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

lines indicates that there is no dependence on Z, which implies that a
simple scaling law exists in the single-sided case, viz.
P ∝ (ωRo) 4 Z. (5.19)
In Fig. 5.6 this law has been used to normalise the axes, but voltage
is used on the ordinate instead of power. The chosen normalisation
of the axes in Fig. 5.6 is general and using the analytical solution of
Eq. (5.2) presented above, it can be shown that this normalisation is
valid also for non-zero initial velocity. It is important, however, to be
careful when scaling to a different radii ratio, since for smaller values
of the characteristic impedance, the single-sided multipactor zones may
not exist at all.
In the double-sided case, it is evident that G is a function of Z.
Consequently a more complicated scaling law should be expected. For
small values of Z, however, the coaxial case becomes similar to the
parallel-plate geometry, where the resonance voltage can be written as
function of the frequency-gap-size product. For the coaxial case, this
scaling law becomes
P ∝ (ω(Ro − Ri)) 4 1
. (5.20)
Z
and for the first order resonance this scaling law is quite accurate (cf.
Fig. 5.3), but for the higher order modes it quickly loses its validity with
increasing Z.
5.1.3 Main findings
A qualitative comparison with experiments [63] shows good agreement
with the present analysis. The experimental data shows an increase in
the multipactor threshold for increasing radii-ratio Ro/Ri. It was also
found that the first multipactor zone became narrower for increasing
Ro/Ri. These features are in agreement with the results of this study
as shown in Figs. 5.3 and 5.7. By mapping the data of Fig. 5.3 into the
voltage vs. frequency-gap-size space, used in the experiments, a clear
threshold increase compared with the parallel-plate case can be seen as
well. Even though the experiments used quite large values of Ro/Ri,
no case of single-sided multipactor was observed. This can be explained
by the fact that a material with a low first cross-over point was used,
where the initial velocity will play an important role when the applied
voltage is not high enough. More importantly, only the first order mode
was studied and in this case, as shown in Fig. 5.3, multipactor will be
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