R.A. Stark

Diocotron instability for relativistic non-neutral electron flow in planar magnetron geometry

Diocotron stability properties of relativistic non‐neutral electron flow in a planar magnetron are investigated within the framework of the cold‐fluid‐Maxwell equations. The eigenvalue equation for the extraordinary‐mode waves in a relativistic velocity‐sheared electron layer is obtained, and is solved in the massless, guiding‐center approximation. Approximating the electromagnetic field in the anode resonator by the lowest‐order mode, the dispersion relation for the diocotron instability is obtained. Although the tenuous beam approximation is assumed, the eigenvalue equation and corresponding dispersion relation are both fully electromagnetic, and valid for relativistic electron flow. The dispersion relation is numerically investigated for a broad range of system parameters. From numerical calculations of the dispersion relation, it is shown that the typical growth rate of the diocotron instability indicates a strong instability. The early evolution of the diocotron instability as an important precursor to the evolution of the full magnetron oscillation is discussed.

Simulation studies of the relativistic magnetron

Summary form only given. Two-dimensional particle-in-cell (PIC) simulations of the high-power magnetron using the codes MAGIC and MASK have been performed. The simulations have been specialized to the A6 magnetron geometry, or slight variations thereof. Several scenarios with both MAGIC and MASK have been run to saturation. With MAGIC the following was observed: (1) mode competition between the π and 2π modes, and, alone, the l=5 mode (5.0 GHz), all in agreement with Buneman-Hartree theory; (2) the density profiles, which depart markedly from those of Brillouin flow, are rounded with a negative density gradient with radius; (3) the RF fields at saturation are comparable in magnitude to the applied fields; and (4) saturation of the RF is accompanied by energetic bombardment of the anode. In simulations using MASK, the π mode and the 2π mode have been observed separately. Also either the π mode or the 2π mode is seen to dominate at saturation, depending on the cathode radius

Phase-locking simulation of dual magnetrons

Summary form only given. The analysis of phase-locking of dual magnetrons is underway by means of direct particle simulation of two coupled magnetrons. The computer code allows two magnetrons to run side by side without any crosstalk other than being coupled through a transmission line. The phase evolution can be simulated with two magnetrons connected by a transmission line with various lengths and impedances. The Physics International magnetron geometry configuration was used. and the preliminary results demonstrate that a half-integral wavelength connector produced 180° out-of-phase operation. The phase-locking time can be observed easily from the phase evolution of two magnetrons

Simulation Of A Dense Plasma Focus X-ray Source

The authors are performing simulations of the magnetohydrodynamics of a Dense Plasma Focus (DPF) x-ray source located at Science Research Laboratory (SRL), Alameda, CA, in order to optimize its performance. The SRL DPF, which was developed as a compact source for x-ray lithography, operates at 20 Hz, giving x-ray power (9--14 Angstroms) of 500 W using neon gas. The simulations are performed with the two dimensional MHD code MACH2, developed by Mission Research Corporation, with a steady state corona model as the equation of state. The results of studies of the sensitivity of x-ray output to charging voltage and current, and to initial gas density will be presented. These studies should indicate ways to optimize x-ray production efficiency. Simulations of various inner electrode configurations will also be presented.

Theory of high power cylindrical magnetron

Summary form only given. Making use of a macroscopic cold-fluid model for the electrons, the authors have formulated a diocotron theory of the extraordinary mode perturbations for a tenuous electron flow. However, this previous theory is limited to a planar geometry and to a very tenuous layer. The authors have therefore extended the previous theory to a cylindrical geometry and to an intense electron flow. Eigenvalue equations of the extraordinary mode perturbations for an electron flow in Brillouin equilibrium in a cylindrical magnetron were derived, within the context of the linearized cold-fluid Maxwell equations. Assuming a tenuous flow density, the simplified eigenvalue equation was used to derive a closed algebraic dispersion relation of the diocotron instability

Linear Theory Of The High-Power Planar Magnetron

Linear stability properties of the extraordinary mode perturbations in a relativistic electron flow generated inside a planar magnetron are investigated. The stability analysis is carried out within the framework of a linearized macroscopic fluid model and the eigenvalue equation is obtained. In a tenuous density limit, an algebraic dispersion relation for the diocotron instability is obtained from this eigenvalue equation. Results of numerical investigation of this dispersion relation are presented. Particle simulation is also carried out for the diocotron instability and it is shown that the simulation results agree extremely well with the analytical results. Making use of finite element methods, the eigenvalue equation of the extraordinary mode is numerically solved and the results are also presented.