Propagation of Waves through Magnetoplasma Slab within a Parallel

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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