0 âhelix angle. Field theory is applied to anafyze the behavior of the planar helix in the presence of a flat electron beans present between the two screens.
IEEE TRANSACTIONS
ON MICROWAVE
5) The feasibility when
adipose
large
lateral
radiators tioned, At
dimensions
the applicator
915 MHz
with
would
frequency.
of 433 MHz,
These results from
statements
because
with
and pork
than these values depth,
thus losing
the required
system, like, for instance, affect
blood
only
frequency
by surface cooling and heat
of the various
to occur
flow.
for
However,
depth
to the interior.
systems should
remain
the in oioo of a living
it is assumed that
penetration
effects of the blood
conduction
by experi-
Fig.
1.
The planar traveling-wave
y“-directions of conduction 0 —helix angle.
of the used
stream and heat The
principal
Field
theory
presence
is applied
to anafyze
of a flat electron
indicate
the presence
attenuation
are shown for current
of three
constant,
[3]
[4] [5]
[6]
[7]
[8]
[9]
[10] [11]
A W. Guy, J. F. Lehmarm, and J. B. Stonebndge “Therapeutic applications of electromagnetic power, Proc. IEEE, vol. 62, pp. 55-75, 1974. J. W. Hand and G. ter Haar, “Heating techniques in hyperthermia~ Brit. J. Radloi., vol. 54, PP. 443-466, 1981. D. A, Christensen and C. H. Dumey, “ Hyperthermia production for cancer therapy: A review of fundamentals and methods,” J. Microwaoe Power, vol. 16, pp. 89-105, 1981. G. Kantor, “Evaluation and survey of microwave and radio-frequency applicators,” J. Microwrzoe Power, vol. 16, pp. 135-150, 1981. G, M. Samaras, A. Y. Cheung, and S. F. Weinmann, “ Focussed microwave radiation therapy for deep tumors,” in Hvpertherwua as an A ntzneoplastlc Treatment Modality, NASA Publ. 2051, 1978, pp. 67-68, A. Y, Cheung, W. M. Gelding, and G. M. Samaras, “Direct contact applicators fOr microwave hyperthermia,” J, Microwave Power, VO1. 16, pp. 151-159, 1981. F. A. Chbbs, “’Clinical evaluation of a microwave/radio-frequency system (BSD Corporation) for induction of local and regional hyperthermia;’ J. Mtcrowuoe Power, vol. 16, pp. 185-192, 1981. M, Melek and A. P. Anderson, “A throned cylindrical array for focussed in Proc. 11th European Microwave Conf. microwave hyperthemna,” (Amsterdam), pp. 427-432, 1981. H. P. Schwan, “Survey of rmcrowave absorption characteristics of body tissue,” in Proc. Trl-Sem. Conf. on B1ologzcal Effects of Microwave Energp, NTIS Dec. AD 131477 and 220124, pp. 126-145, 1958. M. A. Stuchly and S. S. Stuchly, “Dielectric properties of biological substances-Tabulated,” J. Mzcrowaoe Power, vol. 15, pp. 19-26, 1980. J. L. Guerquin-Kem, L, Palas, M. ,Gautherie, C. Foumet-Fayas, E. Gimonet, A. Priou, and S. Samsel, “Etude comparative d’ apphcateurs hyperfrequences (2450 MHz, 434 MHz) sur frmt~mes et sur pi~ces opiratoire, en vne d’une utilisation therapeutique de l’hyperthermie micro-onde en cancirologie,” in Proc. URSI Symp, (Electromagnetic Waoes and Bmkrgp) (Jouy-en-Josas), pp. 241-247, 1980.
modes,
a typicaf
proposed
Abstract
—A
as a slow-wave
constitute
Traveling-Wave
structure
conducting
a planar helix.
for application
one mode having
TWT.
Also.
a negative
TWT.
the effect
Curves of beam
The planar
TWT
considered
of UC screens (Fig. tion.
As
shown,
directions
the y-axis.
cally
located
beam
the
top
An
by a distance the
beam
screens
of thickness extent
the structure
the wave in regions here will
consists of a pair 2a in the x-direc-
be applicable
conduct
make angles 0 and
the two screens. Both
to be of infinite
not disturb
bottom
respectively,
electron
out in [5], limiting
will
and
which,
between
are assumed
here for analysis
1) separated
y’ and y“
with
CONFIGURATION
in – O
2 b is symmetri-
the screens and the in the y-direction.
in the transverse remote
from
As direc-
the ends,
to a structure
several
wavelengths wide. A practicaf structure can be terminated in the y-direction by closing the “helix” by conducting wires. The beam
Tube
current
density
z-component.
SHEEL ADITYA, MEMBER,IEEE,AND K. ARORA, SENIORMEMBER,IEEE
pair of unirfirectiottafly
directions,
planar
in the
INTRODUCTION
II.
by means applied
different
with
helix
the two screens. Remdts
The analysis of a helix-type traveling-wave tube (TWT) has been carried out by Pierce [1], Chu and Jackson [2], and others [3], [4]. In a TWT, a slow-wave structure such as a helix or coupled cavity is used to slow down the electromagnetic wave to the velocity of the electron beam so that a strong interaction between the two can take place. A slow-wave structure in planar geomet~, consisting of a pair of parallel unidirectionally conducting (UC) screens conducting in different directions and separated by some distance, has been studied by Arora [5], Aditya [6], and Aditya and Arora [7]. It appears that this planar slow-wave structure can be used in a TWT. In view of this, a planar helical TWT is analyzed in the present text, Field equations are derived and the modaf solution of the problem is obtained. The variation of the complex propagation constants of different modes with beam voltage is studied.
tion
DEVI CHADHA, RAJENDIb4
of the planar
between
as in the case of the usuaf helix-type
and results obtained
of Planar Helix
.v’ and
is indicated.
pointed
Field Theory
of propagation;
UC screens, resPectiveI~
unchanged.
WFEfLf3NCES
[2]
the behavior
beans present
1,
[1]
tube: z —duection
of top and bottom
tissue. Deviations
of the dynamics
the effective
I
are valid applicator
fair accuracy adipose
are likely
of the presence
this could
features
would
of 14 cm
The same remarks
have been checked
the above
convection,
depth
smaller
where
men-
be 30 cm.
ments using muscle phantom situation,
or three
diameter
to a penetration
dimensions
two
5 cm at 2450 MHz.
decrease of penetration
of the lower
the frequency
diameter
only
fat, the applicator
the applicator
result in a rapid
realistic
Because of the
size. As already
size is approximately
and irradiating
the benefits
to be only
is irradiated.
reasonable
13 cm (corresponding
[1]). Making would
appears
cancer)
of the applicators,
can be grouped
be about
for
of a focaf point
tissue (breast
73
AND TECHNIQUES, VOL. 31, NO. 1, JANUARY 1983
THEORY
is constant In practice,
of the focusing
over the cross section this assumption action
and has onlly a
is very nearly
of a strong
realized
dc magnetic
field
in the z-direction.
screens, conducting in III.
The planar helix is proposed
in a traveling-wave
tube (’ITVT).
The boundary present.
Manuscnpt recewed March 29, 1982; revised August 4, 1982. The authors are with the Department of Electrical Engineering, Institute of Technology, Harrz Khas, New Delhi, 1I 0016, India.
Indian
WAVE EQUATIONS AND ELECTRON DYNAMICS
and are constant equations
0018-9480/83/0100-0073$01.00
conditions
require
both TE and TM modes to be
If the fields are assumed to be varying in the y-direction,
can be written 01983
IEEE
as exp (jut
– ~z),
i.e., ~/ dy = O, then the field
in the following
form.
74
IEEE TRANSACTIONS
ON MICROWAVE
THEORY
AND
TECHNIQUES,
x 4
For the TE mode
rEy +
japoHX
rHx+(dH:/dx)+
,UC
– ~
L__-- ____-----T___ \
(2) r = a + j/3 is the propagation and .TZis the z-component
from
the field
presence
equations
that
constant
ilong
of the current the TE mode
the z-direc-
density.
For
the transverse-symmetric
nents in the different
by the
B1eu(x-
H =
b)~B2e-u(-’
xa
{ Nsinhux,
u~=–rz–k;
by the following
1) Tangential
components
2) Tangential k;
However,
of current
components
changes into
The
With
the help
of
the
z
L/ —Jz
of electric
and magnetic
field
are
of electric
field
are continuous
at
(4)
= O.
field
above
acteristic
components
are continuous boundary
equation
are zero and the magnetic
field
along y’ at x = a.
conditions
result
in the following
for the transverse-symmetric
char-
modes:
J(JC~
continuity
and
force
equations
for
between .T2and E, can be obtained
charges, the relationship
components
3) Electric
because of the presence of the
and the wave equation
#Ez —–UZE. 8.X2
These coefficients
conditions:
x=a;
= U2/.Loco.
the TM mode is affected
z-component
coefficients.
boundary
at x = b;
continuous
and
(9)
x
