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

possible for quite large Ro/Ri-values. In the simulations by Sakamoto et
al [64], the experimental results were confirmed. In addition, single-sided
multipactor was observed, which confirms the result of this theoretical
study.
Among the more important results of this part of the study are the
following. The analytical approximate solution of the nonlinear differential
equation of motion for an electron in a coaxial line. The dual regions
of stable phase, Eqs. (5.13) - (5.17), which explain why single-sided multipactor
will be possible also for smaller values of Ro/Ri. The scaling
law for single-sided multipactor, Eq. (5.19), simplifies the presentation
of multipactor prone regions of the single-sided case. The limit formula
for the transition from double- to single-sided multipactor, Eq. (5.7), is
an interesting feature for future experiments to confirm. The reduced
threshold for the first order zone of single-sided multipactor, which must
be taken into account when constructing the lower boundary of all the
zones. Finally, this analysis shows that the behaviour of resonant multipactor
is significantly affected by the nonuniform field and it shows the
benefits of analytically studying different geometries to understand the
basic behaviours before performing numerical simulations.
5.2 Particle-in-cell simulations
In this part of the coaxial study, which is based on paper F, extensive
PIC-simulations have been performed in order to verify the analytical
results as well as to investigate the importance of initial velocity spread
and different maximum secondary emission. One of the advantages with
PIC-simulations is the ability to include parameters that are stochastic
in nature. The stochastic properties of some of the parameters as well
as the actual value of the maximum secondary emission coefficient may
have significant effects on the multipactor threshold as well as on the
existence of a discharge. This has previously been shown in the case
of plane-parallel geometry [46] and it is demonstrated that the effect is
similar also in coaxial geometry.
5.2.1 Numerical implementation
The geometry and field is described in the analytical section. The code
uses normalised parameters such as G and λ and the SEY follows the
model by Vaughan [22]. The initial velocities of the secondary electrons
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