General Considerations
Plasma waves are generated by the charge separation that arises when ions and electrons are displaced from their equilibrium positions in a plasma. The dispersion properties and the stability of these waves are important in many aspects of plasma physics and are usually studied by kinetic theory methods. They tend to propagate mainly in collisionless plasmas, since other wave phenomena are dominant in the presence of collisions. The kinetic description of plasma waves is inherently nonlinear, since the time evolution of the distribution functions of the plasma species is affected by the self-consistent electric field, itself a function of the charge density. Linearized models have been used by many authors to study the stability properties of plasma waves, most often by analytical tools only. Nonlinear studies have also been carried out, but the difficulties in this case are overwhelming and one has to resort to numerical techniques.
The effect of short range binary collisions on the stability properties of these spatially uniform Vlasov equilibria has also been studied, both analytically and numerically, and the dampening effect of collisions has been shown.
Results
Nonlinear plasma waves.
We present some numerical simulations showing that a nonlinear superposition principle introduced recently by Buchanan and Dorning gives a self-consistent plasma state with the desired properties. In particular, we examine how these nonlinear states evolve under the Vlasov dynamics and compare their evolution with the time evolution of linear superpositions of the same BGK modes.
- 1. L. Demeio, A numerical study of linear and nonlinear superpositions of BGK modes, mandato in pubblicazione a Transport Theory and Statistical Physics, Luglio 1999 (ICTT Atlanta May 1999).
Effect of short range binary collisions on the stability properties of Vlasov equilibria.
A new algorithm has been introduced, which solves the Vlasov-Poisson system in phase space with a BGK collision operator, both with constant and velocity dependent collision frequency. The algorithm has been used to examine the influence of binary collisions on the nonlinear behaviour of Vlasov solutions. A linear stability analysis in presence of collisions, described by the BGK collision operator with velocity dependent collision frequency, has also been performed.
- L. Demeio and G. Frosali, Effects of short-range binary collisions on the stability properties of longitudinal plasma waves, Sommari del III Congresso Nazionale della SIMAI, Salice Terme, PV, 27-31 Maggio 1996, p. 526.
- L. Demeio and G. Frosali, Effects of short-range binary collisions on the stability properties of longitudinal plasma waves, Rapporto Interno 7/1996 del Dip. di Matematica ``V. Volterra", Universita' degli Studi di Ancona.
- L. Demeio, Linear stability of the spatially homogeneous equilibria of the Vlasov-Poisson system with collisions, Reports on Mathematical Physics, 40, 455 (1997).
- L. Demeio, Collisional relaxation of nonlinear plasma waves, IV International Conference on Industrial and Applied Mathematics, Edinburgh, Scotland, July 5-9, 1999, ICIAM99, p. 253.