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

andom spread in emission velocities was done by Riyopoulos et al. [33].
They found that by including the effects of these random parameters,
the effective secondary electron yield, σ ∗ se, was reduced to a number in
the range σse/2 < σ ∗ se < σse. This means that the effective secondary
electron yield will be a function not only of the impact velocity, but also
of the resonant phase as well as the phase spread caused by the spread
in initial velocities and secondary delay times. Another study, which
supports this result, investigated the effect on the different resonance
zones for different values of the maximum SEY due to initial velocity
spread [46]. It was found that, except for the first order mode, a realistic
thermal spread of the initial electrons raised the multipactor SEY
requirement from unity to above unity. For the higher order modes a
SEY greater than approximately 1.5 was necessary to compensate for
the losses incurred. In addition, with increasing velocity spread, the
multipactor zones started to overlap. The increased SEY requirement
will result in an increased threshold for the higher order modes and can
explain the success with increasing the first cross-over point in the Hatch
and Williams charts when fitting experimental data (see Fig.2.5).
The importance of the spread in initial velocities can be seen when
constructing multipactor charts for a constant initial velocity without allowing
compensation for electron losses outside the phase stability range.
In Fig. 2.11 zones bounded by solid lines indicate the region where multipactor
can take place under this assumption. The dashed lines make
up wider zones that encompass the other zones and are identical to the
zones shown in Fig. 2.3.
By including a higher secondary electron yield and a spread in initial
velocities, the multipactor zones will become wider than the solid
line zones. A σse greater than unity, which will be the case when the
impact velocity is greater than the first cross-over point, will compensate
for some of the losses incurred due to phase instability. A spread
in initial velocities will widen the range of possible resonant phases (cf.
Eq. (2.9)) and the left and right limits will not be as sharp as indicated
by the solid line multipactor zones in Fig. 2.11. This widening of the
multipactor zones has been taken into account to a certain extent in the
traditional analytical approach, which is indicated by the wider dashed
line zones in Fig. 2.11. However, the widening should not only be towards
the left side, but also towards the right [39]. Furthermore, the
sharp lower left corner of each dashed line zone is misleading, as that
indicate a point where the secondary electron emission is unity and the
24