Stability of Brillouin flow in planar, conventional, and inverted magnetrons

Abstract

The Brillouin flow is the prevalent flow in crossed-field devices. We systematically study its stability in the conventional, planar, and inverted magnetron geometry. To investigate the intrinsic negative mass effect in Brillouin flow, we consider electrostatic modes in a nonrelativistic, smooth bore magnetron. We found that the Brillouin flow in the inverted magnetron is more unstable than that in a planar magnetron, which in turn is more unstable than that in the conventional magnetron. Thus, oscillations in the inverted magnetron may startup faster than the conventional magnetron. This result is consistent with simulations, and with the negative mass property in the inverted magnetron configuration. Inclusion of relativistic effects and electromagnetic effects does not qualitatively change these conclusions.

Multi-frequency recirculating planar magnetrons

“…2.5. Simon [38] has explicitly shown that the smoothbore magnetron was an adequate description for the equilibrium state. Still, two models dominate the literature: a multistream model based on individual cycloidal particle orbits, and the Brillouin model that idealizes the electron motion as a laminar flow [54].…”

“…Still, two models dominate the literature: a multistream model based on individual cycloidal particle orbits, and the Brillouin model that idealizes the electron motion as a laminar flow [54]. Full derivations of the following equations in planar and cylindrical smoothbore magnetrons have been published in many textbooks [6,45,47,54] and theses [10,38,55,56], and will not be repeated here. The following discussion instead focuses on the relevance of the results as they apply to the design of the MFRPM and the interpretation of the experimental results.…”

“…The large cathode area therefore makes the RPM an especially promising HPM source. The inverted cylindrical magnetron variant (where the cathode resides on the outside, and the anode on the inside) solves the small-area cathode problem with the added advantage of enhanced electron bunching in the circular bends because of the negative mass instability [30][31][32], but suffers from heat dissipation issues from the smaller anode area, and introduces considerable practical challenges for microwave extraction from the anode [33][34][35]. Other RPM advantages include a favorable scaling of the magnetic field volume with cavity number (as N ), a large anode volume that facilitates heat dissipation, and a decoupled relation between the cavity number and Anode-Cathode Gap (AK gap) spacing.…”

“…Different geometric variations of the magnetron have been the focus of research at the University of Michigan (UM) for several years. For example, the effect of conventional, planar, and inverted magnetron configurations on start-up has been theoretically investigated [32,37,38]. Experimental research at UM has largely focused on the first RPM prototype, termed the RPM-12A [10,39,40].…”

Crossed-field flows

“…For a smooth bore magnetron, the negative (positive) mass effect in the inverted (conventional) magnetron geometry was shown to increase (decrease) the severity of the diocotron instability [4] in the Brillouin flow. Including the SWS on the anode, the resonant interaction of the vacuum circuit mode and the corresponding smooth-bore diocotron-like mode is the dominant cause for instability [5].…”