EAD 234B: E&M
Homework #3
Due Thursday, April 22, 2010
(1)
We wish to consider the case of waveguides containing plasmas. To simplify the calculations,
we will assume the waveguides are made from perfect conductors.
(a)
For simplicity, we consider the case of slow waves, which implies that
Show that the resultant equation to be solved is then
or
subject to the appropriate boundary conditions. In the above,
where we have made use of the cold plasma dielectric tensor in cylindrical coordinates,
neglecting ion motion and have also assumed the magnetic field is aligned along the z
axis which we will subsequently take to be the axis of a perfectly conducting cylindrical
waveguide. In addition, we will assume a homogeneous plasma.
(b)
Then, assuming wavelike solutions which are separable, show that this results in a Bessel
equation for
(
)
,
, ,
r
z t
φ
θ
.
(c)
We now look at a simple case and assume that the steady magnetic field is infinite. Show
that the resultant dispersion relationship is
where
p
n
ν
is the
ν
th
zero of
J
n
(
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 Spring '10
 NCL
 waveguide dispersion relation, mode frequencies, long coaxial waveguide, TM mode frequencies, lowest propagating mode

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