ESPIC/Boris-SDC algorithm for particle-in-cell simulations
by
Kristoffer Smedt(University of Leeds)
→
Europe/Stockholm
Description
Particle-in-cell (PIC) schemes are a type of numerical kinetic plasma modelling method for hot diffuse plasmas, which are not suitable for treatment using conventional numerical MHD. Plasma particles are tracked in continuous space while the electric and magnetic fields are discretised and solved on a grid, with charge/current interpolated from particles to grid and vice versa for the fields. Integrating the Lorentz force equation for the particles, `particle pushing', has traditionally used the Boris algorithm which is intrinsically second order accurate. A new method of tuneable order of accuracy called Boris-SDC was developed in a previous study, using the Boris algorithm as a base method for spectral deferred corrections used to converge on a collocation solution. The method was shown to produce the desired high order solutions for particles in a simple Penning trap with an imposed magnetic eld and directly computed electric field.
The current study is investigating the performance of the Boris-SDC algorithm integrated into an electrostatic Particle-in-Cell (ESPIC) scheme, as a first step to ascertain whether Boris-SDC can outperform the traditional Boris algorithm either generally or when high accuracy is needed. Performance evaluation has been successfully carried out for the simple case of a charged particle oscillating in a static electric field as well as for the classic example of the two-stream instability. In both cases, the high accuracy and high order convergence of Boris-SDC was still exhibited when integrated within ESPIC, but limited by the accuracy thereof. A second order ESPIC scheme was used, which was found to impose a lower limit on the error, with the relative performance of Boris-SDC to Boris depending on this underlying level of accuracy.
