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

even though it may be sufficient from an engineering point of view. On
the other hand, the higher order modes have a narrower phase-focusing
range (see below), which makes it difficult to compensate for e.g. initial
velocity spread, and thus a secondary yield of unity may not be sufficient
to sustain a discharge. Consequently, an impact energy somewhat
higher than the first cross-over point will be needed when constructing
the lower multipactor threshold for the higher order modes. This will
be discussed further in the subsection “Effect of random emission delays
and initial velocity spread.”
Voltage amplitude [V]
10 4
10 3
10 2
10 0
10 1
Frequency − Gap product [GHz⋅mm]
Figure 2.5: Hatch and Williams charts for aluminium together with measurement
data by Woode and Petit [31].
When the microwave engineer assesses the risk of having a multipactor
discharge, it is usually not the boundary of the individual breakdown
region that is considered. Typically, the lower envelope of the all
the zones is taken as the “design threshold” (cf. Figs. 2.3 and 2.4). By
setting the phase, α, in Eq. (2.7) to zero, the lowest field amplitude to
achieve a certain vimpact is obtained. Thus the lower envelope, which
is the same for both the Sombrin Chart and the Hatch and Williams
chart, is given by,
E0 = (v1 − v0)mω
. (2.16)
2e
14