On Potentials of Gyrotron Efficiency Enhancement - IEEE Xplore

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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 34, NO. 3, JUNE 2006

On Potentials of Gyrotron Efficiency Enhancement: Measurements and Simulations on a 4-mm Gyrotron Oleg I. Louksha, Bernhard Piosczyk, Gennadi G. Sominski, Manfred K. Thumm, Fellow, IEEE, and Dmitriy B. Samsonov

Abstract—In a 74.2-GHz 100-kW pulse gyrotron, the characteristics of parasitic low-frequency oscillations and their influence on electron energy spread have been determined. A method for suppressing parasitic oscillations by varying the magnetic field distribution in the beam compression region is studied. The results of measurements demonstrate the influence of azimuthal inhomogeneity of electron emission on the excitation of parasitic oscillations and on the gyrotron output parameters. Obtained data allows one to determine the ways of gyrotron efficiency enhancement by improved quality of the helical electron beam. Index Terms—Emission uniformity, energy spread, gyrotron efficiency, space-charge oscillations.

I. INTRODUCTION

I

N GYRO-DEVICES, the microwave energy is extracted from the rotational energy of a helical electron beam (HEB) (see, e.g., [1]–[3]). Therefore, the gyrotron efficiency can be enhanced by increasing the HEB energy related to the transverse motion of electrons in a magnetic field. This energy is characterized by the value of the pitch factor ( and —electron transverse and longitudinal velocities) which typically does not exceed 1.5. The main obstacle for the operation at high pitch factor is a spread of electron velocity in the beam. In the presence of velocity spread, electrons with largest transverse velocity are reflected from the magnetic mirror in the beam compression region. The amount of reflected electrons increases with increasing beam pitch factor. The reflected electrons can be trapped and accumulated in the region between the gun and the resonator. The space charge cloud of the trapped electrons is unstable. When the amount of trapped electrons is large enough, parasitic low-frequency oscillations (LFO) are excited at a frequency which is close to the frequency of the oscillatory movement of an electron in the trap (see, e.g., [4]–[7]). The space charge accumulated in the trap increases the transverse and longitudinal velocity spread [4], [8], [9]. The radio-frequency (RF) field of the parasitic oscillations, excited in the trapped space charge, causes an additional spread of the total velocity (energy spread), as well Manuscript received June 6, 2005; revised December 15, 2005. This work was supported in part by the Forschungszentrum Karlsruhe and in part by INTAS under Grant 03-51-3861. O. I. Louksha, G. G. Sominski, and D. B. Samsonov are with the St. Petersburg State Polytechnical University, St. Petersburg 195251, Russia (e-mail: [email protected]; [email protected]; [email protected]). B. Piosczyk and M. K. Thumm are with the Forchungszentrum Karlsruhe, Association EURATOM-FZK, Institut für Hochleistungsimpuls- und Mikrowellentechnik (IHM), D-76021 Karslruhe, Germany (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TPS.2006.875779

as an electron bombardment of the cathode surface resulting in the appearance of secondary electrons. All these factors cause an additional decrease of the beam quality and the efficiency of energy transformation in gyrotrons [4], [10]–[15]. Thus, the increase of HEB transverse energy can result in an enhancement of the gyrotron efficiency only in combination with reducing velocity spread from trapped electrons or/and with suppressing parasitic trap oscillations. One of the important sources of velocity spread in gyrotrons is inhomogeneous electron emission from thermionic cathodes of magnetron-type injection guns [4], [12], [16]. Typically, these guns operate in the regime of temperature limited emission. Therefore, the inhomogeneities of both the work function and the emitter temperature result in a nonuniform distribution of current density in the HEB cross section. The beam spatial nonuniformities can lead to degradation of the gyrotron efficiency through the increase of velocity spread due to nonuniform space-charge fields and through the excitation of parasitic modes in the resonator [17]. The inhomogeneities of electron emission can result from the imperfections in manufacturing of the large-size conical cathodes used in gyrotrons. Also, the long term performance of the cathode can be affected by several factors, including changes in emission uniformity caused by ion and electron bombardment of the emitter surface. In this paper, the experimental and theoretical data on HEB characteristics and their influence on gyrotron operation are presented. The research objective was to demonstrate the possibilities for gyrotron efficiency enhancement by improving the beam quality. The investigations were performed with a pulse 4-mm gyrotron at the St. Petersburg State Polytechnical University. Section II describes the experimental setup and the measuring procedure. The experimental results on LFO characteristics and the mechanism of generation of the parasitic trap oscillations are discussed in Section III. In Section IV, we describe the results of the measurement of electron energy distributions in the collector region of the gyrotron. The data, presented in Section V, concern the influence of cathode emission inhomogeneity on parasitic low-frequency oscillations and on gyrotron output parameters. Section VI contains the results of the investigation on suppressing parasitic oscillations by using a non-uniform magnetic field in the compression region. Finally, in Section VII, we discuss the results obtained and summarize the paper. II. EXPERIMENTAL SETUP AND MEASURING METHODS The measurements were performed with the experimental gyrotron shown schematically in Fig. 1. The tube includes a triode-type magnetron injection gun which operates in the diode regime with grounded intermediate anode. The main

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LOUKSHA et al.: ON POTENTIALS OF GYROTRON EFFICIENCY ENHANCEMENT

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TABLE I MAIN GEOMETRICAL AND OPERATING-REGIME PARAMETERS OF THE EXPERIMENTAL GYROTRON

Fig. 1. Drawing of the experimental gyrotron cross section.

geometrical and operating-regime design parameters are summarized in Table I. The layout of the gyrotron provides easy disassembly of the tube and replacement of its components. In the experiments, we used both the standard geometry of the tube with high Q-factor resonator placed in the plateau region of the magnetic field distribution and modified geometries of the gyrotron. In one of the modified versions, the resonator was removed. Around the electron beam, a tunnel with constant diameter remained. In the other version, the resonator was replaced by a special graphite RF-absorber with increasing diameter towards the collector. These modifications served to prevent excitation of gyrotron modes and to distinguish effects of space-charge oscillations on the electron energy distribution. The tube is equipped with a room-temperature pulse magnetic system consisting of five coils (see Fig. 1). The magnetic comcan be adjusted by varying the cathode pression ratio coil current. Additional magnetic fields of the collector and the

analyzer coils are used for guiding electrons to the 1-mm input aperture of the electron energy analyzer. It is possible to modify the spatial distribution of the magnetic field in the compression region with a control coil. Magnetic field distribution can and be changed by varying the current of the control coil its polarity (additive and opposite) relative to the current of the . main coil The output microwave power is absorbed in the water load (see Fig. 1) which is part of the thermocouple wattmeter. The power measurement accuracy is equal to 5 kW for beam pulse duration . A part of the power is directed through the 4-mm waveguide to a spectrum analyzer representing a heterodyne system with the frequency-swept driving oscillator, the diode mixer and the 350-MHz storage oscilloscope. In the sectional cathode assembly of the gyrotron, the emitter is changed via replacement of the molybdenum element equipped with an emissive strip. The experiments were peremitters C1 and C2 (operating temperature formed with ), and with an impregnated dispenser . It is possible to rotate emitter C3 the cathode assembly with a bellows-type feed through. In all of the azimuthal positions, the cathode axis misalignment with respect to anode axis does not exceed 0.1 mm. The azimuthal is distribution of the cathode emission current density obtained by measuring the electron current passing through a 1-mm-diameter pinhole in the intermediate anode to the anode probe (see Fig. 1) in dependence of the azimuthal position of the cathode. The measurements have been performed in the absence of applied magnetic field. The relative spread of emission current density is determined as the root mean square (rms) value

where is standard deviation is mean current density. In most and were measured with the azimuthal cases, the dependencies , which corresponds to measuring points step per full turn of the cathode. Two types of probes were used to register the low-frequency instabilities in the HEB and the parasitic low-frequency oscillations outside the tube (Fig. 1). The high-frequency (HF) probe

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placed in the magnetic compression region measures induced signals from the beam near-zone. The external removable HF antenna is used for measurement of the radiation penetrating to the outside of the gyrotron through nonmetallic parts of the tube and the external circuits. Pulse shape and spectral distribution of the external antenna signal agreed closely with those of the beam probe signal. These signals differed only in the amplitude caused by the different sensitivity of the probes. The experimental data on the low-frequency oscillations discussed later were obtained with the external antenna. The spherical electron energy analyzer [18] utilizes the retarding-field method. As it was in other gyrotron experiments [16], the analyzer is located above the collector at a weak magnetic field (see Fig. 1). At the position of the input of the analyzer, the magnetic field is approximately 150 times weaker than at the maximum (plateau) of its distribution. Therefore, the transverse component of the electron velocity and the beam energy related to the transverse motion are negligible, and the measured distribution corresponds to the distribution of the total energy of the electrons. For the working regime of the gyrotron, the maximum current into the analyzer did not exceed 1 mA. Two bellows-type vacuum feed throughs provide a movement of the input aperture of the analyzer in transverse direction to measure energy spectra of electrons at different points of its cross section and an adjustment of the analyzer axis inclination to improve the energy resolution due to correction of the analyzer position with respect to the magnetic field lines. and In the experiments, the pulses of retarding voltage are measured simultaneously. During a analyzer current decreases from a maximum value alpulse, the value of during a single pulse. The enlowing thus to measure ergy spectrum is obtained by differentiation of the measured de. Following the techniques of [16], the value pendence is determined as of energy spread

where the retarding voltages , , correspond to the analyzer current reduction to 0.1, 0.5, and 0.9 of its maximum. Energy resolution, or minimum energy spread that can be registered by the analyzer, was equal to 0.3%–0.4%. The achieved energy resolution is sufficiently high to study the impact of nonstationary space-charge fields on electron energy distributions in the gyrotron.

Fig. 2. Amplitude of low-frequency oscillations A , output power at the main TE mode P and calculated pitch factor as functions of magnetic field B (cathode C1, U = 30 kV, I = 10 A, B =B = 18:0).

LFO signal has been observed in the region above where the main gyrotron mode is oscillating. The gyrotron mode has its maximum power at . The measured maximum values of output power (95 kW) and efficiency (31.7%) are close to the design values. Taking into consideration the data on LFO characteristics obtained in gyrotrons differing in geometry and operating parameters (see, e.g., [4]–[7], [12], [19], [20]), we can conclude that these oscillations result from accumulation and bunching of space charge in the gyrotron trap. Trap oscillations are likely excited if the coefficient of reflection of electrons from the mag. For the netic mirror exceeds a certain threshold value beam in which all particles have the same total energy, this coefficient can be defined as

where and are the total and transverse velocities, respecis distribution function of electrons in the tively, and plateau region of magnetic field distribution. Fig. 3 shows the coefficient of reflection calculated as a function of pitch factor for different rms values of transverse velocity spread in the case of a Gaussian distribution

III. PARASITIC LOW-FREQUENCY OSCILLATIONS The measurements of LFO signals were performed over a wide range of operating parameters: accelerating voltage , cavity magnetic field , beam , magnetic compression ratio current . A typical plot of the pulse-average amplitude of the as a function of magnetic field for one of LFO signal the cathodes (C1) is shown in Fig. 2. In addition, the demode pendencies of output power of the main and the pitch factor calculated with the EGUN code are also presented in this figure. For this cathode being characterized by the highest emission homogeneity (see Section V), no

where and are the mean value and standard deviation of transverse velocity, respectively. Using this plot and the value of the velocity spread as described in the next section, we can from the pitch factor corestimate the threshold coefficient responding to LFO appearance. IV. ELECTRON ENERGY DISTRIBUTION A typical electron energy spectrum measured for the cathode C2 in the regime with an output power of in the main mode is shown in Fig. 4(a). Parasitic LFO


Fig. 3. Calculated coefficient of reflection from magnetic mirror R as a function of pitch factor for different transverse velocity spread v (Gaussian distribution).

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Fig. 5. Experimental gyrotron with graphite absorber: energy spread ", amplitude of low-frequency oscillations A and calculated pith-factor as func: : , B =B tions of magnetic field B (cathode C2, U ,I : ).

17 9

Fig. 4. (a) Measured and (b) calculated electron energy spectra (cathode C2, U : ,I ,B : , B =B : , calculation for and pitch factor velocity spread v : ).

= 28 2 kV

= 10 A = 2 75 T = 10%

= 17 9 =11

were absent in that regime of operation. The interaction of the electron beam with the RF field in the resonator results in a wide energy spread estimated to 103%. The measured spectra were compared with those calculated in a self-consistent model [21] for the same values of operating parameters and different ini. Fig. 4(b) gives tial transverse velocity spread values the calculated spectrum for and pitch factor . In general, calculated spectra for velocity spread value were in satisfactory agreement with the measured ones in the case of gyrotron operation with cathode C2. In case of cathode C1 and C3, the energy spectra have not been measured. As observed in the experiments with the standard high Q-factor cavity, the electron energy spread is very small and

= 11 5kV = 2 4A

=

limited only by the analyzer resolution in the regimes with . In this high magnetic field, when the beam pitch factor case, the electron beam is not disturbed by the RF-fields and no instability of any type develops, at least to the magnitude distinguishable by its contribution to the HEB energy spread. As regards the high pitch factor regimes in the presence of a LFO signal, we failed to avoid millimeter-wave radiation and thus obtained large broadening of the energy distribution under the action of resonator RF fields for a wide range of accelerating voltages from 11 to 30 kV. Moreover, this radiation existed not only for the standard gyrotron configuration but also for the version with removed resonator. In the latter case, the constant-diameter beam tunnel possibly acted as a specific microwave cavity. Substantial suppression of mm-wave radiation was achieved by replacement of the resonator by a graphite absorber. In the gyrotron with the absorber, measurements were performed at different accelerating voltages. For each voltage, the beam current was chosen in agreement with the scaling relations ensuring conservation of electron trajectories [4], [8], [9]. A typical deon magnetic field for the rependence of energy spread is presented in Fig. 5. The deduced voltage meapendencies of the amplitude of the LFO signal sured with the external HF antenna and the calculated pitch are also shown in this figure. The energy spread factor abruptly increases from 0.3%–0.4% up to 3%–5% at and . The LFO signal appears practically at the same values of magnetic field and pitch factor. For fixed voltage and current, we varied the spatial distribution of the magnetic field in the compression region in order to suppress parasitic low-frequency oscillations (see the results in Section VI). Suppression of the oscillations resulted in increasing the threshold pitch factor for LFO appearance. The correlated displacement and dependencies in the direction to lower of was observed. This correlation suggests that the RF fields of the bunched space charge in the trap are responsible for the electron energy spread of 3%–5% in the region near the threshold of LFO excitation. Further decrease of magnetic field is accompanied by increase of the LFO amplitude while the energy spread varies

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Fig. 7. Amplitude of low-frequency oscillations A for cathodes C1, C2, C3 and calculated pitch factor as functions of magnetic field B (U = 30 kV, I = 10 A, B =B = 18:35).

TABLE II COMPARISON OF EMISSION INHOMOGENEITY, MAXIMUM EFFICIENCY, THRESHOLD PITCH FACTOR CORRESPONDING TO LFO APPEARANCE AND TRANSVERSE VELOCITY SPREAD FOR CATHODES C1, C2, C3

Fig. 6. Azimuthal distribution of emission current density sponding spread j for cathodes C1 (a), C2 (b), and C3 (c).

j () and corre-

nonmonotonously with (see Fig. 5). We think that this indicates the presence of other types of instabilities, not connected directly with the instability of the space charge locked in the trap. For example, these can be high-frequency instabilities (see, e.g., [4], [22]–[24]) at frequencies above the band (10–350 MHz) of the receiving apparatus. , where For the region of low magnetic field the LFO signal amplitude is the highest, the energy spread is approximately equal to 7%–11%. These measured values of are 2–2.5 times greater than the spread values calculated with the particle-in-cell (PIC) code GyroTrap [18], [25]. This discrepancy can possibly be attributed to effects that could not be accounted for in these simplified calculations. The additional spread can result from three-dimensional nonuniform electron bunches oscillating in the trap. In particular, this non-uniformity can be caused by cathode emission inhomogeneity. V. ELECTRON EMISSION INHOMOGENEITY The LFO characteristics, described for the cathode C1 in Section III, were also studied for the second cathode C2 and

for the impregnated dispenser cathode C3. Azimuthal distribuof these cathodes and tions of emission current density are given in Fig. 6. As shown the corresponding spreads in this figure, the emission inhomogeneity increases from the cathode C1 to C2 and then to C3. The dependencies of the LFO amplitudes measured for cathodes C1–C3 and the calculated pitch factor versus magnetic field are presented in Fig. 7. For a cathode with better emission uniformity, we obtained a decrease of the LFO amplitude for a fixed magnetic field and an increase corresponding to LFO of the threshold pitch factor value appearance. It was also observed that the increase of emission inhomogeneity resulted in a reduction of the maximum output mode. The values of power and efficiency in the main , threshold pitch factor and maximum emission spread achieved with all cathodes are summarized in efficiency Table II. Most likely, the observed increase of the LFO amplitude in the case of inhomogeneous emission is due to the corresponding increase of the velocity spread in the beam. The inhomogeneous emission caused by nonuniformity of work function or temperature along the emitting surface contributes to the velocity spread due to the nonuniform space charge fields, as well at the cathode surface and along the whole beam path [4], [16]. Concerning the gyrotron efficiency, its degradation with increase of the emission inhomogeneity can be caused by: 1) the increase of velocity spread, 2) the excitation of parasitic modes in the resonator, 3) the increase of energy spread due to the occurrence of parasitic low-frequency oscillations and/or due to the build up of beam instabilities. To estimate the velocity spread resulting from cathode emission inhomogeneity, the values obtained from the measurement


of the energy spectrum in the gyrotron with cathode C2 (Section IV) are used. As it was found, the experimental energy spectrum is in good agreement with calculated one if we assume a transverse velocity spread of 10%. Let us take for the cathode C2 in the regime without parasitic oscillations. and velocity Knowing the values of threshold pitch factor , a threshold reflection coefficient correspread sponding to starting of LFO can be determined. Thus, with the and a threshold reflection values has been obtained (see Fig. 3). Ascoefficient is constant for all cathodes, we suming that the coefficient can estimate the transverse velocity spread for the cathobtained in this manner odes C1 and C3. The values of are shown in the last column of Table II. As followed from Table II, cathode emission inhomogeneity can affect the HEB quality through increase of velocity spread. cathode It should be noticed that the replacement of a (C1 or C2) by the W-Ba cathode (C3) can be accompanied by the variation of velocity spread not only from emission inhomogeneity but also from the difference of emitter material. The latter defines the structure of the cathode surface, in particular, its roughness which is one of the important factors of velocity spread [4]. In the presence of the trap oscillations, the emitter material can influence the amount of space charge in the trap and, therefore, the LFO amplitude, also due to the amount of secondary electrons emitted from the cathode surface. Secondary electrons have larger spread of initial velocities compared to thermo-electrons, and can be emitted both from the emissive strip and from the adjacent regions of cathode assembly [4], [12], [15]. As a result, secondary emission increases the velocity spread in the beam and the coefficient of electron reflection from the mirror. The contribution of secondary electrons in the beam from the W-Ba impregnated cathode must cathodes due to the difference of the exceed that from for W-Ba cathode secondary emission coefficient ( and for cathode) [26]. VI. INFLUENCE OF MAGNETIC FIELD DISTRIBUTION ON LOW-FREQUENCY OSCILLATIONS Taking into account the effect of parasitic low-frequency oscillations on HEB characteristics, a method for suppressing these oscillations is needed to advance gyrotron operation towards high pitch factor regimes without degradation of beam quality. Suppression of the oscillations can be achieved by optimization of the magnetic field distribution in the beam compression region [20]. Two mechanisms of the influence distribution on the dynamics of space charge in of the the trap are assumed to be reasons for LFO suppression. First, distribution results in the change the modification of of the “potential well” profile for the electrons locked in the trap, which influences the development of the instability in the ensemble of nonisochronous electron oscillators. Second, the oscillations can be suppressed by introducing additional losses of trapped electrons by their interception with the metal wall of the surrounding tube. The interception of electrons comes as a result of the decrease of the distance between the HEB and the metal beam tunnel if we reduce the magnetic field at a local area of the magnetic compression region. For a certain

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reduction of magnetic field, it is possible to intercept only electrons from the beam “halo,” where trapped electrons are collected [4], [13], [15], without the interception of the primary beam. In this section, the effect of magnetic field distribution on parasitic oscillations is simulated using the code GyroTrap and is studied experimentally. A. Numerical Simulation With the PIC Code GyroTrap The calculations were performed with the simplified PIC code GyroTrap simulating one-dimensional self-consistent movement of electrons in adiabatic approximation [25]. The code calculates the forming and the dynamics of large-scale (in comparison with the axial step of the helical trajectory of a single electron) space-charge bunches oscillating in the trap. Under the assumptions introduced in GyroTrap, it is possible to analyze space-charge dynamics during a long time, exceeding several hundreds of oscillation periods of an electron in the trap, which distinguishes this code from the typical two-dimensional simulations [13], [14]. versus time for Fig. 8 shows plots of the beam potential the regime with operating values of the parameters , , , and transverse velocity spread pitch factor . The dependencies were calculated in the cell located at the end of the magnetic compression region at 189 mm distance from the cathode (the total length of the compresmm). Fig. 8(a) gives the depension region is dence for the initial distribution of magnetic field . As shown in this figure, accumulation of particles in the trap accompanies initial beam potential growth, whereupon oscillaMHz develop. As an assumptions at the frequency tion, these oscillations are excited as a result of the instability in the ensemble of non-isochronous electron oscillators for which , where and are the oscillation frequency and the energy of an electron [25]. Starting from this assumption, we optimized the distribution of the magnetic field in order to de. crease the number of trapped particles for which for the optimized distriFig. 8(b) shows the dependence . No oscillations exist in this case, at least during the bution simulation time of 3 . Both distributions related to these mm, the calculations are shown in Fig. 9. In the region optimized distribution is equal to the distribution corresponding to additive polarity of the control coil (see Section II). The difference between the two last-mentioned distributions concerns mm where only the end of the compression region was necessary for the the constant gradient of optimized suppression of the trap oscillations. Unfortunately, the parasitic trap oscillations are characterized by high sensitivity of their intensity to fine structure of the “potential well” profile determined, among other factors, by the HEB space-charge potential distribution varying with the beam current. Therefore, even small changes of the operating parameters can greatly influence the degree of LFO suppression for an optimized magnetic field distribution. Thus, the computer simuoptimization, lation should be considered as a first step of followed by its experimental optimization, i.e., achievement of the lowest possible magnitude of parasitic oscillations without substantial deterioration of the basic output parameters of the gyrotron—its output power and efficiency.

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Fig. 8. Calculated beam potential B : , : , v

= 2 75 T = 1 2

U

as a function of time

t for (a) initial and (b) optimized B (z) distributions shown in Fig. 9 (U

= 10:6%, z = 189 mm).

Fig. 9. Initial distribution of magnetic field and the distribution optimized in the calculations for suppressing parasitic low-frequency oscillations.

B. Experiment and EGUN Simulation In the experiments, the distribution of the magnetic field was varied with the control coil connected in series with the main solenoid (see Section II). For the case where the control coil is energized with opposite polarity to the main solenoid, reduction of the magnetic field at the local area near this coil causes the increase of the radius of the electron guiding center and a decrease of the distance between the HEB and the metal beam tunnel. Fig. 10 shows the beam trajectories calculated with the and for the distribuEGUN code for the initial distribution tion corresponding to opposite polarity of the control coil when ( —the current of the main its current , no interception of electrons solenoid). For this value of from the primary beam with the wall of the tube has been observed. The minimum distance between the beam and the wall

= 30 kV, I = 10 A,

mm. The thickness of the beam is is equal to 0.1 mm at above , about 3 mm in this region. At a current the electrons from the outer layer of the HEB are intercepted by the tube wall and do not enter the resonator. All the primary . beam is intercepted at Typical plots of the LFO amplitude versus magnetic field cathode C2 for difmeasured in the gyrotron with the ferent currents of the control coil (opposite polarity) are shown in Fig. 11. Here, the dependence of the calculated pitch factor as a function of magnetic field is shown, the bracket indicates the magnetic field interval corresponding to the main mode of the gyrotron. Because we could not measure the electron current passing into the resonator, the part of the beam intercepted by the tube wall was estimated by the reduction of the gyrotron , the control output power. In the case of coil essentially did not influence either the output power or the LFO amplitude. There must be no interception of electrons in this case, including the electrons from the beam “halo.” On the other hand, opposite polarity of the control coil at provides interception of electrons by the tube wall throughout the HEB, because we did not succeed in the detection of either output power or parasitic oscillations. was characterized by The regime with the loss of the output power in the main mode not exceeding 20%. However, the LFO amplitude was reduced greatly in com. As seen in Fig. 11, parison with the initial regime there is no a LFO signal in the region of the main gyrotron mode and the reduction of the LFO amplitude is 7–10 times at lower . We may suppose that the most of magnetic field the primary beam passes into the resonator and contributes to the generation of microwave power. But the trapped electrons from the beam “halo” are intercepted by the metal wall of the


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Fig. 12. Amplitude of low-frequency oscillations A for different values of (additive polarity) and calculated pitch factor as control coil current I functions of magnetic field B (cathode C2, U = 30 kV , I = 10 A, B =B = 17:9).

Fig. 10. Geometry, electron trajectories and B (z ) dependence for (a) the initial magnetic field distribution and (b) the distribution corresponding to opposite polarity of the control coil (I = 0:87 1 I ).

for different values of Fig. 11. Amplitude of low-frequency oscillations A (opposite polarity) and calculated pitch factor as control coil current I functions of magnetic field B (cathode C2, U = 30 kV, I = 10 A, B =B = 17:9).

tube, which results in a significant suppression of parasitic oscillations. One can note that the control coil current corresponding to the appearance of the interception of the primary beam in the EGUN calculations exceeds slightly the current of this coil at which the output power is reduced. This discrepancy can be explained by the skin effect in metal components of the tube, as well as by possible misalignment of the magnetic system, beam tunnel or cathode assembly.

The experiments demonstrated the suppression of parasitic oscillations by using additive polarity of the control coil as well. , the LFO amplitude reduction was In the case of 2–3 times throughout the magnetic field range corresponding to LFO existence. The results are shown in Fig. 12. This value of the control coil caused practically no decrease of the microwave output power of the gyrotron. We attribute the measured reduction of the LFO amplitude to the effect of magnetic field distribution on the space-charge instability in the ensemble of non-isochronous electron oscillators, which were studied with the PIC calculations (see Section VI-A). VII. DISCUSSION OF THE RESULTS AND CONCLUSION The data of this paper on the LFO characteristics and the electron energy distributions allow to determine the zone of stable operation of the experimental gyrotron, which is characterized by a high quality HEB with low electron energy spread and by the absence of parasitic oscillations. The threshold value of the pitch factor corresponding to LFO appearance can serve as a boundary of this zone. When the pitch factor exceeds the threshold value, simultaneously parasitic oscillations appear and energy spread abruptly increases. Such degradation of the HEB quality results in a significant decrease of gyrotron efficiency, even at relatively low amplitude of parasitic oscillations. It was shown that the inhomogeneity of electron emission has a strong negative influence on the beam quality. The decrease of emission homogeneity causes an increase of the LFO amplitude and a reduction of gyrotron efficiency. For development of a gyrotron with enhanced efficiency, it is desired to extend the zone of stable operation towards high pitch factor regimes. Such broadening seems to be possible by using methods for suppressing parasitic low-frequency oscillations by optimization of the magnetic field distribution in the compression region. The suppression can result from introducing additional losses of the trapped electrons from the beam “halo” due to their interception with the metal wall of the tube, and from decreasing the increment of the instability of space charge locked in the trap. The variation of magnetic field distribution can be achieved with an additional control coil placed in the compression region. Our measurements showed that accurate adjustment

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of the magnetic field was needed for effective suppression of the oscillations. As applied to modern long-pulse and continuous wave (CW) high-power gyrotrons with superconducting solenoids, a wide-ranging variation of the magnetic field distribution can be realized only if the control coil is a part of the solenoid. However, the interception of the beam “halo” can be distribution using achieved by even small correction of the a room-temperature coil, if the designed beam trajectory passes close to the wall of the tube. An alternative to the additional magnetic coil as a method for losing the trapped electrons is a special electrode with adjustable aperture placed in the compression region. In this case, the variation of the aperture diameter allows to achieve considerable losses of the trapped electrons without interception of the primary beam. However, the necessity to combine an adjustable aperture with high power loading of the electrode in the long-pulse and CW regimes makes this technique difficult to achieve. As a next step, the gyrotron microwave cavity will be opti. In combimized for operation at high pitch factor nation with LFO suppression, enhanced gyrotron efficiency is expected.

ACKNOWLEDGMENT The authors wish to thank A. N. Kuftin, V. K. Lygin, M. A. Moiseev, and V. E. Zapevalov of IAP, Nizhny Novgorod, Russia, for assistance in the design and manufacturing of the tube components, as well as K. A. Poduschnikova and S. A. Fefelov of Ioffe Institute, St. Petersburg, Russia, for helpful discussions and manufacturing elements of the experimental setup.

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Oleg I. Louksha was born in 1961. He received the M.Sc. and Ph.D. degrees in physical electronics from the Leningrad Polytechnical Institute (now St. Petersburg State Polytechnical University), Leningrad, U.S.S.R., in 1984 and 1992, respectively. Since 1984, he has been working at the Physical Electronics Department, St. Petersburg State Polytechnical University, first in the investigation of noise and space-charge oscillations in magnetron-type devices. In 1986, he was involved in the gyrotron program. He has been responsible for the theoretical and experimental investigations directed on the formation of high-quality electron beam in gyrotrons. Since 1996, he has been an Associate Professor of the Physical Electronics Department. He is currently a Vice-Dean of the Radiophysical Science and Engineering Faculty, St. Petersburg State Polytechnical University. His current research interests are focused on the experimental study and numerical simulation of physical processes in gyrotron electron beam. He has over 50 research publications.


Bernhard Piosczyk received the Dipl. Ing. degree in physics from the Technical University of Berlin, Berlin, Germany, in 1969, and the Dr. rer. nat. degree from the University of Karlsruhe, Karlsruhe, Germany, in 1974. Since 1970, he has been at the Research Center (Forschungszentrum) Karlsruhe, first in the field of RF-superconductivity for accelerator application, then in the development of CW, high current H+ and H- ion sources, and since 1987, in the development of high-power gyrotrons. He is responsible for the development work on the coaxial cavity gyrotron.

Gennadi G. Sominski was born in Leningrad, U.S.S.R. (now St. Petersburg, Russia), on December 12, 1935. He received the M.Sc. degree in electronics, the Ph.D. degree in physics for the study of magnetrons with secondary-emission cathodes, and the Dr.Sci. degree for the work on investigation of high-power microwave crossed-field devices, from the Leningrad Polytechnical Institute (now St. Petersburg State Polytechnical University), U.S.S.R., in 1960, 1967, and 1984, respectively. Since 1960, he has been at the Physical Electronics Department, St. Petersburg State Polytechnical University. In 1968, he founded the Laboratory of High-Current Electronics and Microwaves and has been leading it up to now. In 1991, he became a Full Professor at the Physical Electronics Department, St. Petersburg State Polytechnical University. His activity is focused on the research of physical processes in electron space charge—specific “active medium” of high-power microwave devices, as well as on the development of methods for improving these devices and for designing new-type microwave systems. He has developed new diagnostics of high-current electron beams and effective methods of the control of space-charge processes in these beams with nonuniform electric and magnetic fields. His research interests also include the study and manufacturing of field emitters with fullerene coating for the formation of high-density electron beams. He has been the author or coauthor of over 200 publications and 17 inventions. Prof. Sominski was elected a full member of the International Academy for Technological Cybernetics. He is a member of the Advisory Committee of the Russian Foundation for Basic Research and a member of the Physical Electronics Division of Russian Academy of Sciences.

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Manfred K. Thumm (SM’94–F’02) was born in Magdeburg, Germany, on August 5, 1943. He received the Dipl. Phys. and Dr. rer. nat. degrees in physics from University of Tübingen, Tübingen, Germany, in 1972 and 1976, respectively. At the University of Tübingen, he was involved in the investigation of spin-dependent nuclear forces in inelastic neutron scattering. From 1972 to 1975, he was Doctoral Fellow of the Studienstiftung des Deutschen Volkes. In 1976, he joined the Institute for Plasma Research, Electrical Engineering Department, University of Stuttgart, Stuttgart, Germany, where he worked on RF production and RF heating of toroidal pinch plasmas for thermonuclear fusion research. From 1982 to 1990, his research activities were mainly devoted to electromagnetic theory in the areas of component development for the transmission of very high power millimeter waves through overmoded waveguides and of antenna structures for RF plasma heating with microwaves. In June 1990, he became a Full Professor of the Institute for High-Frequency Techniques and Electronics at the University of Karlsruhe, Karlsruhe, Germany, and Head of the Gyrotron Development and Microwave Technology Division, Institute for Technical Physics, Research Center Karlsruhe, Forschungszentrum Karlsruhe (FZK). Since April 1999, he has been the Director of the Institute for Pulsed Power and Microwave Technology at FZK, where his current research projects are the development of high-power gyrotrons, dielectric vacuum windows, transmission lines and antennas for nuclear fusion plasma heating, and industrial materials processing. He has authored/coauthored three books, 9 book chapters, 180 research papers in scientific journals, and approx. 800 conference proceedings articles. He holds 10 patents on active and passive microwave devices. Dr. Thumm is Vice Chairman of Chapter 8.6 (Vacuum Electronics and Displays) of the Information Technical Society in German VDE and a member of the German Physical Society. In 2006, he has been appointed to be a member of the IEEE EDS Vacuum Devices Technical Committee. He has been awarded with the Kenneth John Button Medal and Prize 2000, in recognition of outstanding contributions to the Science of the Electromagnetic Spectrum. In 2002, he was awarded the title of Honorary Doctor, presented by the St. Petersburg State Technical University, for his outstanding contributions to the development and applications of vacuum electron devices.

Dmitriy B. Samsonov received the B.S. and M.S. degrees in physical electronics, in 2003 and 2005, respectively, from St. Petersburg State Polytechnic University, St. Petersburg, Russia, where he is currently working toward the Ph.D. degree in physical electronics at the Laboratory of High-Current Electronics and Microwaves, where he is engaged in gyrotron experiments.