Particle-in-cell simulation with Vlasov ions and drift kinetic electrons

There are certain limitations in using gyrokinetic ions for simulations of turbulent transport in tokamak plasmas. Applications where Vlasov ions might be more appropriate include the electron temperature gradient driven turbulence, edge turbulence with steep density gradient, and magnetic reconnection in a weak guide field. In such cases the ion gyrokinetic model presently used in simulations needs to be extended, but a satisfactory extension valid for fully electromagnetic turbulence is not presently available. Even if an accurate model is found, its numerical implementation could be very challenging. We propose a kinetic model that combines Vlasov ions with gyrokinetic electrons to avoid the difficulties with gyrokinetic ions. The field equations of this model are the Faraday's equation and the Ampere's equation without the displacement current. The perturbed fields B-1 and E-1 rather than the scalar and vector potentials are used to formulate the field equations. We have devised an implicit scheme for this model, demonstrated in three-dimensional slab for the Alfven waves, the drift Alfven instability and the ion acoustic waves.