The nonlinear diocotron mode in a pure electron plasma

The nonlinear diocotron mode, discussed by Fine, Driscoll, and Malmberg [Phys. Rev. Lett. 63, 2232 (1989)] is characterized by two equations, one describing the frequency of orbiting, the other giving the quadrupole moment, as functions of size and offset. A new analysis, based on the method of moments, which yields equations more general in their content, is presented here. For example, the new equations describe columns whose shapes are not elliptical and whose densities are not constant

Linear response of the two-dimensional pure electron plasma: Quasimodes for some model profiles

After examining the initial value problem for the linear, diocotron response of a long cylinder of pure-electron plasma, the "quasimodes" associated with convex, power-law density profiles are studied. For these profiles, exact, analytic results are available. The "quasimodes," which are damped by phase mixing, may be characterized by their angular variation, flatness, and the magnitude of the gap separating the plasma from the containing wall

On the collision probability for the infinite cylinder

The derivation of a compact expression for the collision probability for the infinite cylinder involves the reduction of a complicated integral, a reduction attributed to the late D.R. Inglis in a Los Alamos report that is unavailable. We present an alternative evaluation here

On the zero-energy moments of the distribution of fast atoms and cascades

The slowing down of neutrons in capture-free hydrogen is not only a classic problem in transport theory but is a paradigm for several problems in the interaction of energetic ions with matter. Here we are concerned primarily with the distribution of stopped particles. We describe a novel expansion for the transport equation which which gives extremely accurate results for the moments of the distribution and which proves an earlier conjecture made by E.M. Baroody. We discuss additional applications of the expansion, which appears to be an improved “straight-ahead” approximation