Global and kinetic MHD simulation by the Gpic-MHD code

In order to implement large-scale and high-beta tokamak simulation, a new algorithm of the electromagnetic gyrokinetic PIC (particle-in-cell) code was proposed and installed on the Gpic-MHD code [Gyrokinetic PIC code for magnetohydrodynamic (MHD) simulation]. In the new algorithm, the vortex equation and the generalized ohm's law along the magnetic field are derived from the basic equations of the gyrokinetic Vlasov, Poisson, and Ampere system and are used to describe the spatio-temporal evolution of the field quantities of the electrostatic potential φ and the longitudinal component of the vector potential Az. Particle information is mainly used to estimate second order moments in the generalized ohm's law. Because the lower order moments of the charge density and the longitudinal current density are not used explicitly to determine φ and Az, the numerical noise induced by the discreteness of particle quantities reduces drastically. Another advantage of the algorithm is that the longitudinal induced electric field, ETz=-∂Az/∂t, is explicitly estimated by the generalized ohm's law and used in the equations of motion. The particle velocities along the magnetic field are used (vz -formulation) instead of generalized momentums (pz -formulation), hence there is no problem of 'cancellation', which appear when estimating Az from the Ampere's law in the pz -formulation. The successful simulation of the collisionless internal kink mode by new Gpic-MHD with the realistic values of the large-scale and high-beta, revealed the usefulness of the new algorithm. (author)