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

there are different oscillatory velocities depending on whether the electron
starts on the outer or the inner conductor, an average value must
be computed. By setting Vω,o = qEo/mω = v1/2 the corresponding voltage,
VRo, can be derived. Similarly, by setting Vω,i = qEi/mω = v1/2
the voltage VRi can be obtained. The lower threshold voltage is then
approximately equal to:
Uth ≈ VRo + VRi
. (5.12)
2
The upper threshold is computed in a similar manner, only with v2
instead of v1. The hybrid modes, which in general have a lower average
impact velocity will require a stronger electric field to reach an energy
equal to the first cross-over point. Consequently, a threshold higher than
the lower envelope is obtained for these zones (cf. Fig. 5.4).
Amplitude of Conductor Voltage [V]
10 4
10 3
10 2
1 c
2 h
Double sided multipactor: Z c = 20Ω
3 c
10 0
4
Frequency [GHz]
Figure 5.4: Numerically obtained double sided multipactor chart. The
dashed lines are the approximate lower and upper envelopes given
by Eq. (5.12). The sum of the transit time in RF-cycles for each
zone is indicated. Parameters used: W1 = 23 eV, W2 = 2100 eV,
W0 = 0 eV, Ro = 10 mm, and Ri = 7.2 mm.
If the inner radius is sufficiently small, single-sided multipactor becomes
the dominating scenario. Single-sided multipactor is less complicated
than its double-sided counterpart, as the complicated asymmetry
does not appear in this case. This allows an analytical analysis based
76
7
6
10 1