
451Microwave Tubes
υ
µε π
εp
p
p d
=
+{ ( ) }
2 2
(12.64)
A slow wave structure, with a large dielectric constant, is more lossy and
thus less efcient. For small pitch angle, the phase velocity along the coil in
free space is approximately given by
υ
π
β
p
c p
d
≈
=
(12.65)
12.5.8.1 Brillouin Diagram
Figure 12.31 shows the
ω
–
β
(or Brillouin) diagram for a helical slow wave
structure. This curve is very useful in the design of a helix. Once
β
is known,
υ
p
can be computed from Equation 12.65 for a given dimension of a helix.
The group velocity (
υ
gr
) of the wave is simply the slope of the curve and is
given by
gr
/
(12.66)
A slow wave structure has the ...