AstroGK Algorithm Description

NOTE: This section is under construction

The gyrokinetic equation evolves the five-dimensional distribution function for each species s given by g_s(x,y,z,E, \lambda), where particle energy is E=m_s v^2/2 and pitch angle is \lambda=v_\perp^2/(v^2 B_0). Along with the distribution functions, Maxwell's equations in the gyrokinetic limit evolve three scalars---the scalar potential \phi(x,y,z), the parallel component of the vector potential A_\parallel(x,y,z), and the parallel component of perturbmagnetic field \delta B_\parallel(x,y,z)---that describe the fluctuating electromagnetic fields.

The spatial components x and y are handled spectrally in Fourier space, and the z-direction is handled with a compact finite differencing scheme. Integration over the velocity-space grids is accomplished using spectral integration by quadrature in E and \lambda, while the differentiation needed by the collision operator in pitch angle is accomplished using finite differencing. The linear terms are advanced implicitly to avoid the need to satisfy a Courant condition for the fast electron dynamics. Nonlinear terms are evaluated by fast Fourier transform in real space and the term is advanced using a 3rd-order Adams-Bashforth scheme.

A Langevin antenna is used for driving the turbulence at the scale of the simulation domain and a hypercollisionality is used for the removal of energy as the smallest resolved scales.