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

energy for the first order of resonance, as indicated by Fig. 3.7. However,
this figure only shows the behaviour for a given pd-product and in order
to see what happens when the gas density increases, the threshold can be
plotted as a function of the pd-product. This has been done in Fig. 3.9
for a material with a low first cross-over energy and, as expected, the
threshold increases with increasing pressure for the lowest order mode,
N = 1, and after reaching a maximum, the threshold starts to decrease
again. For higher order modes, the threshold decreases monotonically
as the gas becomes dense enough to affect the multipacting electrons.
This behaviour is identical to that found by Gilardini [53] in his Monte
Carlo simulation of low pressure multipactor. He also observed that for
materials with a higher first cross-over point, the threshold does not
increase with increasing pd, instead it falls off monotonically, which is
the behaviour shown in Fig. 3.10. The main reason for this difference
in behaviour is the contribution of electrons from collisional ionisation,
which increases drastically when the electron energy is well above the
ionisation threshold.
Normalised Voltage
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
10 −2
10 −1
10 0
Pressure × gapsize [Pa⋅mm]
Figure 3.9: Normalised multipactor thresholds for varying pd. The thresholds
are normalised with respect to the vacuum threshold. Curves for
the three first orders of resonance are shown. Parameters used
are: W1 = 23 eV, W0 = 3.68 eV, σse,max(0) = 3, ɛ0 = 0, fdN=1 =
0.6 GHz·mm, fdN=3 = 2.4 GHz·mm, and fdN=5 = 4.2 GHz·mm.
For higher order of resonance, N > 1, Gilardini found no difference
in the basic behaviour regardless of material. The threshold falls off
N=1
N=5
N=3
10 1
53