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

where φL and φR are the left and right limits respectively. This difference
is illustrated graphically in Fig. 2.6. However, when v0 ≪ vimpact both
approaches yield the same phase stability limits.
Voltage [V]
10 3
10 2
10 1
Unstable phase range (constant v 0 )
Stable phase range (constant v 0 )
Unstable phase range (constant k)
Stable phase range (constant k)
N=1
10 0
Frequency − Gap product [GHz⋅mm]
Figure 2.6: Lower multipactor thresholds in vacuum for the first 3 orders
of resonance (N = 1, 3, and 5). The curves for the constant k
model are plotted slightly offset as the curves otherwise overlap.
Parameters used are: W1 = 23 eV , W0 = 3.68 eV, and k = 2.5.
Saturation
In order to sustain a multipactor breakdown, the secondary electron
emission yield must be greater than or equal to unity. If the yield is less,
the electron number will quickly decrease and the discharge disappears.
With a σse greater than unity the electron number will grow rapidly with
each impact and if no saturation mechanism is considered the number
of electrons after a time t, if the field frequency is f, will be:
N=3
N=5
Ne(t) = Ne(0)(σse) 2ft
N (2.22)
The rapid growth of the number of electrons can be illustrated with
an example. Suppose σse = 1.5 and f = 2 GHz, then the number of
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