SIMULATED PARAMETERS OF SUBGIGAWATT

SIMULATED PARAMETERS OF SUBGIGAWATT RELATIVISTIC BWOs WITH PERMANENT MAGNETIC SYSTEMS∗ A.V. Gunin, V.V. Rostovξ, E.M. Tot’meninov High Current Electronics Institute SB RAS, 634055, 2/3, Akademicheskii Avenue, Tomsk, Russia

K.A. Sharypov, V.G. Shpak, M. I. Yalandin Institute of Electrophysics UB RAS, 620016,106, Amundsen Street, Ekaterinburg, Russia

A.E. Yermakov, S.V. Zhakov Institute of Metal Physics UB RAS, 620049,18, S.Kovalevskaya Street, Ekaterinburg, Russia

G. Demol ITHPP F-46500 Thegra, France

R. Vezinet CEA/DAM GRAMAT F-46500 Gramat, France

Abstract Report presents the results of calculations and numerical modeling of quasi-stationary, nanosecond relativistic X-band and Ka-band BWOs with peak power exceeding 100 MW where magnetic field guided electron beam (0.5-1.7 T) could be created by permanent magnets made of highly-coercivity materials. Magnetic field interpolation of the permanent magnets was used in numerical models of microwave devices (code KARAT). Particle-in-cell simulations have shown that in the frequency ranges of 8 GHz and 37 GHz, and for the Bfield below cyclotron resonance value, the same parameters of HPM generation are available as it predicted and/or measured experimentally for prototype models with solenoids fed by DC or pulsed current.

of this zone is of special importance and requires to reduce e-beam gun (vacuum diode) overall radial size, including vacuum insulator section. With that, an electric field at the cathode shielding electrode should be minimized. The probability of injection of backward ebeam current is of critical and this requires a special shaping of B-field lines of force in the section between the cathode and vacuum insulator.

II.

BWO with resonant reflector

Relativistic BWO with resonant reflector and increased slow wave structure cross-section (D/λ>1, here D is the mean diameter of the SWS and λ is the wavelength) is schematically depicted in Fig. 1.

I. INTRODUCTION The BWOs equipped with highly-coercivity permanent magnets (for example, made of NdFeB) can enhance essentially autonomy of a prospective HPM generators built around of high-current repetitive electron accelerators type SINUS, RADAN, and ones based on SOS modulators [1-3]. Besides, a stable source of focusing B-field could be important component of multichannel BWO’s providing coherent summation of the radiation [4]. Design of permanent magnets takes into consideration a specificity of the options where solenoidal profile of Bfield is required in the BWOs working zone. It includes the cathode electrode, slow-wave system (SWS), and ebeam collector. The problem of B-field reverse shift out

Figure 1. Design of BWO with resonant reflector; R – reflector, SOL – solenoid, B – electron beam, SWS – slow wave structure. In this oscillator scheme [5], an incident TM01 wave counter-propagating to the e-beam is reflected from the resonant reflector in the idle mode due to excitation of the locked symmetric TM02 mode. The amplitude of z-

∗

This work was supported in part by the French MOD (DGA) and CEA Gramat through a research contract involving ITHPP (Thegra, France) and HCEI SB RAS (Tomsk, Russia), by integrated research projects between HCEI SB RAS, IEP UB RAS, and IMP UB RAS, and by RFBR Grant 11-02-00097. ξ email: [email protected]

978-1-4577-0631-8/11/$26.00 ©2011 IEEE

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component of RF electric field at the beam radius in the reflector region can be several times higher than that one in the corrugated waveguide. Thus in the confined space region, conditions are provided for preliminary efficient modulation of the e-beam. It should be noted that, due to concentration of RF field in the reflector volume, preliminary modulation effect in this system is stronger than in the conventional relativistic BWO with cutoff-neck. The oversized SWS cross-section reduces the probability of RF breakdown. Increasing the SWS (and the cathode) diameter results in reducing the radial component of electric field at the edge of the cathode. This improves quality of electron beam and increases efficiency of the microwave generation at magnetic field below cyclotron resonance [6,7].

III.

It allows calculations of the axial and radial magnetic field components in axially symmetric systems containing permanent magnets and, if necessary, a soft magnetic elements [9]. Permanent magnet was also optimized by magnetostatic section of SAM program package [10].

X-BAND BWO

A. Time domain numerical experiments Numerical optimization of 8-GHz BWO generation regimes was performed with the used of axiallysymmetrical version of PIC-code KARAT [8]. Parameters of SWS and e-beam injector used in simulations were identical for both BWO options based on guiding solenoid coil (Fig.2,a) as well as on the permanent magnet (Fig.2,b). Electron-beam characteristics used in the simulation were as follows: electron energy of 400 keV, beam current of 3.1 kA.

Figure 3. Non-averaged microwave power vs. time (340 MW, if averaged at stationary stage) simulated for BWO with solenoid (Fig.2,a). Windings current set as 95 A; Bzfield at the cathode edge of 0.59 Т.

Figure 4. Microwave power vs. maximum value of guiding magnetic field simulated for BWO with solenoid (Fig.2,a). Point “A” corresponds to PIC-simulation presented at Fig.3.

Figure 2. Comparison of the axial magnetic field distribution and electron beam trajectories in interaction space of BWO for two versions of magnetic field sources. Diagrams has equal scale and the coincident point in the edge of cathode, that is electron beam emission area. For numerical model of the device based on solenoid, B-field was evaluated from the current in the windings of selected geometry. The permanent magnet-based system was preliminary optimized by the boundary integral method using a developed FORTRAN program package.

Figure 5. Non-averaged microwave power flux vs. time (347 MW, if averaged at stationary stage) simulated for BWO with permanent magnet (Fig.2,b). Interpolated Bzfield at the cathode edge of 0.59 Т.

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Simulation of HPM generation in quasi-stationary regime has shown (Fig.3) that for solenoid-based BWO peak power of 340 MW is achievable in magnetic field above 0.5 T. Hereinafter we mean B-field in the maximum of axial distribution (Fig.2). Efficiency of HPM-generation (~27%) is quite high in this case, and microwave power remains practically constant for Bfields above certain value for a rather extended interval until appearance of cyclotron resonance effect. In view of a stable, long-term BWO operation in repetitive mode it’s desirable to increase B-field until no drop of the generation power. This is important to improve homogeneity of electrons emission from the cathode as well as to prevent electrons touch of SWS wall when secondary near-wall discharges can be initiated. Obviously, for the solenoid-based BWO, the rise of Bfield results in the increase of power supply source. As it follows from calculations (Fig.5), the BWO option with permanent magnet can provide microwave power no less than that for the device with solenoid. However, attempt to increase B-field for e-beam quality improvement will be associated in this case with a growth of magnetic material mass and/or with a necessity to increase its residual magnetization.

Figure. 6. Electric field values and backward electrons trajectories in two versions of vacuum diodes. B. Coaxial diode design Design option of coaxial e-beam diode magnetized by the permanent magnet (Fig.6,a) should reproduce all useful properties of the diode equipped with a solenoid coil (Fig.6,b). Shielding electrode of the cathode holder must terminate backward parasitic current emitting from the cathode edge (i). To minimize the probability of parasitic electron emission from entire cathode electrode, electric field should not exceed some critical level. For example, in the case of voltage pulse width of about 40 ns, critical E-field level at finished surface of stainless steel electrode is limited by the value of 300 kV/cm (ii). Long service life of vacuum insulator presupposes the level of E-field at dielectric boundaries as it was realized for the diode geometry presented at Fig.6,a (iii). Numerical electrostatic calculations (Fig.6) were done for the voltage level of -450 kV. This voltage exceeds

somewhat the BWO operating voltage (400 kV) and, in particular, takes into account the factor of probable voltage pulse non-uniformity. As it seen at Fig.6,a, a backward path of B-field lines is terminated by the shield electrode of cathode holder. This stops parasitic current emitting from cathode edge to the grounded wall of diode. Maximum value of electric field at the cathode holder surface attains 255 kV/cm. It exceeds the level of 215 kV/cm calculated for the case of solenoid-based version. However, it is less essentially than above mentioned critical level of 300 kV/cm. Maximum level of E-filed on the insulator boundary is almost the same for both versions of the diode. Thus, the results of simulations demonstrated possibility of reliable vacuum diode configuration when it equipped with a permanent magnet. C. Design and characteristics of permanent magnet For technological reasons, axially symmetric sections of the permanent magnet were interpolated with a set of trapezoidal segments (Fig.7). Estimates have shown that for the option with twelve segments interpolation provided non-uniformity of axial filed distribution less than 0.1% in the BWO beam-to-wave interaction region. Axial repulsion force inside radial-magnetized sections of permanent magnet and repulsion between the sections in whole was estimated. Above forces did not exceed 8000 N for residual magnetization of Вr=1.2 T selected for NdFeB. With that, mechanical strength of a permanent magnet can be provided by rather standard tightening elements. The value of Вr=1.2 T was chosen reasoning from commercial availability of magnetic materials to fit a required residual magnetization spread of numerous individual magnetized elements no worse than 2%. Table 1 presents main characteristics of designed highly-coercivity permanent magnetic systems whose Bfield in critical zone of the BWO is equivalent to that of the pulse solenoid with winding currents of 95A and 75А. For the last case (75 А), when maximum B-field is about 0.47 Т, BWO microwave power drops down to ~150 MW in accordance with simulations similar to that shown at Fig.4 and Fig.5. However, for a decreased-power BWO ebeam parameters were specially reduced (electron energy of 330 keV, beam current of 2.35 kA), and these measures makes more compact the accelerator and 40% - decreases the weight of magnetic material (down to 95 kg). Table 1. Permanent magnets of X-band BWO Characteristics Total length, mm Diameter, mm Mass of the magnet, kg Total weight, including tightening system, kg BWO microwave power, MW

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Version for Bz=0.59 T 565 320 132 172

Version for Bz=0.47 T 547 290 95 130

347

150

It is pertinent to mention here that the BWO prototype with DC solenoid has a weight of copper windings of ~55 kg. Besides, the device also includes a stabilized, controllable mains rectifier (12 kW; weight ~15 kg). Taking into account the necessity of forced cooling of the windings, the total weight of the BWO unit with permanent magnet exceeds one for the solenoid-based option less than two times.

generation was as high as 150-170 MW. This was rather close to the peak power predicted in PIC-simulations [8] (Fig.9). In the experiments and simulations electron beam energy was 275 keV, and e-beam current was 1.7 kA. Thus, efficiency of quasi-stationary HPM generation attained 35%. When dealing with a project of permanent magnetbased Ka-band BWO, one must keep in mind the following peculiarities. Reduction of HPM device sizes proportionally to the radiation wavelength does not presuppose equivalent E-fields scaling in the whole system. On the contrary, this leads to the rise of E-field at the cathode electrode and increases essentially transversal velocities of electrons in the tubular beam. If so, then thickness of hollow e-beam should be minimizing by application Bz field as strong as possible in the region below cyclotron resonance (Fig.9). There is also problem of high E-field at the shield of cathode electrode. This value attains ~600 kV/cm and it can be critical for pulse durations exceeding units of nanoseconds. Development of secondary near-wall microwave discharges in SWS is also highly probable at elongated pulsewidth. Fortunately, in the experiments [11] where e-beam puleswidth was 3-5 ns we did not observe cutting of microwaves due to above limitation factors. This was a background which stimulated design project of Ka-band BWO equipped with a permanent magnet made of NdFeB (Fig.11) possessing maximum Bfield of 1.7 T and predicted peak power of 140 MW.

Figure 8. Schematic cross-section of prototype Ka-band BWO equipped with a pulsed solenoid coil.

Figure 7. Design of high-coercivity magnet integrated with vacuum chamber, electron injector, electrodynamic slow-wave structure and forced-cooled beam collector of X-band BWO.

IV.

Ka-BAND BWO

Design project of Ka-band BWO is based on the prototype of quasi-stationary HPM device with a pulsed solenoid (Fig.8) tested experimentally [11]. For the guiding field of 2.2 T in the maximum of Bz - distribution (similar to that shown at Fig.2,a) an output power of HPM

Figure 9. Microwave power vs. guiding magnetic field simulated for Ka-band BWO with solenoid (Fig.8). Point “A” corresponds to the experiment [11]. Point “B” represents the choice for permanent-magnet-based Kaband BWO.

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V. SUMMARY

Figure 10. Non-averaged microwave power flux vs. time (142 MW, if averaged at stationary stage) simulated for Ka-band BWO with solenoid (Fig.9). Bz-field at the cathode edge of 1.7 Т.

The weight of designed permanent magnet of X-band BWO exceeds one for equivalent dc solenoids. However, the absence of capacitive energy storages, charging devices (rectifiers) and power switches, as well as systems of forced oil cooling of windings, the total weight and sized characteristics of the permanent magnet can be preferable in the case of long-burst or continuous operation. Total weight of permanent magnet of Ka-band BWO (~90 kg) tree times higher as compare with the pulsed solenoid supply source used in the experiments [11] at pulse repetition frequency of 10 Hz (pulse solenoid itself weights less than 1 kg). At the same time, permanent magnetic system has not limitation to increase the repetition rate of HPM device when, for example, SOSbased hybrid modulator [12] can drive e-beam injector as fast as thousand pulses per second and higher. A 2-T direct current, forced-cooled solenoid and associated supply/cooling systems much more heavy and require the mains power above 20 kW [3].

VI.

REFERENCES

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Figure 10. Design of high-coercivity magnet integrated with vacuum chamber, electron injector, electrodynamic slow-wave structure and forced-cooled beam collector of Ka-band BWO. Maximum magnetic field at the cathode emitting region is 1.7 T. Residual magnetization of NdFeB is selected as Br=1.2 T. Total weight of the magnetic material is 70 kg.

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