Collisional effects and dispersion relation of magnetic field structures

The local dispersion relation of weak magnetic modes for an arbitrary wavelength ranging from collisional to collisionless cases is derived. The convection velocity and the growth rate are explicitly computed. The convection effects are emphasized and a significant departure from collisional Nernst law is shown to occur even for rather low wavenumbers. In laser plasma experiments, this prevents the convection of intermediate scale magnetic structures generated near the critical layer toward high densities. An explicit convection velocity formula is proposed that is directly usable for numerical purposes. The mathematical tools used in this work are continuous fractions arising naturally from the Fokker–Planck equation with a Landau collisional operator, so that this method can be used to study collisional effects on other plasma modes.