Proceedings of the 1986 International Linac Conference, Stanford, California, USA

A COHERENT VERY HIGH POWER MICROWAVE SOURCE USING A VIRTUAL CATHODE OSCILLATOR* M. V. Fazio, and R. F. Hoeberling, AT-5, MS H827 Los Alamos National Laboratory, Los Alamos, NM 87545

SUllll1ary results in severe longitudinal charge bunching. The oscillation of the virtual cathode excites the longi­ An oscillating virtual cathode produced by a mul­ tudinal electric field that drives the transverse mag­ tikiloampere relativistic electron beam can generate netic waveguide modes in a cylindrical waveguide. As microwave power at levels from several-hundred mega­ the ratio of the beam current to the space-charge lim­ watts to one gigawatt. This type of source can oper­ iting current increases,s the microwave output fre­ ate from 500 MHz to 40 GHz. To become useful as an Quency in an oscillating virtual cathode varies be­ accelerator driver, it is essential that we control tween the plasma frequency wp and ~ "'p, where the frequency and phase of the microwave radiation. To accomplish this, it may be possible to use the Z resonant interaction between the oscillating virtual "'p2 (4:e yl2 cathode and a microwave cavity that is pumped with a klystron-injected signal to produce a microwave source capable of very high power, narrow bandwidth, narrow­ In this expression, n is the electron density and m band frequency tunability, and phase controllability. is the electron mass. The second mechanism for microwave production in­ Dynamics of the Virtual Cathode Oscillator volves the electrons that are trapped in the potential well between the real cathode and the virtual cathode. A virtual cathode is formed when the electron The electrons reflexing in this potential well can also current from an electron-beam diode, greater than the generate broadband microwave power at a higher frequen­ space-charge limiting current,l is injected into a cy than in the case of the oscillating virtual cathode. cylindrical waveguide, as shown in Fig. 1. A propa­ The frequency is higher because the individual reflex­ gating electron beam produces a negative potential ing electrons can travel at near the speed of light; because of its own space charge, and when the beam whereas, the frequency of the virtual cathode oscilla­ enters the waveguide, the space-charge potential en­ tions is determined by the plasma frequency wp of the ergy increases. At high current levels, the potential electron beam. barrier produced by the beam space charge exceeds the The virtual cathode oscillator is not a well­ beam's kinetic energy, and electrons in the beam are behaved microwave source. It has a broad microwave reflected back to the anode. This current level is spectrum with peaks in a variety of waveguide modes. called the space-charge limiting current. The poten­ Mainly. two factors contribute to this characteristic. tial barrier is called a virtual cathode and is formed The microwave radiation is generated by a combination at the position where the kinetic energy approaches of the two processes: the oscillating virtual cathode zero. For the case of a mildly relativistic electron and the reflexing electrons. Also, frequency chirping beam, an interpolative formula z for the space-charge occurs during the pulse, caused by diode voltage and limiting current (Iscl) in a cylindrical waveguide current-density variations. Consequently, one has a that has good experimental agreement is very unstable free-running oscillator. A number of researchers have reported microwave 17( y2l3 _ 1) 312 generation at the gigawatt level using virtual cath­ ( ink il oamperes) 1 + Z In rw/rb odes formed by high-current relativistic electron beams.. Operating frequencies range from 500 MHz to where y is the relativistic factor of the electron 40 GHz. Efficiencies up to 5~ are reported by U.S. beam, rw is the radius of the waveguide, and rb researchers and up to 40-50% by the Soviets (Didenko).' is the electron beam's outer radius. Didenko has also reported pulsed microwave radiation for half a microsecond at 3 GHz and 500 MW. In spite of these achievements, there has not been much effort toward developing these devices as reliable, effi­ cient, very high power, microwave sources. The ability of an oscillating virtual cathode to produce very high levels of peak power leads one to consider it as a candidate for an accelerator driver. To become viable in this role, it is essential that MICROWAVE ELECTRIC the device be made to operate predominately at a sin­ FIELO gle frequency. There should also be some means to .. • ANTENNA control the device's output phase . Frequency and Phase Locking It may be feasible to produce a frequency-locked oscillating virtual cathode by surrounding the oscil­ REFLEXING VIRTUAL lating virtual cathode with a resonant microwave CATHODE structure. A microwave cavity resonator has several properties of particular use to us in this application. Fig. 1. Typical virtual cathode oscillator source. First, it is frequency selective. The cavity supports a number of well-defined modes of oscillation, and each mode occurs over a very narrow bandwidth. Sec­ Currently there are two models for microwave pro­ ondly, microwave energy can be effectively coupled duction. The first is the oscillating virtual cathode out of a cavity resonator using the same techniques in which the virtual cathode oscillates in space and employed for coupling energy into rf accelerating time with a well-defined period.". This oscillation structures. Examples of microwave generation by passing an electron beam through a resonant structure are the *~ork supported by U.S. Dept. of Energy.

157 MO3-47 Proceedings of the 1986 International Linac Conference, Stanford, California, USA cavity klystron and the magnetron. A series of micro­ virtual cathode is much less than its steady-state wave cavities are used first to bunch the dc electron value. beam and then to extract the power from it at the Successful experimental work on injection locking microwave frequency. The dynamics of the oscillating magnetrons together has been done by Varian,'l virtual cathode is much more complicated and less Raytheon,'2 and P. F. Lewis at English Electric Valve understood than the previous examples. However, there (EEV) Co., Ltd. '3 In the case of Varian and EEV, the is no reason to believe that a resonant cavity sur­ locking power in the steady state was 32 to 35 dB be­ rounding the oscillating virtual cathode would not low the oscillator output power. With Raytheon's also affect its dynamics. If one can tune the oscil­ experiment, the locking power required was 26 dB below lating virtual cathode by varying the beam-current the output. density so that its dominant free-running oscillation frequency is near the passband of a microwave-cavity Proposed Experiment resonator surrounding the oscillating virtual cathode, then it should be possible to create a strong beam/ Now under construction is an experiment to pro­ cavity interaction. Because of this interaction, the duce an injection-locked virtual cathode oscillator cavity field induced by either the oscillating virtual at 1.3 GHz. The device to be tested will use the cyl­ cathode or some other source feeds back on the oscil­ indrical geometry of Fig. 2. The l-MeV, 20-kA space­ lating virtual cathode, forcing it to oscillate in the charge-limited electron beam is accelerated into a desired mode at the cavity resonant frequency fo. The cylindrical resonator where the TM020 transverse magnet­ formation of the virtual cathode is a beam-bunching ic mode is excited. The field pattern for the TM020 is phenomenon; thus, if one can affect the dynamics of shown in Fig. 3. the bunching process, then it should be possible to The fields in the TM020 mode have the following influence the behavior of the oscillating virtual fonn: cathode. Utilizing this feedback interaction, the oscillating virtual cathode and the cavity field E c J 5 , and should lock together in phase and in frequency, con­ z O C· ;0 r) verting beam power to microwave power with improved efficiency. Brandt, et al.," have investigated the H « J ' (5.5:0 r) effect of feedback on the microwave output of a re­ 4> O flexing electron device. Their simulations added a 100-kV/cm external sinusoidal electric field at where JO and JO' are the zero-order Bessel function 9.B GHz to the l-MV/cm field generated by the applied and its derivative, a is the cavity radius. and r is diode voltage. The sinusoidal field increased the the radial position. The radial dimension of the cyl­ microwave energy density at the pump frequency by a inder will be selected to place the TM020 mode at factor of 40. 1.3 GHz, which results in a cylinder diameter of ap­ A further refinement to the frequency-locking proximately 40 cm as shown in Fig. 2. The electric concept involves exciting the cavity resonator with a field is axial in the z-direction, with maxima at the microwave signal at the cavity resonant frequency, axis r a 0, and at r a 14 cm from the central axis, before injecting the electron beam. The power level as shown in Fig. 2. The diameter of the electron beam of this microwave pump would be a few percent of the will be chosen to be within the region of the central power produced by the electron beam. The role of the peak in the electric field shown in Fig. 2. This ge­ microwave pump is to build up the microwave field in ometry will result in a strong coupling between the the cavity so that. when the electron beam enters the electric field from the oscillating virtual cathode cavity. the beam will interact with the existing cav­ and the cavity TM020 mode electric field. Wall ity field. With this technique, the beam should be currents should be induced by the virtual cathode forced to oscillate at the same frequency as the oscillations that set up the electric and magnetic microwave pump instead of waiting for the virtual fields characteristic of the TM020 mode. cathode oscillation to stochastically build up from We will begin experimentation with the microwave noise voltage. The current density of the electron cavity in place downstream of the diode. We Io/i 11 op­ beam would be adjusted by altering the diode geometry timize the electron-beam diode parameters such as to ensure that the free-running frequency of the os­ anode-cathode gap spacing and diode voltage to adjust cillating virtual cathode would be close enough to the the electron-beam current density so that the micro­ cavity frequency for the beam/cavity interaction to wave radiation peaks in the 1.3-GHz regime. If the be significant. One then would no longer have a truly presence of the cavity does indeed affect the dynamics free-running oscillator, but instead a device that must interact with a resonant structure that affects the bunching process and, hence, the oscillation frequency. MICROWAVE The concept of injection locking a free-running RAOIATlOIi microwave oscillator to an external signal is one that ) QUTPUT WAVEGUIDE has been around for some 40 years. An extensive (TYPICAL Qf 41 .,/ amount of theoretical work on injection locking has been done by persons such as E. E. David,' J. C. Slater,lO and numerous others. David's work has • • • • H dealt primarily with magnetrons. The work of both • indicates that if the coupling between the two sources • E is strong enough and if their frequencies are close enough together, frequency and phase synchronization • (or locking) occurs. o 0 0 {-~ In these microwave oscillators, coherent oscil­ VIRTUAL lations spring up from preoscillation noise already CATHODE VACUlJIII.WAVEGUIOE present in the system. If an external sinusoidal sig­ WIIiDOW nal is impressed upon the oscillator, the initial os­ cillations start from the vector sum of this external signal and the noise voltage. During the rf build-up, the effect of the locking signal is enhanced (over the steady-state case) because the rf voltage due to the Fig. 2. Cylindrical resonator configuration.

MO3-47 158 Proceedings of the 1986 International Linac Conference, Stanford, California, USA

TMII211MOOE E Conclusions If a virtual cathode source can be phase and Fre­ quency locked to a relatively low-power injection sig­ nal, and if the problems associated with duty factor and pulse length can be solved, a variety of new possibilities in the microwave area become available , = a to accelerator technology. For example, a single gigawatt-level injection-locked virtual cathode source could replace a large number of klystron sources. To achieve even higher levels of power, several virtual cathode sources could be run coherently in parallel by having all of them frequency and phase locked to a single injection signal. ~ 0 0 ~ 0 References 0 ~ 0 -H °10 ~ 0 1. L. S. Bogdankevich and A. A. Rukhadze, ·Stability t 1~ of Relativistic Electron Beams in a Plasma and f-. a= 20 C1II ~ the Problem of Critical Currents," Sov. Phys. AT 1.3 GHz Usp. 14, 163 (1971). .\ TMII20 = 1.14a 2. R. F.Hoeberling and D. Payton, III, "Ion Accel­ eration in the Evacuated Drift-Tube Geometry,· J. Appl. Phys., i, 48 (1977). Fig. 3. Electric field distribution in a TM020 3 C. K. Birdsall and W. B. Bridges, "Space Charge cavity. Instabilities in Electron Diodes and Plasma Con­ verters," J. Appl. Phys. 32, 2611 (1961). of the virtual cathode oscillations, we should observe 4. D. J. Sullivan, Proc. 3rd Int. Topical Conf. on an improvement in efficiency and a rise in microwave High-Power Electron and Ion-Beam Research and power output as we tune the oscillating virtual cath­ Technology, Novosibirsk, USSR, 1979 (Institute of ode frequency through the cavity resonant frequency. Nuclear Physics, Novosibirsk, USSR, 1979), Vol. Having tuned the free-running frequency of the II. 769; D. J. Sullivan, Proc. 4th Int. Topical virtual cathode oscillator close to the cavity's Conf. on High-Power Electron and Ion-Beam 1.3 GHz, we can then apply power from the 1.3-GHz Research and Technology, Palaiseau, France, 1981, klystron that is used as the injection-signal source. edited by H. J. Doudet and J. M. Buzzi, Eds. With this configuration, we will be able to see the (Ecole Poly technique, Palaiseau, France, 1981), effect of the cavity resonator on the oscillation VO I. r. 371. frequency of the virtual cathode with and without the 5. M. A. Mostrom, T. J. T. Kwan, and C. M. Snell, microwave injection signal. The use of the external "Simulation of Virtual Cathode of a Scattered injection signal allows the microwave field in the Electron Beam," Bull. Am. Phys. Soc. 27, 1075 cavity to be initialized, so that the virtual cathode (1982). -- from its time of formation sees a strong cavity field 6. D. J. Sullivan, "High Power Microwave Generation with which to interact. The klystron would be turned From a Virtual Cathode Oscillator (VIRCATOR)," on to pump the cavity before firing the electron beam. IEEE Trans. on Nucl. Sci., 30, (4), 3426 (1983). which would allow the cavity field to ring up to its 7. A. N. Didenko, A. G. Zherlitsyn, A. S. Sulakshin, steady-state value in a time equal to several e-folding G. P. Fomenko, V. I. Tsvetkov, and Yu. G. Shtein, times. "The Generation of High Power Microwave Radiation The microwave cavity enhances the effect of the in a Triode System by a Heavy-Current Beam of klystron output power by storing the klystron-produced Microsecond Duration," Pis'ma Zh. Tekh. Fiz. 9, energy in the cavity electromagnetic field over a rel­ 151 0 (1 983) . - atively long period of time. The electric field in 8. H. E. Brandt, A. Bromborsky, H. B. Bruns, R. A. our cavity, assuming a 0 of 1000, is about 220 kV/cm Kehs, "Microwave Generation in the Reflex at 10 MW of klystron output as compared with a field Triode," Proc. 2nd Int. Topical Conf. on High­ of around 500 kV/cm in the oscillating virtual cathode Power Electron and Ion-Beam Research and Technol­ itself. It must be kept in mind that the rf voltage ogy, Cornell University, Ithaca, New York, in the oscillating virtual cathode starts from near 6496( 1977) . zero amplitude in the presence of the 220-kV/cm cavity 9. E. E. David, Jr., "RF Phase Control in Pulsed field. Because our injected signal is comparable in Magnetrons," Proc. of the IRE (Institute of Radio amplitude to the diode field, it seems quite possible Engineers) 40, 669 (1952). that we should be able to injection lock the oscilla­ 10. J. C. Slate~ Microwave Electronics, (Van ting virtual cathode with the klystron. Nostrand, New York, 1950), 205-210. Microwave slot apertures will be used to couple 11. "Notes on Phase Locked Magnetrons," Varian Asso­ the klystron power to the cavity and to extract power ciates Radiation Division, Palo Alto, California, from the device. The coupling occurs through the private communication. circumferential magnetic field in the cavity that 12. W. C. Brown, "Microwave Beamed Power Technology penetrates the slot and excites the TE10 mode in the Improvement - Final Report," Raytheon Co., Micro­ rectangular waveguide. The short dimension of the wave and Power Tube Division, Waltham, Massachu­ slot is parallel to the cavity's center line. The setts 02254, PT-5613, (1980). slots will couple to appropriately sized waveguide. 13. P. F. Lewis, "An Experiment in the Parallel Operation of High-Power Magnetrons," Microwave Journal, ll, (4), 82, (1970).

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