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

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of detection. The global methods are characterised by being able to discern whether or not microwave breakdown is taking place somewhere within the tested system. However, it can not pinpoint the location of the discharge. For flight hardware it is important to completely avoid multipactor in the entire microwave system and consequently this type of testing is preferred. During the product development stage, it may be of interest to know not only that a discharge is taking place, but also its exact position within the system. In such a case, a local method can be useful, since it can be used to monitor a certain area inside a device. 6.1.1 Global methods When performing systems tests on flight hardware, global methods of detection are normally used and there are several reasons for this. The methods can usually be applied without modifying the component, which is advantageous as modifications can affect the electromagnetic properties and give inadequate measurement results. In cases where the discharge is weak, many local methods are unable to detect the phenomenon and thus the often more sensitive global ones are a better choice. Furthermore, it is a requirement of the ESA standard [50] that two methods of detection should be used and at least one of them should be global. By using two methods of detection, the risk for misinterpretations is reduced. The most common global methods of detection will be described in the following subsections. Close-to-carrier noise Multipacting electrons will be accelerated to high velocities by the electric field and at regular intervals, 2/N times per field cycle, the electrons will hit an electrode or device wall and experience a sudden deceleration. The radiated power is a function of the electron acceleration and it is described by Larmor’s formula, P = 2 e 3 2 ˙v 4πɛ0 2 c3 (6.1) where ˙v is the acceleration, ɛ0 the dielectric constant of vacuum, and c the speed of light. For an applied sinusoidal electric field, the electrons will experience a sinusoidal acceleration, except for the sudden interruptions when colliding with the electrodes. Fig. 6.1 shows what the acceleration may look like for first order multipactor (N = 1), where the electrons hit the electrodes once every half cycle of the electric field. 94
Amplitude of acceleration [Gm/s 2 ] x 10 1.5 6 C2C−Noise Timedomain 1 0.5 0 −0.5 −1 −1.5 1.76 1.78 1.8 1.82 1.84 1.86 x 10 −8 Time (s) Figure 6.1: A qualitative plot of the electron acceleration for multipacting electrons with N = 1 (average value for a large number of electrons). The regular deviation from a pure sinusoid will generate harmonics, but these will be discussed in the next subsection. Due to variations in the time between impact and emission of new electrons, in the time it takes to decelerate the electrons, and also in the number of electrons, close-to-carrier noise will be generated. In fact, most noise is generated at the carrier frequency, but this can not be seen in a measured spectrum, as the signal amplitude masks the noise. By performing a Fast Fourier Transform (FFT) of a sequence like the one shown in Fig. 6.1, the noise generated close to the carrier can be seen (see Fig. 6.2). Very close to the carrier, the noise level is even higher than what can be discerned in Fig. 6.1 and by using a bandpass filter with high rejection at the carrier frequency, the noise increase close to the carrier can be detected with a spectrum analyser. In combination with a low-noise amplifier, this can be a very sensitive method of detection. This method of detection can be used for both single and multicarrier signals. Care should be taken, however, when using a pulsed signal, since such a signal will generate harmonics and if the pulse length and type is not chosen properly, the harmonics may be generated in the measurement band [31]. A risk with this method is that other sources of 95
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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
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where φL and φR are the left and
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(cf. Fig. 2.7). When taking the env
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2.1.4 Methods of suppression Many o
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Noise (dBm) Power #1 (dBm) Match #1
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andom spread in emission velocities
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Figure 2.12: Multipactor experiment
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where kn is a factor determining th
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allows for another design margin, w
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Boundary function Method One of the
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carriers, because the NLSQ method r
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multipactor discharge. Using a Mont
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the assumption of a constant ratio
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Voltage (V) 10 3 10 2 10 1 10 −2
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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,
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: Chapter 6 Detection of multipactor
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
Page 133 and 134: [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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