
416 Microwave Engineering
When a microwave signal is applied to the input terminals of the buncher
cavity, its gap voltage in grid space will appear as
V
s
= V
1
sin(
ω
t) (12.2)
As assumed, V
1
≪ V
0
, the average transit time (
τ
) through the buncher gap
(d) is
τ
≈ d/
υ
0
= t
1
– t
0
(12.3)
The voltages (V
s
and V
1
), times (t
1
and t
0
) and buncher gap d are shown in
Figures 12.1 and 12.4.
The average gap transit angle can be written in terms of average transit
time (
τ
) as
θ
g
=
ωτ
=
ω
(t
1
− t
0
) =
ω
d/
υ
0
(12.4)
The average microwave voltage in buncher gap can be obtained by inte-
grating V
s
, dividing the outcome by average transit time (
τ
), and on using
Equation ...