
476 Microwave Engineering
circuit, V
0
is the (dc) anode voltage and I
0
is the (dc) anode current. Thus, the
RF power generated by electrons can be given by
P V I P V I I
m
e
E
B
N V
C
Q
z L
gen loss
= − = − + =
0 0 0 0 0
0
2
2
2
0
2
1
2
β
max
| |
(12.120)
In Equation 12.120, N is the total number of resonators, V is the RF voltage
across the resonator gap, E
max
(= M
1
|V|/L) is the maximum electric eld,
β
is
the phase constant, B
z
is the magnetic ux density, L is the centre-to-centre
distance between the vane tips and M
1
is the gap factor for a
π
-mode opera-
tion. The gap factor M
1
is given by
M
n n1
2 2= sin( ) ( )β δ β δ/ / /
(12.121)
M
1
≈ 1 for small values of ...