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

The step-like behaviour of the increasing threshold is due to the fact
that several multipactor zones are involved (f · h ≈ 11.5 GHz·mm).
Starting with mode number N = 7 for ’current model a)’, the lower
threshold for the parallel-plate case is found and as the h/l-ratio increases,
the zone corresponding to N = 7 shrinks until, with an almost
sudden voltage step, the next threshold, being determined by the N = 5
zone, is reached. Finally the last N = 3 zone determines the threshold
before it also vanishes.
In addition to the experimental comparison, Fig. 4.5 brings forward
the importance of different parameters of the current model as well as of
the used model for SEY [22]. By increasing the initial velocity (’current
model b)’), the overall threshold decreases as a lower field strength will
be sufficient to reach the same impact velocity (cf. Eq. (2.7)). The effect
of an increased thermal spread, WT, is that the electron losses increases
and the threshold starts to increase for lower h/l-values (also shown
in ’current model b)’). By lowering the first cross-over point (’current
model c)’), the parallel-plate threshold decreases, since an additional
zone, N = 9, comes into play. However, as it shrinks away, the threshold
increases in a sudden step to the same level as in case ’a)’ and then it
follows ’a)’ except that the steps occur at higher h/l-values. An increased
first cross-over point, case ’d)’, shows a change of behaviour opposite to
’c)’, except for the parallel-plate threshold as it is still the N = 7 zone
that determines this threshold.
In the current model a uniform electric field has been used. Due to
the geometry of the iris, the actual electric field will tend to be curved
outwards at the edges of the slot instead of being straight (cf. Fig. 4.1).
Since the field amplitude is higher in the centre of the iris than at the
edges, the Miller force [10], which is proportional to the negative gradient
of the square of the electric field amplitude, will tend to push the
electrons out of the iris. This effect is most important for the higher
order resonances, where several RF-cycles are required to cross the gap.
In addition to the Miller force, the curved electric field will have a component
in the z-direction, which, in particular for the first order mode,
will drive the electrons toward the iris edges. This means that the electron
losses will be greater than in the case of a uniform field, which
will lead to an even further increase of the multipactor threshold. This
effect should be more pronounced for thin irises and could explain why
the current model predicts the existence of a discharge beyond a certain
h/l-ratio where experiments cannot detect it (cf. Fig. 4.5).
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