An evaluation is made of the performance of a Relativistic Klystron Amplifier (RKA) at 1.3 GHz. Problems are found to be associated with the RKA's RF pulse generation which place an upper limit on the RKA's operating range. RF-breakdown initiated by the X-ray flux also puts a limit on the electron-beam voltage. Large RF output pulses require use of the phase-locking property of the RKA.

The operation of the Relativistic Klystron Amplifier (RKA) was extended to higher frequencies. A 5 kA, 4 cm-diameter, 0.5 MeV Intense Relativistic Electron Beam (IREB) was fully modulated at 3.5 GHz. The RF from this IREB was extracted into a coaxial transmission line, in a TEM mode, and subsequently converted adiabatically into a rectangular TE11 mode. Finally, the RF was radiated into the atmosphere through a rectagular horn sealed with a lucite vacuum window. In a related experiment a 5 kA IREB was self-modulated by a mechanism similar to the RKA at a frequency of 8 GHz.

The limiting current that can flow across a parallel, planar gap under ac conditions is computed. As the limiting current is approached, the intense space charge of the beam may increase the gap capacitance by a factor of two to three over the vacuum value. Our numerical calculations show that a fully modulated beam may deliver up to 60 percent of its beam power to a load without forming a virtual cathode.

A coaxial drift tube allows propagation of an ultra high power relativistic electron beam (500 keV, not less than 100 kA, 100 ns). In this paper we study the modulation of a large diameter (12.6 cm) intense relativistic electron beam (500 keV, 16 kA) by an external microwave source via particle simulation. The annular beam, enclosed within a coaxial drift tube, is found to be fully modulated by a low-power external RF source at a frequency of 1.3 GHz. We further show that the coaxial configuration is easily scaled to high power. Here, a very large diameter (26 cm) intense beam (460 keV, 100 kA) is fully modulated at 1.3 GHz to obtain 31 GW of RF beam power.

Results are presented from recent research carried out on the development of high efficiency, high power traveling wave tube amplifiers. A rippled wall traveling wave tube is used as a slow wave structure for wave interactions with an 850 kV, 1 kA electron beam. A 100 kW signal from a magnetron is injected at the front end of the device and amplified by 15-30 dB giving an output power of 100 MW from a single stage amplifier. At higher gains the system tends to oscillate due to feedback from impedance mismatches at the structure ends. To overcome this we have used a severed amplifier consisting of two identical amplifiers in series and separated by an absorbing graphite section between the two amplifiers. With this device we have obtained 400 MW output power with an energy conversion efficiency of 48%. We shall present a comparison between the amplifier characteristics for the single and two stage amplifiers. Peak output powers are obtained in the severed amplifier at a beam current of 900 A; however, sidebands have developed and the output is no longer single frequency. It should be noted that the relative distribution of power in the sidebands compared to the center frequency varies with the beam current and that the sideband power can approach 50% of the total radiated intensity at high beam currents. The sidebands are asymmetrically located on either side of the carrier frequency with the upper sideband displaced from the carrier by about three times the frequency shift for the lower sideband. The authors discuss mechanisms leading to the sideband behavior described. It seems likely that most of the phenomena observed can be accounted for by finite structure length effects, which lead to resonances in the transmission coefficient for the structure. Other effects of importance include a substantial spread in the electron energy spectrum as the wave develops.

The beam-wave interaction in a Cerenkov traveling wave tube is considered theoretically. The system is assumed to operate at 8.75 GHz either as an amplifier or as an accelerator. The injected electrons have a kinetic energy of 0.85 MeV and the beam at the entrance can be prebunched or uniform. To avoid saturation, two kinds of tapering are considered: one which is adaptable, in the sense that the phase velocity follows exactly the particle's velocity; in the other, the dielectric coefficient varies algebraically in space. In the case of an accelerator (Eo equals 5 MV/m, I equals 1 A and d equals 0.8 m) the adaptable tapering causes the system to be almost three times more effective than in a uniform device. An analytical solution corresponding to the case 2(gamma) (r)(2) >> 1, is discussed. The other case considered is when the injected beam has a uniform distribution of phases relative to the wave. The construction of the bunching is illustrated as well as the regime in which the amplitude of the wave increases linearly; our simulation reveals that almost 50% of the interaction region is exploited for the former process. The authors show that by tapering, both the gain and the efficiency increase. When operated as an amplifier (E0 equals 1.0 MV/m, I equals 450 A and d equals 0.3 m) with an optimal linear variation of the dielectric coefficient, the efficiency is improved to about 30% from the 5% in the uniform device.

Recent results of this novel amplifier-oscillator system are reported. Parameterization of the TWT's gain and amplification bandwidth as well as the phase coherence between the two TWT's rf outputs as a function of BWO operating frequency are presented. The experimental apparatus is designed to simultaneously generate three intense annular electron beams and propagate them through twin Traveling Wave Tube (TWT) amplifiers and a Backward Wave Oscillator (BWO). The high power BWO and TWTs are composed of cylindrical waveguide with a sinusoidally varying wall and are designed to operate in the X-band frequency range at a total system power level of a few 100 MWs. A broad-band microwave coupler built into the system is used to extract the spontaneously generated microwave radiation from the BWO and redirect it into two TWTs for amplification. The system is frequency tuned by independently varying the parameters of the electron beam driving the BWO while maintaining constant beam conditions for the TWTs. The performance of each amplifier is individually investigated for gain and amplification bandwidth as a function of BWO operating frequency and for gain as a function of beam current. Since the TWTs operate below device saturation levels, the gain and amplification bandwidth results are compared to linear theory. The two TWT output signals are further compared for phase coherence. Techniques used to eliminate mode competition between the TWT's primary TM01 amplifier mode and higher modes which behave as oscillators are also reviewed.

The authors report the injection locking results of a long-pulse (200-400 ns) high power (20-30 MW) relativistic magnetron. The cold-cathode magnetron structure is driven by a high power modulator to generate S-band output at 3.3 GHz. Phase-locking with reproducible locked angle is achieved with an injection power ratio as low as 1:200. The locked states are phase stable to within +/- 3 degree(s) during the pulse. Repetition-rated operation at 5 Hz produces average powers higher than single shot systems. Phase locking physics is studied by parametrically scanning the injection frequency and varying the injection power. Important effects due to frequency pushing are identified. The measured locking bandwidth agrees well with a theory which takes into account frequency pushing effects. The measured dependence of final locked phase on injection frequency and injection power also agrees well with theory.

Phase-locked relativistic magnetrons in both 'half module' and 'full module' configurations were operated at power levels of 2.0 and 2.9 GW rms peak (4.1 and 5.8 GW instantaneous peak), respectively, at 2.8 GHz. Different interconnection geometries are investigated; the authors verify that the 'hybrid' geometry works best, as previously predicted by numerical modeling.

Until the present work, experience with repetitive relativistic magnetrons was sparse, consisting of $OM 1 Hz cooled devices and $OM 100 Hz bursts in uncooled resonators. The highest average power reported is approximately 500 W. The authors have modified an existing magnetron to include water cooling for repetitive operation. The system is designed for five second bursts at 200 Hz. Earlier single shot operation produces rf energies exceeding 50 Joules per micropulse. The authors have achieved 40 Joules per micropulse at a repetition rate of 100 Herz, or an average power of 4 kW for 0.5 seconds. The authors discuss issues in interfacing magnetrons with repetitive pulsed power and the operating characteristics during a burst of pulses.

The driven van der Pol-Duffing equation has been used to model the behavior of a relativistic magnetron driven by an external locking signal. The authors continue the study of the driven van der Pol-Duffing equation and present initial results of the investigation of coupled van der Pol-Duffing equations as models of mutually coupled relativistic magnetrons. A method is presented for determining the amplitude and phase of a signal in the slowly-varying amplitude approximation in the case that both the signal, X(t), and its time derivative, X(t), are available. When second-order differential equations and coupled systems of such equations are used as models of driven and coupled nonlinear oscillators, both X(t) and X(t) are available. In this case, it is possible to determine the amplitude and phase without averaging over a fast time scale. Thus certain dynamical information is retained that is lost if it is necessary to average over a fast time scale. In the case of two oscillators linearly coupled with time delays in the mutual drive configuration, the slowly varying amplitude and phase approximation has been used in order to simplify the problem. In general, behavior of the oscillator amplitudes, as well as the phase difference between oscillators, must be considered. An essential step in studying this system is the determination of stationary amplitudes and phase difference. In the case of zero frequency mismatch between oscillators and optimum coupling delay phase, stationary amplitudes and coupled power are obtained analytically as functions of coupling quality factor and ratio of oscillator growth rate to natural frequency. Unless these parameters are sufficiently large, the potential increase in coherent power delivered due to coupling will not be realized.

Four magnetron oscillator models are constructed and analyzed for the study of relativistic magnetron phase locking physics: the extended spoke model, the magnetron-specific equivalent model, the van der Pol equation, and the magnetron oscillator equation. The spoke model reproduces the magnetron specific conductance and susceptance features that are incorporated into other models. The equivalent circuit model and the magnetron oscillator equation model generate the same set of predictions concerning phase-locking condition, locking time, saturation amplitude and final phase. Both models predict a wider locking bandwidth and a shorter locking time as results of the frequency pushing effect. The van der Pol model solved in the fast time scale reveals the dependence of locking time on injection power and oscillator growth rate as well as on injection frequency.

Phase locking in driven relativistic magnetrons is demonstrated using 2D particle-in-cell simulations. It is found that injecting a driving signal prior to the onset of magnetron oscillations can decrease the locking time substantially from the characteristic time required to achieve phase locking by injecting the driving signal after the onset. Simulation indicates that magnetrons with small aspect ratio oscillate predominantly in the (pi) mode, while ones with large aspect ratio can oscillate in various modes which depend upon system parameters. Moreover, it is shown that the frequencies of magnetron oscillations decrease as the effects of nonlinear beam loading become more pronounced.

Stability properties of the extraordinary mode perturbations in a relativistic electron flow in a cylindrical magnetron are investigated within the framework of the linearized Vlasov-Maxwell equations. The stability analysis is carried out under the assumptions that the layer is thin and relatively tenuous and that the phase velocity of the perturbed waves is very close to the mean drift velocity of the layer. The perturbed distribution function is calculated by integrating along the electron orbit. The eigenvalue equation is derived and solved in the vacuum and layer regions. Solution in the vacuum region includes the resonator influence and cylindrical curvature effects. A closed algebraic dispersion relation is obtained for the synchronous modes. Analytical investigation of the dispersion relation is carried out for the resonance modes, which are very close to the vacuum modes in the magnetron circuit. The necessary and sufficient condition for instability is obtained for the resonance modes. It is shown that typical growth rates of the instability are few percents of the electron cyclotron frequency.

Simulations of the relativistic magnetron were performed with the 2-D fully electromagnetic particle-in-cell code MAGIC. These simulations reveal that the operating principles of the relativistic magnetron differ fundamentally from those generally thought to apply in these devices; in the fully oscillating state there is no synchronism between the azimuthal motion of the electrons and the rf wave; the gain mechanism has been identified as a negative resistance interaction. Other results of the simulations include rough quantitative agreement with published results of relativistic magnetron experiments performed at Physics International.

High-power microwave sources have been developed intensively during recent years for applications in high-power radars and communications, high-energy charged particle accelerators, thermonuclear plasma heating, and electronic defense warfare. A novel approach is described to generate large numbers of high-power microwave sources which not only operate at the same frequencies but also have their phases under control. One immediate application is by combining this large number of sources coherently to produce much higher power levels which a single device could not possibly reach. Using magnetron arrays to produce such unique microwave sources is feasible and has been demonstrated by computer particle simulations. However, this concept can very well be applied to other microwave devices.

Work begun in 1986 has continued on the reflex-diode oscillator mounted on one of the four Aurora $OM10-MV, $OM22-(Omega) pulse lines. This is a preliminary report on the most recent work, which extracted microwaves radially into 18 rectangular WR-975 waveguides around the virtual cathode. Two additional arms upstream of the anode extracted microwaves around the real cathode. Vestigial-loop, waveguide directional couplers measured the radially extracted microwave energy. The output is typically 50 to 100 J/arm, for the frequencies between 0.6 and 1.0 GHz. Effects were compared from two cathode tips differing by a factor of $OM2 in diameter. Additional parameter variations have included the anode/cathode spacing and the positioning of a second foil.

A reflex diode operating from 1 to 8 GHz is powered by the TEMPO pulser at Harry Diamond Laboratories. High-power microwave (HPM) pulses (60 ns FWHM) are radiated into a large anechoic chamber. These pulses are monitored with waveguide rf couplers, and open-ended waveguide. Two configurations of the reflex diode are compared. The configurations differ by the polarity of the applied voltage pulse. These two configurations are studied experimentally and numerically, using the particle-in-cell code MAGIC.

This paper discusses the design motivation for a microwave calorimeter using a semiconductor, and reports on the implementation status of the device.

The resonance at which high-efficiency operation of virtual cathode oscillators is obtained occurs when the beam frequency equals the reflex frequency to within 2%. This tolerance limit in the frequency ratio implies that cathode closure in the anode-cathode gap is not acceptable. The authors have developed and tested a 6-cm2 cathode that will operate longer than 1 microsecond(s) at 300 A/cm2 without significant closure. As yet, the full-scale (>80 cm2) cathode has not worked quite as well. In many tests, the cathode will operate in the emission-limited temperature/field (T/F) mode for approximately 300 ns, and then transition into explosive emission with a relatively slow ($OM0.5 cm/microsecond(s) ) closure rate. The current density was 45 to 90 A/cm2. High-power rf-emission tests have not been run under conditions where the diode stays open and in resonance for the duration of the rf pulse at a current density of 250 A/cm2, which is required for 3-GHz operation; that test remains the focus of continuing research. Long (600-ns) duration rf pulses have been obtained at low power. The data base on microwave generation at lower power also has been extended and has shown that high-efficiency resonances will occur when a multiple of the reflex frequency equals the beam frequency. This allows greater flexibility in the design and scaling of microwave device.

The interaction of transverse eigenmodes with a relativistic electron beam in an overmoded cyclotron autoresonance maser amplifier is analyzed using a nonlinear self-consistent model and kinetic theory. It is shown that all of the coupled modes grow with the dominant unstable mode at the same growth rate, but suffer different launching losses. The phases of coupled modes are locked in the linear and nonlinear regimes. Simulations indicate that the rf power distribution among the interacting modes at saturation is insensitive to input power distribution but sensitive to detuning.

High-power CARM and FEL research on a long-pulse (1 microsecond(s) ) high-voltage (700 kV) modulator at the MIT Plasma Fusion Center is described. The experimental results on a Ka-band, long-pulse CARM oscillator experiment are presented. In this experiment, a SLAC 5045 klystron gun produced an electron beam at 250-320 kV and 10-20 A; a beam (alpha) equalsV (rho) (perpendicular)/(rho) (parallel), variable from 0 to 1, was produced on this electron beam with a wiggler magnetic field near guide field resonance. CARM operation was observed for many parameter settings, and for frequencies ranging from 29 to 32 GHz. Output powers as high as 110 kW were achieved with an efficiency of up to 1.8%. Higher frequency radiation at 74.5 GHz was also obtained and is attributed to second harmonic CARM operation. Recent operation of an FEL experiment using a 580 kV, 0.27 (mu) (Rho) electron gun, built by Thomson Tubes Electroniques, and a permanent magnet helical wiggler with (lambda) (omega ) equals 3 cm and B(omega ) equals 500 G is described. Results include measurement of small signal gain, gain-bandwidth, and oscillation at 30 GHz, with power levels of approximately 1 MW.

The negative energy cyclotron wave will couple to a positive energy, slow waveguide mode with a growth rate which can be even larger than the space charge mode for intense, high voltage electron beams. In addition to high power, this unique cyclotron resonance device offers a large cyclotron frequency upshift ratio ((omega) /(Omega) c) and considerable tolerance to the beam's velocity spread. 2-D fluid theory, 1-D Vlasov theory and 11/2-dimensional simulations are presented along with the design parameters for a proposed proof-of-principle experiment.

A cyclotron autoresonance maser (CARM) inherently demonstrates high efficiency due to its autoresonant feature. Tapering the axial magnetic field can further enhance the CARM's already attractive efficiency. A self-consistent, three-dimensional, nonlinear numerical simulation code has been developed and used to optimize the design of CARM amplifiers, including an axial magnetic field taper. There are usually two free parameters involved in tapering the magnetic field linearly, namely, the tapering rate and taper-starting position. It will be shown in the simulation results that these parameters can be reduced to only one, that is, the tapering rate. By starting the magnetic field taper directly before the first electron crossover occurs, both optimum efficiency and growth rate can be obtained.

Design and experimental results are presented from two high power microwave generation experiments utilizing a high repetition rate induction linac generated electron beam. A relativistic klystron has generated more than 100 MW microwave pulses in X-band for 50 ns without pulse shortening or breakdown. Design studies for the first cyclotron autoresonance maser (CARM) amplifier using an induction linac electron beam are also presented.

A Bragg reflector composed of periodic cylindrically symmetric corrugations can provide a reflection of nearly unity through the principles of constructive interference, allowing the creation of a frequency selective resonator. Measurements of reflectivity and Q of the resonator for sinusoidal corrugations are presented. Measurement and simulation results for an improved reflector with a Hamming-Window amplitude distribution are also presented.

1407_27Computer simulations of plasma-filled backward wave oscillators reveal that the gain of voluminous beam-plasma cyclotron interactions is significantly larger than that of the conventional backward wave oscillation. This slow plasma cyclotron wave is emitted from plasmas and its gain is substantially enhanced only if it also satisfies the dispersion relation of a ripple wall waveguide which couples the slow wave to fast wave. The observation may be employed to interpret previous experiments which display a strong dependence of output power on the magnetic field and can be utilized to build high gain microwave beam-plasma devices.

1407_28Experimental and theoretical studies of high power microwave generation from a short pulse backward-wave oscillator (BWO) experiment are reported. The electron beam has an energy of about 600 keV with currents in the 2 kA range. Microwave radiation at a frequency above 12.6 GHz is observed to be generated. Measurements thus far are consistent with the TM01 mode that is predicted to be excited with the electron beam and slow wave structure parameters.

A coherent radiation source which uses an electron beam to drive a resonator which consists of two short sections of metal grating embedded in a parallel-plate waveguide structure has been operated in the millimeter-wavelength regime. The fields in the first of the grating sections imparts velocity modulation to the beam and the second extracts power from a bunched beam. Thus, the device functions like a twocavity klystron. However, the open quasi-optical coupling structure can be utilized at wavelengths which are shorter than those that are practicable in a conventional closed cavity Idystron design. The electron beam energy and current employed in these experiments are modest (10's ofkv and 1-2 A) and the primary motivation for the work is to develop convenient moderate power sources for various applications of millimeter- and submillimeter-wavelength radiation. It is interesting to note, however, that the topology of the resonator is similar to that used by Bugayev et al.1'2 in very-high-power radiation sources at centimeter-millimeter wavelengths.

30Cross field amplifiers (CFA) have been used in many applications where high power, high frequency microwaves are needed. Although these tubes have been manufactured for decades, theoretical analysis of their properties is not as highly developed as for other microwave devices such as klystrons. The authors have developed a simulation model for CFAs using the PIC code CONDOR. Their simulations indicate that there are limits to the maximum rf field strength that a CFA can sustain. When the fields become too high, efficiency becomes very poor, and the currents drawn may become so large that secondary emission cannot be maintained. It is therefore desirable to reduce the circuit impedance of a very high power tube. One method for doing this, proposed by Feinstein, involves periodically coupling a standard CFA circuit to an internal waveguide. Most of the power flows in the waveguide, so the overall impedance is much reduced. By adjusting the guide dimensions one can vary the impedance. Thus one can retain high impedance at the low power end but low impedance at the high power end. In principle one can maintain constant rf voltage throughout the tube. CONDOR simulations have identified a good operating point at X band, with power generation of over 5 MW/cm and total efficiency of over 60%. ARGUS simulations have modeled the cold test properties of the coupled structure. The nominal design specifications are 300 MW output, 17 db gain, frequency 11.4 GHz, DC voltage 142 kV, magnetic field 5 kG, anode cathode gap 3.6 mm, total interaction length about 60 cm. Results of code simulations are discussed and the status of the experimental effort is reported.

An experiment is conducted to examine the tail erosion phenomenon which occurs to an intense microwave pulse propagating in air breakdown environment. In the experiment, a 1 MW microwave pulse (1.1 microsec) is transmitted through a large plexiglas chamber filled with dry air at about 1-2 torr pressure. Two different degrees of tail erosion caused by two different mechanisms are identified. This experimental effort leads to the understanding of the fundamental behavior of tail erosion and provides a data base for validating the theoretical model. A theoretical model based on two coupled partial differential equations is established to describe the propagation on an intense microwave pulse in air breakdown environment. One is derived from the Poynting theorem, and the other one is the rate equation of electron density. A semi-empirical formula of the ionization frequency is adopted for this model. A transformation of these two equations to local time frame of reference is introduced so that they can be solved numerically with considerably reduced computation time. This model is tested by using it to perform the computer simulation of the experiment. The numerical results are shown to agree well with the experimental results.

33In the study of the propagation of high power microwave pulse, one of the main concerns is how to minimize the energy loss of the pulse before reaching the destination. In the very high power region, one has to prevent the cutoff reflection caused by the excessive ionization in the background air. A frequency auto-conversion process which can lead to reflectionless propagation of powerful EM pulses in self-generated plasmas is studied. The theory shows that under the proper condition the carrier frequency (Omega) of the pulse will indeed shift upward with the growth of plasma frequency (Omega) pe. Thus, the plasma during breakdown will always remain transparent to the pulse (i.e., (Omega) >(Omega) pe). A chamber experiment demonstrating the frequency auto-conversion during the pulse propagation through the self-generated plasma is then conducted in a chamber. The detected frequency shift is compared with the theoretical result calculated by using the measured electron density distribution along the propagation path of the pulse. Good agreement between the theory and the experimental results is obtained.

An electromagnetic (EM) missile launched from a hyperboloidal lens has been investigated experimentally. The system includes a hyperboloidal lens made of wax and a V-conical antenna (with a 30 degree(s) apex angle) located at the focal point of the lens. As expected, the lens system performs like an aperture field similar to that from a parabolic reflector. Both the measurement and simulation show that the EM missile launched from the hyperboloidal lens has a slow rate of energy decay and a waveform consisting of a pair of opposite pulses--properties similar to those of a parabolic reflector.

35The resonant properties of large circular arrays of parallel, nonstaggered dipoles have been analyzed specifically when only one element is driven. The approach involves using tubular cylindrical dipoles and the integral equations of antenna theory. The parameters that are involved in the adjustment to any one of many possible resonant distributions of current around the array include the length and radius of the (Nu) identical tubular dipoles and the distance between them as fractions of the operating wavelength. Extremely sharp resonances have been obtained at properly selected values of the parameters. The very large resonant amplitudes of the currents in the elements can have any one of a variety of different symmetrical distributions of phase around the array including 180 degree(s) shifts from element to adjacent element. Typical field patterns consist of many extremely sharp peaks. The study of the circular array has been carried out using the method of symmetrical components. In order to study closed loops of dipoles other than the circle, e.g., ellipses, egg-shaped curves, etc., the analysis is being generalized.

n order to verify the existence of the theoretically predicted, extremely sharp resonances that occur in a circular array with many identical elements but only one driven, an experimental investigation of such an array has been carried out. The circular array consists of 90 monopole elements equally spaced around a 6-meter circumference. The properties of the array are observed through three windows: the input admittance of the array, the relative currents on the parasitic elements, and the radiation patterns. It is found that resonance -- at which the conductance becomes very large and the susceptance very small -- does occur. The experiment shows that the quality of the resonance, Q(equals f/(Delta) f), depends strongly on the equality of the spacing between the elements and good conductive contact between the monopoles and the ground plate.

1467_37A number of proposed applications of electromagnetic waves require that the radiation beam maintain a high intensity over an appreciable propagation distance. An example of this is the possibility of a power satellite providing electrical energy to a host of other satellites by means of directed radiation beams. This is referred to as power beaming. Another example is the possibility of accelerating particles to ultra-high energies by utilizing high-power laser beams. Other applications include advanced radar and directed-energy sources. The quest to achieve these objectives has led to a resurgence of research on propagation of radiation beams and diffraction theory. Diffraction causes a beam of radiation to spread out in the lateral direction and, from energy conservation, the intensity drops off correspondingly. Briefly, the objective of much of the research being carried out is: 'Can diffraction be overcome?' The authors present a survey and critique of the analyses and experimental tests of solutions of the wave equation in connection with so-called diffractionless and other directed radiation beams. The examples discussed include electromagnetic missiles, Bessel beams, electromagnetic directed energy pulse trains, and electromagnetic bullets.

1407_38The attainment of high densities in inertial confinement fusion is reached through the coalescence of convergent waves in time. According to the laws of gas dynamics there exists a corresponding solution where the coalescence takes place instead in space. Applied to inertial confinement fusion, this solution may provide a configuration for a continuous plasma focus. If such a configuration can be upgraded to yield a net release of thermonuclear energy, the generation of very intense plasma jets may become possible.

1407_39The reduction of the lowest-order nonlinear bremsstrahlung recoil force on the bare charge of an unperturbed relativistic test particle in a nonequilibrium beam-plasma system is derived from first principles. The purpose is to identify many of the important physical assumptions and mathematical techniques involved in the theory of nonlinear-bremsstrahlung radiative instability.

1407_40It has previously been shown that all causal finite energy solutions of the time-dependent acoustic and Maxwell's equations have forms which, except for a factor (1/r), behave like one-dimensional solutions propagating outward along each radial direction (or ray) when the time and distances are large. The region where the one-dimensional form dominates is called the wave zone. The authors have previously given exact solutions of the acoustic and Maxwell's equations in which the solutions in the wave zone differ from zero only for rays in a right circular cone and for a given finite radial interval within the cone. The exact solutions are called 'bullets' because asymptotically they represent packets of energy which are 'shot' through the cone which is a kind of 'rifle.' In the present paper it is shown graphically how the exact solution in the acoustic case develops into its wave zone form with increasing time. Also considered are solutions of the acoustic equations such as the focus wave mode solutions, and the wave zone forms are given. These solutions are compared with each other and with the bullets in the wave zone region.

1407_41Several exact, nonseparable, space-time solutions of the scalar wave and Maxwell's equations have been found recently. These localized wave (LW) solutions contain very broad-bandwidth components and can be optimized to exhibit enhanced localization properties. Moreover, by driving an array with these LW solutions, one can generate beams that also exhibit these LW characteristics. A new type of array is required to try to realize these localized wave effects -- one that has independently addressable elements. The enhanced localization effects are intimately coupled to the proper spatial distribution of broad-bandwidth signals driving the array; i.e., by shading not only the amplitudes, but also the frequency spectra of the pulses driving the array. A LW pulse-driven array generates a moving localized, interference pattern, i.e., a set of pulses whose shapes are reconstituted as they propagate by the frequency components arriving at different times from the various aperture sources. Analytical bounds on the characteristics of beams generated by an arbitrary pulse-driven array have been derived and are supported by numerical and experimental values. These bounds extend the meaning of near-field distances or diffraction lengths to the situation where the array driving functions can be broad-bandwidth signals. It has been demonstrated theoretically and experimentally that an acoustic array driven with a designed set of localized wave (LW) solutions of the scalar wave equation generates a robust, well-behaved, transient pencil-beam of ultrasound in water that outperforms the beams generated by related continuous wave excitations of the same array. Numerical models predict similar results for an electromagnetic LW pulse-driven array.

1407_42Localized scalar and electromagnetic wave solutions in a variety of complex environments will be reviewed. Like their free-space counterparts, these acoustic and electromagnetic localized wave (LW) solutions can be optimized so that they are localized near the direction of propagation and their original amplitude is recovered out to extremely large distances from their initial location. Pulses with these very desirable localized transmission characteristics may have a number of potential applications in the areas of directed energy transmission, secure communications, and remote sensing.

1407_44An experiment to evaluate the feasibility of the spiral line induction accelerator (SLIA) as a compact high current accelerator is currently underway at Pulse Sciences, Inc. The experiment involves injecting a 3.5 MeV, 10 kA electron beam into a strong focusing racetrack spiral transport line with two passes through two 1.5 MV induction accelerating units, giving a nominal 9.5 MeV output. The status of hardware fabrication and full-scale component tests are summarized with emphasis on the electrical design of the injector and accelerating cells. Initial experimental results at 1 MeV are reported on beam matching and transport in stellarator fields, and on the design and testing of the shielded (coaxial) accelerating gaps to minimize the beam breakup (BBU) instability.

1407_46The generation of nonlinear plasma wakefields by an intense, short laser pulse and the relativistic optical guiding of intense laser pulses in plasmas are studied with a nonlinear, self-consistent model of laser-plasma interactions. Nonlinear steepening and period lengthening of the plasma waves are observed, and expressions are obtained for various nonlinear wakefield quantities. Relativistic focusing with the self-consistent plasma response shows that laser pulse fronts and laser pulses shorter than a plasma wavelength, 2(pi) c/(omega) (rho ), are not relativistically guided and will continuously erode due to diffraction.

1407_47Since the previously reported successful demonstration of acceleration of electrons to $OM 12 MeV, higher trapped beam current and longer beam lifetime have been obtained. The improved confinement has led to a higher peak energy $OM 18 MeV, and is the result of increasing the strong focusing and toroidal magnetic fields, reducing magnetic field errors, and optimizing the betatron flux condition. Modifications to the electromagnet buswork are in progress to further reduce field errors, and a fast pulsed magnet system to provide dynamic stabilization of the cyclotron resonances is being studied.

1407_48Electron trapping and acceleration have been successfully accomplished in the modified elongated betatron at UC Irvine. About 150 nC of electrons have been trapped and accelerated for $OM900 microsecond(s) until the betatron field reached its maximum, establishing an electron layer with $OM80 (Alpha) of circulating current and $OM1.6 MeV of energy in the cylindrical chamber. No minimum current is required to start the beam trapping in the betatron. There are essentially no electron losses during the acceleration at low injection currents; the electron losses at high injection currents are probably caused by the space charge effects, resistive chamber walls, and betatron field ripple. By filling the chamber with plasma, an electron beam of $OM120 (Alpha) current ($OM230 nC of charge) and $OM1.6 MeV energy has been observed. No instabilities have been found during the acceleration except the precessional instability which has been effectively controlled by the toroidal magnetic field. An electron orbit simulation has been carried out; it has shown that practically no resonance instabilities can be developed in the stretched betatron due to its unique geometry and field configuration, which has been confirmed by the experiment.

1407_49Following Budker's proposal, experiments on plasma betatrons were carried out in several laboratories. Large conduction currents were observed as a result of gas breakdown, but the current of energetic electrons did not exceed 10 (Alpha) . Plasma injection to start a beam in good vacuum has been adopted. The chamber consisted of outer and inner glass pipes lined with stainless steel mesh at radii of 5 cm and 2 cm, respectively. A toroidal field of 2-3 kG was applied along with a vertical field of up to 1.4 kG. Plasma was injected by coaxial guns, 1/4 inch in outer diameter, without increasing the neutral pressure significantly. A 20 (Alpha) beam was accelerated to a peak energy of 1 MeV with little loss and then dumped to the chamber wall by a spiller field. The current was enhanced to more than 100 (Alpha) by the addition of electron injection using a field emission cathode.

1407_50The tandem betatron is a compact, high-current induction accelerator that has the capability to accelerate electrons to an energy of order one gigavolt. Based upon the operating principle of a conventional betatron, the tandem betatron employs two synchronized induction cores operating 180 degrees out of phase. Embedded within the cores are the vacuum chambers, and these are connected by linear transport sections to allow for moving the beam back and forth between the two betatrons. The 180 degree phase shift between the core fluxes permits the circumvention of the flux swing constraint that limits the maximum energy gain of a conventional betatron. By transporting the beam between the synchronized cores, an electron can access more than one acceleration cycle, and thereby continue to gain energy. This added degree of freedom also permits a significant decrease in the size of the magnet system. Biasing coils provide independent control of the confining magnetic field. Provided that efficient beam switching can be performed, it appears feasible that a one gigavolt electron beam can be generated and confined. At this energy, a high current electron beam circulating in a one meter radius orbit could provide a very intense source of short wavelength ((lambda) < 10 nm) synchrotron radiation. This has direct application to the emerging field of x-ray lithography. At more modest energies (10 MeV-30 MeV) a compact tandem betatron could be employed in the fields of medical radiation therapy, industrial radiography, and materials processing.

1407_51Saturnus is an infrared FEL operating in the 10 micrometers wavelength region, driven by a compact 20 MeV linac with a photoinjector, under construction at UCLA. The 1.5 cm period, 0.6 (Tau) peak field undulator is being built at the Kurchatov IAE. The FEL is designed to operate primarily in the self-amplified spontaneous emission mode. This paper covers the start-up from noise, optical guiding, saturation, sidebands and superradiance, with emphasis on the effects important for future short wavelength operation of FELs. The photoinjector follows closely the Brookhaven design. Electrons are injected into an accelerating section based on the plane-wave transformer design developed by Swenson at SAIC. Simulation of the linac and FEL show a gain length of 10 cm, and a saturation power of 50 MW.

1407_52Novel techniques are described by which electromagnetic energy can be stored, compressed and then used to accelerate high current particle beams to high energy.

One may well ask: at this late stage, what more do we need to learn about the old subject of beam breakup instabilities (BBU) in linear accelerators? The physical mechanism is well-understood. Various stabilization mechanisms have been explored and implemented. The theoretical techniques that have been developed in treating the instabilities have become standard tools, and except for the cases where the focusing force is a nonlinear function of the beam's transverse displacement, the governing equations are linear. On the other hand, BBU is perhaps the most fundamental instability in a linear accelerator——its excitation requires no more than the passage of a charged particle beam through a sequence of cavities. The resurgence of interest in this instability naturally accompanied the construction of high current accelerators. In fact, our interest in this instability was originally stimulated by the two— beam accelerator experiment that was recently conducted at the Naval Research Laboratory. As we gained more experience with BBU, we are confronted with various nagging issues. Some of these are well-known and are, in fact, generic to all stability theories. Others are of a more specific nature. We shall describe them in this paper. A key issue, in our opinion, is the adequacy of the "conventional" models and the confidence in their use to assess the danger of BBU growth in a given experimental situation. The predictive capability is very important, as BBU growth depends on many parameters: beam current, beam energy, pulse length, pulse separation, cavity separation, machine length, acceleration gradients, focal strength breakup mode frequency and their spectra, their Q values, and transverse shunt impedances. Half of these parameters span over four orders of magnitudes, depending on the machine. Some important ones cannot even be determined accurately. Below, we shall discuss the various issues which arose in the course of our research. We provided answers to a small fraction of them, while the others await future investigation. Needless to say, the list is not exhaustive.

1407_54It is shown that cross-coupling among cavities may reduce beam breakup (BBU) growth in a recirculating accelerator. The main reason for this growth reduction is the sharing of the deflecting mode energy among coupled cavities. This result is based on a numerical study of the proof-of-principle experiment currently planned for the spiral line induction accelerator (SLIA, 35 ns, 10 kA, 8.5 MeV). Reduction of BBU amplitude by factors of several hundreds is also predicted for a SLIA upgrade (35 ns, 10 kA, 25 MeV) which consists of a 7-turn, 70-cavity system. Various issues are addressed.

1407_55This paper describes work being done to develop high-power 11.4-GHz relativistic klystrons suitable for driving future linear colliders. Peak rf power levels of 330 MW have been achieved using an 11.4-GHz, high-gain tube with multiple output structures. In these experiments the rf pulse is of the same duration as the beam current pulse. Experiments have been performed on two short sections of high-gradient accelerator using the rf power from a relativistic klystron. An average accelerating gradient of 84 MV/m has been achieved with 80-MW of rf power. The use of the front end of the Advanced Test Accelerator at Lawrence Livermore National Laboratory will allow future tests of new rf sources and tests of two-beam accelerator concepts.

Proposed future positron-electron linear colliders1 would be capable of investigating fundamental processes of interest in the 0.5—5 TeV beam-energy range. At the SLAC Linear Collider (SLC) gradient of about 20 MV/m this would imply prohibitive lengths of about 50—250 kilometers per linac. We can reduce the length by increasing the gradient but this implies high peak power, on the order of 400- to 1000-MW at X-Band. One possible way to generate high peak power is to generate a relatively long pulse at a relatively low power and compress it into a shorter pulse with higher peak power. It is possible to compress before DC to RF conversion, as is done using magnetic switching for induction linacs, or after DC to RF conversion, as is done for the SLC. Using RF pulse compression it is possible to boost the 50- to 100-MW output that has already been obtained from high-power X-Band klystrons to the levels required by the linear colliders. In this note only radio frequency pulse compression (RFPC) is considered. The advantages of RFPC are: 1. Generally the higher the power the harder it is to increase it further. This is not the case with RFPC because the control elements operates at low power. 2. With RFPC we can alternate between low power un-compressed pulses and high power compressed pulses by turning the modulation off and on. It is much more difficult to design tubes that function both at low and high peak power levels. 3. RFPC may have lower capital, maintenance and replacement costs per watt of peak power. 4. For a given compression ratio, the cost of RFPC is independent of pulse energy or peak power. Three methods of RF pulse compression that are in use or have been proposed at SLAC will be reported on. The SLAC Energy Development (SLED),2 where RF energy is stored in cavities; the Resonant Line SLED (RELS),3 where the energy is stored in long resonant lines; and the Binary Pulse Compressor (BPC) ,where the energy is stored in traveling wave delay lines.

1407_57The SBS_1 experiment at Sandia National Laboratories is designed to demonstrate the feasibility of the Scanning Beam Switch for high-power rf generation. The primary application is to pulsed rf linacs and high-frequency induction accelerators. It is expected that the apparatus will generate rf output power exceeding 100 MW at 50 MHz over a 5 microsecond(s) pulse. The device can operate as an oscillator or high gain amplifier. To achieve the capability for long-macropulse and high-duty-cycle operation, SBS_1 uses a large dispenser cathode and vacuum triode input driver.

A development program is underway to apply rf superconductivity to the design of continuous-wave (cw) linear accelerators for high-brightness ion beams. Considerable progress has been made both experimentally and theoretically toward this application. Recent tests of niobium resonators for ion acceleration have yielded average accelerating gradients as high as I 8 MV/m. In an experiment with a radio-frequency quadrupole geometry, niobium was found to sustain cw peak surface electric fields as high as 1 28 MV/rn over large (1 0 cml surface areas. Theoretical studies of beam impingement and cumulative beam breakup have also yielded encouraging results. We have also made extensive measurements of the if properties of high-Ta superconductors. In this paper, we summarize our progress and identify current and future work in the areas of accelerator technology and superconducting materials which will build upon it.

We wish to replace this energy recovery scheme with a new concept -a high power rectenna, that directly converts the rf power generated by the decelerator unit to dc that can be utilized to drive the rf source for the accelerator. It thus avoids the drawbacks of the LANL scheme. We will illustrate the main features and advantages of the rectenna approach to energy recovery by discussing its use in the High Current RF (HCRF) Space Based FEL concept. This concept employs the highest peak power if sources (200 MW per source) of any of the FEL concepts, so it represents the most stressing environment for the application of the rectenna based energy recovery method. Section 2 will review the HCRF space based FEL concept, and section 3 will discuss the high powered rectenna design. Section 4 provides a summary of our work to date.

1407_60 An analytic model of cumulative beam breakup has been developed which is applicable to both low-velocity ion and high-energy electron linear accelerators. The model includes arbitrary velocity, acceleration, focusing, initial conditions, beam-cavity resonances, and variable cavity geometry and spacing along the accelerator. Both the steady-state and transient displacements of the beam bunches are calculated. As examples, the solution is applied to hypothetical high-current ion accelerators comprised of superconducting coaxial half-wave resonators. The steady-state transverse motion of particles comprising a longitudinal halo between bunches is also calculated, and effects of nonzero bunch length and arbitrary bunch shape are investigated. The role of focusing in controlling beam breakup is quantified for these cases.

1407_61Experiments have been performed to investigate the beam breakup (BBU) instability in electron beams transported through rf cavity systems. Experiments have utilized two accelerators: 1) a Febetron accelerator operating with energy equals 100-300 keV, extracted current equals 10-100 (Alpha) , and pulse length equals 300 ns, and 2) the Michigan Electron Long Beam Accelerator (MELBA), with energy equals 0.6-0.9 MeV, extracted current equals 100-400 (Alpha) and pulselength equals 0.5-2 microsecond(s) . The transport system consists of 5 or 10 rf cavities with Q equals 210 +/- 30. the cavities are connected by cutoff waveguide sections, which prevent electromagnetic coupling between cavities in order to eliminate the regenerative BBU. Each cavity has a microwave probe to detect growth of e-beam emission in the non-axisymmetric TM110 mode at 2.5 GHz, corresponding to the BBU. Solenoidal magnetic fields of 1-3.5 kG are applied. Initial experimental data on the Febetron show strong (>40 dB) growth of rf at 2.5 GHz between the first and tenth cavity. MELBA data shows about 20 dB rf growth between the second and fifth cavities in a 5 cavity system. Up to 85% of the injected current is transported through the cavity system. The magnitude of BBU growth, its dependence on current and magnetic field, and the onset time to rf peaking are consistent with theory.

1407_62Beams of charge- and current-neutralized plasma will cross a transverse-magnetic field by a combination of collective-plasma processes. These processes were studied for a high-to-low beta ((beta) equalsV plasma energy density/magnetic field energy density) hydrogen-plasma beam injected into a vacuum transverse magnetic field with nominal parameters: (Tau) i approximately equals 1 eV, (Tau) e approximately equals 5 eV, n 14 cm-3, vi 6 cm/s, tpulse < 70 microsecond(s) , (Beta) z (Rho (i)) (Rho (i)), where a is the beam radius, x is the downstream distance, and (Rho (i)) is the ion gyroradius. A brief state of initial diamagnetic propagation is observed, followed by a rapid transition to $Ex$B propagation. $Ex$B propagation is accompanied by beam compression transverse to $B with as much as a factor of four increase in density and a slight drift of the beam in the ion Lorentz force direction. As the magnetic field increases, the observed magnetization time decreases from that calculated using classical Spitzer conductivity, approaching an order of magnitude. This rapid magnetization can be accounted for using classical Hall conductivity, rather than invoking anomalous processes or instabilities to calculate the magnetization time.

1407_63In testing a gas puff cathode, it was found that a hydrocarbon gas, butane, gave better results than hydrogen or ammonia. Butane's long molecule may provide both a larger collision cross section and probably some ability to absorb excess collision energy in internal vibration. The butane puff diode gave much lower current density than a solid polyethylene cathode and the difference might be attributed to the lower density of the butane puff versus the solid cathode. The emittance of the puff diode was much better with an angular spread of only a few milliradians. A new generation of puff valves have been developed which have demonstrated opening speeds faster than the existing valve by about a factor of two. Use of the new valve will let one determine if gas density really helps and if it does, the design of the valves can be further refined for about another factor of three improvement. UV irradiation of solid polyethylene cathodes is studied. A titanium hydride active cathode remains an option if it proves to be the best performer. Magnetic insulation much stronger than the 8 kG used to date may be necessary to obtain the best results. As a first step a cathode is being developed with internal insulation coils and an internal capacitor bank requiring no outside connection during a shot. Magnetic field lines in such a diode always close back on the cathode providing minimum leakage for a given field strength. External coils can be added to enhance the insulation if needed. Such a design will be relatively self-contained and so could be installed on beam generators in the USSR.

1407_64A diagnostic technique has been developed to determine the negative hydrogen ion (H-/D-) thermal energy in a variety of conditions in a volume production ion source. The method is based on Nd:YAG laser photodetachment of the negative ions. The photodetachment produces local changes in the ion and electron densities, whose space and time evolution are traced by the use of a probe and a time-delayed second Nd:YAG laser pulse. The results of measurements using this technique for deuterium ions are described. Information was collected from the center of the source to near the plasma electrode. The effects of the presence of electric and magnetic fields near the probe during measurements are addressed. The present study demonstrates that the extracted ion current is equal to the thermal flux through the extraction aperture.

1407_65The conceptual design of an electrostatic quadrupole (ESQ) system for focusing and matching a 30 mA, 35 kV H- beam into a radio frequency quadrupole (RFQ) accelerator has been developed. The design procedure involves two steps. First, a linear beam optics code which solves the K-V envelope equations is used to design a lens system based on a hard-edge focusing function. The beam envelope, in conjunction with the lens parameters, should satisfy several constraints concerning electric breakdown, image forces, spherical and chromatic aberrations. Next, a practical lens design is developed. The field gradient is calculated numerically with a 3-D Laplace solver and the fringe-field integrals are evaluated to obtain the nonlinear forces up to the third order. The results from the Laplace solver generate input to a modified PARMILA code, and the beam propagation and emittance growth in the system are evaluated. Preliminary analysis shows an emittance growth of about 50%. Design of the apparatus and experimental plans are discussed.

Space charge effects are introduced to the superradiant free electron laser solution which now shows interference pattern in the intensity envelope at high densities.

1407_68The standing-wave free-electron laser (FEL) differs from a conventional linear-wiggler microwave FEL in using irises along the wiggler to form a series of standing-wave cavities and in reaccelerating the beam between cavities to maintain the average energy. The device has been proposed for use in a two-beam accelerator because microwave power can be extracted more effectively than from a traveling-wave FEL. A simplified numerical simulation indicates that, with appropriate prebunching, the standing-wave FEL can produce an output signal that is effectively the same in all cavities. However, changes in the beam energy of less than 1% are found to introduce unacceptably large fluctuations of signal phase along the device. Analytic calculations and single-particle simulations are used here to show that the phase fluctuations result from beam synchrotron motion in the initial signal field, and an approximate analytic expression for the signal phase is derived. Numerical simulations are used to illustrate the dependence of phase fluctuations on the beam prebunching, the beam-current axial profile, and the initial signal amplitude.

1407_69Using a simple mean field model of the electron-electron interaction, study has been done of the effect of space charge in a planar diode. Results show, in particular, that the classical value for the limiting current in such a diode can be exceeded by a large factor due to the effect of tunneling. The smooth transition of the solutions from the quantum to the classical (non-quantum) regime is demonstrated.

1407_70It is shown that the acceleration by net inverse bremsstrahlung of a laser light is a classical phenomenon in which high-energy electrons, whose momenta and energies are modulated by the laser light, obey strictly the momentum and energy conservation laws and the time-reversal invariance of the transition probability. Net inverse bremsstrahlung acceleration of high-energy electrons traveling in a strong laser light and an electrostatic wave propagating in an oblique direction with respect to the laser light is investigated by using the relativistic quantum-kinetics based on the Dirac equation. The quantum kinetics treats the classical phenomenon exhibited by high-energy electrons through the correspondence principle. The dc force in the laser light direction by the net inverse bremsstrahlung is independent of the spread of the electron beam energy, and increases with the electron beam energy. Also, the dc force increases with the laser intensity if the potential amplitude of the laser wave is smaller than the electron rest energy.

1407_71The trajectories of electrons emitted from a sharp protrusion with corners are calculated, where the electric field is intense and the radius of curvature tends to zero. The calculations include the effects of a longitudinal magnetic field but ignore the space charge effects. The arbitrarily large electric field at a mathematically sharp corner does not necessarily impart to the electrons an excessive amount of transverse momentum, whether or not the external magnetic field is present. Scaling laws are derived for the beam's transverse displacement in terms of macroscopic quantities, such as anode-cathode voltage drop, gap separation, magnetic field, and the protrusion dimensions. The implication of these findings on the electron sources generated from micro-tips is addressed.