No abstract

We present a new fast solver to calculate fixed-boundary plasma equilibria in toroidally axisymmetric geometries. By combining conformal mapping with Fourier and integral equation methods on the unit disk, we show that high-order accuracy can be achieved for the solution of the equilibrium equation and its first and second derivatives. Smooth arbitrary plasma cross-sections as well as arbitrary pressure and poloidal current profiles are used as initial data for the solver. Equilibria with large Shafranov shifts can be computed without difficulty. Spectral convergence is demonstrated by comparing the numerical solution with a known exact analytic solution. A fusion-relevant example of an equilibrium with a pressure pedestal is also presented.

We propose the use of sparse grids to accelerate particlein-cell (PIC) schemes. By using the so-called 'combination technique' from the sparse grids literature, we are able to dramatically increase the size of the spatial cells in multi-dimensional PIC schemes while paying only a slight penalty in grid-based error. The resulting increase in cell size allows us to reduce the statistical noise in the simulation without increasing total particle number. We present initial proof-of-principle results from test cases in two and three dimensions that demonstrate the new scheme's efficiency, both in terms of computation time and memory usage. arXiv:1607.06516v1 [physics.comp-ph]