A fluid description is used to study the properties of two-stream instability due to interaction of a non-relativistic electron beam with quantum magnetized plasma and transverse wiggler magnetic field. It is assumed that the background plasma provides charge and current neutralization of the electron beam. The dispersion relation is obtained by solving and linearizing fluid-Maxwell equations. The resulting dispersion equation is analyzed numerically over a wide range of system parameters. The results of quantum and classical treatments are compared numerically, with including the effects of wiggler on the dispersion relation. It is found that the transverse wiggler magnetic field can strongly improve the instability of quantum plasma as well as classical plasma.

In this paper, we propose a new conservative semi-Lagrangian (SL) finite difference (FD) WENO scheme for linear advection equations, which can serve as a base scheme for the Vlasov equation by Strang splitting [4]. The reconstruction procedure in the proposed SL FD scheme is the same as the one used in the SL finite volume (FV) WENO scheme [3]. However, instead of inputting cell averages and approximate the integral form of the equation in a FV scheme, we input point values and approximate the differential form of equation in a FD spirit, yet retaining very high order (fifth order in our experiment) spatial accuracy. The advantage of using point values, rather than cell averages, is to avoid the second order spatial error, due to the shearing in velocity (v) and electrical field (E) over a cell when performing the Strang splitting to the Vlasov equation. As a result, the proposed scheme has very high spatial accuracy, compared with second order spatial accuracy for Strang split SL FV scheme for solving the Vlasov-Poisson (VP) system. We perform numerical experiments on linear advection, rigid body rotation problem; and on the Landau damping and two-stream instabilities by solving the VP system. For comparison, we also apply (1) the conservative SL FD WENO scheme, proposed in [22] for incompressible advection problem, (2) the conservative SL FD WENO scheme proposed in [21] and (3) the non-conservative version of the SL FD WENO scheme in [3] to the same test problems. The performances of different schemes are compared by the error table, solution resolution of sharp interface, and by tracking the conservation of physical norms, energies and entropies, which should be physically preserved.

When an intense ion beam propagates through a dense background plasma, its current is partially neutralized by the electron plasma return current. Due to the non-uniformity of the background plasma electrons longitudinal velocity profile (r), the flow can be unstable. The instability is similar to the Kelvin-Helmholz instability for the non-uniform flow of an incompressible neutral fluid, with the electrostatic potential playing the role of pressure. For the case of electron return current flow, the significant new feature is the presence of the partially self-neutralized magnetic field of the ion beam, which significantly affects the evolution of small-amplitude excitations. In this paper the stability properties of the flow of electrons making up the plasma return current is investigated using the macroscopic cold-fluid-Maxwell equations. It is shown that this flow may become unstable, but the instability growth rates are exponentially small. This unstable body mode is qualitatively different from previously studied surface-mode excitations of the electron plasma return current for an intense ion beam with a sharp radial boundary, which is found to be stable due to the stabilizing influence of the partially neutralized magnetic field of the ion beam.

A thorough analysis of the electromagnetic instabilities encountered in the beam plasma interaction physics shows that the most unstable modes are not the ones which are usually studies. We characterize these most unstable modes and determine the patterns they create.

In the fast ignition scenario for inertial fusion, a relativistic electron beam is supposed to travel from the side of the fusion pellet to its core. One one hand, a relativistic electron beam passing through a plasma is a highly unstable system. On the other hand, the pellet core is denser than its side by four orders of magnitude so that the beam makes its way through a important density gradient. We here investigate the effect of this gradient on the instabilities. It is found that they should develop so early that gradient effects are negligible in the linear phase.

We will consider relativistic electron beam interacting with plasma and study the electromagnetic instabilities obtained for arbitrarily oriented wave vectors ranging from two-stream to filamentation instabilities. For these unstable modes, we will study every temperature effects, namely beam and plasma normal, and parallel temperatures. Temperatures are supposed to be non-relativistic and modeled through water bag distributions. It is found that only normal beam temperature and parallel plasma temperature have a significative influence over the growth rates for wave vector making an angle with the beam larger than a critical angle θc which is determined exactly. The largest growth rate being reached for a wave vector making an angle with the beam smaller than θc, it is not damped by any kind of temperatures. We finally explore collisions effects and show they can reduce the largest growth rate.

We investigate intermediate unstable modes between two stream and filamentation instabilities. We detail the problem of the angle between the wave vector and its electric field and use an electromagnetic formalism allowing for any value for this angle. We display analytical results for 3 different models: cold beam-cold plasma, cold beam-hot plasma and cold relativistic beam-hot plasma. We demonstrate that plasma temperature prompts a critical angle for which waves are unstable at any k and show that for a relativistic beam, the most unstable waves are obtained for wave vectors which are neither normal nor perpendicular to the beam.

Ion–electron two-stream instabilities in high intensity heavy ion fusion beams, described self-consistently by the nonlinear Vlasov–Maxwell equations, are studied using a three-dimensional multispecies perturbative particle simulation method. Large-scale parallel particle simulations are carried out using the recently developed Beam Equilibrium, Stability, and Transport (BEST) code. For a parameter regime characteristic of heavy ion fusion drivers, simulation results show that the most unstable mode of the ion–electron two-stream instability has a dipole-mode structure, and the linear growth rate decreases with increasing axial momentum spread of the beam particles due to Landau damping by the axial momentum spread of the beam ions in the longitudinal direction.