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

stability factor becomes:
G = (νc
ω
ω
(CΦ − 1) + C (Φ − 1))tan α + 1 − C
νc
ω
νc
(1 − CΦ)tan α − (CΦ + 1)
(3.8)
where C = (k + 1)/(k − Φ). In Fig. 3.3 the phase limits, where |G| = 1,
have been plotted together with the non-returning electron limit. Both
the positive and negative phase error limits tend to decrease with increasing
pressure. However, the limit for non-returning electrons increases,
which is a more important limit when the electron impact energy exceeds
the first cross-over energy, thus reducing the width of the multipactor
zone.
Phase limit (degrees)
40
20
0
−20
−40
−60
−80
10 −3
−100
Postive phase error
Negative phase error
Non−ret. el. in vacuum (Semenov et. al.)
Numerical non−returning electron limit
10 −2
Phase Limits
10 −1
Pressure (Pa)
Figure 3.3: Phase limits in a low pressure gas based on the simple analytical
model. The dashed line and the solid line (dashed at the end)
show the upper and lower phase limits beyond which a phase
error will start growing. The dash-dot line is the phase below
which emitted electrons will not be able to escape from the wall
of emission. The dotted line is the phase limit obtained using
Eq. (2.15) and is an approximation of the dash-dot line in the
vacuum case. Parameters used are: σc = 6.9 × 10 −19 m 2 , N = 1,
k = 7.6, d = 0.1 m, and W1 = 23 eV.
10 0
10 1
41