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

analytical. Attempts were made to find a purely analytical implementation
as well, but due to the strong non-linearities in the functions for the
cross-sections, no accurate such implementation could be found. Details
concerning the two implementations are presented in paper C and will
not be reproduced here.
As mentioned in chapter 2, when constructing the complete multipactor
zones, the multipactor thresholds corresponding to impact velocities
between the first and second cross-over points are determined
for a specific order of resonance within the phase range from the nonreturning
electron limit to the upper phase stability limit. The zone
for that order of resonance is then the envelope of all these curves (cf.
Fig. 2.3). However, to explore the basic effects on the multipactor phenomenon,
it is sufficient to study the threshold corresponding to unity
SEY. Thus, in most of the following charts, only the lower multipactor
threshold will be considered. However, in keeping with the multipactor
tradition, the complete zones will be presented as well.
One concern that appears when making low pressure multipactor
charts is the parameters which should be used on the chart axes. Classical
vacuum multipactor charts use engineering units with voltage as a
function of the frequency-gap size product, like in Fig. 2.3. By multiplying
Eq. (3.11) by the gap size, d, to get the voltage and rearranging
Eqs. (3.12), (3.13), and (3.14), these expressions can all be written as
functions of two natural parameters, viz. fd and pd, i.e. the frequencygap
size and the pressure-gap size products. Thus, for a given pd the
multipactor zones can be constructed in the classical engineering units
as shown in Fig. 3.7. Note that three different pd-values are used, one
for each zone. The chosen values are close to the limit of stability of the
numerical implementation for each zone.
In Fig. 3.7 both the analytical (semi-analytical) and the numerical
implementations are used to plot the thresholds. Very good agreement
between the two implementations is found and therefore the faster analytical
version is used to produce all other figures. The most striking
first impression of the graphs in Fig. 3.7 is the difference in behaviour
between the first and the higher order modes. The first order mode
shows an increased threshold, which is a consequence of the friction
force experienced by the electrons due to collisions with neutrals. This
is in agreement with the model presented in paper B, which only considered
the friction force. However, for higher order modes, the result
is the opposite. Instead of an increased threshold as in the friction
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