reaction theory, a variational propagation in a parallel-plate guide within which a magnetized inhornogeneous lossy plasma slab is inserted. Tbe equation.
IEEE TRANSACTIONSON MICROWAVETHEORYAND TECHNIQUES,VOL MTT-34, NO 1, JANUARY 1986
Propagation of Waves Through Magnetoplasrna Slab Within a Parallel-Plate Guide HUA-CHENG
CHANG,
SHYH-KANG
AND CHUN
,4mtract
—By
equation guide
within
inserted. with
applying
is established which
solution
and the field dMribution which may influence These factors
and the direction slab,
solution bility
and
With
a variational
lossy
plasma
include
electron
is also incorporated
of the guide
density,
the strength
field, the midtb and the thickness
collision
Iosses.
to investigate
with the present
In this study,
characteristics
the plasma electron
A special
modal
an anomalous
numerical
is
of
expansion
numericaf
line where a magnetized
In this study,
along
the reflection
in the slab are obtained.
insta-
the governing
pendix),
the validity
Finally
included
density)
sandwich
filter
tuning
and with has been
structure
voltage reported
Consider
(and, hence, recently
[1].
guide
an
slab material
that
plicated For
the
the guide is anisotropic
associated
and is difficult a simplified
problem
then
and inhomoge-
becomes
very
com-
propagation
resolved ic
by the methodology
through
guiding
for
specifying
structure.
the previous
This
clifficulty
of variaticmal reaction
FORMULATION
permeability the
and
(PoL(.x,
tensors,
the region
by a TEM
metallic
plate
a slab of anisotropic, Y), ~ o=(x,
E( x, y) represent
permittivity
occupies
is illuminated
parallel
which
10SSY rn~terial
ji ( x, y)
and slab
extended 1 within
respectively.
O< x G
Y))
the relative Assume
a, O G y < b, and
wave
jlZ;exp(–
jkox)
a oneqo~:
= ~~~exp(–
jkox)
ko=om As usual,
the
throughout In
the
slab,
factor
(1) exp (jut)
is adopted
study. we shall c xx
;=
electromagnet-
Vo={x.
time-harmonic
this
has been
tlheory [8].
let c
XY
Cxz
~ yx
6YY
~yz
c Zx
c
c,=
[1
2Y
=
studies, this paper deals with
the guided wave problem in which a magnetized plasma slab is placed within an infinitely extended parallel-plate metallic guide. The reason to select this parallel-plate structure is that it may reduce the mathematics involved and still allow a simplified analysis for a more practical strip Manuscnpt
a~d
Here,
plasma slab in an unbounded [4], [5] made use of a special
anisotropy.
[6], [7] and the variational By extending
is inserted.
~;=
problem
technique to figure out the governing variational equation and then used the finite-element method to find out the field distribution. The extension of this technique to the same propagation problem in the presence of an external static magnetic field was unsuccessful owing to the introof material
infinitely in Fig.
to access.
dimensional inhomogeneous region, some investigators
duction
is first
can be confirmed.
results
of the particular
VARIATIONAL
as shown
inhomogeneous,
neous,
equation
used
With only layers of isotropic and homogeneous media, this sandwich structure can be easily handled by the conventional transmission-line techniques [2], [3]. However, if the within
of the approach
are the numerical
II.
electron
variational
derived, using the variational reaction theory. The equation is then solved by the finite-element method coupled with the frontal solution algorithm. In comparison with the previous works and the modal expansion solutions (Ap-
the characteristics
algorithm.
PLASMA–DIELECTRIC as a microwave
plasma slab is incor-
INTRODUCTION
1.
A
WU,
porated.
slab
method
RUEY-BEEI
CHEN
transmission
in a parallel-plate
such an approach,
the propagation
of the static magnetic the
associated
inhornogeneous
algorithm.
coefficient
the
theory,
wave propagation
is then solved by the finite-element
the factors are stndled.
reaction
variational
a magnetized
Tbe equation
the frontal
the
for handling
JENG,
HSIUNG
received September 18, 1984; revmed August 27, 1985. Tlus
work was supported in part by the National Science Council, Republic of China, under Grant NSC-71-0201-EO02-14. The authors are with the Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan, R.O.C. IEEE Log Number 8405925.
(2) where the
the
of
a matrix.
outside
and
n=,
(Ez, Hz) sources
00118-9480/86/0100-0032$01.00
the
component
the superscript
Obviously,
these
two
transverse
T means tensors
the
to
transpose
are unit
tensors
the slab.
By the variational (~:,
t means
subscript
z-direction
reaction
theory
[8], we can achieve
the
formulation by choosing the longitudinal fields as unknowns. First, we constrain the transverse (~, J4t ) to be zero and represent 01986
IEEE
Authorized licensed use limited to: National Taiwan University. Downloaded on February 25, 2009 at 00:14 from IEEE Xplore. Restrictions apply.
the transverse
CHANG
fields
et (II.:
PROPAGATION
(~,, Et)
OF WAVES
THROUGH
MAGNETOPLASMA
in terms of the longitudinal
33
SLAB
ones, i.e.,
1.
—i;l.
Et=
jticoz,,E.)
(vHz x 2-
j~co
(Lb@
Then,
we
further
constrain
(.lz, MZ) to be zero outside (Ez, Hz)’ fields are
the
longitudinal
the slab “so that
sources
z
the exterior
BOK------7 I
z
Fig. 1.
Parallel-plate
/
guide with magnetized, inbomogeneous, and 10SSY plasma slab.
(E=, Hz) fields as follows:
the unknown
(4) where R and T are the modal coefficients
to be determined
andl
k;=k&(m~/b)2, The exterior
rn=l,2,...
(5)
.
(~,, ~,) fields can be expressed easily in terms
of the boundary ( EZ,”HZ) fields by (3). Also, these modal coefficients can be expressed in terms of boundary fields by matching
the continuity
1jb[E&
Rp’1 = – bo
conditions,
i.e., .~bEzsin(?)dY]
x=o,a
TJOH=(X= 0)] dy
d..
TfM= :~b@Z(X=U)
+ ;~bH;(x Here, (~;,
m 7ry
2b .~R=z~Ez(x=O)sin
—
() b
dy,
m=l,2,
= O) dy. ~b(;oHz(x
~;)
are related
III.
FINITE-ELEMENT
to (E;,
=0)–2E~)
H:)
dy.
(8)
be solved
by
by
...
AR:M= ;J%oHz(x=mf&)dY
lnM=;Jb,oHz(x=.)
(6)
cos(y)dY.
Now
the variational
formula
The
becomes the
81=0 I=
(7)
– H~J4=) dydx
JZ=.2. (V Xfi– MZ=2. By substituting plifications,
(–V
(3)–(6)
we finally
into obtain
ju~O~”@.
(7) and making the variational
equation
technique
[7],
[9],
(8) will [10].
First,
the
whole
0< y
