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Microwave Engineering
book

Microwave Engineering

by Ahmad Shahid Khan
May 2014
Intermediate to advanced content levelIntermediate to advanced
800 pages
24h 50m
English
CRC Press
Content preview from Microwave Engineering
456 Microwave Engineering
In Equations 12.84 and 12.85,
υ
0
is the dc electron velocity,
υ
e
is the magni-
tude of the velocity uctuation in the velocity-modulated electron beam,
ω
e
is the angular frequency of velocity uctuation and
θ
e
is the phase angle of
the velocity uctuation.
Substitution of Equation 12.85 in Equation 12.83 gives
m
υ
e
ω
e
sin (
ω
e
t +
θ
e
) = e E
1
sin(
ω
t +
β
p
z) (12.86)
There will be interaction between the electric eld and the electron beam,
provided the velocity of the modulated electron beam and the dc electron
velocity are approximately the same, that is,
υ
υ
0
. Thus, the distance trav-
elled by the electrons is
z =
υ
0
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Publisher Resources

ISBN: 9781466591417