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

Phase [degrees]
60
50
40
30
20
10
α 3
0
0 5 10
N (rf−cycles)
15 20
α 2
α 1
Figure 5.5: Stable resonant phase for single-sided multipactor. Analytically
obtained stable phases are shown as diamonds (red) and the ones
obtained numerically are indicated with dots (blue). Eqs. (5.15) -
(5.17) are shown as solid lines. The dashed line indicates α =
π/4 .
zones as there are phases that are smaller than π/4 (cf. Fig. 5.5), which
will yield a higher impact velocity and consequently a lower threshold.
Furthermore, in the numerical solution of Eq. (5.2) for the first order
mode, an impact velocity of as much as four times Vω,o can be observed.
This results in a threshold much lower than the envelope. The maximum
impact velocity of the second zone is slightly lower than 2Vω,o, resulting
in a somewhat higher threshold. The following higher order modes then
quickly converge to the analytical limit (cf. Fig. 5.6).
When the initial velocity is zero, the only parameters left to vary are
G and the ratio Ro/Ri. Since the characteristic impedance in ohms of
a coaxial line in vacuum is given by Z ≈ 60ln (Ro/Ri), it follows that
only two parameters remain to be varied, viz. G and Z. By following
trajectories for different values of G and Z, stable phase points were
found in this parameter space and the result is plotted in Fig. 5.7, which
was produced using a numerical solution of the equation of motion (a
version of this figure using the analytical expressions can be found in
paper E).
The straight lines in Fig. 5.7 on the right hand side are regions of
stable single-sided resonances. The fact that these appear as straight
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