Abstracts Engineering

Equilibrium and Stability of Brillouin Flow in Planar, Conventional, and Inverted Magnetrons

by David Henry Simon

The Brillouin flow is considered to be the prevalent state in many electron devices that operate with a crossed electric and magnetic field, including magnetrons. An investigation of equilibrium and stability of the Brillouin flow is undertaken in this thesis, motivated by simulations of the novel magnetron device, the Recirculating Planar Magnetron (RPM). These simulations showed faster startup in the inverted configuration when compared to the conventional configuration. This thesis first examines the equilibrium properties of the Brillouin flow for both planar and cylindrical geometries, and discovers new relations between the vector potential, scalar potential and electron velocity that mirror the Buneman-Hartree (B-H) and Hull Cutoff conditions. The B-H condition derived from the Brillouin flow model shows a better match to simulation and experiment of relativistic magnetrons than the single particle model B-H condition. The stability of the equilibrium Brillouin flow is studied by perturbation analysis. The perturbation fields are matched to the vacuum field solution to find the complex eigenvalue frequency. The first focus is on smooth-bore magnetrons. Analysis of a planar magnetron recovers the familiar diocotron-like instability growth. The Brillouin flow instability growth rate is found, for the first time, to be enhanced in the inverted cylindrical magnetron and decreased in the conventional cylindrical magnetron, relative to the planar magnetron. This shows that the negative mass effect on a thin electron beam in a cylindrical crossed-field device is not eliminated by the significant intrinsic velocity spread associated with the velocity shear in the Brillouin flow. A slow-wave structure (SWS) is then added to the anode, introducing a resonance between the wave on the slow-wave circuit and electrons. The space harmonics in the vacuum electromagnetic fields and within the flow are included in the analysis, also for the first time. The result is that the real part of the eigenvalue frequency closely matches the cold tube circuit frequency. The growth of the instability is slightly higher for the conventional magnetron, compared to the inverted magnetron, unlike the smooth-bore anode. The resonant instability appears to be dominant over the negative mass instability when a SWS is added to the anode. Advisors/Committee Members: Lau, Yue Ying (committee member), Kushner, Mark (committee member), Gilgenbach, Ronald M (committee member), Foster, John Edison (committee member).