SPACE POWER An International Journal on Systems, Technology, Economics, Environment and Policy Formerly Space Solar Power Review Volume 6, Number 3, 1986 Papers presented at the 1985 International Symposium on Antennas and Propagation (ISAP ’85) PERGAMON PRESS New York / Oxford / Beijing / Frankfurt / Sao Paulo / Sydney / Tokyo ! Toronto
SPACE POWER An International Journal on Systems, Technology, Economics, Environment and Policy Published under the auspices of the SUNSAT Energy Council Editor-in-Chief Dr. John W. Freeman Space Solar Power Research Program Rice University, P.O. Box 1892 Houston, TX 77251, USA Associate Editors Dr. Eleanor A. Blakely Lawrence Berkeley Laboratory Dr. William C. Brown Raytheon Company Colonel Gerald P. Carr University of Texas Dr. David Criswell California Space Institute Mr. Hubert P. Davis Raytheon Company Mr. Gerald W. Driggers, President Combustion Engineering Mr. Arthur M. Dula Attorney: Houston, Texas Mr. I.V. Franklin British Aerospace, Dynamics Group Professor Norman E. Gary University of California, Davis Dr. Peter E. Glaser Arthur D. Little, Inc. Dr. Arthur Kantrowitz Dartmouth College Mr. Richard L. Kline Grumman Aerospace Corporation Dr. Klaus Schroeder Rockwell International Professor Harlan J. Smith University of Texas Mr. Gordon R. Woodcock Boeing Aerospace Company Editorial Assistant: Diana White Editorial Office: John W. Freeman, Editor-in-Chief, Space Solar Power Research Program, Rice University, P.O. Box 1892, Houston, TX 77251, USA.
Papers presented at the 1985 INTERNATIONAL SYMPOSIUM ON ANTENNAS AND PROPAGATION (ISAP ’85) Kyoto, Japan August 20-22, 1985
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0883-6272/86 $3.00 + .00 Copyright © 1986 SUNS AT Energy Council INTRODUCTION Seven papers in this issue are the presentations given at the 1985 International Symposium on Antennas and Propagation (ISAP'85) held in Kyoto, Japan, August 20-22, 1985. The symposium, the third ISAP in Japan, was sponsored and organized by the Institute of Electronics and Communication Engineers of Japan, and was supported by the Antennas and Propagation Society of the Institute of Electrical and Electronics Engineers and the International Union of Radio Science (URSI). Two hundred and seventy papers from 27 countries were presented at 52 sessions. The seven papers were included in the session of Radio Energy Transmission which is regarded as one of frontier technology and systems that await active cooperation of antennas and propagation engineers. Also, this session was closely related to the theme of the Symposium: A step to new radio frontiers. Three papers in the session, all of which were contributed from Japan, concern Solar Power Satellite, and four papers consisting of three from Japan and one from the USA concern Fusion Plasma Heating. A program of the session is as follows: 1. Nonlinear Interaction of Strong Microwave Beam with the Ionosphere — MINIX Rocket Experiment N. Kaya, Kobe University, Kobe, Japan; H. Matsumoto, RASC, Kyoto University, Kyoto, Japan; S. Miyatake, University of Electro-Communications, Tokyo, Japan; I. Kimura, Kyoto University, Kyoto, Japan; M. Nagatomo, T. Obayashi, Institute of Space and Astronautical Science, Tokyo, Japan. 2. Nonlinear Excitation of Electron Cyclotron Waves by a Monochromatic Strong Microwave — Computer Stimulation Analysis of the MINIX Results H. Matsumoto, T. Kimura, RASC, Kyoto University, Kyoto, Japan. 3. Rectenna Composed of a Circular Microstrip Antenna K. Itoh, T. Ohgane, Y. Ogawa, Hokkaido University, Sapporo, Japan. 4. Analysis of Aperture Antenna Attached to Cutoff Cavity for ICRF Plasma Heating K. Sawaya, S. Adachi, Tohoku University, Sendai, Japan. 5. A Ridged Waveguide Slotted Coupler for Large Tokamaks H. Arai, N. Goto, Tokyo Institute of Technology, Tokyo, Japan. 6. Reflector Antennas for Electron Cyclotron Resonance Heating of Fusion Plasma O. Wada, M. Nakajima, Kyoto University, Kyoto, Japan.
7. Submillimeter Wave Propagation in Tokamak Plasmas C.H. Ma, D.P. Hutchinson, P.A. Staats, K.L. Vander Sluis, Oak Ridge National Lab., USA; D.K. Mansfield, H. Park, L.C. Johnson, Princeton University, USA. The symposium chairman and the chairman of the technical program committee were Prof. F. Ikegami of Kyoto University and Prof. N. Goto of Tokyo Institute of Technology, respectively. On behalf of them and the contributors, I would like to express our appreciation to Prof. John Freeman for the kind invitation to publish all of these seven papers more completely in the Space Power Journal. Some authors have taken advantage of this opportunity to rewrite their papers which were condensed in the limited pages in the original proceedings. My role in the symposium was to organize the session as one of the members of the technical program committee. I hope these papers are useful for relating two different field engineers of the energy and the antennas and propagation. PROF. KIYOHIKO ITOH Department of Electronic Engineering Hokkaido University Sapporo, Japan
0883-6272/86 $3.00 + .00 Copyright ® 1986 SUNSAT Energy Council NONLINEAR INTERACTION OF STRONG MICROWAVE BEAM WITH THE IONOSPHERE MINIX ROCKET EXPERIMENT N.KAYA Faculty of Engineering Kobe University Rokko, Kobe 657, Japan H. MATSUMOTO RASC Kyoto University Uji, Kyoto 611, Japan S. MIYATAKE Electro-communication University Chofu, Tokyo 182, Japan I. KIMURA Faculty of Engineering Kyoto University Kyoto 606, Japan M. NAGATOMO and T. OBAYASHI Inst. Space and Astronaut. Sci. Komaba, Tokyo 153, Japan Abstract — A rocket-borne experiment called MINIX was carried out to investigate the nonlinear interaction of a strong microwave energy beam with the ionosphere. The MINIX stands for A/icrowave-Zonosphere Nonlinear/nteraction eA'periment and was carried out on August 29, 1983. The objectives of the MINIX is to study possible impacts of the SPS microwave energy beam on the ionosphere such as the Ohmic heating and plasma wave excitation. The experiment showed that the microwave with f = 2.45 GHz nonlinearly excites various electrostatic plasma waves, though no Ohmic heating effects were detected. INTRODUCTION One of the important issues of the Solar Power Satellite (SPS) is to make an assessment of possible impacts of the SPS on the Earth's environment prior to the design of the SPS. The microwave-ionosphere interaction is one of such topics which needs to be studied prior to the realization of the SPS. In order to meet such a need, a rocket-borne experiment called MINIX was carried out by a Japanese S-520-6 sounding rocket on August 29, 1983. The MINIX stands for A/icrowave-/onosphere Nonlinear /nteraction eA'periment. One of the objectives of the MINIX is to measure plasma wave spectra during the microwave transmission and collect quantitative
data of nonlinear excitation of plasma waves caused by the strong microwave energy beam. The other is to measure the possible electron heating and associated phenomena, such as density depletion, caused by the microwave transmission. Both the plasma wave excitation and density modulation of the ionosphere by the SPS microwave may affect the short wave communications and may result in a strong modification of the natural ionospheric and magnetospheric plasma environment of the Earth. In order to obtain as quantitative data as possible on such effects, we transmitted a microwave energy beam with a frequency 2.45 GHz and a power density of the order of 230 watt/m2. Those values are the same as the frequency and power density planned for the future SPS. EXPERIMENTAL INSTRUMENTS The MINIX was performed by a mother-and-daughter rocket. The payload section is divided into two parts, mother and daughter, as illustrated in Fig. 1, which shows a test scenery of the payload final check at the launching site at Kagoshima Space Center of ISAS, located at Uchinoura in Kyushu Island. The mother part contains the power supply composed of a DC-battery and DC-DC converter, the microwave transmitter composed of the magnetrons with a controller, two sets of truncated wave-guide antennas, a Langmuir probe for the measurement of electron temperature and density, wide band telemetry set, a neutral gas plume which is capable of emitting a neutral nitrogen gas, and a TV monitor camera which was used to monitor the separation of the mother and daughter rocket. The configuration of
these instruments is depicted in Fig. 2. The mother section is below the plane denoted by “separation.” The microwave transmission was made by one of the two truncated wave-guide antennas connected to magnetrons. The magnetrons used in the MINIX are those designed for a home-use microwave oven with a transmitting power of 830 W. Most of the diagnostic instruments such as a VLF wide band receiver, an HF sweep frequency receiver, geomagnetic aspect meter, electron density and temperature meter and microwave detector are installed on the daughter section as illustrated in Fig. 2. The receiving antennas of the VLF and HF plasma waves are extended radially from the top portion of the daughter rocket as seen in Figs. 1 and 2. Each antenna element is 2 m in length and is used as a monopole antenna or is combined to form a dipole antenna. The HF sweep frequency receiver covered a frequency range of 0.1 MHz to 18 MHz with a sweeping time of 250 msec. The VLF receiver covers a frequency range of 60 Hz to 25 kHz. Three rectenna type antennas are installed at the bottom of the daughter rocket and extended radially to form four paddles as seen in Fig. 1. One of the four paddles is used not as an antenna but as a mirror to view down the Earth by a TV monitor camera which is looking up to the daughter rocket from the mother rocket. EXPERIMENTAL TIME SEQUENCE Figure 3 shows the trajectory of the S-520-6 rocket and MINIX experimental schedule along the orbit. The separation of the daughter rocket was made at t = 209
sec after launching at an altitude of about 220 km. The experimental period was divided into three categories. The first period (I) was mainly devoted to the study of the Ohmic heating. As the Ohmic heating requires a reasonable amount of electronneutral collisions, a long duration (10 sec) transmission of the microwave was made during the period (I) when the rocket passes through the lower ionosphere where the collision frequency is high. In the second (II) and third (III) period, main focus is laid on the study of the nonlinear plasma wave excitation. The microwave was transmitted intermittently with a 5 sec transmission followed by a 5 sec pause. In the second phase, the dependence is studied of the nonlinear process on the ionospheric plasma parameters such as the electron density and the geomagnetic field which change with altitude. In the third phase after the daughter rocket separation, main interest was laid on the dependence of the nonlinear process of the plasma wave excitation on the distance between the mother-and-daughter rocket, i.e., the local intensity of the microwave field. MAIN RESULTS The magnetron transmitter system which is reinforced against the rocket vibration and shocks worked perfectly during the flight. All the other diagnostic instruments were also perfect in their operation. A videotape was resumed by the resuming team. The tape contained the video information of the separation of the daughter rocket. It was taken by the monitor TV camera installed on the top of the mother rocket. Some of the video frame will be shown at the oral presentation. The measurement of the electron temperature showed no temperature increase was detected both in the phase (I) and at the timing when an artificial neutral nitrogen gas was injected to increase the electron-neutral collisions. It turned out that the estimated temperature increase is of the order of 100 degrees which is not measurable by the temperature or Langmuir probes used in the MINIX. However, it should be noted that this result does not mean at all that the SPS microwave energy beam does not cause the Ohmic heating in the ionosphere. Even though the power density
of the transmitted microwave from the rocket was the same as that of the SPS microwave, the effective time of exposure of the microwave to the ionospheric plasma was too short compared with the characteristic time of the Ohmic heating because the rocket passes through the ionospheric plasma too quickly. As to the nonlinear excitation of the plasma waves, the result was clearly positive. The HF receiver showed a clear difference in the frequency spectra of the plasma waves when the microwave transmission was on and off. One example of the dynamic spectrum of the measured plasma wave for the period from 120 to 210 sec after launching is shown in Fig. 4. The second horizontal line from the top shows the on and off of the microwave transmission. The vertical axis is the frequency from 0.1 to 9 MHz. The horizontal axis show a time scale from 120 to 210 sec. The dark and light bar on the line indicate the timings of the transmission and pause, respectively. The horizontal line appearing at the frequency 3.1 MHz is an interference from the beating of the two frequencies used for the telemetry. Two different types of strong waves are seen excited only during the periods of the microwave transmission. One is the waves around 1.5 MHz and its harmonics. The frequency does not change much but shows only a slight decrease in time, i.e., with altitude. This wave turns out to be the electrostatic electron cyclotron harmonic waves judging from the comparison with the local electron cyclotron frequency. The second type of plasma waves excited by the microwave changes its frequency from 4 MHz to 6 MHz with altitude. The frequency of the wave turns out to be almost equal to the local electron plasma frequency. Thus this wave is supposed to be the electron plasma wave excited by the Raman scattering process of the transmitted microwave. The present MINIX revealed that the strong microwave energy beam is subject to nonlinear decay instabilities and causes the nonlinear excitation of electron cyclotron and plasma waves in the ionosphere.
The MINIX was the first trial of transmission of high power microwave in situ the ionosphere. We carried out this experiment in a hope that a local effect of the high intensity microwave of the SPS microwave beam can well be simulated and examined by a rather small scale experiment such as the MINIX. The Ohmic heating and associated density depletion could not be measured showing that the heating effect is of large-scale and slow-time-scale phenomenon. However, it was demonstrated that various plasma waves are excited in the microwave beam column. This may not be important from a viewpoint of the energy loss because the loss of the energy transmission due to the excitation of the plasma waves is less than 1%. However, the effect is significant in a sense that strong electrostatic waves are produced in the ionosphere and magnetosphere which may affect the high energy particle population through Landau and cyclotron resonances and diffuse them in both energy and pitch angles. Such secondary effect should be investigated in detail in the future before the realization of the SPS. Support of the MINIX by the rocket and telemetry teams at ISAS and KSC is greatly acknowledged.
0883-6272/86 $3.00 + .00 Copyright ® 1986 SUNSAT Energy Council NONLINEAR EXCITATION OF ELECTRON CYCLOTRON WAVES BY A MONOCHROMATIC STRONG MICROWAVE Computer Simulation Analysis of the MINIX Results H. MATSUMOTO AND T. KIMURA RASC Kyoto University Uji. Kyoto. Japan Abstract — Triggered by the experimental results of the MINIX, a computer simulation study was initiated on the nonlinear excitation of electrostatic electron cyclotron waves by a monochromatic electromagnetic wave such as the transmitted microwave in the MINIX. The model we used assumes that both of the excited waves and exciting (pumping) electromagnetic wave as well as the idler electromagnetic wave propagate in the direction perpendicular to the external magnetic field. The simulation code used for the present study is one-and-two-half dimensional electromagnetic particle code named KEMPO. The simulation result shows the high power electromagnetic wave produces both the back-scattered electromagnetic wave and electrostatic electron cyclotron waves as a result of nonlinear parametric instability. Detailed nonlinear micro-physics related to the wave excitation is discussed in terms of the nonlinear wave-wave couplings and associated ponderomotive force produced by the high power electromagnetic waves. 1. INTRODUCTION A rocket experiment named MINIX was carried out to study nonlinear effects of a high power microwave beam on the ionosphere. The results of the MINIX showed that electron cyclotron harmonic waves and electron plasma waves are excited by the transmitted microwave from the rocket. The excitation of the electron plasma waves may be due to the well-known Raman scattering process. However, the excitation mechanism of electrostatic electron cyclotron harmonic waves is not well-understood and needs to be clarified. The results are highly nonlinear so that no analytic theory is effective while yet the experimental data are not sufficient to understand the micro-physics in the nonlinear process of the wave excitation. We, therefore, carried out a computer simulation to understand the micro-physics underlying the phenomenon. In Section 2, a brief review of the MINIX results on the plasma wave spectra. Section 3 presents a model and a code hired in the present computer simulation. Section 4 describes the results of the computer simulation. 2. PLASMA WAVE SPECTRUM EXCITED BY THE MINIX MICROWAVE As discussed in the companion paper (Kaya et al., this conference), a clear difference was seen in the plasma wave spectra by on and off of the transmission of the microwave. Figure 1 shows the plasma wave spectra for both periods of microwave
transmission and of pause of the transmission. The shaded area shows the enhancement of the spectrum caused by the transmission of the 2.45 GHz microwave from the rocket. The local electron cyclotron frequency FH and its harmonics as well as the local electron plasma frequency is shown in the figure for reference. The biggest enhancement appears at a frequency in between the first and second harmonics of the electron cyclotron frequencies. It is inferred that this enhancement is due to the excitation of the electron cyclotron harmonic waves excited by the transmitted electromagnetic microwave. The reason for the inference is that this peak in the spectrum decreases in frequency with altitude showing a good correlation of the decreasing cyclotron frequency. A broad but less intense enhancement around 5 MHz-8 MHz showed a good correlation with the local electron plasma frequency and is inferred to be the electron plasma waves excited by the Raman scattering of the transmitted microwave. 3. MODEL AND CODE OF COMPUTER SIMULATION Electrostatic electron cyclotron harmonic waves are known to show the least damping when they propagate perpendicularly to the external magnetic field. The observed cyclotron waves may, therefore, well propagate in this direction because the necessary energy input from the microwave is minimum for this angle of propagation. Taking this fact into account, we hired a model in which all waves are assumed to propagate in the perpendicular direction relative to the external magnetic field. The exciting electromagnetic wave is assumed to be the O-mode wave for the present study. In other words, we examined a possibility of a nonlinear decay process of a high intensity O-mode electromagnetic wave into another electromagnetic wave and the electrostatic electron cyclotron wave. A schematic w-k diagram of this nonlinear decay process is depicted in Fig. 2. The simulation parameters are as follows:
Number of wavelengths in the system (mode number; m) = 16 Amplitude of the magnetic field of the pump wave = 0-1 External magnetic field = 1.0 The computer code is a full electromagnetic particle code, called KEMPO (Matsumoto and Omura, 1985). The KEMPO is a two-and-half dimensional code, but is used as one-and-two-half D for the present study. In the code, electron dynamics in their self-consistent electromagnetic fields are traced together with the nonlinear evolution of the EM fields. Total number of super-electrons handled in the present simulation is 32,768. 4. SIMULATION RESULTS Figure 3 shows the results of the dispersion analysis of the electromagnetic electric field component Ey and electrostatic electric component Ex. The former Ev component is decomposed into positive and negative k components separately. As seen in the figure, the w-k diagram of Ey with positive k's clearly shows that a large amplitude O-mode wave with m = 16 is propagating in the system as a pump wave. The other two diagrams show that both the back-scattered O-mode waves m = — 14, —15, —16 and —17 and the electrostatic electron cyclotron wave with m = 30 are excited. The most intense back-scattered wave is that with k = -14. The examination of the frequencies of the most intense back-scattered wave and the excited wave shows that the necessary conditions of energy and momentum conservation law of the resonant three wave interaction of the following form is satisfied. where the suffixes o, i, and e denote the pump, idler and excited wave components, respectively. Figure 4 shows a time history of energy density of the electric field of the mode 16, 14 and 30, respectively.
The energy density shown for the mode 16 is the difference from its initial values indicating the fluctuations. As seen in Fig. 4(c), the energy density of the excited wave with k = 30 increases with time roughly exponentially with a modulation of a period of about 120. Correspondingly, as seen in Fig. 4(b), the idler wave with k = —14 shows that the similar periodic change with the same period. The fluctuations shown in Fig. 4(a) is a rather complicated evolution. It consists of three factors. One is a beating component with the pump and oppositely propagating weak O-mode wave with the same k, and a component coming from a nonlinear frequency shift of the large amplitude of the pump wave and finally a slow variation due to the coupling with the idler and excited waves. The details of the last variation is hardly seen. However, a clear exponential damping with a slight modulation with almost the same period of about 120 is seen as the average change of the energy evolution. The present computer simulation could basically reproduce the experimental results obtained in the MINIX experiment. Detailed physics will be discussed in the oral presentation. Acknowledgement — The authors would like to thank members of the MINIX rocket experiment for their discussion. REFERENCES 1. N. Kaya, H. Matsumoto, S. Miyatake, 1. Kimura, M. Nagatomo, and T. Obayashi, Nonlinear Interaction of Strong Microwave Beam with the Ionosphere — MINIX Rocket Experiment Conference, 1985. 2. H. Matsumoto and Y. Omura, Particle Simulation of Electromagnetic Waves and its Application to Space Plasmas. In: Computer Simulation of Space Plasmas. 43, edited by H. Matsumoto and T. Sato. Terra Sci. Pub. Co. and Reidel Pub. Co., 1984.
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0883-6272/86 $3.00 + .00 Copyright ® 1986 SUNS AT Energy Council RECTENNA COMPOSED OF A CIRCULAR MICROSTRIP ANTENNA KIYOHIKO ITOH, TAKEO OHGANE AND YASUTAKA OGAWA Department of Electronic Engineering Hokkaido University Sapporo, 060 Japan Abstract — One of the big problems in the SPS system is reradiation of the harmonic waves generated by the rectifying diode. We have proposed the use of a circular microstrip antenna (CMSA), since the CMSA has no higher resonance-harmonic of integer multiple of the dominant resonance frequency. However, characteristics of a large rectenna array of CMSA’s have not been clarified. This paper is concerned with the absorption efficiency of the rectenna composed of the CMSA. The efficiency is estimated explicitly using an infinite array model. The results show that the absorption efficiency of the infinite rectenna array composed of the CMSA is 100%. Also, this paper considers the effect of the losses of the CMSA. INTRODUCTION "Rectenna,” the Earth Station Terminal in the Solar Power Satellite (SPS) system converts the microwave power (2.45 GHz) transmitted from SPS into the DC. The structure of the rectenna is divided roughly in two parts — receiving antenna and rectifying circuit. One of the big problems in the SPS system is reradiation of the harmonic waves generated by the rectifying diode. Therefore, the low-pass filter must be inserted between them in order to prevent the harmonic polluting radio communication environments. The SPS baseline rectenna has been developed by Raytheon Company, and they have adopted a dipole antenna with ground plane as the receiving antenna (1). Also, Gutmann et al. have investigated the possibility of using the Yagi-Uda antenna. However, all of the above-mentioned antennas belong to the linear antenna and have the characteristic that higher resonance-harmonic of integer multiples of its dominant resonance frequency exist. These features are undesirable for suppression of higher harmonic reradiation. We have proposed the use of a circular microstrip antenna (CMSA) as a competitor to the linear antenna for the rectenna in the SPS system (2), since the CMSA has no higher resonance-harmonic of integer multiple of the dominant resonance frequency. Moreover, the microstrip antenna can be printed on the same substrate with other devices. It can realize the very thin rectenna. And this configuration makes manufacture and maintenance very easy.
Some papers have already reported on the rectenna of dipole antennas with ground plane. It was concluded that the infinite array of the dipole antennas with reflector could absorb all power of incident plane wave. This paper is concerned with the absorption efficiency of the rectenna composed of the CMSA. The efficiency is estimated explicitly using an infinite array model. THE RESONANT CHARACTERISTICS OF A CMSA The general geometry of the CMSA is show in Fig. 1. The microstrip antenna has many unique and attractive properties — low in profile, light in weight, compact and conformable in structure, easy to fabricate, and to be integrated with solid-state devices. All of these features are desirable for the receiving antenna of the rectenna. The resonant frequencies of the antenna correspond to eigenvalues. For the CMSA, its resonant angular frequency wr is given by the root of where Jn(x) is the Bessel Function of n order, a is the effective radius of the CMSA, and er is the relative dielectric constant of substrate. Solving this equation, the harmonic resonant frequencies are 1.66f0, 2.08f0, 2.9f0, 3.64f0, and so on, where f0 is the dominant frequency. Therefore, it can be expected that there exists almost no higher harmonic reradiation from the CMSA. The experimental results showed that the insertion losses at 2f0, 3f0 were 16.4 dB and 7.2 dB, respectively (2).
ABSORPTION EFFICIENCY OF THE RECTENNA OF AN INFINITE CMSA ARRAY Generally, an infinite array model can apply approximately to the analysis of the large rectenna array. Although the edge effect cannot be evaluated under such approximation, we obtain very simple and useful results. Consider an infinite array of CMSA's shown in Fig. 2. An angle 6 is the direction of propagation of the incident plane wave and is restricted to the x-z plane. Polarization is parallel to the x-z plane. Therefore, we ignore the polarization mismatch loss. Here, we assume that thickness of the substrate is very small compared with the wave length. So, we can consider a very simplified model — single mode (TMno) excitation model of a magnetic current loop on the ground plane. Using the Stark’s method (3), we obtain the active admittance
k is the wave number of the incident wave, and /3m, hn, and ymn are propagation constants of the (/»,«)th space harmonic wave along x, y, and z respectively. These higher waves correspond to grating lobes. When all higher waves are evanescent, the active conductance is expressed using Eq. (2) as follows: where p = ka sinfl. The absorption efficiency of the infinite rectenna array is defined as a ratio of the maximum receiving power of one element to the incident power per an element (4). Then the absorption efficiency is represented by Here, the numerator denotes the absorption cross section. And the denominator denotes the cross section of the cell. The absorption cross section Ae is given by where Grad and D are the radiation conductance and the directivity of a singh element respectively, and G the active conductance. Therefore, Ae is rearranged a: follows: Here, we consider the case of no grating lobes. The substitution of Eq. (3) into Eq. (7) shows that the absorption efficiency r) is 100%. This means that the infinite rectenna array of CMSA’s can absorb the incident power perfectly under the condition of no grating lobes. This result is identical to that on the dipole antenna with ground plane. Figure 3 shows the absorption efficiency vs. element spacing in the case of a square lattice (Lx = Ly = L). When the grating lobe generates, the efficiency be-
comes zero, since all of the incident power flow is along x-z plane or in the direction of propagation of the grating lobe. This phenomenon cannot be observed for an infinite array of dipoles with ground plane where the cancellation occurs between dipoles and their images (3). However, the above discussion ignores the effect of the thickness of the substrate. In fact, it is predicted that the efficiency is greater than zero because the surface wave generates before the grating lobe. This discussion can be extended to the case of the CMSA with losses. When we consider the ohmic and the dielectric losses of the CMSA, the active conductance is rewritten as follows: Both the ohmic and the dielectric losses of the CMSA are affected by the thickness of the dielectric substrate. Figure 4 shows the absorption efficiency under the existence of losses, where the relative dielectric constant of the substrate is 2.6 and tan8 = 2.2x 10-3. As may be seen from this figure, the greater spacing provides the smaller efficiency. In other words, the efficiency becomes less than 100% even if there is no grating lobe. Therefore, it is necessary to define the limit of the absorption efficiency when we design the rectenna practically. CONCLUSION We have estimated the active admittance and the absorption efficiency of the infinite array of the CMSA’s. The infinite array model made these equations very simple, and this paper shows that the absorption efficiency of the infinite rectenna array composed of the CMSA is 100% . The results indicate the possibility of realization of the very thin rectenna which uses the CMSA as the receiving antenna. Acknowledgment — This research project is supported by a grant from the Ministry of Education, Science and Culture under project 56460102. REFERENCES 1. R.J. Gutmann et al.. Directional Receiving Elements and Parallel-Series Combining Analysis, NASA-CR-151866 (N79-16039), 1978. 2. K. Itoh. Y. Akiba, T. Ohgane, and Y. Ogawa, Fundamental Study on SPS Rectenna Printed on a Sheet of Copper Clad Laminate, Space Solar Power Review 5, 149-162, 1985. 3. L. Stark, Microwave Theory of Phased-Array Antennas — A Review, Proc. IEEE 62, 1661-1701, 1974. 4. S. Adachi, O. Suzuki, and S. Abe, Receiving Efficiency of an infinite Phased Array Antenna above a Reflecting Plane, IECE Japan, J64-b, 6, 566-567, 1981.
0883-6272/86 $3.00 + .00 Copyright ® 1986 SUNSAT Energy Council ANALYSIS OF APERTURE ANTENNA ATTACHED TO CUTOFF CAVITY FOR ICRF PLASMA HEATING KUNIO SAWAYA and SABURO ADACHI Department of Electrical Engineering Faculty of Engineering Tohoku University Sendai 980, Japan Abstract — Basic characteristics of an aperture antenna attached to a cutoff cavity for ICRF plasma heating are investigated. The analysis is performed for antennas radiating into semiinfinite free space rather than a magnetoplasma. Good agreement between theory and experiment is observed, indicating the validity of the analysis. INTRODUCTION RF plasma heating in the Ion Cyclotron Range of Frequency (ICRF) has proven to be very efficient in plasma experiments (1). In these experiments, antennas to heat plasmas have been half-turn loop antennas located inside tokamaks. Such antennas, however, have some disadvantages in a fusion reactor, where high power will be applied and impurity ions are produced from metallic materials of antennas and surrounding Faraday shields (1). Under this circumstance, aperture antennas located on a tokamak wall and attached to cavity outside of vacuum vessel are proposed (2—4). Since available dimensions of a port area of tokamak is limited and the frequency used to heat plasma is the order of 100 MHz, the attached cavity would be cut off even if a large tokamak is used. The purpose of this report is to show the basic properties of such an aperture antenna attached to a cutoff cavity. THEORY The geometry of the aperture antenna attached to a rectangular cutoff cavity is illustrated in Fig. 1, where the width of the aperture h is less than X/5 even for large tokamaks. The surface current of the antenna conductor J(x,y) and the tangential electric field E,,(x,y) on the aperture are expressed respectively as follows:
are the vector mode functions of LSEX and LSEy modes, respectively. The antenna current and the aperture field expressed by Eqs. (1) and (2) are substituted in the integral equations which satisfy boundary conditions on the aperture and the antenna surface. Applying the Galerkin's method, one can obtain a (K+L + 2) x (K+L + 2) matrix equation involving unknown lk and V, which can be easily solved numerically. Driving delta gap voltage is assumed at* = 0 and (b-w)!2 <y< (b+w)!2.
COMPARISON WITH EXPERIMENT Figure 2 shows the input impedance of the aperture antennas attached to cutoff cavity comparing with experimental data. It is found that resonance occurs below the frequency of «=0.25X. Good agreement between theory and experiment can be observed indicating the validity of the analysis. NUMERICAL RESULTS Input admittance of the aperture antenna is plotted in Fig. 3 for the varying values of b/a. The sensitivity Q obtained from the admittance characteristics in the vicinity of resonant frequency and the shortening coefficient defined by T7=[a/x]r{,sonanc<, /0.25 are plotted in Fig. 4. As seen in Fig. 3 and Fig. 4, the conductance increases and
the corresponding value of Q decreases rapidly with increasing b/a. This tendency indicates the significance of selecting dimension has large as possible. Figure 5 and Fig. 6 show the sensitivity Q and the shortening coefficient 17 as functions oidia and sla, respectively. Since the cavity is cutoff, it is expected that the sensitivity Q can be improved by decreasing the depth of the antenna s. However, Fig. 6 illustrates the saturating tendency of Q as s decreases. This tendency can be interpreted as follows. For the case of large 5, the aperture electric field is weak and the radiation resistance becomes also small. For a small value of 5, the distribution of electric field is not uniform as shown in Fig. 7 and only the field in the vicinity of the driving point is strong which yields rather a small radiation resistance and a large value of Q.
CONCLUSION Basic characteristics of the aperture antenna attached to a cutoff cavity are investigated. Good agreement between theory and experiment is observed indicating the validity of the analysis. Further investigation of the aperture antenna in the presence of an anisotropic plasma medium can be performed by extending the present analysis. Acknowledgement — This work was supported in part by Scientific Research Grant-in-Aid (grant 59050003, ‘Antennas and related problems for heating in plasmas') from the Ministry of Education. Science and Culture of Japan.
REFERENCES 1. Equipe TFR, 1CRF Results on TFR at Megawatt Power Levels, Plasma Phys. 24(6), 615-627, 1982. 2. H. Arai and N. Goto, A Cutoff Waveguide ICRF Coupler for Large Tokamaks, IEEE Trans. Plasma Sci. PS-13(3), 135-143, 1985. 3. F.W. Perkins and R.F. Kluge, A Resonant-Cavity ICRF Coupler for Large Tokamaks, IEEE Trans. Plasma Sci. PS-12(2), 161-172, 1984. 4. K. Theilhaber, Theory of the JET ICRF Antenna, Nuclear Fusion 24(1), 1383-1392, 1984.
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0883-6272/86 $3.00 + .00 Copyright ® 1986 SUN SAT Energy Council A RIDGED WAVEGUIDE SLOTTED COUPLER FOR LARGE TOKAMAKS HIROYUKI ARAI and NAOHISA GOTO Department of Physical Electronics Faculty of Engineering Tokyo Institute of Technology Ohokayama, Megura-Ku, Tokyo 152, Japan INTRODUCTION A ridged waveguide was proposed to transfer the waves into the plasma through the small cross section for the ICRF heating experiments (1,2). It can be fabricated compactly with all-metal, which is free from the damage of insulators in the coupler. In order to apply the ridged waveguide to the tokamak, this paper newly proposes the slotted coupler which can reduce the VSWR in the ridged waveguide. THE RIDGED WAVEGUIDE SLOTTED COUPLER The maximum transmission power Plm is the power in the case of no reflection from the load. However, the load is not matched to the ridged waveguide, the maximum launching power to the load Pm is given as follows (1). where T, p are the reflection coefficient from the load and the VSWR in the waveguide, respectively. Equation (1) shows that the maximum launching power is inversely proportional to the VSWR in the waveguide. The following experiments are devoted to reduce the VSWR in the ridged waveguide. Simulated Coupler Geometry A ridged waveguide slotted coupler has a short circuit in the mouth and a series of slots like a Faraday shield. Figure 1 shows the overall configuration. The frequency of ICRF heating in JT-60 is planned to be 110 MHz-130 MHz. The simulated coupler was about one-tenth of actual size, and the VSWR in the waveguide was measured around 1 GHz. Design parameters of the coupler are shown in Fig. 2. A polyethylene water tank (260 mm x 260 mm x 300 mm) filled with 20 liter water is used as dielectric instead of the fusion plasma, where the thickness of the polyethylene is 3 mm. In our experiments, there was not a large flange around the mouth for the simplicity of set up. Additionally, the distance to the water tank d could be varied in order to simulate the change in distance to the plasma.
The ridged waveguide consists of a rectangular waveguide of 4 GHz band and a T-shaped aluminum ridge. Three kinds of gap spacing G, 2 mm, 4 mm and 6 mm between the waveguide wall and the plane plate on the ridge were provided. Cutoff frequency for respective waveguide is calculated by the equivalent circuit method (2) as 0.47 GHz, 0.66 GHz and 0.81 GHz. The slotted coupler (coupler II) is compared with the coupler I which has a simple open end. As an other parameter of the slotted coupler, gap spacing g at the mouth were varied for each waveguide. The VSWR generally increases in the absence of water which corresponds to the
plasma being away from the aperture. To overcome this difficulty, the simple matching is tried by inserting a quarter-wave matching section into the coupler as in Fig. 2(III). The coupler with matching section consists of two guides with the different gap spacings, Gj and G2. The detailed length 1 of matching section is determined through the experiment.
Measurement Results The dependence on the distance to the water tank is presented in Fig. 3. In Fig. 3(a), the VSWR of coupler II is always less than that of coupler I, and the increase of the former is more gradual than the latter. The VSWR of slotted coupler is less than half that of coupler I except for the large distance to water tank (d>6 cm). This result indicates that the matching between the ridged waveguide and the water load can be improved by the slotted coupler. The VSWR of g=2.5 mm is a little bit smaller than g=4 mm in the range of d>3 cm, while the VSWR varies considerably by the g for G=6 mm in Fig. 4(b). The VSWR curve of coupler I with G=6 mm is smaller than that of slotted coupler with g=6.4 mm for d>l cm. However, the VSWR of coupler II is improved by the small g, for example, that of g= 1.7 mm is less than half that of coupler I for d<4 cm. The VSWR of the slotted coupler for water load with G=6 mm is also improved, provided the gap spacing g at the mouth is smaller than the G. Though the VSWR for air load is not improved by the slotted coupler, the matching section reduces it less than one-third. One typical result of the slotted coupler with matching section is contrasted with the couplers I and II. It is shown in Fig. 4. The VSWR for air load is reduced from 20-30 less than 7 at the matching frequency. In this paper, we call the frequency of the minimum VSWR the matching frequency. In addition, the effect of matching section is more obvious for water load. The matching section reduces its VSWR less than one-third of coupler II and less than one-fourth of coupler I at the matching frequency. The slotted coupler with matching section is proved to be very effective to reduce the VSWR for the air load. DISCUSSION For the estimation of the maximum power capability of the ICRF coupler, electric fields around the short circuit at the mouth should also be considered. However, those electric fields are expected to be smaller than those in the waveguide, since a node of standing wave is located at the bottom of short circuit. At this stage, the maximum launching power of the slotted coupler by Eq. (1) represents the maximum power capability of the ICRF coupler. According to this procedure, we estimate the maximum launching power of the slotted coupler for water load using the measured VSWR in the waveguide. The maximum transmission power of the ridged waveguide with G=4 mm as in Fig. 3(a), for example, is 10 MW (3). Consequently, the maximum launching power is 3.4 MW for d = 5 mm and 2 MW for d=10 mm by substituting the measured VSWR into Eq. (1). This power capability is sufficient for the ICRF coupler to large tokamaks which need a few million watts incident power. CONCLUSION The ridged waveguide slotted coupler has lower VSWR for water load than that of the simple open ended coupler. The matching section reduces its VSWR to one-third of coupler I for air load and one-fourth for water load. These results suggest that the ridged waveguide slotted coupler is very attractive for ICRF coupler. The applicability of this coupler to the plasma load together with its optimum design is left for future problem.
Acknowledgement — The authors would like to thank Dr. N. Nagashima, Japan Atomic Energy Research Institute for his helpful suggestions. Thanks are also due to K. Sakurai and H. Inoue for their assistance with experiments. REFERENCES 1. H. Tanabe and N. Goto, A Ridged Waveguide Aperture Antenna, Paper of Technical Group, AP-80-22, Institute of Electronics and Communication Engineers of Japan, June 1980. 2. F.W. Perkins, ICRF Couplers. IAEA Technical Committee Meeting on Radio Frequency Heating in Large Fusion Experiments, Princeton Univ. PPL, 19-22, October 1981. 3. Y. Yano, N. Goto, and T. Nagashima, An ICRF Ridged Waveguide Coupler, IAEA Technical Committee Meeting on Radio Frequency Heating in Large Fusion Experiments, Princeton Univ. PPL, 19-22, October 1981.
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0883-6272/86 $3.00 + .00 Copyright ® 1986 SUNSAT Energy Council REFLECTOR ANTENNAS FOR ELECTRON CYCLOTRON RESONANCE HEATING OF FUSION PLASMA OSAMI WADA and MASAMITSU NAKAJIMA Department of Electronics Kyoto University Kyoto 606, Japan Abstract — For electron cyclotron resonance heating (ECH) of fusion plasma, transformation is required of the millimeter wave output from a gyrotron, circular TE„„ mode, into a linearly polarized wave beam. It is easily realized by use of a parabolic cylinder reflector. Vlasov el al. proposed this type of reflector antenna which has a stair-cut aperture at an end of a circular waveguide (1). On the other hand, we proposed another type of antenna which also uses a parabolic cylinder and has an obliquely cut aperture (2). In this paper, the transformation efficiencies of polarization and radiation fields of the two types of antennas are calculated by means of geometrical optics and the Kirchhoff-Huygens principle. Then we propose a mode converter, in which the output of this type of parabolic reflector is led to a rectangular waveguide and transformed into TEW mode. In addition, another reflector antenna is proposed which focuses the wave beam using an elliptic cylinder reflector and a parabolic one. GEOMETRICAL-OPTICS TREATMENT The longitudinal magnetic field of TE()n mode from a gyrotron is given by where kcn = p' onla, p'on is the root of J (p) =0, and a is the radius of the circular waveguide. By virtue of Hansen’s Integral, Eq. (1) is written as where IJUn is a transverse wave vector and A is the angle between \kcn andlr. According to Eq. (2), TE()n mode is represented by a superposition of plane waves which propagate at an angle a with the waveguide axis, where The electric field vectors are perpendicular to the waveguide axis. Radiation from a highly oversized waveguide can be approximately treated by means of geometrical optics. From the aperture of the waveguide, each plane wave above-mentioned is radiated in free space at the same angle a. If the aperture is perpendicular to the waveguide axis, the radiation is axi-symmetric. But when the
lower half of the waveguide is cut away by a length L( = 2«cota) as shown in Fig. 1(a) (1), radiation occurs in the range of Tr/2<i^<37r/2 shown in Fig. 2. If it is cut obliquely at the angle a as shown in Fig. 1(b), most of the radiation is directed into the lower-half. After reflection from the parabolic cylinder reflector whose focal axis coinsides with the waveguide axis, the electric field of each plane wave is oriented in the direction of y-axis of Figs. 2 and 3. Treated by the geometrical optics, the beam width of the stair-cut type in the E-plane is 4/and that in the H-plane is 4</cosa, where /is the focal distance of the parabolic cylinder in Fig. 2. For all of the plane waves from the aperture to be reflected by the parabolic reflector, the height of the reflector It should be equal to/ or higher. For the whole beam from the parabola not to be interrupted by the waveguide,/ should be larger than 1.5a. The field distribution in the H-plane is uniform. The E-plane field distribution is obtained as follows: The radiation power in unit angle is constant and power in Ay at A of Fig. 2 on the reflector (y=2/sint///( 1 - cost//)) is proportional to Ai/z/Ay, so that |£'(y)2<x l/|dy/dt//| and The radiation from this antenna is regarded equivalent to that from a square plane wave source (4/ X 2acosa) having the field distribution as Eq. (4) (see Fig. 4).
In the case of the obliquely-cut type, cut at the angle a,/'can be made as short as a. From this aperture, some of the plane waves are radiated upwards, and the equivalent plane wave source is not square but spreads infinitely in width as shown in Fig. 5. The field distribution is expressed by Eq. (4), most of the power being concentrated around the center of the reflector. So even a reflector with height h = f can catch about 82% of the power. For // = 2/, 3/, and 4/, the efficiency is as large as 91%, 94%, 96%, respectively (Fig. 6). This efficiency t? is derived from the ratio of the reflected power to the whole power. Using a variable t = y/lf, the reflected power from the parabolic reflector with height /t(=/to) is calculated as
RADIATION FIELDS OF THE REFLECTOR ANTENNAS In this section we will calculate the radiation fields from the equivalent plane wave source derived in the previous section. From the equivalence theorem, the radiation from an aperture antenna is equivalent to that from electric and magnetic currents J and M on the aperture. where In is an outward unit normal vector on the aperture 5 and the subscript t denotes tangential components of the field. The electromagnetic fields from the currents are expressed in terms of vector potentials 14 and 14'.
From Eq. (8), the far fields are calculated in spherical coordinates as In the calculation of the far fields, we have used the normalized sizes fa and h/f, and the normalized frequency F(=k/kcn = l-n-a/kp'o„). F is proportional to frequency, F = I corresponding to cut-off. Figure 7 shows the radiation field pattern from the obliquely-cut type antenna. Incident mode is TE01 with F = 1.5 (a = 41.8°) and f/a = 1. In the E-plane the beam is sharpened as the reflector is made deeper and tj is improved. But in the H-plane the beam width does not change. Figure 8 shows the radiation field pattern from the stair-cut type. In this case h/f = 1 and 7? = 100% . The greater the focal distance is, the wider the width of the source in the E-plane is and the sharper the beam. But the beam width in the H-plane does not change. Compared in Fig. 9 are (a) the stair-cut type (F = 55, f/a = 2.0, h/f = 1.0) and (b) the obliquely-cut type (F = 1.55, f/a = 1.19, h/f = 4.53). The aperture width in the E-plane is about (a) 8« and (b) 10a, respectively (see Fig. 10). Half-value angles in the E-plane are (a) 7° (6°), (b) 9° (9°), and those in the H-plane are (a) 18° (17°), (b) 20° (23°). The values in the parentheses are measured half-value angles. Although the
size of (a) is smaller than (b), the half-value angle is smaller. But side lobes of (a) are larger than those of (b). When the incident wave is in higher mode than TE01, the beam is sharper. TE$n-TEn10 MODE CONVERTER Figure 11 shows the configuration of a circular-TE()n to rectangular-TE1(l mode converter. The linearly polarized output wave beam (h0 x 4/) is deflected by a plane conductor and enter a rectangular waveguide («i x b). When the height of the waveguide («,) is appropriate, most of the power of the beam is converted to TEl0 mode. Figure 12 shows numerical results for circular TE(I1 incidence, x = is normalized frequency (x = Fp' On/lTr). The efficiencies have peaks near ax/h0 = 1.3-1.4. ELLIPTIC CYLINDER REFLECTOR ANTENNA ‘ An elliptic cylinder can be used to focus wave beams in the transverse direction. To focus in the longitudinal direction, another parabolic cylinder reflector is used. Figure 13 shows the configuration of the reflector antenna. The beam can be concentrated at an arbitrary point by proper settings of the two reflectors. CONCLUSIONS Two types of parabolic reflector antennas have been compared, (a) the stair-cut type and (b) the obliquely-cut type. The latter antenna (b) can be made compact when h/f is equal to 2 or 3. If the sizes of reflectors are the same, the beam of (a) is sharper than that of (b). The side lobe level of (b) is lower than that of (a). The obliquely-cut type antennas (b) have been used in Gamma-10 (Tsukuba Univ.) and other fusion plasma devices, and satisfactory results have been obtained (3). This research was supported by the Grant-in-Aid for Fusion Research, Ministry of Education, Japan. REFERENCES 1. S.N. Vlasov and I.M. Orlova, Radiophysics and Quantum Electron. 17(1), 1974 (Eng. Trans.). 2. M. Nakajima and O. Wada, Report of the Special Research Project on Nuclear Fusion, 1983 (in Japanese). 3. T. Saito et al., Conf. Digest 9th Int. Conf, on Infrared and Millimeter Waves, Osaka, 1984.
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