pressure, the required threshold will first increase and, after reaching a plateau, it will make a smooth transition to the low pressure branch of the Paschen curve. This behaviour is confirmed by the investigations made by Gilardini [53] for materials with a low first cross-over point, close to the ionisation energy of the gas, and for N = 1, i.e. for the first order of multipactor. For materials with a higher first cross-over energy and for higher order multipactor, Gilardini found no initial increase in the multipactor threshold, instead a monotonically decreasing breakdown voltage was seen. A possible explanation for the differences between the result obtained by the simple analytical model and the result of Gilardini is also presented in paper B and it is suggested that the reason is that for materials with a higher W1 and for N > 1 the contribution of electrons from impact ionisation decreased the required W1 (see Fig. 3.4). However, as will be seen in the next section, electron contribution from impact ionisation is not the only reason for this behaviour. The collisions will also cause an electron velocity spread, which will result in a larger total impact velocity and thus a lower voltage is needed to achieve the necessary first cross-over energy. A comparison was made with experiments by Höhn et al. [18] in low pressure argon as well as with PIC-simulations by Gilardini [54] in the same gas (see Fig. 7 in paper B). However, the fd-product chosen by these authors was located in the middle of the right boundary of the first multipactor zone, an area dominated by the hybrid modes [39]. The simple model used in the presented analytical approach is not applicable to these modes and consequently the behaviour found in the experiments and simulations could not be confirmed. Furthermore, the impact energy of the electrons at this fd-product is several times higher than the ionisation energy of argon and thus a significant contribution of electrons from collisional ionisation would be expected. In addition, the required W1 would be reduced due to the electron velocity spread and thus a behaviour similar to curves (b) or (c) in Fig. 3.4 should be expected and it is also what is found. To further analyse multipactor in a low pressure gas, a better ana- 42
Voltage (V) Threshold curves in a low pressure gas Multipactor in a low pressure gas without ionisation Multipactor in vacuum Corona a b c Pressure (Pa) Figure 3.4: Qualitative form of the dependence of breakdown threshold with pressure in the region between which multipactor and corona, respectively, dominate the breakdown process: (a) the friction force due to collisions with neutrals dominates, (b) electron velocity spread reduces the required W1 and collisional ionisation contributes significantly to the total number of electrons, (c) intermediate situation. 43
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Thesis for the degree of Doctor of
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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 54 and 55: Voltage (V) 10 3 10 2 10 1 10 −2
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
Page 104 and 105: 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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