Vlasov gyrokinetic simulations of ion-temperature-gradient driven instabilities

An Eulerian code that solves the gyrokinetic Vlasov equation in slab geometry is presented. It takes into account the ExB and polarization drifts in the plane perpendicular to the magnetic field, and kinetic effects in the parallel direction. The finite Larmor radius is modelled by a convolution operator. The relation is established between this model and others proposed previously, and they are shown to be equivalent in the limit of long wavelengths and small Larmor radii. The code is applied to investigate ion-temperature-gradient modes in the quasi-neutral regime, with adiabatic electrons. Numerical results are reported for a wide range of parameters, including density and temperature profiles, magnetic field strength, and ion to electron temperature ratio. Normally the plasma evolves towards long wavelength structures, although in some cases (when Landau damping is very weak) more strongly turbulent regimes are observed. Test particles are used to compute diffusion coefficients both in real space and velocity space. For the most strongly turbulent regimes, particle diffusion coefficients are of order 20 m2s-1. The saturation mechanism is also investigated. Many previous numerical results obtained with particle codes are confirmed, but the Vlasov Eulerian technique allows a much finer resolution of structures both in real space and velocity space