ELECTRON cyclotron heating (ECH) using high-power

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1 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 11, NOVEMBER Experimental Verification of Phase Retrieval of Quasi-Optical Millimeter-Wave Beams Hiroshi Idei, Takashi Shimozuma, Michael A. Shapiro, Member, IEEE, Takashi Notake, Shin Kubo, and Richard J. Temkin, Fellow, IEEE Abstract The accuracy of a phase-retrieval procedure for microwave beams was analyzed and verified using an 84-GHz quasi-optical beam transmitted by a corrugated waveguide. The output intensity and phase profiles of the beam were directly measured with a microwave receiver. The beam intensity was also measured at several planes and the data were used with a phase-retrieval algorithm to yield an independent estimate of the phase. Moment and matching coefficient methods were used to analyze the retrieved profiles. In the higher order moment analysis, the intensity profiles, which were calculated from the retrieved phase profiles, coincided well with the measured profiles in terms of the beam size, asymmetric property (skewness), and flatness/peakedness (kurtosis) over the entire profile. Analysis indicated that the mode content of the beam obtained by phase retrieval matched that of the direct measurement with a matching coefficient of 0.97 using both the intensity and phase profiles. Index Terms Electron cyclotron heating (ECH), Gaussian beam, gyrotron, phase measurement, phase retrieval, quasioptical mirror. I. INTRODUCTION ELECTRON cyclotron heating (ECH) using high-power millimeter waves is an attractive method for plasma production, auxiliary heating, and current drive in a nuclear fusion research. In planned fusion experiments at the International Thermonuclear Experimental Reactor, Cadarache, France, the injected ECH will have a total power of 20 MW. To couple into oversized circular corrugated waveguides in the ECH system, an output beam from a high-power gyrotron oscillator leads to a matching-optics unit (MOU), which is transmitted to the launcher by the waveguide transmission line in the mode of the waveguide. The output beam from the gyrotron is then converted into a pure Gaussian beam to attain a high coupling efficiency between the MOU and waveguide. The phase-correcting mirror array at the MOU for the large helical device (LHD) project at the National Institute for Fusion Science, Manuscript received April 17, 2006; revised July 6, This work was supported in part by the Japan U.S. Collaboration in Nuclear Fusion Research under the Personal Exchange Program. The work of M. A. Shapiro and R. J. Temkin was supported by the U.S. Department of Energy, Office of Fusion Energy Sciences, Washington, DC. H. Idei is with the Advanced Fusion Research Center, Research Institute for Applied Mechanics, Kyushu University, Kasuga , Japan ( idei@triam.kyushu-u.ac.jp). T. Shimozuma, T. Notake, and S. Kubo are with the Radio Frequency Plasma Heating Research Division, National Institute for Fusion Science, Toki , Japan. M. A. Shapiro and R. J. Temkin are with the Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA USA. Digital Object Identifier /TMTT Toki, Japan, was designed at the Massachusetts Institute of Technology (MIT), Cambridge [1]. The phase profiles were retrieved from the intensity profiles using the iteration methods explained in [2] [4] because precise phase measurements are unavailable in high-power applications. The retrieval process is necessary to design phase-correcting mirrors. The mirror array designed for the LHD project has been evaluated at the low-power test facilities [5]. To obtain a high transmission efficiency in the corrugated waveguide line, the beam center position and tilt must be aligned within tolerable limits to provide coupling into the mode [6]. Precise quantifications of the beam center and tilt angle are required to investigate their effects on the transmission/coupling efficiency. In this coupling study, a Gaussian-like beam was coupled into a corrugated waveguide at the tilted injection in the - and -directions, which were perpendicular to the propagating -axis [7]. The tilted injection excites the unwanted coupling modes, which causes high transmission losses and arcing events in the high-power transmission. The intensity profiles of the output beam from the waveguide after coupling were offset from the waveguide axis and sidelobes appeared in the - and -directions due to the tilted injection. The beam center and tilt were analyzed from the first moments of the moment theory of a quasi-optical beam [8]. The desired Gaussian content in the output beam was analyzed using the matching-coefficient method. The output beam profile after coupling in the tilted injection is used to compare the retrieved profiles to the measured profiles. The distorted intensity profiles are measured along the propagation. The phase profiles are retrieved from the measured intensity profiles by the iteration method [9]. In this paper, the intensity profiles, which are calculated with the retrieved phase profiles, are compared to the measured profiles. The intensity profiles are analyzed by the moment theory (using higher order moments). Recently, a new approach using the higher order moments to retrieve the phase has been proposed and developed [10], [11]. This paper also evaluates the matching coefficients from both of the intensity and phase profiles measured and calculated in the phase retrieval. Finally, the phase-retrieval process is experimentally tested with the direct intensity and phase measurements at a low power level. This paper is organized as follows. Section II describes the experimental setup and results at the low-power level. The intensity and phase profiles calculated in the phase retrieval are shown in Section III. Section IV discusses the intensity and phase profiles based on the moment theory and matchingcoefficient method, while Section V presents a conclusion /$ IEEE

2 3900 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 11, NOVEMBER 2006 Fig. 1. Experimental setup for the low-power test measurements. Fig. 2. Measured intensity and phase profiles of the input beam in the tilted injection. Data from [9]. II. EXPERIMENTS A. Low-Power Test Facilities The low-power test facilities were used to directly measure the phase profiles of the propagating waves, as well as the intensity profiles with a high resolution and stability of the measuring frequency. The operating frequency was 84 GHz. One synthesizer, which was a microwave ( 20 GHz) source for the multiplier, generated a millimeter wave, while the other was a local oscillator (LO) for the harmonic mixers on both the launcher and receiver sides. Since the conversion losses at the harmonic mixers were not low (typically 35 db), additional IF amplifiers were prepared. The frequency of the IF signal was 20 MHz. The intensity ratio and phase difference between the IF signals on the two sides were detected at a vector network analyzer. To operate the harmonic mixers, an LO pumped amplifier was also prepared. In this system, the dynamic range was more than 90 db for the intensity measurement. The error in the phase measurement was approximately 5 at a power level of 80 dbm [12]. The power level at the launcher was more than 0 dbm, and this study used the precise phase measurement. A three-dimensional stage system controlled the detector-stage position. The setting resolution at the -plane perpendicular to the propagating -axis was mm, while the resolution for the -axis was mm. The setting resolutions of the detector-stage position were on the order of 1/100 for the wavelength at the frequency. The test components were set up by the position control of the three-dimensional stage. A helium neon laser was used to align the components. B. Experimental Setup A corrugated horn antenna and two quasi-optical mirrors prepared the Gaussian beam, which was injected into a 1-m-long circular corrugated waveguide with an 88.9-mm diameter. As shown in Fig. 1, the beam was injected into the waveguide at a tilt angle of 1 with respect to the waveguide axis in the -direction. A small WR-06 waveguide was used for probing the beam in order to avoid the field disturbance. A microwave absorber was used to prevent wave scattering at the probing. Fig. 2 shows the intensity and phase profiles of the injected beam measured in the - and -directions. A Fig. 3. (a) Intensity I(x; y) and (b) phase patterns 8(x; y) of the output beam at z = 150mm. I(x; y) and 8(x; y) are plotted by 2 db and 0.5-rad steps, respectively. From [9]. Gaussian beam with a beam size, mm and a phase curvature, mm explains the beam. The 23-mm beam is slightly smaller than the optimum size (29 mm) to couple into the 88.9-mm-diameter waveguide, but the phase profiles were flat with a large phase curvature (2356 mm) in the main beam part. The beam size and phase curvature evolution along the propagation direction are expressed by Gaussian optics, as explained in [5]. The intensity and phase patterns of the output beam from the waveguide were measured at the propagating positions of and mm, where the origin of the coordinate is the output aperture of the waveguide. C. Measured Intensity and Phase Profiles Fig. 3(a) and (b) shows the intensity and phase patterns and, respectively, of the output beam from the waveguide at the propagating position of mm. Since the input beam was tilted with respect to the waveguide axis, various modes of the waveguide, including a Gaussian-like mode, were excited. The intensity pattern of the output beam was off center in the coordinate. Thus, the intensity pattern was deformed with a sidelobe. The phase front of the beam was not parabolic and contained some aberrations. The tilt in the -direction mainly distorted the beam in the -direction. Fig. 4(a) and (b) shows the measured intensity and phase distributions, respectively, in the -direction at mm. At mm, the intensity sidelobe was large and the peak of an intensity main lobe had a negative coordinate. The main lobe shifted to the positive -direction and the sidelobe became smaller along the propagation direction. The beam power density center positions can be expressed by the first

3 IDEI et al.: EXPERIMENTAL VERIFICATION OF PHASE RETRIEVAL OF QUASI-OPTICAL MILLIMETER-WAVE BEAMS 3901 Fig. 5. First moment evolution along the propagation directions hxi(z) and hyi(z) of the output beam from the waveguide. Dashed lines show the tilted propagation axes, which are defined by the normalized integrals at z = 150 mm. Data from [9]. Fig. 4. (a) Measured intensity and (b) phase distributions in the x-direction at y =0mm. From [9]. moments. Here, the th moments, and are defined with the intensity distribution as The first moment evolutions along the propagation direction and are written in terms of the quasi-optical moment theory as follows [8]: The gradients of the phase in the - and -directions determine local values of the wavenumber. The integrals of the gradients in the -plane with an intensity weight, which were normalized by the total intensity and wavenumber of the beam, expressed the propagating directions of the beam. In the phase distribution shown in Fig. 4(b), the local minimum near the main lobe peak is located at a more negative coordinate than that of the main lobe peak. Thus, there was a phase gradient at the main lobe peak. The phase rapidly changes near the sidelobe. These results were consistent with the intensity profiles along the propagation direction, indicating that the main part of the beam was tilted and the sidelobe part might be expanding. Fig. 5 shows the first moment evolution along the propagation directions and. The first moment is defined as the center of the intensity (1) (2) (3) (4) distribution. The moment at mm was at approximately mm, but the peak of the intensity distribution was at approximately 19 mm. The sidelobe affected the beam center or the moment. Along the propagation direction, the center of the beam moved toward the positive -direction and the sidelobe was expanded. The dashed lines show the tilted propagation axes defined by the normalized integrals at mm. The first moment evolutions were explained well by the tilted propagation axes. The first moments at various positions were in the slope of the tilted propagation axes, indicating that the -plane in the experimental setup was well aligned with the propagating -axis. III. PHASE RETRIEVAL The phase profiles were retrieved from three intensity profiles along the propagation direction. Two data sets at mm and at mm were used for the phase retrieval. Interpolating converted the measured array intensity data into a array. In the phase-retrieval process, the calculated intensity profiles were compared to the measured intensity profiles at the reference plane. Thus, the intensity profiles were calculated with the retrieved phase profiles along the propagation direction. Figs. 6 and 7 show the intensity distributions measured and calculated in the retrievals with the data sets in the - and -directions, respectively, at mm and mm. The distributions were at the beam center lines, which were and The intensity distributions in the retrievals agreed well with the measured distributions down to a level of db below the central peak. Figs. 8 and 9 show the retrieved and measured phase distributions at mm and mm in the - and -directions, respectively. The profiles were also at the beam center lines, which were and The retrieved and measured phase data were interpolated in the intensity dynamic range of 30 db. The phase profiles were normalized at the beam centers. The figures also show the measured intensity distributions. Fig. 8 shows an excellent agreement between the retrieved and measured phase profiles in the intensity dynamic range of 15 db, even near the sidelobe. In Fig. 6, the intensity distributions in the retrieval also coincide with the measured distribution in the dynamic range. The profiles away from the sidelobe,

4 3902 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 11, NOVEMBER 2006 Fig. 6. Intensity distributions in the x-direction measured and calculated in the retrieval at: (a) z =150 mm and (b) 350 mm. Distributions in the retrieval are obtained from two data sets of the measured intensity profiles at z = 150=250=350 mm and at z = 200=300=400 mm. Fig. 8. Retrieved and measured phase distributions in the x-direction at: (a) z = 150 mm and (b) 350 mm. Retrieved phases are obtained from two data sets of the measured intensity profiles at z = 150=250=350 mm and at z = 200=300=400mm. Measured intensity distributions are also shown. with a basis of the phase retrieval may collect a sidelobe in the dynamic range when the intensity profiles, which are calculated in the retrievals, reproduce the measured profiles. Fig. 7. Intensity distributions in the y-direction measured and calculated in the retrieval at: (a) z = 150 mm and (b) 350 mm. Distributions in the retrieval are obtained from two data sets of the measured intensity profiles at z = 150=250=350mm and at z = 200=300=400mm. IV. DISCUSSION The intensity and phase profiles in the retrievals were compared to the measured profiles at the beam center lines in Figs To discuss the validity of the phase retrieval, the similarities of the intensity and phase profiles measured and calculated in the retrieval should be quantified throughout the beam. First, the intensity profiles calculated in the retrievals are discussed with the measured intensity profiles using higher order moments. In [10] and [11], the th moments of were used in the analysis. However, the intensity profiles in this study are mainly deformed in the -direction due to the tilted injection in the -plane as shown in Fig. 3. The th moments, which are uncoupled in the - and -directions, and, are used to compare the calculated and measured intensity profiles. Higher order th moments around the beam centers are defined as follows: shown in Figs. 8 and 9, agree well in the dynamic range of 22 db. The phase profiles retrieved from the two intensity data sets are consistent. It is noteworthy that a quasi-optical mirror designed (5) (6)

5 IDEI et al.: EXPERIMENTAL VERIFICATION OF PHASE RETRIEVAL OF QUASI-OPTICAL MILLIMETER-WAVE BEAMS 3903 Fig. 11. Evolution of the skewness along the propagation direction S (z) of the intensity profiles measured and calculated in the phase retrievals. Fig. 9. Retrieved and measured phase distributions in the y-direction at: (a) z =150 mm and (b) 350 mm. Retrieved phases are obtained from two data sets of the measured intensity profiles at z = 150=250=350 mm and at z = 200=300=400 mm. Measured intensity distributions are also shown. Fig. 12. Evolution of the kurtosis along the propagation direction K (z) of the intensity profiles measured and calculated in the phase retrievals. Fig. 10. Evolution of the effective beam radii along the propagation direction a (z) of the intensity profiles measured and calculated in the phase retrievals. The effective beam radii in the - and -directions are, respectively, expressed with the second moment as The effective beam radii are defined for the intensity distribution. Twice the effective radius corresponds to the beam size (7) (8) in Gaussian optics. Fig. 10 shows the evolution of the effective beam radii along the propagation direction. The evolution of the effective radii in the measured intensity profiles are well explained by those in the calculated profiles. The third moments are used to discuss the asymmetric properties of the intensity distributions. The skewness, which is a measure of the degree of the asymmetry, is defined from the third moment as. A positive or negative skewness expresses the shape of the distribution when the tail expands in the positive or negative direction, respectively. Fig. 11 shows the evolution of the skewness along the propagation direction. The skewness in the -direction is positively larger than that in the -direction due to the sidelobe in the positive -direction. The sidelobe expands along the propagation direction, but a tail with a relative intensity level of more than 20 db is perpetuated, as shown in Fig. 6(b). The skewness due to the sidelobe roughly maintains a constant value along the propagation in the -direction. The fourth moments give the flatness/peakedness of the distribution. The kurtosis to express the flatness of the distribution are defined from the fourth moments as. The kurtosis of a Gaussian distribution is 3. A distribution that has a kurtosis greater than 3 is termed leptokuritic, while a value smaller than 3 is termed platykuritic. Fig. 12 shows the evolution of the kurtosis along the propagation direction. The kurtosis in

6 3904 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 11, NOVEMBER 2006 The phase-retrieval process was experimentally confirmed to be a robust solution for designing phase-correcting mirrors. ACKNOWLEDGMENT Author H. Idei would like to thank the staff of the TRIAM Experimental Group, Kyushu University, Kasuga, Japan, for their continuous support. The authors express their gratitude to Prof. O. Motojima and Prof. N. Noda, both with the National Institute for Fusion Science, Toki, Japan, for promoting the Japan U.S. Collaboration in Nuclear Fusion Research. Fig. 13. Matching coefficient between complex amplitudes measured and calculated in the retrievals along the propagation direction C (z). the retrieval was evaluated at the output aperture of the waveguide. The kurtosis in the -direction, i.e.,, at the aperture is smaller than a Gaussian kurtosis of 3. Thus, the intensity distribution in the -direction is flatter than a Gaussian beam and is mode-like at the waveguide aperture. The intensity distributions calculated in the retrievals agree with the measured distributions in the higher order moments. To discuss both the retrieved phase distribution and intensity distribution, the matching coefficients were evaluated. The matching coefficient compares two complex amplitudes and, and is written as where the complex amplitude is defined from the intensity and phase profiles as. Fig. 13 shows the matching coefficient between the complex amplitudes, which were measured and calculated in the retrievals along the propagation direction. The matching coefficients are approximately 0.97 along the propagation direction. The high matching coefficient indicates that both the intensity and phase profiles calculated in the phase retrievals closely resemble the measured profiles. Precise measurements at the low-power level experimentally verified the intensity and phase profiles calculated in the retrieval. V. CONCLUSION The intensity and phase profiles were precisely measured to compare to the profiles calculated in the phase retrievals at the low power level. The retrieved phase profiles agreed well with the measured phase profiles in the intensity dynamic range of 15 db as the intensity profiles calculated in the retrieval reproduced the measured profiles. From higher order moment analysis, the intensity profiles calculated in the retrieval coincided well with the measured intensity profiles in terms of the beam size, asymmetric property, and flatness/peakedness over the entire distribution. The mode content of the beam in the retrieval to that in the measurement, which was expressed by the matching coefficient, was This high matching coefficient indicated that both the intensity and phase profiles calculated in the phase retrievals agreed very well with the measured profiles. (9) REFERENCES [1] M. A. Shapiro, T. S. Chu, D. R. Denison, M. Sato, T. Shimozuma, and R. J. Temkin, Design of correcting mirrors for a gyrotron used at large helical device, Fusion Eng. Des., vol. 53, pp , [2] A. P. Anderson and S. Sali, New possibilities for phaseless microwave diagnostics. Part I: Error reduction techniques, Proc. Inst. Elect. Eng., vol. 132, pp , Aug [3] A. V. Chirkov, G. G. Denisov, and N. L. Aleksandrov, 3D wavebeam field reconstruction from intensity measurements in a few cross sections, Opt. Commun., vol. 115, pp , [4] D. R. Denison, T. S. Chu, M. A. Shapiro, and R. J. Temkin, Gyrotron internal mode converter reflector shaping from measured field intensity, IEEE Trans. Plasma Sci., vol. 27, no. 2, pp , Feb [5] T. Notake, H. Idei, T. Shimozuma, M. Sato, S. Kubo, S. Ito, Y. Takita, K. Ohkubo, Y. Yoshimura, S. Kobayashi, Y. Mizuno, T. Watari, R. Kumazawa, M. A. Shapiro, and R. J. Temkin, Evaluation of phase correcting mirrors for an 84 GHz gyrotron based on direct phase measurements at low-power level, Fusion Eng. Des., vol. 73, pp. 9 18, [6] K. Ohkubo, S. Kubo, H. Idei, M. Sato, T. Shimozuma, and Y. Takita, Coupling of tilting Gaussian beam with hybrid mode in the corrugated waveguide, Int. J. Infrared Millim. Waves, vol. 18, pp , [7] H. Idei, T. Shimozuma, T. Notake, S. Ito, S. Kubo, M. A. Shapiro, J. P. Anderson, R. J. Temkin, and K. Ohkubo, Beam alignment of ECH transmission line using moment method, in Proc. 27th Int. Infrared Millim. Waves Conf., 2002, pp [8] S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov, Averaged description of wave beams in linear and nonlinear media (method of moments), Izv. Vyssh. Uchebn. Zaved. Radiofiz., vol. 14, pp , [9] H. Idei, T. Shimozuma, M. A. Shapiro, T. Notake, S. Kubo, R. J. Temkin, and K. Ohkubo, Comparison between retrieved and measured phase profiles of quasi-optical beams, in Proc. 28th Int. Infrared Millim. Waves Conf., 2003, pp [10] J. P. Anderson, M. A. Shapiro, R. J. Temkin, and D. R. Denison, Phase retrieval of gyrotron beams based on irradiance moments, IEEE Trans. Microw. Theory Tech., vol. 50, no. 6, pp , Jun [11] M. A. Shapiro, J. P. Anderson, and R. J. Temkin, Synthesis of gyrotron phase-correcting mirrors using irradiance moments, IEEE Trans. Microw. Theory Tech., vol. 53, no. 8, pp , Aug [12] T. Notake, H. Idei, S. Kubo, T. Shimozuma, Y. Yoshimura, S. Kobayashi, Y. Mizuno, S. Ito, Y. Takita, K. Ohkubo, W. Kasparek, T. Watari, and R. Kumazawa, Real time polarization monitor developed for high power electron cyclotron resonance heating and current drive experiments in large helical device, Rev. Sci. Instrum., vol. 76, 2005, Hiroshi Idei received the B.S. degree in physics from Shizuoka University, Shizuoka, Japan, in 1988, and the M.S. and Ph.D. degrees in physics from the Nagoya University, Nagoya, Japan, in 1990 and 1995, respectively. From 1993 to 2003, he was a Research Associate with the Plasma Heating Division, National Institute for Fusion Science. Since 2003, he has been an Associate Professor with the Advanced Fusion Research Center, Research Institute for Applied Mechanics, Kyushu University, Kasuga, Japan. His research interests include plasma confinement research, plasma heating/current drive using microwaves and millimeter waves, plasma diagnostics using microwaves and millimeter waves, and microwave and millimeter-wave components.

7 IDEI et al.: EXPERIMENTAL VERIFICATION OF PHASE RETRIEVAL OF QUASI-OPTICAL MILLIMETER-WAVE BEAMS 3905 experiments. Takashi Shimozuma was born in Sanjo, Japan, in He received the B.Sc. (with honors) and Ph.D. degrees in physics from Kyoto University, Kyoto, Japan, in 1979 and 1985, respectively. From 1984 to 1993, he was with the Central Research Laboratory, Mitsubishi Electric Corporation, Amagasaki, Japan, as a Gyrotron and Plasma Researcher. Since January 1994, he has been with the National Institute for Fusion Science, Toki, Japan. His research interests are the research and development of gyrotrons, ECH systems, and ECH Shin Kubo was born in Matsuyama, Japan, in He received the B.Sc. and Ph.D. degrees in physics from Kyoto University, Kyoto, Japan, in 1978 and 1984, respectively. Since 1984, he has been a Member of the Scientific Staff with the Institute of Plasma Physics, Nagoya University, Nagoya, Japan, which, in 1990, was reorganized as the National Institute for Fusion Science, Toki, Japan, where he is currently an Associate Professor with the Radio Frequency Plasma Heating Division. His research interests are wave processes in plasma, particularly in the microwave region, including microwave-heating systems. Michael A. Shapiro (M 01) received the Ph.D. degree in radio physics from the University of Gorky, Gorky, Russia, in In 1995, he joined the Plasma Science and Fusion Center, Massachusetts Institute of Technology (MIT), Cambridge, where he is currently Head of the Gyrotron Research Group. His research interests include vacuum microwave electron devices, high-power gyrotrons, dynamic nuclear polarization spectroscopy, high gradient linear accelerator structures, quasi-optical millimeter-wave components, and photonic-bandgap structures. Takashi Notake received the B.S. degree from Ritsumeikan University, Kyoto, Japan, in 1999, and the M.S. and Ph.D. degrees from Nagoya University, Nagoya, Japan, in 2001 and 2005, respectively. He is currently a Post-Doctoral Fellow with the Radio Frequency Plasma Heating Research Division, National Institute for Fusion Science. His current interests are pressure and current profiles control of magnetically confined plasmas by use of electron cyclotron resonance heating and current drive (ECRH/ECCD). Richard J. Temkin (F 94) received the B.A. degree in physics from Harvard University, Cambridge, MA, in 1966, and the Ph.D. degree in physics from the Massachusetts Institute of Technology (MIT), Cambridge, in From 1971 to 1974, he was a Research Fellow with the Division of Engineering and Applied Physics, Harvard University. From 1974 to 1979, he was a Staff Member and an Assistant Group Leader with the National Magnet Laboratory, MIT. In 1980, he became Group Leader of the Gyrotron and Advanced Millimeter Sources Group, Plasma Fusion Center, MIT. Since 1985, he has been a Senior Research Scientist with the Physics Department, MIT. Since 1986, he has been Head of the Waves and Beams Division, Plasma Science and Fusion Center, MIT, where he currently serves as the Associate Director.