J.W. Luginsland

Beyond the Child–Langmuir law: A review of recent results on multidimensional space-charge-limited flow

Space-charge-limited (SCL) flows in diodes have been an area of active research since the pioneering work of Child and Langmuir in the early part of the last century. Indeed, the scaling of current density with the voltage to the 3/2’s power is one of the best-known limits in the fields of non-neutral plasma physics, accelerator physics, sheath physics, vacuum electronics, and high power microwaves. In the past five years, there has been renewed interest in the physics and characteristics of SCL emission in physically realizable configurations. This research has focused on characterizing the current and current density enhancement possible from two- and three-dimensional geometries, such as field-emitting arrays. In 1996, computational efforts led to the development of a scaling law that described the increased current drawn due to two-dimensional effects. Recently, this scaling has been analytically derived from first principles. In parallel efforts, computational work has characterized the edge enhancement of the current density, leading to a better understanding of the physics of explosive emission cathodes. In this paper, the analytic and computational extensions to the one-dimensional Child–Langmuir law will be reviewed, the accuracy of SCL emission algorithms will be assessed, and the experimental implications of multidimensional SCL flows will be discussed.

Cathode effects on a relativistic magnetron driven by a microsecond e-beam accelerator

Experiments have been performed on a relativistic magnetron driven at e-beam accelerator peak parameters: voltage = -0.4 MV, current = 16 kA, and pulselength = 0.5 /spl mu/s. The magnetron is a six-vane device operating at about 1 GHz with extraction from two cavities. For equal power in both extraction waveguides, the peak microwave power of this device is between 200 and 300 MW. Microwave pulse-shortening limits pulselengths to the range of 10-100 ns. Time-frequency analysis of microwave emission indicates operation at about 1.03 GHz, close to the pi mode frequency identified from cold tests and the three-dimensional MAGIC code. Two cold cathodes were tested: 1) an emitting aluminum knob in the vane region with no endcap and 2) an extended cathode with a graphite fiber emission region in the vanes and endcap outside the vanes. Electron endloss current has been measured for the two cathodes. With no endcap, the cathode exhibited endloss current fraction up to 50% of the total; with one endcap, the cathode reduced the endloss current fraction to as little as 12%. Both cathodes produced peak total-electronic efficiency in the range of 14%-21%.

Effects of tapering on gyrotron backward-wave oscillators

Computer modeling has been utilized to guide gyrotron backward-wave oscillator (gyro-BWO) experiments at the University of Michigan over a wide range of tapered interaction regions and tapered magnetic fields. E-GUN code is used to examine beam and diode characteristics, while MAGIC is used to analyze the dynamics of the problem, such as particle kinematics and microwave power production. Several innovative techniques are used to create matching boundary conditions for a backward propagating wave. MAGIC simulations predict optimum performance of the gyro-BWO operating in a TE/sub 01/ mode within a combination of uniform interaction region and a tapered axial magnetic field which increases 7.5% in the direction of beam propagation. Experiments have been performed to investigate the effects of tapering magnetic fields and tapered interaction region radii on the high-power microwave emission from the gyro-BWO over the frequency range from 4.0 to 6.0 GHz. These experiments were performed on the Michigan Electron Long-Pulse Accelerator (MELBA) with parameters: V=-0.7 to -0.9 MV, I/sub diode/=1-10 kA, I/sub tube/=1-4 kA, T/sub e-beam/=0.4-1.0 /spl mu/s. Tapered interaction regions of 37%, 23%, 9.4%, and 6.4% were built and tested to determine their effect on microwave power, pulselength, and inferred energy compared to the uniform interaction region. Magnetic tapering trim coils with a range of -10.6%</spl Delta/B/B/sub 0/<+15.0% were constructed which allow the orientation of the field taper to be changed without breaking the vacuum. The peak microwave power from individual shots was from 30 to 55 MW. Experiments on magnetic field tapering indicate that positive tapered fields improve microwave power and energy output.

Magnetic priming effects on noise, startup, and mode competition in magnetrons

Azimuthally varying axial magnetic fields have been utilized to perform magnetic priming of magnetrons for rapid startup, low noise, and mode control. An overview of the latest magnetic priming experimental and simulation results are presented in this paper. Magnetic priming experiments in dc-operating microwave oven magnetrons show sideband elimination, even with the cathode heater turned off. Simulations using three three-dimensional (3-D) improved concurrent electromagnetic particle-in-cell (ICEPIC) codes with two different computational algorithms recover the oven magnetron experimental results obtained with magnetic priming including fast mode growth, rapid spoke formation, and the tendency toward lower noise operation. A new, axially symmetric, azimuthally varying magnetic field geometry for oven magnetrons is explored and preliminary results are reported. Simulations using two-dimensional (2-D) MAGIC code for the University of Michigan/Titan relativistic magnetron show that the oscillation startup time can be dramatically decreased (almost by a factor of 3) and mode competition can be suppressed with magnetic priming.

A simulation study of beam loading on a cavity

Beam loading exerts a strong influence on the operation of high-power and medium-power microwave sources. This paper reports a simulation study of beam loading on a cavity using the two-dimensional particle-in-cell code, MAGIC. We vary the beam voltage, the beam current, the degree of current modulation on the dc beam before the beam enters the cavity, and the degree of charge neutralization on the beam. We deduce the beam-loaded quality factor Q and the beam-loaded resonant frequency from a Lorentzian fit of the numerical data on the gap voltage response as a function of the driving frequency. The MAGIC simulations have revealed several unanticipated results. The beam loading is observed to be a function of perveance. Constant perveance beams, of varying voltage and current, exercise about the same degree of beam loading on the model klystron cavity (except, of course, for the cases with very small beam current). The inclusion of an ac component on the dc beam current has no effect on the degree of beam loading; neither does the neutralization of the electron beam. Many of these simulation results cannot be explained by existing theories that ignore ac space charge effects.

Relativistic magnetron driven by a microsecond E-beam accelerator with a ceramic insulator

Relativistic magnetron experiments performed on a six-cavity device have generated over 300 MW total microwave power near 1 GHz. These experiments were driven by the long-pulse electron beam from an accelerator with parameters as follows: voltage of *300 kV, current of 1-10 kA, and typical pulselength of 0.5 ms. This paper reports investigations of high-power microwave generation, mode competition, and pulse shortening for the relativistic magnetron with a ceramic insulator compared to a plastic insulator. The ceramic insulator improves the vacuum by a factor of ten (to 10/sup *7/ torr range) and flattens the voltage of the accelerator. Relativistic magnetron performance with the ceramic insulator shows increased microwave power and pulselength over the plastic insulator. Effects of RF breakdown in the extraction waveguide on peak microwave power and pulselength are also investigated by utilizing SF/sub 6/ in one or both of the extraction waveguides.

Virtual cathode formation due to electromagnetic transients

The process of virtual cathode formation in a gap is critically examined via particle simulations. It is found that the limiting current obtained from the electrostatic approximation is valid only in the deeply nonrelativistic regime. For injection energy as low as 30 keV, the transients in the injected current may produce an inductive voltage that can significantly lower the limiting current from the classical, electrostatic value. Although the source of the virtual cathode is transient in nature, the virtual cathode formed due to this inductive voltage persists long after the injected current has reached a steady-state value. The self-magnetic field is unimportant, however, at this low energy. This result has implications for scaling devices with rapid current rise times to weakly nonrelativistic energies as well as for Particle-In-Cell (PIC) codes which use field emission models with electric field thresholds.

High-power transit-time oscillator: Onset of oscillation and saturation

A simple circuit model is used to investigate the transit-time oscillator (TTO) driven by a high-current diode. A novel condition for the onset of oscillation is derived in terms of the diode impedance. It is shown that a low impedance is required for the production of high-power microwaves in a TTO. The initial growth is calculated, and the saturation level is numerically computed using the one-dimensional model. These one-dimensional (1-D) results are in excellent agreement with a full scale two-dimensional Particle-in-Cell simulation. The success of the much simpler 1-D model allows a close examination of the roles played by the convection current and by the displacement current, as well as the modification in the transit time due to the intense space charge within the gap.

Magnetic perturbation effects on noise and startup in DC-operating oven magnetrons

Previous experiments demonstrated that imposing an azimuthally varying axial magnetic field, axially asymmetric, in dc-operating oven magnetrons causes rapid mode growth (by magnetic priming) and significant noise reduction. This configuration was previously implemented by adding five perturbing magnets on the upper existing magnet of the magnetron. Experiments reported here add five perturbing magnets on each of the two existing magnets of the magnetron, restoring the axial symmetry of the magnetic field, while maintaining the five-fold azimuthal magnetic field symmetry. Compared with the unperturbed magnetic field case, it has been observed that the noise close to the carrier is reduced by up to 20 dB, while the sidebands are not completely eliminated for medium and high currents. Magnetron start-oscillation currents are somewhat higher for this axially symmetric, azimuthally varying magnetic field as compared to the baseline unperturbed magnetic field.

Experiments on peer-to-peer locking of magnetrons

Experiments on peer-to-peer locking of 2 kW magnetrons are performed. These experiments verify the recently developed theory on the condition under which the two nonlinear oscillators may be locked to a common frequency. Dependent on the coupling, the frequency of oscillation when locking occurs does not necessarily lie between the free running frequencies of the two isolated, stand-alone magnetrons. Likewise, when the locking condition is violated, the beat frequency is not necessarily equal to the difference between these free running frequencies.