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

h
l
Figure 4.1: The geometry used in the considered model.
coordinate is outside the iris area |z| > l/2, i.e. one of the gap edges
has been passed, the electron trajectory is lost. The probability of survival,
p(k) (see Fig. 4.2), for the electron trajectory decreases with the
number of transits, k, and for a general one-dimensional random walk
problem, with the jump size governed by a continuous distribution function,
Φk(z), an explicit solution for this, the first passage time problem,
is not always possible. However, in paper D it is explained that the
asymptotic behaviour of p(k) is determined by the largest eigenvalue γ0
of the expansion of Φk(z), i.e.
E
y
p(k) ∝ γ k 0 . (4.2)
A detailed description of how to determine p(k) is given in paper D
together with approximate solutions for γ0 when the normalised iris
length, η = l/(vTtg), is either very small or very large. This summary,
however, will focus on the effect the random electron drift has on the
multipactor susceptibility zones.
Each seed electron inside the iris gap will start to multiply with the
successive wall collisions. Due to the stochastic losses, the number of
electrons will sometimes become large and sometimes small. However, if
on average the generation of electrons due to wall collisions is larger than
the loss over the gap edges, there is a finite probability that a sufficiently
z
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