Simulation of Finite-Beta Effects in Gyrokinetic Plasmas

A generalization of the original split-weight scheme for finite-beta plasmas [W. W. Lee, J. Lewandowski, Z. Lin and T. S. Hahm, Phys. Plasmas {\bf 8}, 4435 (2001)] to multi-dimensional plasmas is developed. The scheme is based on the concept of perturbative particle simulation, where only the non-adiabatic response of the electrons, $\delta h$, is followed in time, where $\delta h = F- (1+\psi) F_0$, $F$ is the electron dunstibution function, $F_0$ is the background electron distribution function, $\psi =\phi + \int A_\parallel d x_\parallel/c$, and $\phi$ and $A_\parallel$ are the perturbed potentials. The procedure involves the Poisson solvers for $\phi$, $A_\parallel$, $\partial \phi / \partial t$, $\partial A_\parallel /\partial t$, and $\partial^2 A_\parallel / \partial t^2$, which, in turn, need up zeroth, first, second and third velocity-space moments for input. The use of the scheme for turbulence and MHD studies [Lee and Qin, Phys. Plasmas {\bf 10}, 3196 (2003)] will be presented.