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

Probability of survival
1
0.8
0.6
0.4
0.2
0
l=2 mm
l=8 mm
l=16 mm
50 100 150 200 250 300 350 400 450 500
Number of collisions
Figure 4.2: The probability of survival, p(k), for an electron emitted in the
center of the iris gap, z = 0, for three different iris lengths. Parameters
used: f = 1 GHz, N = 1, and WT = 2 eV (corresponding
to vT, the rms-velocity of the Maxwellian distribution
of initial velocity in the z-direction).
strong discharge will appear. The generated number of electrons over
the initial number of electrons after k collisions is given by,
Ne
N0
≡ g(k) = p(k)σ k se. (4.3)
Depending on the start position of the seed electrons, the initial behaviour
of Ne can vary. If the start position is close to the iris edge,
the average electron number will first decrease and then if σse is large
enough, it will start increasing again. But if the start position is in
the center, it may first start to increase, but after a number of transits,
it will start decreasing (cf. Fig. 4.3). Eventually, it is the asymptotic
behaviour of p(k) that will determine whether or not there will be a
discharge. Thus from Eq. (4.2) and Eq. (4.3) one can conclude that the
asymptotic change in the electron number is given by,
g(k) ∝ (σseγ0) k . (4.4)
Thus the average number of electrons will grow if
62
σseγ0 > 1 (4.5)