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

where kn is a factor determining the frequency spacing
kn = fn/f0 − 1, n = 0,1,...,N − 1 , (2.27)
f0 is the lowest carrier frequency and ω0 = 2πf0. When assessing the
worst case scenario from the multipactor point of view, it is important
to study a whole envelope period. For arbitrarily spaced frequencies, the
envelope period, T, can be found by solving the following Diophantine
systems of equations:
T = ni
, ni ∈ N i = 1,2,...,N − 1 (2.28)
∆fi
where N is the number of carriers, f0 is the signal with the lowest frequency
and ∆fi = fi − f0. The envelope period will be the solution
with the smallest possible integers. For equally spaced carriers, the solution
becomes n1 = 1, n2 = 2,...,nN−1 = N − 1, which is implies that
T = 1/∆f, like before.
When studying multicarrier multipactor it is common to make certain
simplifications that will allow using single carrier methodology to
asses also the multicarrier case, e.g. the mean frequency of all the carriers
is used as the design frequency. Thus, most of what has been said
about single carrier multipactor will then be valid also for the multiple
signals case.
2.3 Design guidelines
From an industrial point of view it is important not only to understand
the physics of multipactor, but also how the theoretical and experimental
results should be applied when making multipactor-free microwave
hardware designs. In Europe, most space hardware designers follow the
standard issued by ESA [50]. This standard includes both the single
and the multicarrier cases, but for the latter it is stated that the design
guidelines are only recommendations. Most research support these
recommendations, but not enough tests have been performed to verify
the theoretical findings. When using the standard it is important to be
aware of the fact that it is primarily based on the parallel-plate model
with a uniform electric field. Design with respect to this approach for
other geometries is normally a conservative and safe way. However, in
many common microwave structures, the geometry is such that losses
of electrons is much higher than in the parallel-plate case. Thus the
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