Study of the diffusion across a magnetic field in a beam–plasma interaction using a drift-kinetic Vlasov code

Abstract

A drift-kinetic Eulerian Vlasov code, with fluid equations for the ions, is developed to study the problem of the injection of an electron beam into a two-dimensional magnetized plasma, often referred to as direct current (dc) helicity injection. The diffusion of electrons across a magnetic field in the presence of a beam–plasma instability is studied. The case of a magnetic field tilted with respect to the beam direction is considered. The competition between the velocity shear Kelvin–Helmholtz (KH) and the beam–plasma (BP) instabilities is investigated in order to analyze the plasma heating and current drive mechanism induced by the beam injection. The KH instability generates low-frequency plasma convection motion associated with cE×B/B2 drift. In particular, the diffusion coefficients Dy and Dv ∥ describing, respectively, the anomalous diffusion process induced in space across the magnetic field by the KH instability, and the velocity diffusion process due to the kinetic effects induced in velocity space along the magnetic field by the BP instability, are computed using test-particle diagnostics. In the present Cartesian model, it is found that Dy = Dv∥ tan2 θ/ωce2 where θ is the angle between the magnetic field and the x axis. This relation which links the electron dynamics in the x-y real space and in the x-v∥ phase space is verified by the numerical code. The Vlasov code provides a powerful tool to study particle diffusion in space and in phase space, especially in the low-density regions of the distribution function.