Modelling of Beam Plasma Interaction in Strongly Inhomogeneous Plasma

We consider an interaction of a beam with a plasma in the solar wind. The properties of plasma waves are described by 1D Zakharov's equation, the beam is modelled describing particles moving in the electric field of Langmuir waves by means of PIC code. We show that the whole description has Hamiltonian structure and the code is written in simplectic form. We take into account the presence of high level of density fluctuations that are known to occur in the solar wind. It is shown that when the level of density fluctuations is low (δn / n_0) << ( 3 k^2 (λ_D)^2 ) the regime of beam relaxation is very similar to the one in homogeneous plasma and as described by quasilinear (QL) equation. The relaxation length in this case is very short. On the contrary when the level of density fluctuations overcomes certain limit (δn / n_0) > α( k^2 (λ_D)^2 ), where α ≈ 1 the effects of plasma inhomogeneity crucially influence the process of relaxation. Linear wave growth becomes localized and clearly identifiable wave packets dominate wave spectrum due to kinematics of wave propagation and wave-particle resonant interaction. Most of wave packets grow in regions of density gradients. Another important feature of the relaxation consists in formation of the tail of electron distribution in the range of velocities V > Vb . Beam width grows in the direction of lower velocities as well as in the direction of higher velocities and the number density of accelerated electrons can reach 10 - 20 % of the beam density and the energy flux carried by this population can be as large as 40% of the initial energy flux carried by the beam.