Magdi M. Shoucri

Splitting schemes for the numerical solution of a two-dimensional Vlasov equation

Abstract Splitting schemes are applied to the numerical solution of a two-dimensional Vlasov equation. Results obtained when solving the equation in configuration space, by treating the convective term and the acceleration term separately, are compared with results previously obtained using a different method where the two-dimensional Vlasov equation was transformed in velocity space using Hermite polynomials expansion.

The excitation of microwaves by a relativistic electron beam in a dielectric‐lined waveguide

The dispersive properties of a relativistic electron beam in a dielectric‐loaded waveguide are investigated. The linearized fluid and Maxwell’s equations are used to derive the dispersion relation and to study the eigenmodes for the system. The Cerenkov microwave radiation mechanism is investigated.

Nonlinear evolution of the bump-on-tail instability

The nonlinear evolution of a bump‐on‐tail Maxwellian distribution function, to an initially unstable perturbation, is studied numerically. The results indicate that the time asymptotic solution is a Bernstein–Greene–Kruskal equilibrium.

Nonlinear behavior of a monochromatic wave in a one‐dimensional Vlasov plasma

The nonlinear evolution of a monochromatic wave in a one‐dimensional Vlasov plasma is studied numerically. The numerical results are carried out far enough in time for phase mixing to dominate the asymptotic state of the system. A qualitative comparison with previously reported simulations is given.

Numerical solution of the vlasov equation by transform methods

A method is described whereby a pseudo collision operator is formally added to the Vlasov equation in order to eliminate the recurrence effect when numerically solving the Vlasov equation via a hermitian polynomials expansion. This is done with the intent of developing a two-dimensional scheme for the numerical solution of the Vlasov equation. (MOW)

Dispersion relation for a relativistic electron beam in a plasma

The dispersion relation for a relativistic electron beam in a plasma, in the absence of an external magnetic field, is derived. It is shown that the plasma oscillations excited by the beam are linearly coupled to the electromagnetic TM mode.

Computer simulation of the sideband instability

The physical origins of the growth of sidebands of a large amplitude plasma wave are studied numerically. It is shown that in the first phase of the nonlinear evolution of a large amplitude plasma wave the spatially averaged distribution function shows the formation of a stable bump and, for the case presented, the phase velocity of the lower sideband falls on the side of the bump having a positive slope. In the second phase of the evolution of the system, the sidebands saturate and the bumpy region of the spatially averaged distribution function takes a shape close to a flat plateau.

A multistep technique for the numerical solution of a two-dimensional Vlasov equation

Abstract This work describes a multistep technique for the numerical solution of a two-dimensional Vlasov equation. The equation is first transformed, with respect to the two velocity variables v x and v y , , by expanding the distribution function f(x, y, v x , v y , t) in terms of Hermite polynomials. The transformed equation is then integrated at each time step first in the x direction, and next in the y direction and vice versa. The numerical scheme is tested by studying the two-dimensional free streaming case and the linear Landau damping. The results show very good agreement with the theory.

Numerical solution of a two-dimensional Vlasov equation

Abstract By means of a Hermite polynomials expansion in velocity space of the distribution function, the two-dimensional Vlasov equation is solved numerically by applying a multistep technique. We first study the case of a two-dimensional strongly nonlinear Landau damping, where a large amplitude oscillation is initially applied to the system. A second case is considered where an initially stable oscillation is applied to two-dimensional counter-streaming plasmas. The time evolution of these systems is studied and the performance of the numerical code is analyzed.

Destruction of trapping oscillations by sideband instability

The nonlinear evolution of a beam‐plasma instability is studied numerically by direct solution of the Vlasov–Poisson equations. It is shown that the trapped particle oscillations which follow the saturation of a single launched wave can be destroyed by growing sidebands. The results are in agreement with previously reported experimental results.