Crossed-field Amplifier Research Articles

Разработка усилителя со скрещенными полями W-диапазона

The results of the development of a W-band crossed-field amplifier are presented. The optimal geometry of the slow-wave system was determined and its dispersion characteristics were calculated. Three-dimensional modeling using the large-particle method is performed, which demonstrates a gain of up to 15 dB and a maximum output power level of more than 1 kW.

Simulation of a Pulsed 4.7 MW L-Band Crossed-Field Amplifier

It is critical to have a standard reference model for crossed-field amplifiers (CFAs) for the research community. We use the TechX 3-D particle-in-cell (PIC) code TechX to model the Stellant Systems L-4953 CFA. This CFA is a pulsed, reentrant, backward wave device with a thermionic cathode operating in the space-charge limited regime. The basic operating parameters are: peak output power <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${P}_{\text {out}}^{\text {peak}}\approx 5 \text {MW}$ </tex-math></inline-formula> , gain <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${G}\approx 11.2 \text {dB}$ </tex-math></inline-formula> , pulse duration <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${t}_{\text {pulse}}={1.8} \mu \text {s}$ </tex-math></inline-formula> , pulse rate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${f}_{\text {pulse}}={360} \text {Hz}$ </tex-math></inline-formula> , duty cycle <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text {Du}={0.06}8\%$ </tex-math></inline-formula> , and a frequency bandwidth from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${f}={1.28} \text {to} {1.35} \text {GHz}$ </tex-math></inline-formula> . This work will present device dimensions, the dc and radio frequency (RF) connection assemblies, and characterize the device performance. Simulations in VSim are used to determine the gain, bandwidth, and transmission characteristics. With the specified anode current of 98 A, a stable 3-electron spoke operation is observed with the simulated gain matching the device within 1 dB. The simulation model is directly compared with supplied device data from 13 devices and accurately predicts the operating voltages within 3% and output power within 10% except for an outlier at 1.28 GHz.

Theoretical Linkage of Thermionic, Field, and Space-Charge Limited Emission for a Vacuum Crossed-Field Gap

Crossed-field devices, such as magnetrons and crossed-field amplifiers, where an external magnetic field is orthogonal to the electric field across the gap, are used in radars, communications systems, and material processing. Improving the efficiency and power density of crossed-field devices requires a robust understanding of electron emission, particularly when multiple emission mechanisms may contribute, such as for thermionic and field emission. Previous studies of nonmagnetic diodes have theoretically identified the transitions, or nexuses, between multiple electron emission mechanisms by examining the relevant equations defining each individual mechanism and then derived exact theoretical solutions that combined these mechanisms and approached the standard emission equations under appropriate limits. This work extends those studies by incorporating the orthogonal magnetic field and assessing the transitions between the Richardson–Laue–Dushman (RLD) formulation for thermionic emission, the Fowler–Nordheim (FN) equation for field emission, the space–charge limit given by both the general (for nonzero electron injection velocity) and (zero electron injection velocity) Child–Langmuir (CL) (generalized CL (GCL) and CL, respectively) laws for space–charge limited current, and the space–charge limited current for a noninsulated (magnetic field below the Hull cutoff) and insulated (magnetic field above the Hull cutoff) diode. We derive exact solutions for the current density for these mechanisms and demonstrate their asymptotic behavior under relevant conditions. Furthermore, we plot the exact solution of current density <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$J$ </tex-math></inline-formula> as a function of applied voltage <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V$ </tex-math></inline-formula> by incorporating the general thermo-field emission theory for the current source and demonstrate the transition between each emission mechanisms with increasing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V$ </tex-math></inline-formula> for various temperatures and fixed ratios of magnetic field to the Hull cutoff. We also construct nexus plots to identify transitions between the various regimes for different conditions.

High-Power Amplification Experiments on a Recirculating Planar Crossed-Field Amplifier

The recirculating planar crossed-field amplifier (RPCFA) was designed, constructed, and tested at the University of Michigan. The RPCFA was driven by a number of RF sources ranging in frequency from 2.40 to 3.05 GHz and powers of 1 to 800 kW. Pulsed voltage was delivered to the cathode by the Michigan electron long beam accelerator with ceramic insulator (MELBA-C) which was configured to supply pulses of −300 kV, 1–10 kA, with 0.3–1.0- $\mu \text{s}$ pulse lengths. The RPCFA demonstrated zero-drive stability and a bandwidth of 15%. Amplification of microwave signals, at the design frequency of 3 GHz, below 150 kW, was observed with a mean gain of 7.87 dB and high variability, $\sigma = 2.74$ dB. Filtering this data set to only include shots with identical voltage and current profiles yielded a gain of 6.6 ± 1.6 dB. The mean gain increased to 8.71 dB and the variability decreased to $\sigma =0.63$ dB when the injected microwave power increased beyond 150 kW. Peak output powers of nearly 6 MW were achieved with RF breakdown limiting the maximum output power of the device.

Simulation of a Time-Varying Distributed Cathode in a Linear Format Crossed-Field Amplifier

The effects of a temporally modulated, distributed cathode in a linear format crossed-field amplifier (CFA) are simulated in VSim and analyzed. A linear format, 150 MHz, low power (100 W), moderate gain (7 dB), meander line CFA is used as the basis for the simulation model. This paper describes simulations with different time-varying distributed cathodes in which electron injection is modulated at the RF both in-phase and out-of-phase with the RF input. At low RF input power, the modulated electron injection dominates the operation. Injecting in-phase with the RF input shows gain increases from 23 dB at 150 mA to 32 dB at 1 A for low cathode modulation power (<0.1 W). The CFA efficiency increased from 2%–4% to 20%–24% using the electron modulation. The simulation shows distinct cylindrically shaped electron bunches as opposed to spokes because of the synchronous injection. These results suggest that for high power magnetrons electron modulation could improve gain.

Simulation of a Distributed Cathode in a Linear-Format Crossed-Field Amplifier

The effects of a distributed cathode in a linear-format crossed-field amplifier are simulated in VSim and analyzed. A linear-format, injected-beam, 150-MHz, low-power (~100 W), moderate-gain (7 dB), meander-line crossed-field amplifier (CFA) designed and tested at Northeastern University is used as the basis for the simulation model. The simulation results were validated by the experimental results from that CFA. The injected-beam model was then replaced with a distributed cathode requiring electron injection with an energy below the sole electrode. A new method, which uses a divergence-free region, was developed to simulate this distributed cathode. This model was validated and studied using three different current injection profiles. The distributed cathode offered no improvements to gain or the signal-to-noise ratio (SNR). Increasing the cathode area lowers the noise but is counteracted by the corresponding decrease in gain. The limits to the gain in this particular device are due to the current space charge limit for the higher power operation and the SNR for the lower power operation.

High-Power Recirculating Planar Crossed-Field Amplifier Design and Development

The recirculating planar crossed-field amplifier (RPCFA) was designed and simulated using the finite-element frequency-domain code ANSYS HFSS and the particle-in-cell (PIC) code MAGIC. The RPCFA is a high-power microwave device adapted from the recirculating planar magnetron, developed at the University of Michigan, Ann Arbor, MI, USA. Electromagnetic (EM) PIC simulations of a planar, meander line, and slow wave structure demonstrated 13.5-dB amplification of a 1.3-MW, 3-GHz signal to approximately 29 MW. The RPCFA is designed to be driven by pulsed power from the Michigan electron long beam accelerator-ceramic insulator, which is currently configured to deliver pulses at −300 kV, 1–10 kA, with 0.3– $1~\mu \text{s}$ pulse lengths. The RF input-drive signal will be provided by an MG5193 magnetron which delivers 5- $\mu \text{s}$ pulses up to 2.6 MW at 3 GHz. EM PIC simulations also demonstrated zero-drive stability of the design and were used to evaluate changes in performance resulting from variations of several experimental parameters. Variation of the drive frequency suggested that the RPCFA is expected to have a 3-dB amplification bandwidth of 300 MHz or 10%.

An overview of my efforts to bridge the gap in the microwave tube area between what universities provide and what the industry needs

My efforts to “bridge the gap” span a period of nearly 40 years and consist of over 100 courses on microwave tubes presented to well over 2000 scientists, engineers, and technicians. I developed the first five-day course for the US Navy. After several more courses, I wrote Microwave Tubes. In 1988, I developed the equivalent of a one-semester course on traveling wave tubes for the Navy and presented it several times each at Teledyne, Litton, Varian, and Hughes. In 1994, I wrote Principles of Traveling Wave Tubes, which was translated and published in Russia. I continued expanding and refining the courses and, in 2011, I wrote Klystrons, Traveling Wave Tubes, Magnetrons, Crossed-Field Amplifiers, and Gyrotrons, which was translated and published in China. Most recently, my courses have been attended by scientists and engineers from China, Sweden, Turkey, the United Kingdom, and Germany as well as the United States.

Drift resonance in high density non-neutral plasmas

Theoretical studies of the operation of crossed-field electron vacuum devices such as magnetrons and crossed-field amplifiers (CFA) have usually centered on their initial growth, taking this as an indication of their operating modes. In such an analysis one solves the equations for the density profile, the operating frequency, the growth rate, and other features of these devices. What one really obtains then are only the conditions for the device to turn on. The dominant interaction in this stage is a Rayleigh-type instability which initiates a quasilinear diffusion process whereby the electron density profile redistributes itself into a profile which will be in equilibrium with the ponderomotive-like forces produced by the growing rf fields. Eventually the rf fields will saturate and an operating device will settle into a stationary operating regime. This stage of a device’s operation is called the “saturation stage.” This latter stage involves a different set of physical interactions from the initiation stage. No longer is there a growth rate; rather the rf amplitudes have saturated and as a result, the ponderomotive-like forces have also vanished along with the quasilinear diffusion. In this saturation stage, we find that new rf modes appear. In fact, there are a total of five rf modes, two of which are the usual slow modes of the initiation stage, and three of which have fast oscillations in the vertical direction. One fast mode corresponds to a drift plasma oscillation while the other two fast modes are drift cyclotron modes. In this paper, we will describe how the drift plasma oscillation interacts and couples with the slow rf modes at the diocotron resonance.

Novel concepts of vacuum microelectronic microwave devices with field emitter cathode arrays

Field emitter arrays (FEA) are promising electron sources for vacuum microelectronic microwave amplifiers and oscillators. In this paper, microelectronic analogs of “classic” microwave devices are considered. Traveling wave klystrons, klystrodes and cross-field amplifiers with FEA are described. Basic output parameters (gain, efficiency, etc.) of these devices are calculated. A model of a self-excited vacuum microtriode oscillator is developed. The oscillator is studied numerically, as well as by experimental investigation of the circuit analog model. Chaotic generation in the oscillator under external harmonic driving is analyzed. The rf interaction with the electron beam modulated by the field emission in a twystrode is investigated using a particle-in-cell code and a one-dimensional nonlinear code.

Crossed-field amplifier simulations using a moving wavelength computer code

A moving wavelength particle in cell computer code has been used to study the interaction in emitting sole crossed-field amplifiers (CFAs). Results of the study of magnetrons using a related code have been published previously. The CFA results echo many of the features of the magnetron results. Application of the code to a cold cathode, pulsed CFA showed the existence of chaotic fluctuations in the space charge which we believe are related to noise in experimental CFAs. A major feature of these fluctuations is voids in the charge above the cathode which propagate slower than the RF wave (and, hence, travel backward in the moving reference frame). As the voids pass beneath the base of the spokes they modulate the amount of charge entering the spokes and enhance the chaotic behavior. The spokes recirculate from output to input becoming partially debunched in the process. Differing amounts and distributions of the space charge recirculated result in the computed power and phase pushing varying from pass-to-pass of the moving wavelength around the CFA anode. The fluctuations in field at the cathode and the pass-to-pass fluctuations are used as a measure of the fluctuation of the simulation. Two alternative designs have been investigated in an attempt to reduce CFA noise. A nonreentrant design eliminates the pass-to-pass fluctuations. However, the simulations show internal fluctuations commencing shortly after the space charge has built up. Experimentally, noise of this CFA was improved over the baseline design by from 4 to 8 dB depending on the operating frequency. Simulation of an alternate reentrant design with a thermionic cathode capable of a current density which will support a Slater solution of the sheath trajectories, showed elimination of the internal space-charge fluctuations. Experimentally, noise of this CFA was improved by 10-30 dB over that of the baseline CFA. Fluctuations observed in the simulations are believed to be a qualitative model of noise generation phenomenon and may help point the way to future reduction of such noise.

Smooth-bore magnetron simulations using a moving wavelength computer code

A moving wavelength computer code developed for crossed-field amplifier simulations has been used to simulate the operation of a smooth-bore magnetron. Simulations using thermionic emission and a mixture of thermionic and secondary emission have been conducted. The simulations were run for about 24 000 cyclotron periods and were stationary for at least the last 18 000 of these periods. The results show the space charge does not settle to an approximation of a Brillouin state, but instead a charge distribution of lower density extends well beyond the edge of a theoretical Brillouin sheath. A small current reaches the anode. Trajectories extracted from the simulation show a mixture of shapes-some with substantial cycloiding, others with little cycloiding.

Theoretical modeling of crossed-field electron vacuum devices

The modeling of crossed-field electron vacuum devices, such as magnetrons and crossed-field amplifiers with a dc background mode and an rf pump mode is discussed. The dominant interaction in these devices is the wave-particle interaction (diocotron). This interaction drives the classical Brillouin flow nonlinearly unstable through a Rayleigh-type instability in a shear flow. This linear instability triggers the nonlinear instability, which is a second-order nonlinear diffusion process. This diffusion process is driven by the density gradient at the edge of the sheath, which causes the electron density to evolve into a new density profile, one which will be in equilibrium with the nonlinear diffusion process. The general physics of the various processes contained in this model is discussed, including a possible explanation for the ultra-low noise phenomena.

Parametric interactions inside a magnetron

The purpose of this work is to understand theoretically what are the possible noise levels in a magnetron or a crossed-field amplifier (CFA), due to parametric three-wave interactions in the electron plasma, at various operating parameters. Our approach is to use the cold-fluid equations and their Fourier decomposition into a background (DC) mode, a pump (RF) mode, and two other noise (RF) modes. The two RF noise modes are assumed to interact parametrically with the large RF pump mode, and to satisfy the standard resonance conditions for the sum of the wave vectors and sum of the frequencies. We use our previous results to determine the background mode and the RF pump mode. Any strong RF electric field propagating in a crossed-field electron vacuum device can drive a Brillouin sheath unstable by means of a Rayleigh instability, whenever a wave–particle resonance can be found inside the sheath. What happens physically is that, at the resonance, the laminar flow of the electrons is strongly disturbed, and a diffusion process ensues, whereby the electrons diffuse away from the resonance region. This upsets the balance in the Brillouin flow, causing the electrons to redistribute into a new average DC density profile – which may be far from the original Brillouin profile, but is a stationary solution of a nonlinear diffusion equation. Using these stationary density profiles, we can then study the propagation of small RF signals on such a DC background, as well as their parametric interactions with the RF pump wave, at various DC voltages and magnetic fields. In addition to being able to predict the operating regime and the DC current flow, these studies demonstrate that parametric interactions probably limit the operating voltage range of a typical magnetron or crossed-field amplifier to about 20% above the Hartree voltage.

Microelectronic crossed-field cold-cathode amplifier

The results of theoretical investigation of the structure of a microelectronic two-compartment crossed-field SHF amplifier with distributed cold cathode are presented.

Simulation and modeling of self-modulated re-entrant beam crossed-field amplifier

The operation of a new re-entrant beam, cold-cathode, crossed-field amplifier (CFA), modulated by pulsing only the RF input signal (self-modulation) is described in this paper. The results of experimental and theoretical investigations are presented. It is shown that the self-pulsed CFA has a gain of more than 12 dB and an electronic efficiency above 40% over a 6-8% bandwidth in X-band. The output power reaches 4.5 kW at the anode voltage of 8.2 kV.

Ultra-low B-field magnetron operation at the drift-cyclotron resonance

In magnetrons operating near the Buneman-Hartree resonance ku-/spl omega/=0, u being the E/spl times/B drift velocity, the energy stored in the cyclotron motion is not converted into microwaves, and the efficiency decreases at low magnetic fields. By operating at the drift cyclotron resonance ku-/spl omega/=/spl Omega/, both the electrostatic and the cycloidal motion energy are converted to radiation and the efficiency increases at low magnetic fields. At optimum efficiency all normalized operation parameters are expressed solely in terms of the cyclotron-to-RF frequency ratio. For a specified anode circuit it is shown that the DC electric and magnetic field can be reduced by a factor 6-10 relative to the conventional operation, with electronic efficiency in the 50%-70% range. Moderate power S-band crossed field amplifier operation at 400 Gauss magnetic field is demonstrated by numerical simulations. UHF operation is conjectured at 40-50 Gauss produced by solenoids without iron cores.

New improved formulas for magnetron characteristic curves

Improved analytic formulas for the magnetron characteristic curves (V/sub 0/ versus I/sub 0/ and P/sub RF/ versus I/sub 0/ for fixed B) are derived using the authors guiding-center fluid model. It is shown that if the anode voltage V/sub 0/, the Hartree voltage V/spl circ//sub s/, and the RF voltage V/sub 1/ satisfy the inequality |V/sub 0/-V/spl circ//sub s/|/spl les/V/sub 1/ then the anode current is directly proportional to the RF voltage. Under these (typical) conditions, explicit expressions for the V-I and P-I relations may be obtained. The new equation for V versus I, which differs significantly from the classical relation of J. Hull predicts that current is drawn to the anode for voltages both above and below the Hartree voltage, in direct contradiction with the traditional view of magnetron operation; this result is closely related to the fact that the gain in a crossed-field amplifier (CFA) is an even function of the difference between the phase velocity of the wave and the drift velocity of the electrons, when space-charge effects are small. A new expression is given for the Hartree voltage that includes the effect of the space charge in the spoke. It is also shown that the best quantitative agreement between the new formula and experimental measurements of magnetron V-I curves is obtained when the hub density is taken to be about 1/2 of Brillouin density.

Phase noise reduction and photoelectron acceleration in a high-Q RF gun

The phase noise and jitter characteristics of the laser and RF systems of a high-gradient X-band photoinjector have been measured experimentally. The laser oscillator is a self-mode-locked titanium:sapphire system operating at the 108th subharmonic of the RF gun. The X-band signal is produced from the laser by a phase-locked dielectric resonance oscillator and amplified by a pulsed TWT and klystron. A comparison between the klystron and TWT amplifier phase noise and the fields excited in the RF gun demonstrates the filtering effect of the high-Q structure, thus indicating that the RF gun can be used as a master oscillator and could be energized by either an RF oscillator, such as a magnetron, or a compact source, such as a cross-field amplifier. In particular, the RF gun can play the role of a pulsed RF clock to synchronize the photocathode laser system; direct drive of a synchronously mode-locked AlGaAs quantum well laser has been achieved using the X-band gun RF fields. This novel, gigahertz repetition rate, laser system is being developed to replace the more conventional femtosecond Ti:Al/sub 2/O/sub 3/ system. Some advantages include pumping this laser with a stabilized current source instead of a costly, low-efficiency pump laser. Finally, dark current measurements and initial photoelectron measurements are reported.

Stationary operating density profiles in a crossed-field amplifier

We demonstrate with numerical WKB solutions that stationary density profiles can exist in a crossed-field amplifier. These are density profiles that can exist in equilibrium with a high-frequency (RF) wave propagating in the slow-wave structure. These density profiles are very different from the usual Brillouin profiles. They have a finite and negative density gradient, and extend from the cathode to the anode. They carry a DC current proportional to the RF power in the slow-wave structure. The source of the DC current is a wave–particle resonance that occurs toward the top of the sheath. This resonance drives any Brillouin electron flow unstable. The electrons then redistribute themselves into a new flow – one that can be stationary in the presence of the wave–particle resonance. The new flow has a spoke-like structure, where the spokes carry the current to the anode. Various plots are given, including the DC voltage operating range, DC current flow, phase shifts, and density profiles of the total electron distribution, for various ambient magnetic fields and DC voltages. Numerical values agree reasonably well with the modelled experimental device.