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

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andom spread in emission velocities was done by Riyopoulos et al. [33]. They found that by including the effects of these random parameters, the effective secondary electron yield, σ ∗ se, was reduced to a number in the range σse/2 < σ ∗ se < σse. This means that the effective secondary electron yield will be a function not only of the impact velocity, but also of the resonant phase as well as the phase spread caused by the spread in initial velocities and secondary delay times. Another study, which supports this result, investigated the effect on the different resonance zones for different values of the maximum SEY due to initial velocity spread [46]. It was found that, except for the first order mode, a realistic thermal spread of the initial electrons raised the multipactor SEY requirement from unity to above unity. For the higher order modes a SEY greater than approximately 1.5 was necessary to compensate for the losses incurred. In addition, with increasing velocity spread, the multipactor zones started to overlap. The increased SEY requirement will result in an increased threshold for the higher order modes and can explain the success with increasing the first cross-over point in the Hatch and Williams charts when fitting experimental data (see Fig.2.5). The importance of the spread in initial velocities can be seen when constructing multipactor charts for a constant initial velocity without allowing compensation for electron losses outside the phase stability range. In Fig. 2.11 zones bounded by solid lines indicate the region where multipactor can take place under this assumption. The dashed lines make up wider zones that encompass the other zones and are identical to the zones shown in Fig. 2.3. By including a higher secondary electron yield and a spread in initial velocities, the multipactor zones will become wider than the solid line zones. A σse greater than unity, which will be the case when the impact velocity is greater than the first cross-over point, will compensate for some of the losses incurred due to phase instability. A spread in initial velocities will widen the range of possible resonant phases (cf. Eq. (2.9)) and the left and right limits will not be as sharp as indicated by the solid line multipactor zones in Fig. 2.11. This widening of the multipactor zones has been taken into account to a certain extent in the traditional analytical approach, which is indicated by the wider dashed line zones in Fig. 2.11. However, the widening should not only be towards the left side, but also towards the right [39]. Furthermore, the sharp lower left corner of each dashed line zone is misleading, as that indicate a point where the secondary electron emission is unity and the 24
Voltage [V] 10 4 10 3 10 2 10 0 10 1 Frequency − Gap product [GHz⋅mm] Figure 2.11: Multipactor charts based on the same parameters as in Fig. 2.3. The solid line zones indicate the zones within which phasefocusing is active. The dashed line zone is produced by including also unstable phases until the non-returning electron limit. phase is very unstable, thus making a discharge impossible. A more correct boundary would be a rounded shape, which starts in the lower left corner of the solid line zone and smoothly joins the dashed left hand side [47]. This is confirmed by experiments [30,48], cf. Fig. 2.12, which shows measurement data from one of the early multipactor experiments by Hatch and Williams [48]. A similar rounded shape can also be seen in numerical simulations and examples of this is shown in chapter 5, which includes PIC simulations of multipactor in a coaxial line. 2.2 Multicarrier Modern satellites operate in multicarrier mode, i.e. several signals at different frequencies exist simultaneously in the microwave and electronic systems. An example of such a system is Sirius 3, which is one of the Nordic satellite [49]. It has 15 channels in the frequency range 11.7 - 12.5 GHz and each channel has a bandwidth of 33 MHz. Assume that each channel has a power of 200 W. Then the maximum instantaneous power of the system, the peak power, is equal to 45 kW. The peak power increases with the square of the number of carriers. Such a high instan- 25
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 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 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 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,
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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
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Amplitude of acceleration [Gm/s 2 ]
Page 111 and 112:
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
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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
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
Page 135 and 136:
[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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