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

the increased threshold is losses of electrons out of the iris region [60]. In
this analysis, we show that one of the contributing factors to this electron
loss is a random drift due to the axial component of the initial velocity
of the secondary emitted electrons. Other loss mechanisms, which are
due to the inhomogeneity of the field, tend to further enhance the losses
and these effects will be more pronounced for small gap lengths. This
means that by taking only losses due to the random drift into account,
a conservative increase of the breakdown threshold should be obtained.
4.1 Model and approximations
The geometry used in the model is the 2-dimensional structure shown
in Fig. 4.1. The iris has a gap height h in the y-direction, a length l
in the z-direction and is assumed to be fitted into a waveguide with a
height that is much greater than h. The harmonic electric field E is
assumed uniform in the gap, as a simple approximation of the actual
field. There are two main reasons for choosing a uniform field. Firstly,
the deterministic model developed for the parallel plate case, which is
described in chapter 2, can be used to describe the basic behaviour
of an electron trajectory inside the gap. Secondly, the effect of the
initial velocity spread of the secondary electrons along the z-axis on the
multipactor threshold can be analysed separately from the drift force due
to inhomogeneities in the electric field. In addition, it gives a convenient
base for comparing the results with those of the parallel plate model.
By assuming a uniform E-field in the y-direction, the electron motion
along the z-direction is not affected by the field. The motion in this
direction, the drift motion, will occur with a fixed velocity vz between
the impacts. Lets assume that a seed electron is emitted inside the gap at
the coordinate z0, −l/2 < z0 < l/2, at one of the walls. As the electron
traverses the gap and hits the opposite side of the iris, it has become
displaced a distance ∆z in the z-direction. This drift is determined by
the velocity in the z-direction, vz , together with the transit time, tg,
and is given by ∆z = vztg. For a fixed mode order, N, and frequency,
f, of the field, each transit time is the same and is given by,
tg = Nπ
, (4.1)
ω
where ω = 2πf.
The electron trajectory in the z-direction will perform a random
walk with a change of velocity, vz, after each impact. When the impact
60