Explicit Brillouin Flow Solutions in Magnetrons, Magnetically Insulated Line Oscillators, and Radial Magnetically Insulated Transmission Lines

Abstract

This article re-examines the Brillouin flow solutions in crossed-field diodes, with applications to magnetrons, magnetically insulated line oscillators (MILOs), and magnetically insulated transmission lines (MITLs). The Brillouin flow solutions are constructed for various geometries, including planar magnetrons, MILOs, and MITLs, cylindrical magnetrons with electrons flowing in the azimuthal direction, cylindrical MITLs and MILOs with electrons flowing in the axial direction, and radial MITLs and MILOs with electrons flowing in the radial direction. A common theme of this analysis is that two main external parameters are used to characterize the Brillouin flow: the anode-cathode voltage (V a ) and the total magnetic flux within the crossed-field diodes ( A a ). These two parameters are equivalent to the gap voltage and a specification of the degree of magnetic insulation, which is approximately equal to the ratio of the magnetic field to the Hull cutoff (HC) magnetic field.The magnetic flux may be provided externally by a magnet (as in a magnetron) or by the wall currents without an external magnet (as in a MILO or MITL), or by some combination of the two, as in the intermediate case of a magnetron-MILO hybrid. Once these two parameters are specified, the electron flow speed at the top of the Brillouin hub is uniquely determined. This immediately yields the Buneman-Hartree (BH) condition according to the Brillouin flow model, whether it be a planar magnetron or a cylindrical MILO. In so doing, we have obtained, for the first time using the Brillouin flow model, the BH condition for a cylindrical MILO, and we show that the same condition is obtained from the single-particle orbit model. We also found that, in general, the electron current within the Brillouin hub Manuscript

Electron Trajectories and Critical Current in a Two-Dimensional Planar Magnetically Insulated Crossed-Field Gap

“…The assessments potentially connect the newly developed metrics and the traditionally used critical current density for VC formation and transition to nB state for 𝐵 > 𝐵 H in 1D [2], [3], [7], [17], [19] or 2D with 𝐵 𝑦 [23]. Moreover, the presented methodology of assessing the electron flow may be applied and extended to other crossedfield devices [16], [41]- [43].…”

“…If 𝐵 > 𝐵 𝐻 , in which the electrons execute cycloidal orbits (without space-charge) and return to the cathode, a critical current 𝐽 𝐶𝑅 , which may also be considered as a modified 𝐽 CL , may be found to mark the transition or collapse from a stationary cycloidal flow to the non-stationary near-Brillouin (nB) flow [3], [6], [23], [35]. The nB flow consists of the classical Brillouin flow [3], [16], [36] superimposed by a turbulent background characterized by virtual cathode (VC) oscillation [2], [3], [18], [19]. The classical Brillouin flow is a laminar flow with all electrons moving parallel to the cathode (and zero velocity orthogonal to the cathode) and may be considered as a stable solution of minimum energy [13].…”

“…While neither our metrics nor Slater's orbits describe an oscillating magnetron, they may elucidate the behavior in the oscillatory range [13]. Similar to the methods developed for analyzing oscillating magnetrons based on PIC data [40], the present assessments may be applied and extended to other similar devices or physical models, such as magnetically insulated line oscillators [16], two-species Brillouin flow [41], Hall thrusters [42], and Z-pinch [43].…”

Induced Current Due to Electromagnetic Shock Produced by Charge Impact on a Conducting Surface

“…We tentatively conclude that the shock-induced surface current will not cause additional damage in multipactor discharge, because of the low-impact energies of the multipactoring electrons. However, the shock-induced currents could be important in MILOs and relativistic magnetrons, in which spoke electrons, a significant fraction of which may have high energies (a few tens to hundreds of keV), always strike the anode circuit [14], [15]. The shock-induced current, in this case, would introduce additional beam loading that is omitted in the classical RS theory.…”

“…3) Linear beam tubes, such as the traveling wave tubes and klystrons would not be affected as much by this shockinduced current because there is little beam interception in the interaction region. One may wonder if the additional beam loading due to the electromagnetic shocks, as described in 2) for relativistic crossed-field devices, is one reason for the characteristically low efficiencies experienced in relativistic magnetrons (compared with microwave oven magnetrons) and in MILO experiments [14], [15].…”