High power gyrotrons using oversized cylindrical resonators, tapers and ... spatially distributed in the far-field radiation of the open-ended wave- guide.
METHOD FOR IDENTIFICATION OF MODES IN OVERSIZED WAVEGUIDE OF HIGH-POWER 150 GHz GYROTRON M. Kitlinski*, G. Hochschild**, W. Wiesbeck***
ABSTRACT High power gyrotrons using oversized cylindrical resonators, tapers and waveguides are subject to provide a multitude of modes. For characterisation of the gyrotrons under development a measuring system is required to identify the individual modes in an arbitrary TE mode mixture and to determine fractional power contributions. The new menthod uses four sensors spatially distributed in the far-field radiation of the open-ended waveguide. The measurement is based on the processing of linear combinations of the four high frequency signals.
INTRODUCTION The Electron Cyclotron Resonance Heating (ECRH) for the large plasma experiments of the next generations requires several megawatts of power at -2mm wavelength which might be generated by future gyrotrons using resonators operated in high order modes. For the experimental verification of alternative methods of mode stabilisation in overmoded gyrotrons a measuring system for mode identification is required. This system has to operate for the whole spectrum of possible modes from rotational symmetric modes to whispering gallery modes simultaneously propagating in the cylindrical output waveguide.
There are many different methods used to identify the modes in oversized cylindrical waveguides and to determine the fractional power belonging to each of them. Among known measuring procedures one can generally distin-
guish: -
-
methods based on internal detection (direct measurement of the field components, perturbation methods, visualisation of the electromagnetic field distribution). methods of external detection (near-field pattern or far-field pattern determination and analysis) methods using special transmission or reflection devices (coupled wave transduces, pulsed or frequency modulated systems).
Recently proposed [1] visual field indicators like liquid cristals give acceptable results, when only few low order modes coexist at the gyrotron output. However, in high order mode operation we want to study mode competition phenomena and to observe the resulting complex mode spectrum in the
* ** ***
UniversitAt Karlsruhe, Institut fOr H6chstfrequenztechnik und Elektronik, Kaiserstr. 12, 7500 Karlsruhe, Federal Republic of Germany (on leave Techn. University of Gdansk, Gdansk, Poland) Kernforschungszentrum Karlsruhe GmbH, Institut fUr Kernphysik II, P.0.Box 3640, 7500 Karlsruhe, Federal Republic of Germany 3Universitct Karlsruhe, Institut fOr H6chstfrequenztechnik und Elektronik, Kaiserstr. 12, 7500 Karlsruhe, Federal Republic of Germany
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cylindrical output waveguide. Therefore, taking into account the undetermined number of TE modes,the expected power level (200kW to 1MW), frequency range (130mOp 160 GHz) as well as availability of the commercial components only far-field mapping outside of the waveguide is feasible. Up to now this method has been used to identify mode families with a first index m S 2 [2,3]. Nevertheless, far-field pattern measurements can be applied to mixtures of arbitrary modes.
The analytical expressions describing far-field radiated from an openended circular waveguide propagating the TEmn mode were found by Risser
[+l4WU eR m r 2 R [kmn
E
(1n (L -coso ) J (k a) mksinO 2s(M) k -M mn (1)nt o2 mn
M+1
-jkR
8
2
_
imn Ose+r
Wjilj m-~. e E[
m =
mn
R
0 ) (1-cos mn k
k
J Jm (k a)2 mn
asin___ sine
(kasine)
si(@
(2)
where: k
V
mn
mn -, a
v mn
-n-th zero point of J'm
J
-inm-order Bessel function
Prelectin coeficien
uin'te waveguid
mn
8mn = into k(e)o(kmn1)2 account the dependence on 0 and * in the spherical coordinate Taking system one can rewrite relations (1) and (2) in a shorter form:
=o E
=
A
inn
(a)
cos(ino)
(3)
Binn (e) sin(mi)
which will be used to find the relations shown in Fig. 2
FOUR-ANTENNA MAPPING SYSTEM The proposed mode identification method uses the four-antenna axrangement (Fig. 1) placed in the far-field region at a distance R>2 (2a) /A ) from the circular waveguide. The antennas A,B,C,D are spatially distributed on a circle (r=const.): A()
B
(o'ff ),
C4
D(003 ff
+Tr)
Mapping is done by varying radial and angular positions of the antennas. The information about certain mode groups (m=4k,2k+2,2k+l1,k=0,1,...) is obtained from three vector-combinations of the four signals. In this way the unknown mode spectrum is divided into three groups of the mode families (the same "m'). pependgnt on the chosen antenna polarisation (Fig.2) the power related to E or E components is measured.
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x
r =R
sine
z
Y' gyrotron output: open-ended cylindrical oversized waveguide D 2a 2>> A0 R - 2D 2/A0 =
Fig. 1: Mapping system for mode identification
Polarisation of receiving
6
sensors
Combination of received signals
t
Th
IjA+B-C+D)
4kO A4kn
|4
n=1
|(A-B+C-D)
J(A-C)
4 )
k=O n=1
2
k=O
n=1I Fig. 2:
1 B4k,n sin(4k) n=1
ncos(2k+2)¢0 A2k+2 2k'2nk=O A
2kn=n
4
0
n=1
cos(2k+1 )0 |2
82k+2, 2,
sin(2k+2)0
B2k+
sin(2k+
n=1
Different combinations of high-frequency signals received using four antennas system
A SIMPLIFIED APPLICATION In the simplest case when k=O the relations shown in Fig. 2 are restricted to the mode families TE0 , TE in TE2n* In the angular pos-ition 4A=0 of the mapping system each of Whe considered vector combinations is related to only one mode family:
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j
I(A+B+C+D)
~(A-B+C-D)
I(A-C)
=>
4
AOn
> P
Pon
=>
4 A2n
P2n
=>
2 Am
> P => P
(4)
Pn
-
The identification of the individual modes within the same mode family requires radial positioning of the antennas. The necessary values of the angle 0 (r=Rsin0) result from the roots of J' in (1). This means: m
)=0) 0=001 (JV(oi 01001 0=002 ( 002)
for
(J'2( 21)=O)
0= 021
for
or
or for
=> P - P
~~~~01
0
=> P
2
P21 P
)=O) 0=0 22 (J'(0 2 22
=> P
0=01111 (J'(0~~11 )=O)
=> p
P11
> P
12
012 (J(o12)0)
22
GENERAL CASE Let us consider an arbitrary number of modes in each of the mode groups given in Fig.2. To describe this case we introduce new variables: q q t t
[Em,n] - mode number, q Q -expected number of modes under identification =1,2,.., Q, - measurement number T - number of measurements. = 1,2,.., T,
Fjr a chosen polarisation of the receiving sensors (for example to measure E ) the power determined in the "It"-th measurement is:
(6)
) I ( q=1 (IE q,Pt q-1 q,t )*
P
To find an unknown amplitude A and unknown phase a of the q-mode, we assume, that in the far-field Fegion the electric fi% ld components have the form: Eft=
q,t
E0
q,Pt
=
AOq e jaq 0
Aq e
.0aq
S 0 (0a,rP q,ttt
S
9
et(
(7)
(8)
t
- the coefficients describing the field distribution in the where S plane oPriteasurement for given q,Bt,ft,
To determine 2Q unknown values (A ,a ) in that case it is necessary to do T=2Q measurements and to solve a 3et %f algebraic equations resulting from (6) which are written shortly in matrix form:
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[PI []2QX1 where:
[P] =
[S qst I Qx2Q P 2Q] [P1 'P2'*
[Al
[A 1
=
[S Iq q ,t
e=
1
vector of measured power
I
...w A e
S[Q11Q* SQi
(9)
[AI*[S qtt I
[Al [A1xQ
=
S1
.
Q
~*
2Q
vector of unknown amplitudes and phases
matrix of the coefficients
distribution
Q, 2Q
TECHNICAL REMARKS For the experimental verification of the described mode identification method a far-field analyzer is under construction. The mapping system uses the arrangement of four antennas shown in Fig.1 with a moving capability in polar coordinates. The field mapping is performed by control of the common radial distance of the antennas from the z-axis and of the rotation angle ¢ of the 4 antenna arrangement. The rectangular fundamental mode waveguide antennas are linearly polarised as shown in Fig.2. The fourchannel signal processing system (see schematic diagram in Fig.3) consists of four coherent down converters using harmonic mixers with a common local oscillator, the combining network at X-band and a power meter. The combining network contains two switches and three microwave 1800-hybrid junctions to provide the different linear combinations of the microwave signals (Fig.2). Because in most experimental applications a moderate num-
1 1 2
Al
3 1
:
U
Fig . 3:
Four-channels processing system. 1 Mapping system 2 Four-channels down converter 3 Combining network 14 Power meter
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4
ber of contributing modes can be expected this method may evolve as a handy tool for gyrotron research if computer control and data processing is added. At the same time system calibration and error correction can be performed by computer.
REFERENCES
[1] Y. Carmel, K.R. Chu, M.E. Read, V.L. Granatstein, G. Faillon, P. Boulanger, E. Kammerer, G. Mourier, A technique to identify electromagnetic modes in oversized waveguides, IEEE Trans. on MTT, vol. MTT32, No. 11, Nov. 1984, pp. 1493 to 1495 [2] Z.X. Zhang, G. Janzen, G. MOller, P.G. SchOller, M. Thumm, R. Wilhelm,
Mode analysis of gyrotron radiation by far field measurements, Proc. of VIII th Intern. Conf. on Infrared and Mm Waves, Miami Beach, Florida, 1983, paper T4.3 [3] Z.X. Zhang, M. Thumm, R. Wilhelm, Far field radiation patterns from open-ended oversized circular waveguides and identif'ication of multimode outputs of gyrotrons, Rep. IPF-83-5, Inst. f-ur Plasmaforschung, Univ. Stuttgart, June 1983 [4] J.R. Risser, Microwave Antenna Theory and Design (ed. S. Silver), McGraw-Hill, New York 1949, pp. 334 to 337
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