
421Microwave Tubes
The value of 2I
0
J
n
(nX)|
n=1
= 2I
0
J
1
(X) = I
f
is the fundamental component of
beam current (i
2
), which has its maximum value at X = 1.841. The optimum
distance (L
opt
) at which this fundamental component (I
f
) becomes maximum
is given by
L
V
V
i
opt
=
3 682
0 0
1
. υ
ωβ
(12.20)
In Equations 12.19 and 12.20, I
0
is the dc current, J
n
(nX) is the Bessel’s func-
tion of order n and argument (nX), and
β
i
is the beam coupling coefcient.
Parameters X, V
0
, V
1
,
υ
0
, T
0
,
τ
and t
2
were given earlier.
Induced current (i
2 ind
) in catcher cavity
i
2 ind
=
β
0
i
2
=
β
0
2I
0
J
1
(X) sin{
ω
(t
2
−
τ
− T
0
)} (12.21)
where
β
0
is the beam coupling coefcient of the catcher ...