Coaxial Gyrotrons: Past, Present, and Future (Review) - IEEE Xplore

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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 32, NO. 3, JUNE 2004

Coaxial Gyrotrons: Past, Present, and Future (Review) Olgierd Dumbrajs, Senior Member, IEEE, and Gregory S. Nusinovich, Fellow, IEEE

Invited Paper

Abstract—Most of the present-day millimeter-wave gyrotrons developed for plasma experiments in controlled fusion reactors utilize cylindrical cavities operating in high-order modes. The choice of modes should obey certain restrictions dictated by the achievable mode selection and the maximum admissible level of the density of microwave ohmic losses in the cavity walls. Even with these restrictions, developers have successfully manufactured quasi-continuous-wave gyrotrons operating in the short millimeter wavelength bands that are capable of delivering microwave power on the order of 1 MW. To upgrade gyrotron power to the level of several megawatts, more complicated coaxial microwave circuits should be used. This statement is also valid for relativistic gyroklystrons, which are currently under development for driving future linear accelerators. This paper presents an overview of the history of the development of coaxial gyrodevices, a discussion of the physicsbased issues which are the most important for their operation, a description of the state of the art in the development of coaxial gyrodevices for the above-mentioned applications, and a brief forecast for their future. Index Terms—Coaxial resonators, gyroklystrons, gyrotron oscillators, millimeter-wave radiation.

I. INTRODUCTION

I

N THE development of any microwave source for practically any application, two of the main goals are to increase the radiated power and to shorten the wavelength. Both of these goals require an enlargement of the interaction volume (at least, in terms of the wavelength) and hence lead to operation in higher order modes. This, sooner or later, makes the problem of mode selection unavoidable. For many years, the development of gyrotron oscillators (hereafter referred to simply as “gyrotrons”) was primarily motivated by applications in controlled fusion experiments, where they are used for electron cyclotron resonance plasma heating (see, e.g., [1]–[3] and the references therein), current drive [4], [5], and, more recently, suppression of plasma instabilities [6], [7]. On the other hand, the development of

Manuscript received October 14, 2003; revised January 5, 2004. This work was supported in part by the Office of High Energy Physics and by the Office of Fusion Technology, U.S. Department of Energy. O. Dumbrajs is with the Forschungszentrum Karlsruhe, Institut für Hochleistungsimpuls-und Mikrowellentechnik, Association Euratom—FZK, D-76344 Eggenstein—Leopoldshafen, Germany, and also with the Department of Engineering Physics and Mathematics, Helsinki University of Technology, Association Euratom—Tekes, FIN-02015 HUT, Finland (e-mail: [email protected]). G. S. Nusinovich is with the Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD 20742-3511 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TPS.2004.829976

gyroamplifiers has been, so far, primarily motivated by their use in millimeter-wave radars [8]–[10] and linear accelerators [11]. For all of these applications, the dual goals of increasing radiated power and frequency are important, and thus the issue of mode selection is one of the most critical for the successful development of gyrodevices. In gyrotrons, from the very beginning of their development, it was proposed to use resonators that were open in the axial direction (see, e.g., [12]). This axial openness enables the selection of modes with different axial indexes, since the diffractive losses of modes with only one axial variation in such resonators are much smaller than those for modes with a larger axial index. However, such resonators do not provide the selection of modes with different transverse indexes. Therefore, in the late 1960s, Goldenberg proposed using coaxial resonators for this purpose, because these types of resonators can offer an improved selectivity of modes with different radial indexes. The theory of such resonators was described in [13]. These resonators have been successfully used in gyrotrons for more than 25 years. The aim of this paper is to provide a review of the history of the development of the theory of coaxial resonators and their use in experimental devices, to describe their present status, and to discuss their future. II. HISTORY OF GYROTRONS WITH COAXIAL RESONATORS A. Electron Selection of Modes in Gyrotrons Before we describe the history of the development of gyrotrons with coaxial resonators, it is worthwhile to explain some basic features of their mode selectivity. Typically, in gyrotrons, thin annular electron beams are used. Their coupling to the transverse-electric (TE) modes of cylindrical resonators , where are described [14] by Bessel functions is the azimuthal mode index, is the cyclotron resonance harmonic number, and “minus” and “plus” signs correspond to the co- and counter-rotating modes with respect to the gyration of the electrons in the external magnetic field; is the transverse wavenumber, which is determined by the mode and the resonator wall radius ; and is eigennumber the radius of the electron guiding centers. (For modes, .) As this eigennumber is the th root of the equation is well known, the Bessel functions have the largest maximum closer to the axis, i.e., where the radial coordinate is close to (see, for example, [15]). the caustic radius, Thus, by locating the beam at this position, one can provide the maximum coupling to the field of the desired mode. Simultaneously, for the modes with smaller radial indexes, the beam

0093-3813/04$20.00 © 2004 IEEE

DUMBRAJS AND NUSINOVICH: COAXIAL GYROTRONS: PAST, PRESENT, AND FUTURE

Fig. 1. Dependence of TE-mode eigenvalues on the ratio of the outer to inner radii in a coaxial resonator.

is located inside their caustics, where the field exponentially decays with the radial coordinate, and the beam coupling to these modes is correspondingly small. It is more difficult to provide the selection with regard to modes with larger radial indexes; however, these modes occupy a larger cross section, and therefore their starting currents can be higher than those for the desired mode. This method of selective mode excitation by a proper positioning of a thin annular electron beam was called the “electron selection.” Of course, the effectiveness of this method of mode selection depends on the density of the mode spectrum in the vicinity of the desired mode. Spectrum Rarefaction: In a coaxial geometry, the presence of an inner conductor, first of all, changes the spectrum of mode eigenfrequencies. In the coaxial resonator, the cutoff frequencies depend on the ratio , where and are the outer and inner wall radii, respectively. More exactly, these frequencies are determined by (1) . A typical example of this dewhere modes in Fig. 1, which pendence is given for low-order is similar to [13, Fig. 2]. As is seen in this figure, all nonsymmetric TE modes have a region of ratios , in which the dependence of cutoff frequencies on this ratio is anomalous. By this, we mean that typically the cutoff frequencies increase with the increase in the waveguide transverse dimensions. In our case, however, there is a region, in which the increase in caused by the decrease in the diameter of the coaxial insert results in . As one can the increase of the cutoff frequency see in Fig. 1, at large ratios of coaxial radii these dependences asymptotically approach their values in cylindrical resonators. As follows from the dependences shown in Fig. 1, even in the case of using a coaxial insert of a constant radius, one can rarify the spectrum in the vicinity of the desired mode and improve the mode selectivity this way. It should be noted, however, that in the case of operation at very high order modes, in order to suppress the modes having just one more radial variation than the desired one, it is necessary to position the inner coax so close to the caustic region of

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the operating mode that the ohmic losses of the latter mode become too high for continuous wave (CW) operation. (This issue will be discussed in more detail.) Conductor Tapering: The coaxial insert can also be tapered axially, which yields an additional opportunity for mode selection. Intuitively, this seems quite obvious, because one can distinguish the modes with small radial indexes, whose fields should be weakly disturbed by the coaxial insert, and the modes with large radial indexes, which should experience significant disturbance by this coax, when their caustic radius in a cylindrical cavity is smaller than the radius of a coaxial insert. Since any mode can be represented as a set of rays propagating in the cavity and reflecting from its walls, one can easily imagine the rays (see, e.g., [1]), which upon being reflected from a down-tapered coaxial insert propagate toward an open output end of the cavity. Clearly, this reflection from the down-tapered insert, which increases the axial wavenumber and, hence, the group velocity of the wave, increases the diffractive losses of modes with large radial indexes. This argument can also be illustrated by considering the inhomogeneous string equation, which, being treated together with corresponding boundary conditions, determines the axial structure of the mode (here, “ ” is the mode index), in a so-called cold-cavity approximation (i.e., neglecting the effect of the electron beam on the axial distribution of the mode). As is well known [16], this equation has a form

(2) where is the mode axial wavenumber determined by the equation . In cylindrical resonators, the transverse wavenumber depends on the resonator wall radius, and this dependence is essentially the same for all modes. In coaxial resonators, this number depends on the radii of both the outer and inner wall. When these radii are slightly tapered , (here and are some initial or unperturbed values of can these radii), the normalized transverse wavenumbers be expanded in a Taylor series in the vicinity of their values for and . Correspondingly, the axial wavenumber can be determined by

(3) From (2) and (3), it follows that for coaxial resonators with tapered conductors, in contrast to conventional cylindrical resonators, the modes that are closely separated in frequency but have different derivatives have different axial structures and, correspondingly, different diffractive losses. To make the consequences of the long formula of (3) more transparent, one can consider, as was done in [13] and [17], an is deterequivalent empty resonator, whose axial structure results mined by (2), but the tapering of its wall radius

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in the same axial dependence of the axial wavenumber as that given by (3), i.e.,

(4) Consider, for instance, the case where the outer wall of the coaxial resonator has a constant radius and the inner wall is down-tapered ( , ). In such a case, the modes with have an axial structure corresponding to the axial structure of modes in an empty resonator . Clearly, this with a down-tapered outer wall down tapering reduces diffractive losses of the outgoing radiation, or, in other words, increases the diffractive of the resin onator. On the contrary, the modes with the same resonator have an axial structure similar to that in a , cylindrical resonator with an up-tapered wall which results in large diffractive losses, i.e., low diffractive s. It should be noted that, in parallel with the analysis of coaxial resonators with tapered walls, resonators with a periodically slotted outer wall and an absorbing inner coax were also studied [18]. This concept was driven by the idea that in the process of their azimuthal rotation, all modes whose azimuthal indexes are not equal to the number of azimuthal variations in the corrugation will be transformed by the corrugated outer wall into the modes with large radial indexes whose fields penetrate into the inner absorber. It was found, however, that this method of mode selection is sufficiently efficient only for operating modes with very small radial indexes. The effect of azimuthally periodic axial slots in the walls on the mode-selective properties of coaxial resonators will be discussed in detail. Restrictions on the Choice of Operating Modes: In the CW and high-average power regimes of operation, one of the most critical issues in gyrotron design is accounting for ohmic heating in the resonator walls. Since the ohmic factor can be estimated by the ratio of the radial distance occupied by the RF , to field, which in cylindrical resonators is the distance the skin depth, it is obvious that to increase ohmic one should operate at modes with larger radial indexes. However, when the radial index becomes very large and the beam is still positioned near the caustic of the mode of choice, the voltage depression becomes significant. This results not only in the decrease of the electron kinetic energy, but also in the increase in the electron velocity spread. In such situations, the introduction of an inner coaxial insert is extremely beneficial, because locating this insert near the beam solves the problem of voltage depression. As was noted above, however, there is a tradeoff between efficient mode selection and maintaining sufficiently low ohmic losses in the coax. For efficient mode selection, the radius of the coaxial insert should be close to the caustic radius of the mode; in this case, the modes with larger raoperating dial indexes will experience a strong influence from this insert, which will result in increasing their diffractive losses. Such a positioning, however, can lead to unacceptably high ohmic losses of the operating mode power in the coax, because close to the caustic, the field of this mode can be sufficiently strong.

B. First Experiments With Coaxial Gyrotrons—Inverted MIG The first experiment with gyrotrons utilizing coaxial resonators was carried out in the U.S.S.R. in the early 1970s [19]. In that experiment, the competing modes were the and modes. It was shown that in an empty cylindrical resonator, when the electron beam radius is about 80% of the mode dominates and generates up wall radius, the to almost 400 kW of power with the maximum efficiency of about 45%. The introduction of a coaxial insert provided a shift mode, increasing of the cold-cavity frequency of the the frequency separation between the modes from less than 2% to about 6% [20]. This made it possible to avoid mode competition and, hence, to use a beam with a radius that was smaller than the caustic radius of the mode with one radial variation in order to locate the beam in the area where the beam coupling to the field of this mode was rather small. This resulted in rather high starting and optimum operating currents, and, correspondingly, the efficiency and the output power mode in the gyrotron with the coaxial obtained at the resonator was approximately the same as in the conventional mode. gyrotron operating at the The second experiment was conducted soon after, in 1973, and featured two types of down-tapered inner coaxes—one with a lossy dielectric on the surface and another with a metallic rod [21]. This experiment was the first in which the gyrotron power exceeded the 1-MW level. The first mention of this experiment in an English language reference can be found in [22], which briefly refers to a gyrotron generating an output power of 1.25 MW at an efficiency of 35%, operating at a wavelength of 6.7 mm and pulse length of 100 s. Later [20], it was explained that a down-tapered inner coax was used and that the . It should be noted (although this operating mode was was not clearly stated in the first publications) that to achieve reliable operation at 1.25 MW using a coaxial gyrotron configuration, an inverted magnetron injection gun (MIG) was used, which allowed for the axial support of an inner coax without interception of the beam electrons by radial supporting pins required by a noninverted design. The principle of such an inverted gun, in which an inner rod plays the role of the anode in the gun region and then becomes an inner coaxial conductor providing the mode selection in the resonator region, was described in the open literature much later [23]. The schematic of such an inverted gun and an example photograph are shown, respectively, in Figs. 2 and 3, reproduced from [23]. In the 1980s, an experiment with a 2.1-MW 100-GHz coaxial mode was performed [1]. In gyrotron operating at the this short-pulse experiment (100 s), the fact that the peak density of ohmic losses was less than 1.5 kW/cm made this choice of mode acceptable for CW operation. As mentioned in [24], this record power level was achieved with an efficiency approaching 30%. Despite the success of these experiments, there was a certain lack of interest in coaxial gyrotrons during the late 1970s and the 1980s. This can be explained by at least two reasons. First, during this period of time, the plasma community was satisfied with gyrotrons that could generate several hundred kilowatts of microwave power at frequencies below 100 GHz with pulses


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III. RECENT PROGRESS ON GYROTRONS WITH COAXIAL RESONATORS

Fig. 2. Schematic of the geometry of electrodes and electron trajectories in an inverted magnetron-type electron gun.

Fig. 3.

Photograph of an inverted electron gun.

on the order of 0.1 s. To fulfill these requirements, it was sufficient to operate at modes that could be selected using the method of electron selection as described above. (In addition, improved methods for cooling the resonator walls enabled an increase in the maximum allowable power density of ohmic losses.) For a certain period of time, the modes of choice were the modes with , two radial variations and increasing azimuthal index ( , and then .) Later, the radial index was increased up to 6, but it was still possible to provide an efficient electron modes at mode selection even in the case of operation at a 1-MW level [25]. Thus, at that time, there was no real need to make gyrotrons more complicated, albeit the operation at modes with six radial variations was already accompanied with substantial voltage depression, and selective mode excitation was not an easy problem. The second reason was, possibly, due to the limitations on the maximum level of microwave power that could be sustained in long-pulse and CW operation using the then current state-of-the-art in vacuum windows. At that time, beryllia and alumina were the two most common materials used for the output windows. At first, the windows were fabricated in a single-disk configuration that was cooled on the periphery; later, windows were fabricated in a double-disk configuration that allowed coolant to flow between the two disks, cooling the inner faces [2]. However, at millimeter-wave frequencies, operation with these windows was limited to only several hundreds of kilowatts of CW power.

During the 1990s and early 2000s, significant progress was made in the development of coaxial cavity gyrotrons. The most impressive progress was demonstrated by the gyrotron team of the Kernforschungszentrum Karlsruhe [(KfK), which was later renamed as Forschungszentrum Karlsruhe (FZK)] in Germany, where this work was done as an International Thermonuclear Experimental Reactor (ITER) task in European Fusion Development Agreement (EDFA) cooperation between FZK Karlsruhe and HUT Helsinki. During the early stage of development, this team greatly benefited from collaboration with the Russian gyrotron team at Nizhny Novgorod. Work on coaxial gyrotrons also continued independently in Russia. In addition, some studies of coaxial gyrotrons were performed in the U.S., Brazil, and Japan. In particular, in Brazil, at the beginning of 1990s, some theoretical and experimental work was done at the Plasma Physics Laboratory at the National Institute for Space Research (Sao Jose dos Campos). This work included the design mode of a 1-MW 280-GHz gyrotron operating in the [26], a redesign of this gyrotron for operation in the mode [27], experimental studies of the selective properties of coaxial resonators [28], experimental studies of ohmic losses in coaxial resonators with a silicon carbide coaxial insert [29], and the analysis of space-charge limited currents in coaxial resonators [30]. Unfortunately, this activity was subsequently terminated. Results of the studies of coaxial gyrotrons in the U.S. and Japan are presented in Section III-E. In the U.S., in addition to the development of coaxial gyrotron oscillators for use in controlled fusion experiments, the University of Maryland also developed the first coaxial gyroklystrons for driving future linear accelerators. Impressive experimental achievements will be described at the end of this section. In Section III-A, we will first discuss the innovations made in coaxial gyrotrons and the theoretical results. A. Corrugated Inner Conductor Analyses of coaxial gyrotrons with a smooth-walled tapered inner conductor have shown that in order to provide efficient mode selection to enable the discrimination of modes with radial indexes larger than that of the operating high-order mode, it is necessary to locate the inner coax rather close to the caustic region of the desired mode. Such a location, as we discussed above, results in excessive ohmic losses of microwave power, which leads to overheating of the coax in CW and long-pulse operation (see, e.g., [17]). Also, diffractive factors of the modes increase, with the positive slope of the derivative complicating the problem of mode selection. To address these issues, it was proposed to use an inner conductor with axial slots, instead of a smooth-walled coax [31]. (Note that this concept was proposed in the early 1990s by Denisov [32].) The transverse cross section of such a resonator is shown in Fig. 4. is When the number of slots on the surface of the coax large enough (5)

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Fig. 4. Transverse cross section of a coaxial cavity with a corrugated insert.

this surface can be characterized by an average surface impedance that greatly simplifies the treatment of such cavities. The first papers on the theory of such resonators based on this approach were published in 1996 [33], [34]. We briefly outline only the most important elements of this theory; interested readers are referred to [33], [34], and other papers for details. When the condition given by (5) holds, the normalized surface impedance can be determined as (6) is the period, is the width, and is the Here, depth of corrugations (azimuthal angles corresponding to the and , respectively, period and the width of corrugations, are shown in Fig. 4). As follows from (6), when the corrugation , the surface impedance becomes infinitely depth is equal to large and, correspondingly, the RF magnetic field at the surface becomes very small. Since just this field penetrates into the wall of a metal with finite conductivity, this means that ohmic losses in such a corrugated insert can be rather small, much smaller than in inserts with smooth walls. (We believe that this issue was analyzed for the first time in [35].) This fact alone is extremely important for multimegawatt class gyrotrons intended for operation in the CW and long-pulse regimes. Of course, in such a case, the Helmholtz equation, which determines the membrane function describing the transverse structure of the magnetic field of TE modes, should be supplemented by the Neumann boundary condition (as in the case of TM modes) instead of the Dirichlet condition typical for TE modes. The use of this impedance in corresponding boundary conditions results in the following characteristic equation, which replaces (1):

(7) As one can easily see, when the depth of the corrugations is , (7) reduces to (1). At finite values made vanishing small, of , however, (7) yields solutions whose topology is quite different from those shown in Fig. 1. In general, the axial corrugations offer a way to avoid the positive slope of the eigenvalue curve in terms of the parameter . The part of the eigenvalue

curve with positive slope does not disappear, but as the corrugation depth increases, it moves toward higher values of beyond the typical operating range. Considering the fact that the minin a noncorrugated system imum of the eigenvalue curve corresponds to the caustic radius of the mode, modes with larger radial indexes than that of the operating one will exhibit a posat even higher values of . In the opitive slope erating range of , an even greater number of modes with large , which radial indexes will have negative slopes means that their diffractive factors become smaller. On the other hand, there are always modes with eigenvalues that are close to the eigenvalue of the operating mode with large posiin the operating range. Such modes, tive slopes however, are strongly perturbed by the inner conductor and their field energy is almost completely localized inside the grooves. , these modes Due to their large positive slope could become serious competitors for the operating mode. However, when the coaxial insert contains some absorbers, the ohmic factor of these modes is very low, and thus they should not cause problems with mode competition. An important conclusion from the results presented in [33] is that to improve the stability of the operating mode against competing modes at the fundamental and second cyclotron harmonics, it is reasonable to choose the depth of corrugations close to 20% of the cutoff wavelength. When the presence of second harmonic modes in the spectrum is not important, the depth of corrugations can be increased up to 3/8 of the wavelength. In addition to these first papers on gyrotrons with slotted coaxial resonators, [36] should also be mentioned. This document (a doctoral thesis containing over 200 pages) was prepared by Kern; as it was written in German, its use is somewhat restricted in the international gyrotron community. Nevertheless, it is well written and is actively used by the gyrotron group at FZK. A further improvement of coaxial resonators based on the use of a corrugated insert with longitudinal corrugations of a variable depth was proposed in [37]. Here, both the corrugation depend on depth and the normalized impedance parameter the longitudinal coordinate . This changes the topology of the eigenvalue curves obtained by solving (7) in comparison with the case of constant and . An example of these solutions is shown in Fig. 5. Here, Fig. 5(a) plots the eigenvalue of the mode, which was chosen as the operating mode in a 1.5-MW 165-GHz coaxial FZK gyrotron, which will be discussed, for three cases: 1) smooth-walled inner coax (solution of (1) is shown by the dotted line); 2) slotted inner coax with a constant depth of corrugations (solution of (7) for constant is shown by the solid line); and 3) inner coax with a variable depth of corrugations (dashed line). Fig. 5(b) shows similar dependencies for one of the most dangerous parasitic modes, i.e., . Note that the vertical scale in these two figures is different. From comparison of these figures it follows that the variable depth leads to a much larger relative increase of the slope of the eigenvalue curve of the parasitic mode than for the operating mode (see Fig. 5). In these calculations, it was assumed mm between mm and mm and that that mm between mm the depth increases linearly to mm. In general, the variable and the cavity end at


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140-GHz 1.5-MW coaxial gyrotron operating at the mode. It was found that displacements of the order of could be tolerated. C. Frequency Tunability

Fig. 5. Eigenvalues of (a) operating mode and (b) one of the parasitic modes as functions of the outer-to-inner radii ratio in a coaxial gyrotron with a corrugated insert.

depth of the grooves acts quite differently on different modes; , , and the quality factors of the triplet change very little, whereas the quality factors of the parasitic , , and modes significantly decrease. This improves the mode competition situation. Another beneficial effect of the use of a variable depth of longitudinal corrugations is related to the redistribution (smearing) of ohmic losses in the insert along the axial direction. Before closing this section, let us mention that there are some attempts to characterize coaxial resonators with corrugated inserts without using the concept of an equivalent surface impedance as discussed above, which becomes incorrect when the width of slots is on the order of the wavelength. These approaches and corresponding results can be found in [38] and [39]. B. Tolerances Since coaxial gyrotrons, especially those in which inverted electron guns are used, are more complicated than standard cylindrical gyrotrons, the issue of the sensitivity of the operation of such tubes to various misalignments is extremely important. The effect of the parallel displacement of an inner coax on the gyrotron operation was analyzed in [40]. It was shown that such a displacement leads to a frequency shift, factor, causes some changes in the reduces the diffractive gyrotron startup scenario, and redistributes the ohmic losses of the microwave power in the walls. In [40], the theory and the accompanying effects were illustrated by considering a

For a number of gyrotron applications in controlled fusion experiments, it is desirable to have frequency tunable gyrotrons. This is particularly important in the case of gyrotrons used for the suppression of such plasma instabilities as neoclassical tearing modes (NTMs) [6], [7]. Typically, the radial width of “magnetic islands,” in which the NTM can be triggered, and hence, where the gyrotron power should be deposited for generating the current drive stabilizing the NTM, is rather narrow (on the order of a few centimeters). Also, its localization depends on the magnetic fields and other operational parameters. Therefore, it is desirable to have, if not continuously tunable, then at least step-tunable gyrotrons with frequency steps of about 1%–2%. It is also important to have the ability to tune the gyrotron frequency fast enough, before the instability can significantly deteriorate the plasma confinement. Estimates indicate that typically, to suppress the NTM modes, the gyrotron frequency should be capable of being tuned on a 100-ms time scale. This relatively short time excludes the variation of the magnetic field of the main superconducting solenoid from consideration as a means of frequency tuning. On the other hand, applications with relatively long time scales, such as the startup procedure in large tokamaks, can use gyrotrons that are frequency tuned by variation of the magnetic field. This quite complicated issue is discussed in [41] and is beyond the scope of our paper, since it is equally important for gyrotrons with conventional cylindrical and coaxial resonators. Compared with cylindrical gyrotrons, coaxial gyrotrons, however, can offer an additional opportunity of a relatively slow continuous frequency tuning by moving the tapered inner conductor in the axial direction. This concept has been analyzed in [42] where it was shown that in a 140-GHz gyrotron the frequency could be continuously tuned within a bandwidth of about 1 GHz. We will describe some experiments with frequency tunable gyrotrons in Section III-E. D. Energy Recovery At the first glance, as seen in Figs. 2 and 3, the use of inverted electron guns in coaxial gyrotrons makes the devices more complicated because it requires the presence of two insulators separating the cathode from the body and the inner coax. This configuration, however, makes it possible to recover the electron energy in these devices without the use of depressed collectors separated from the body of the tube. Indeed, since it is desirable for the beam to be located near the caustic of the operating mode in order to enable efficient coupling of the electrons to that mode, and since the inner coax should also be located in this area to provide for mode selection, the beam potential is predominantly determined by the potential of the inner coax. This means that when the potential of this coax is higher than the potential of the body of the tube, the energy of a spent electron beam will decrease as the beam departs from the interaction space and approaches the collector, which can be grounded together with the

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tube body. So, the only concern with regard to this natural depression of the beam potential is the possibility of appearance of reflected electrons similar to the same effect in conventional gyrotrons with depressed collectors. In other words, to avoid the appearance of reflected electrons, this voltage depression and the magnetic decompression of the beam in the region between the cavity and the collector should be consistent. To the best of our knowledge, this idea and corresponding successful experiments with 1-MW 50% efficiency 140-GHz gyrotrons were reported first time in [43]. E. Experiments With Coaxial Gyrotron Oscillators Since we just started to describe experimental achievements, it makes sense, first, to explain the reason why this will be done in a separate section. This reason is motivated by the fact that in many of the experiments, a number of physical issues discussed above were studied simultaneously. Therefore, in this section, we will try to describe the most significant experiments and highlight the most important features of them. First of all, we note the development of a 1-MW-CW mode with 170-GHz coaxial gyrotron operating at the an inverted electron gun. This device was developed by the Toshiba Corporation in Japan during the first half of 1990s [44]. At that time, available output windows were limited to about 0.5 MW of millimeter-wave power in CW operation, so the gyrotron was designed with a dual output. The outgoing radiation was split into two wave arms, each forwarded to a separate window located 120 apart with respect to the gyrotron axis. Unfortunately, this project was terminated later. As a major step on the road to construction of powerful coaxial gyrotrons, we also should mention a particular tube which was developed within a framework of German–Russian collaboration [45]. Since [45] contains a review of previous papers describing the first steps in the development of this tube, we will simply provide a summary of its most important features. The tube was designed for 1.5-MW level operation mode at 140 GHz. The inverted electron gun at the (90 kV, 50 A) for this tube is described in [23]. The inner rod was negatively tapered (with a taper angle of 1 ) and contained 72 longitudinal grooves with a period smaller than one-half of the free-space wavelength. The quasi-optical output system was based on a two-step mode conversion scheme. First, a rippled-wall mode converter consisting of 104 axial slots transmode with the eigennumber formed the corotating mode with equal to 87.36 into the counterrotating the eigennumber equal to 87.38 (these modes are practically degenerate and can easily be converted from one into another when the azimuthal index of the converter equals the sum of azimuthal indexes of two modes). Then, the counterrotating mode, which was localized near the outer wall, was transformed output wave beams. Since the azimuthal angle into two mode is rather of divergence of the radiation of the small (less than 60 ), it was possible to use a rather compact double-cut quasi-optical mode converter to convert this mode into the desired wave beams. From this launcher, two narrow output wave beams were radiated in opposite directions. Then, two pairs of parabolic mirrors directed these wave beams


toward the output windows. In this experiment, which was the first experiment with a dual RF output, a power level of about 1 MW was achieved at an efficiency of 20%. The measured efficiency was lower than predicted by simulations. This discrepancy was explained by the unsatisfactory performance of the rippled-wall mode converter, possibly due to insufficient precision in its fabrication. In addition, the efficiency may have been further degraded by a lack of sufficiently high beam quality that could result in the appearance of trapped particles. Of course, the two-step mode conversion realized in these experiments limited the operation of the tube to a single operating mode only, thus making it impossible to use such devices in applications where the frequency tuning is required. We should note that when reliable CVD diamond windows became available [46], the concept of gyrotrons with dual RF outputs was rendered less important. Present-day estimates indicate that CVD diamond windows can successfully transmit CW power up to about 2 MW at short millimeter wavelengths. Nevertheless, the dual output concept can still be viable for next-generation coaxial gyrotrons, which will be discussed in Section IV. In the second half of the 1990s, there was a certain activity among U.S. researchers aimed at the development of 3-MW 140-GHz coaxial gyrotrons. The first such device was designed [47] and experimentally evaluated [48]. However, for a number of reasons, in short-pulse experiments the maximum power reached the 1-MW level with an efficiency of only 16%. It was found that the reduced efficiency could be attributed to poor azimuthal uniformity of the cathode emission. Also, it appeared that the alignment of the electron gun, cavity, and coaxial insert was not sufficiently accurate. At FZK, the frequency step tuning in coaxial gyrotrons was studied experimentally over the range of frequencies from 134 GHz to about 170 GHz [49]. In order to avoid the effect of window reflections, this gyrotron was equipped with a broadband Brewster window. By that time, in single-mode experiments with the coaxial gyrotron operating at the mode at 165 GHz, the FZK group had already achieved 1.7 MW of output power with more than 26% efficiency [50]. Therefore, it was decided to use this gyrotron with a down-tapered grooved inner coax as a prototype for experiments with frequency tuning. The measurements on step-frequency tuning were performed using a slow variation of the main magnetic field. Simultaneously with varying the field of the main superconducting solenoid, the field of an additional solenoid located in the gun region was varied to adjust the orbital-to-axial electron velocity ratio. This variation also resulted in a change in location of the electron beam in the cavity. As a result, a set of modes with 14, 15, 16, and 17 radial variations was excited in the above-mentioned frequency range. Altogether, there were 19 modes in this frequency range. It was found that the power in the excited modes varied from 0.6 MW to about 1.5 MW. The upper frequency in these experiments was limited by the available magnetic field of a superconducting solenoid. All modes were transformed into wave beams with the use of a so-called Vlasov launcher followed by two mirrors, one with a quasi-elliptic and the other with a nonquadratic phase correcting surface. The measurements of the RF output wave


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Fig. 6. Schematic layout of the 1.5-MW 165-GHz coaxial FZK gyrotron and its cavity.

beam showed that the generated power of all modes was well transmitted through the Brewster window, which was made of Si N . Finally, we should mention the latest results on coaxial gyrotrons that culminate this FZK activity. First, we note that the feasibility of fabrication of 2-MW 170-GHz coaxial gyrotrons for ITER has been demonstrated [51]. In the first set of experiments at FZK [51], the gyrotron was operating at mode at a frequency of 165 GHz. The schematic the layout of this tube and its cavity, including a down-tapered inner coax, are shown in Fig. 6 reproduced from [51]. A maximum output power of 2.2 MW was achieved with an efficiency of 28%; at the 1.5-MW power level, an output efficiency of 30% (without depressed collector) was realized. Operation with a single-stage depressed collector resulted in an enhancement of the efficiency from 30% to 48%, while maintaining a constant 1.5 MW output power level. The experiments reported in [51] were mostly performed with a pulse length of about 1 ms. In these experiments, a new coaxial electron gun was used, which is described in detail in [52]. As shown in Fig. 7 (reproduced from [52]), in this gun the electrons are accelerated toward the outer anode as in conventional gyrotrons, and the coaxial insert is supported from the bottom of the gun. The insert is water-cooled and is adjustable while the gun is in operation. The dipole coils shown in Fig. 6 can be used to radially displace the beam, which is of great advantage for alignment. It was shown that such a gun is more compact than an inverted gun with similar parameters.

Fig. 7. gun.

Electron trajectories and potential lines in a novel 4.5-MW electron

Results of studies of various phenomena in the coaxial gymode at 165 GHz are summarotron operating in the rized in a recent paper [53] which contains all references to relevant publications. These studies include: 1 ) investigation of stable operating conditions and of efficient microwave power generation; 2 ) investigation of the performance as a function of increasing pulse lengths; 3 ) measurements of the mechanical stability of the coaxial insert under operating conditions with intense water cooling; 4 ) measurements of losses in the coaxial insert and comparison with calculations; 5 ) investigation of the deposition of stray microwave radiation captured inside the tube;

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6 ) study of the possible mechanisms of parasitic low frequency ( 100 MHz) oscillations; 7 ) measurements of the influence of the misalignment of the coaxial insert on the operating conditions of the gyrotron; 8 ) fast frequency tuning (within 0.1 ms) by applying a bias voltage at the insert; 9 ) investigation of Penning discharge and ways to suppress it; 10 ) investigation of the hysteresis effect, which can be important for evaluating the impact of voltage overshooting during the voltage rise [54]; 11 ) investigation of the leakage current to the body/coax insert. -mode coaxial At present, the studies on the 165-GHz gyrotron at FZK have been completed and the tube has been disassembled. F. Coaxial Gyroklystrons In addition to the development of coaxial gyrotron oscillators for controlled fusion experiments, coaxial gyroklystrons driven by relativistic electron beams are under development at the University of Maryland. This program is aimed at the development of high-power high-frequency microwave sources for driving future linear accelerators and is sponsored by the Office of High Energy Physics, U.S. Department of Energy. The program was started more than 15 years ago [55]. Initially, the goal was to develop X-band and Ku-band relativistic gyroklystrons operating at a power level of about 30 MW. These steps were realized in a series of successful experiments described in [11]. First, several X-band gyroklystrons operating at the fundamental cymode in all cavities were develclotron resonance in the oped and tested. In these two- and three-cavity experiments, the output power level was close to 30 MW (in 1–2- s pulses), the efficiency was 30% and higher, and the gain achieved was higher than 30 dB in the two-cavity gyroklystron and about 50 dB in the three-cavity devices [56]. Subsequently, a series of experiments were performed with two-cavity frequency-doubling gyroklystrons. In these devices, the operating mode in the output mode. As the result, more than 30 MW cavity was the output power was produced at frequencies close to 20 GHz at an efficiency of about 30% and a gain close to 30 dB. The next step in this program was to upgrade the system to increase the power up to 100 MW level. Since it was impossible to realize this power level operating at such a low-order , it was decided to choose the next symmetric mode as mode as the operating mode in the output cavity. Since the annular relativistic electron beam used to drive this device has rather large transverse dimensions, it was necessary to have the drift tunnel of a rather large diameter. In the case of using simple cylindrical waveguides, this drift section could not be mode, which can either apmade below cutoff for the pear as a result of mode transformation at cavity walls, therefore causing the coupling between the cavities leading to parasitic self-excitation in the tube, or as a result of excitation by the beam in a drift section. To eliminate crosstalk between the cavities and the self-excitation of the drift section itself, it was decided to use a coaxial configuration, in which case the drift tube


mode. In order to not can be made below cutoff for the overly complicate the tube from the very beginning, a standard magnetron injection gun was used, which generated an electron beam with a voltage of up to 500 kV and a current up to 500 A. In the interaction region, the inner coax was supported by two thin tungsten pins: one immediately preceding the input cavity and one preceding the output cavity. Experiments with such a three-cavity tube operating at the frequency close to 8.6 GHz resulted in producing the peak output power of about 80 MW in about 2- s pulses with more than 30% efficiency and a gain approaching 30 dB [57]. This success of the experiments at the fundamental harmonic was followed by some efforts to develop high-power coaxial frequency-doubling Ku-band gyroklystrons [58]. Corresponding experiments were not quite successful for a number of reasons. First, it was found that the emission was strongly nonuniform in the azimuthal direction, with the unfortunate circumstance that the current emitted from the hottest spot on the emitter surface was partially intercepted by the support pins. This interception, which caused the erosion of pins, limited the number of shots. Also important is the fact that in the case of second harmonic operation, the optimum region of operating parameters is much smaller than at the fundamental resonance. Moreover, this region cannot be determined by simulation alone. Very often, in the course of experiments, it is necessary to detune the operating parameters from their optimal values found in the design procedure in order to avoid parasitic effects. These effects are associated with the excitation of parasitic modes, the self-excitation of cavities or drift sections, and the effect of beam instabilities. Therefore, in second harmonic devices, it usually takes a longer time to identify the optimal range of realizable parameters compared with experiments with fundamental resonance devices. Because of the presence of all these factors, experiments with a three-cavity frequency-doubling Ku-band gyroklystron only demonstrated about 27 MW of output power level before the pins were destroyed by the intercepted current [59]. These results have initiated an interest in the development of an inverted electron gun, which would allow one to avoid beam interception by the supporting pins, since the inner conductor can be supported axially, as was discussed earlier. In the design reported in [60], an inverted electron gun was shown to be capable of producing electron beams with a nominal beam voltage and current of 500 kV and 550 A, respectively. A beam with these parameters and an orbital-to-axial velocity ratio equal to 1.5 can have a perpendicular velocity spread caused by the beam optics of less than 1% over a wide range of operating currents from 100 to 600 A. (Of course, practical matters such as the cathode surface roughness and thermal effects will add somewhat to the spread.) The configuration of the inverted gun and all elements supporting the inner conductor are shown in Fig. 8, reproduced from [60]. The electric field gradients, which must be kept under control to avoid RF breakdown at the metal surfaces, were also computed in [60]. The results show that the peak electric field is about 80 kV/cm at the cathode and is close to 150 kV/cm at the anode. For high-power microwave tubes operating in microsecond pulses, these fields are considered to be quite moderate (cf., corresponding data for high-power klystrons in [61]).


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Fig. 8. Geometry of the electrodes and corresponding supporting elements of the inverted electron gun designed for a relativistic gyroklystron. TABLE I STATUS OF COAXIAL GYROTRONS

Presently, the work in both directions, viz. the improvement of the azimuthal uniformity of the emission and the work on inverted electron guns, is in progress. In particular, the work on improving the emission uniformity includes not only the improved fabrication of cathodes with a temperature limited emission and improved diagnostic methods, but also the development of new magnetron-type electron guns operating in the space-charge limited emission regime. We would like to conclude this section with an illustration of the progress in the development of coaxial gyrotrons given by Table I, which provides a decade-by-decade summary of the performance characteristics of coaxial gyrotrons. IV. SOME PREDICTIONS ABOUT THE FUTURE OF COAXIAL GYRODEVICES In our attempts to foresee the future of coaxial gyrodevices, it makes sense to distinguish near-term and long-term plans. A. Prospects for the Near Term This section contains our brief forecast for the next several years. In the development of gyrotron oscillators for controlled fusion, the primary goal is the development of high-power gyrotrons for ITER. It may be stipulated that the physical basis for

Fig. 9. Draft integral design of a 2-MW 170-GHz CW gyrotron for ITER.

fabrication of a 2-MW CW 170-GHz coaxial gyrotron as specified by the ITER team has already been proven. As the first step toward such a gyrotron, some theoretical work has already been done. Presently, this activity is continued by the joint efforts of the European Association (CRPP Lausanne, Switzerland, FZK, Karlsruhe, Germany, and HUT, Helsinki, Finland) together with the European tube industry (Thales Electron Devices, Velizy, France) [62]. To a large extent, these efforts are based on the results of studies of 165-GHz coaxial gyrotrons at FZK, which were described in Section III-E. The draft integral design of the ITER prototype tube is shown in Fig. 9 reproduced from [62]. In [62], it is stated that, for transmission of 2-MW CW microwave power at 170 GHz, one can use a single-disk CVD diamond

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window with a thickness of five half-wavelengths. Therefore, such tubes can be fabricated as single-window devices. There is also a certain interest in developing coaxial gyrotrons operating at the second cyclotron harmonic: two designs of second harmonic 340-GHz 100-kW CW coaxial gyrotrons are presented in [63]. In addition to the coaxial gyrotron activity in the framework of Euroatom Association, there are plans to develop 2-MW CW gyrotrons for ITER in Russia. According to [43], there are near-term plans to test the operation of such tubes in one of the , , and . following modes: Regarding the development of relativistic gyroklystrons, the immediate goals are to test a four-cavity frequency-doubling Ku-band relativistic gyroklystron and to design, fabricate, and test a new gun with a space-charge limited emission and subsequently perform experiments with relativistic gyroklystrons utilizing this gun [64]. B. Prospects for the Long Term The more distant plans of gyrotron developers will be focused on the further escalation of the CW output power of coaxial gyrotrons together with further enhancement of their efficiency and reliability. There are some attempts to investigate the possibilities to increase the power of CW coaxial gyrotrons up to the 5-MW level. For example, [43] includes design data for 5-MW coaxial gyrotrons at frequencies of 95/130 and 170 GHz. (This choice of frequencies corresponds to the requirements of the ITER program.) In the case of a tube operating either at 95 GHz and , or 130 GHz, the modes of choice are respectively. In tubes intended for operation at 170 GHz, the . The operating voltage and desired operating mode is beam current are 150 kV and 100 A, respectively. Similar design studies of coaxial gyrotrons delivering 4–5-MW CW power at frequencies ranging from 140 to 170 GHz for the plasma fusion reactor DEMO have also been done in Europe. [65] contains some design data for these tubes, which should operate at modes with eigennumbers between , , 140 and 180. Possible candidate modes are . Operating voltages and currents will range from and 120 to 140 kV and from 100 and 110 A, respectively, which is quite close to the Russian design data. Of course, these first steps should be supplemented with much more detailed analyses of numerous technical issues important for such “super-power” tubes. For instance, the current limitations on the CW power-handling capabilities of CVD diamond windows implies that the next generation of coaxial gyrotrons will, of necessity, be dual-window devices. Hence, the earlier experience accumulated in the experiments with such configurations will be extremely useful. Also, the use of single-stage and multistage depressed collectors in such tubes operating with electron beams with more than 10-MW CW power is of great importance, as well as the related thermal management issues that include the intense cooling of large-diameter resonators and small-diameter inserts. Clearly, the replacement of 1-MW tubes by 4–5-MW devices will greatly reduce a number of cryomagnets required for gyrotron operation and reduce a number of transmission lines required


for delivering the gyrotron power to the plasma chamber. All of these advances will simplify the microwave facility required for plasma experiments and substantially reduce its cost. Regarding the future of relativistic gyroklystrons, the authors express their hope that the use of electron guns allowing for the axial support of an inner conductor will significantly improve the reliability and lifetime of these tubes. ACKNOWLEDGMENT The second author would like to thank D. Sutter and J. Peters for the discussion which stimulated the preparation of this paper and M. Petelin for valuable discussions of the topics related to this paper. The first author would like to thank B. Piosczyk for innumerable discussions on various aspects of coaxial gyrotrons. The authors would also like to acknowledge the help of D. Abe in editing the manuscript. REFERENCES [1] V. A. Flyagin and G. S. Nusinovich, “Gyrotron oscillators,” Proc. IEEE, vol. 76, pp. 644–656, June 1988. [2] K. Felch, H. Huey, and H. Jory, “Gyrotrons for ECH applications,” J. Fusion Energy, vol. 9, pp. 59–75, 1990. [3] M. Makowski, “ECRF systems for ITER,” IEEE Trans. Plasma Sci., vol. 24, pp. 1023–1032, June 1996. [4] V. V. Alikaev et al., “Electron cyclotron current drive experiments on T-10,” Nucl. Fusion, vol. 32, pp. 1811–1821, Oct. 1992. [5] V. Erckmann et al., “ECRH and ECCD with high power gyrotrons at the stellarators W7-AS and W7-X,” IEEE Trans. Plasma Sci., vol. 27, pp. 538–546, Apr. 1999. [6] G. Gantenbein et al., “Complete suppression of neoclassical tearing modes with current drive at the electron-cyclotron-resonance frequency in ASDEX upgrade tokamak,” Phys. Rev. Lett., vol. 85, pp. 1242–1245, 2000. [7] R. J. La Haye et al., “Control of neoclassical tearing modes in DIII-D,” Phys. Plasmas, vol. 9, pp. 2051–2051, 2002. [8] I. I. Antakov et al., “Gyroklystrons—Millimeter wave amplifiers of the highest power,” in Proc. Int. Workshop “Strong Microwaves in Plasmas”, vol. 2, A. G. Litvak and N. Novgorod, Eds., Russia, 1994, pp. 587–596. [9] A. A. Tolkachev, B. A. Levitan, G. K. Solovjev, V. V. Veytsel, and V. E. Farber, “A megawatt power millimeter-wave phased-array radar,” IEEE AES Syst. Mag., pp. 25–31, July 2000. [10] M. T. Ngo, B. G. Danly, R. Myers, D. E. Pershing, V. Gregers-Hansen, and G. Linde, “High-power millimeter-wave transmitter for the NRL WARLOC radar,” in Proc. 3rd Int. Vacuum Electronics Conf., IVEC2002, Monterey, CA, Apr. 23–25, 2002, pp. 363–364. [11] V. L. Granatstein and W. Lawson, “Gyro-Amplifiers as candidate RF drivers for TeV linear colliders,” IEEE Trans. Plasma Sci., vol. 24, pp. 648–665, June 1996. [12] V. A. Flyagin, A. V. Gaponov, M. I. Petelin, and V. K. Yulpatov, “The gyrotron,” IEEE Trans. Microwave Theory Tech., vol. MTT-25, pp. 514–521, June 1977. [13] S. N. Vlasov, L. I. Zagryadskaya, and I. M. Orlova, “Open coaxial resonators for gyrotrons,” Radioeng. Electron. Phys., vol. 21, pp. 96–102, 1976. [14] M. I. Petelin and V. K. Yulpatov, “Linear theory of a CRM-monotron,” Radiophys. Quantum Electron., vol. 18, pp. 212–219, 1975. [15] L. A. Weinstein, Open Resonators and Open Waveguides. Boulder, CO: Golem, 1969, ch. 5. [16] S. N. Vlasov, G. M. Zhislin, I. M. Orlova, M. I. Petelin, and G. G. Rogacheva, “Irregular waveguides as open resonators,” Radiophys. Quantum Electron., vol. 12, pp. 972–978, 1969. [17] G. S. Nusinovich, M. E. Read, O. Dumbrajs, and K. E. Kreischer, “Theory of gyrotrons with coaxial resonators,” IEEE Trans. Electron Devices, vol. 41, pp. 433–438, Apr. 1994. [18] V. S. Ergakov and M. A. Moiseev, “Mode selection in an open cylindrical resonator with a corrugated wall” (in Russian), in The Book of Collected Papers “Gyrotrons” Gorkiy, USSR, 1980, pp. 98–111.


[19] Y. V. Bykov, A. L. Goldenberg, L. V. Nikolaev, M. M. Ofitserov, and M. I. Petelin, “Experimental investigation of a gyrotron with whisperinggallery modes,” Radiophys. Quantum Electron., vol. 18, pp. 1141–1143, 1975. [20] A. V. Gaponov, V. A. Flyagin, A. L. Goldenberg, G. S. Nusinovich, S. E. Tsimring, V. G. Usov, and S. N. Vlasov, “Powerful millimeter-wave gyrotrons,” Int. J. Electron., vol. 51, pp. 277–302, 1981. [21] Y. V. Bykov, S. N. Vlasov, A. L. Goldenberg, A. G. Luchinin, I. M. Orlova, M. I. Petelin, V. G. Usov, V. A. Flyagin, and V. I. Khizhnyak, “Mode selection in high-power gyrotrons” (in Russian), in The Book of Collected Papers “Gyrotron”. Gorky, USSR: Publ. Inst. Appl. Phys., Acad. Sci., 1981, pp. 185–191. [22] A. A. Andronov, V. A. Flyagin, A. V. Gaponov, A. L. Goldenberg, M. I. Petelin, V. G. Usov, and V. K. Yulpatov, “The gyrotron: High-power source of millimeter and submillimeter waves,” Infrared Phys., vol. 18, pp. 385–393, 1978. [23] V. K. Lygin, V. N. Manuilov, A. N. Kuftin, A. B. Pavelyev, and B. Piosczyk, “Inverse magnetron injection gun for a coaxial 1.5 MW, 140 GHz gyrotron,” Int. J. Electron., vol. 79, pp. 227–235, 1995. [24] A. L. Goldenberg, A. B. Pavelyev, and V. I. Khizhnyak, “Modeling of CW, MW-class gyrotrons under conditions of mode competition in a resonator” (in Russian), in The Book of Collected Papers “Gyrotrons”. Gorky, USSR: Publ. Inst. Appl. Phys., Acad. Sci., 1989, pp. 20–39. [25] V. E. Myasnikov, A. P. Keyer, S. D. Bogdanov, and V. I. Kurbatov, “Soviet industrial gyrotrons,” in Proc. 16th Int. Conf. IR MM Waves, SPIE, vol. 1576, SPIE, Lausanne, Switzerland, Aug. 26–30, 1991, Paper M8.6, pp. 127–128. [26] J. J. Barroso and R. A. Correa, “Coaxial resonator for a megawatt, 280 GHz gyrotron,” Int. J. Infrared Millimeter Waves, vol. 12, pp. 717–728, 1991. , “Design of a TE coaxial cavity for a 1 MW, 280 GHz gy[27] rotron,” Int. J. Infrared Millimeter Waves, vol. 13, pp. 443–455, 1992. [28] P. J. Castro, J. J. Barroso, and R. A. Correa, “Cold tests of open coaxial resonators in the range 9–17 GHz,” Int. J. Infrared Millimeter Waves, vol. 14, pp. 383–395, 1993. [29] , “Ohmic selection in open coaxial resonators: An experimental study,” Int. J. Infrared Millimeter Waves, vol. 14, pp. 2191–2201, 1993. [30] R. A. Correa and J. J. Barroso, “Space charge effects of gyrotron electron beams in coaxial cavities,” Int. J. Electron., vol. 74, pp. 131–136, 1993. [31] V. A. Flyagin, V. I. Khiznyak, V. N. Manuilov, A. B. Pavelyev, V. G. Pavelyev, B. Piosczyk, G. Dammertz, O. Hochtl, C. T. Iatrou, S. Kern, H.-U. Nickel, M. Thumm, A. Wien, and O. Dumbrajs, “Development of a 1.5 MW coaxial cavity gyrotron at 140 GHz,” in Dig. 19th Int. Conf. Infrared Millimeter Waves, Sendai, Japan, 1994, JSAP AP 941228, pp. 75–76. [32] M. I. Petelin, Private Commun., 2003. [33] C. T. Iatrou, S. Kern, and A. B. Pavelyev, “Coaxial cavities with corrugated inner conductor for gyrotrons,” IEEE Trans. Microwave Theory Tech., vol. 44, pp. 56–64, 1996. [34] C. T. Iatrou, “Mode selective properties of coaxial gyrotron resonators,” IEEE Trans. Plasma Sci., vol. 24, pp. 596–605, 1996. [35] P. J. B. Clarricoats and P. K. Saha, “Attenuation in corrugated circular waveguide,” Electron. Lett., vol. 6, pp. 370–372, 1970. [36] S. Kern, “Numerische Simulation der Gyrotron-Wechselwirkung in Koaxialen Resonatoren,” Forschungszentrum Karlsruhe, FZKA 5837, 1996. [37] O. Dumbrajs, “A novel method of improving performance of coaxial gyrotron resonators,” IEEE Trans. Plasma Sci., vol. 30, pp. 836–839, 2002. [38] O. Dumbrajs, Y. V. Gandel, and G. I. Zaginaylov, “Full wave analysis of coaxial gyrotron cavity with corrugated insert,” in Dig. 27th Int. Conf. Infrared Millimeter Waves, R. J. Temkin, Ed., Sept. 22–26, 2002, pp. 185–186. [39] A. Grudiev, J. Y. Raguin, and K. Schunemann, “Numerical study of mode competition in coaxial cavity gyrotrons with corrugated insert,” Int. J. Infrared Millimeter Waves, vol. 24, pp. 173–187, 2003. [40] O. Dumbrajs and A. B. Pavelyev, “Insert misalignment in coaxial cavities and its influence on gyrotron operation,” Int. J. Electron., vol. 82, pp. 261–268, 1997. [41] O. Dumbrajs, J. A. Heikkinen, and H. Zohm, “Electron cyclotron heating and current drive control by means of frequency step-tunable gyrotrons,” Nucl. Fusion, vol. 41, pp. 927–944, 2001. [42] O. Dumbrajs and A. Möbius, “Tunable coaxial gyrotrons for plasma heating and diagnostics,” Int. J. Electron., vol. 84, pp. 411–419, 1998.

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[43] V. E. Zapevalov, V. I. Khizhnyak, M. A. Moiseev, A. B. Pavelyev, and N. I. Zavolsky, “Advanced coaxial cavity gyrotrons,” in Dig. 27th Int. Conf. Infrared Millimeter Waves, R. J. Temkin, Ed., San Diego, CA, Sept. 22–26, 2002, pp. 335–336. [44] Y. Hirata, K. Hayashi, Y. Mitsunaka, Y. Itoh, and T. Sugawara, “Design of a 1-MW, CW coaxial gyrotron with two gaussian beam outputs,” Int. J. Infrared Millimeter Waves, vol. 16, pp. 713–733, 1995. [45] B. Piosczyk, O. Braz, G. Dammertz, C. T. Iatrou, S. Illy, M. Kuntze, G. Michel, A. Mobius, M. Thumm, V. A. Flyagin, V. I. Khizhnyak, A. B. Pavelyev, and V. E. Zapevalov, “Coaxial cavity gyrotron with dual RF beam output,” IEEE Trans. Plasma Sci., vol. 26, pp. 393–401, June 1998. [46] R. Heidinger, G. Dammertz, A. Meier, and M. K. Thumm, “CVD diamond windows studied with low- and high-power millimeter waves,” IEEE Trans. Plasma Sci., vol. 30, pp. 800–807, June 2002. [47] M. E. Read, G. S. Nusinovich, O. Dumbrajs, G. Bird, J. P. Hogge, K. Kreischer, and M. Blank, “Design of a 3-MW, 140-GHz gyrotron with a coaxial cavity,” IEEE Trans. Plasma Sci., vol. 24, pp. 586–595, June 1996. [48] R. Advani, J. P. Hogge, K. E. Kreischer, M. Pedrozzi, M. E. Read, J. R. Sirigiri, and R. J. Temkin, “Experimental investigation of a 140-GHz coaxial gyrotron oscillator,” IEEE Trans. Plasma Sci., vol. 29, pp. 943–950, Dec. 2001. [49] B. Piosczyk, A. Arnold, G. Dammertz, M. Kuntze, G. Michel, O. S. Lamba, and M. K. Thumm, “Step-Frequency operation of a coaxial cavity gyrotron from 134 to 169.5 GHz,” IEEE Trans. Plasma Sci., vol. 28, pp. 918–923, June 2000. [50] B. Piosczyk, O. Braz, G. Dammertz, C. T. Iatrou, S. Illy, M. Kuntze, G. Michel, and M. Thumm, “165 GHz, 1.5 MW-coaxial cavity gyrotron with depressed collector,” IEEE Trans. Plasma Sci., vol. 27, pp. 484–489, Apr. 1999. [51] B. Piosczyk, A. Arnold, G. Dammertz, O. Dumbrajs, M. Kuntze, and M. K. Thumm, “Coaxial cavity gyrotrons—Recent experimental results,” IEEE Trans. Plasma Sci., vol. 30, pp. 819–827, June 2002. [52] B. Piosczyk, “A novel 4.5-MW electron gun for a coaxial cavity gyrotron,” IEEE Trans. Electron Devices, vol. 48, pp. 2938–2944, 2001. [53] B. Piosczyk, G. Dammertz, O. Dumbrajs, O. Drumm, S. Illy, J.. Jin, and M. Thumm, “A single-stage depressed collector for a 2-MW CW coaxial cavity gyrotron,” IEEE Trans. Plasma Sci., submitted for publication. [54] O. Dumbrajs, T. Idehara, Y. Iwata, S. Mitsudo, I. Ogawa, and B. Piosczyk, “Hysteresis-like effects in gyrotrons,” Phys. Plasmas, vol. 10, pp. 1183–1186, 2003. [55] K. R. Chu, V. L. Granatstein, P. E. Latham, W. Lawson, and C. D. Striffler, “A 30-MW gyroklystron-amplifier design for high-energy linear accelerators,” IEEE Trans. Plasma Sci., vol. PS-13, pp. 424–434, Dec. 1985. [56] S. Tantawi et al., “High-Power X-band amplification from an overmoded three-cavity gyroklystron with a tunable penultimate cavity,” IEEE Trans. Plasma Sci., vol. 20, pp. 205–215, June 1992. [57] W. Lawson et al., “High-Power operation of a three-cavity X-band coaxial gyroklystron,” Phys. Rev. Lett., vol. 81, pp. 3030–3033, Oct. 1998. [58] G. P. Saraph et al., “100–150 MW designs of two-and three-cavity gyroklystron amplifiers operating at the fundamental and second harmonics in X-and Ku-bands,” IEEE Trans. Plasma Sci., vol. 24, pp. 671–677, June 1996. [59] M. Castle, “Operation of a high-power, second harmonic coaxial gyroklystron,” Ph.D. dissertation, Univ. Maryland, College Park, 2001. [60] M. Read, G. Nusinovich, and L. Ives, “Design of an inverted magnetron gun for a high power gyroklystron,” in Proc. 6th Workshop High Energy Density and High Power RF , vol. 691, AIP Proc., S. H. Gold and G. S. Nusinovich, Eds., Berkeley Springs, WV, June 22–26, 2003, pp. 136–140. [61] R. M. Phillips and D. W. Sprehn, “High-Power klystrons for the next linear collider,” Proc. IEEE, vol. 87, pp. 738–751, May 1999. [62] B. Piosczyk et al., “A 2 MW, CW, 170 GHz coaxial cavity gyrotron for ITER,” in IAEA Tech. Meeting ECRH Physics and Technology for ITER, Kloster Seeon, July 14–16, 2003. [63] K. A. Avramides, C. T. Iatrou, and J. L. Vomvoridis, “Design consideration of powerful continuous-wave, second-cyclotron-harmonic coaxialcavity gyrotron,” IEEE Trans. Plasma Sci., vol. 32, pp. 917–928, June 2004. [64] E. S. Gouveia, W. Lawson, B. Hogan, K. Bharathan, and V. L. Granatstein, “Current atatus of gyroklystron research at the University of Maryland,” in Proc. 6th Workshop High Energy Density and High Power RF, vol. 691, AIP Proc., S. H. Gold and G. S. Nusinovich, Eds., Berkeley Springs, WV, June 22–26, 2003, pp. 79–88.

946

[65] M. V. Kartikeyan, E. Borie, B. Piosczyk, and M. Thumm, “In quest of a 170 GHz coaxial super gyrotron,” in Dig. 28th Int. Conf. Infrared Millimeter Waves, Otsu, Japan, Sept. 2003, JSAP Catalog 031 231, pp. 169–170.

Olgierd Dumbrajs (SM’98) was born in Riga, Latvia. He received the B.S. degree in theoretical physics from the Latvian State University, Riga, in 1965, and the Ph.D. degree in theoretical particle physics from Moscow State University, Moscow, U.S.S.R., in 1971. From 1971 to 1985, he was with the Joint Institute for Nuclear Research, Dubna, U.S.S.R., and at several European Nuclear Research Centers. At that time, he published many papers on nuclear and particle physics. In 1985, he joined the Gyrotron Project at the Forschungszentrum Karlsruhe, Karlsruhe, Germany. Since 1995, he has been a member of the Experts Group, Coordinating Committee, European Commission for Development Program for the Electron Cyclotron Wave Systems. He is a Professor of Theoretical Physics at Riga Transport and Telecommunication Institute. He is now a Special Research Worker with the Academy of Finland and with the Department of Engineering Physics and Mathematics at the Helsinki University of Technology, Espoo, Finland. His current research interests are in the field of gyrotron theory, nonlinear dynamics, and plasma physics. Dr. Dumbrajs is a life member of the American Physical Society. In 2001, he was elected a full member of the Latvian Academy of Sciences.


Gregory S. Nusinovich (SM’92–F’00) received the B.Sc., M.Sc., and Ph.D. degrees from Gorky State University, Gorky, U.S.S.R., in 1967, 1968, and 1975, respectively. In 1968, he joined the Gorky Radiophysical Research Institute, Gorky. From 1977 to 1990, he was a Senior Research Scientist and Head of the Research Group at the Institute of Applied Physics, the Academy of Sciences of the U.S.S.R., Gorky. From 1968 to 1990, his scientific interests included developing high-power millimeter- and submillimeter-wave gyrotrons. He was a Member of the Scientific Council on Physical Electronics of the Academy of Sciences of the U.S.S.R. In 1991, he immigrated to the U.S. and joined the Research Staff at the Institute for Plasma Research (presently, the Institute for Research in Electronics and Applied Physics), University of Maryland, College Park. Since 1991, he has also served as a Consultant to the Science Applications International Corporation, McLean, VA, the Physical Sciences Corporation, Alexandria, VA, and Omega-P, Inc., New Haven, CT. He is the author of Introduction to the Physics of Gyrotrons (Baltimore, MD: The Johns Hopkins University Press, 2004). He has authored and coauthored more than 150 papers published in refereed journals. His current research interests include the study of high-power electromagnetic radiation from various types of microwave sources. Dr. Nusinovich is a Member of the Executive Committee of the Plasma Science and Application Committee of the IEEE Nuclear and Plasma Sciences Society. He is a Fellow of the American Physical Society (APS). In 1996 and 1999, he was a Guest Editor of the Special Issues of the IEEE TRANSACTIONS ON PLASMA SCIENCES on High-Power Microwave Generation and on Cyclotron Resonance Masers and Gyrotrons, respectively. Presently, he is an Associate Editor of the IEEE TRANSACTIONS ON PLASMA SCIENCES.