Exactly Energy Conserving Semi-Implicit Particle in Cell Formulation

TL;DR

The paper introduces ECSIM, a novel semi-implicit PIC method that conserves energy exactly, is unconditionally stable, and does not require nonlinear iterations, improving efficiency and stability over previous methods.

Contribution

The paper presents ECSIM, a semi-implicit PIC method that conserves energy exactly without nonlinear iterations, maintaining explicit-like computational cycles and enhancing stability.

Findings

ECSIM conserves energy to round-off error for any time step.

ECSIM is unconditionally stable, independent of plasma frequency.

ECSIM eliminates finite grid instability constraints.

Abstract

We report a new particle in cell (PIC) method based on the semi-implicit approach. The novelty of the new method is that unlike any of its semi-implicit predecessors at the same time retains the explicit computational cycle and conserves energy exactly. Recent research has presented fully implicit methods where energy conservation is obtained as part of a non linear iteration procedure. The new method (referred to as Energy Conserving Semi-Implicit Method, ECSIM), instead, does not require any non-linear iteration and its computational cycle is similar to that of explicit PIC. The properties of the new method are: i) it conserves energy exactly to round-off for any time step or grid spacing; ii) it is unconditionally stable in time, freeing the user from the need to resolve the electron plasma frequency and allowing the user to select any desired time step; iii) it eliminates the constraint of the finite grid instability, allowing the user to select any desired resolution without being forced to resolve the Debye length; iv) the particle mover has a computational complexity identical to that of the explicit PIC, only the field solver has an increased computational cost. The new ECSIM is tested in a number of benchmarks where accuracy and computational performance are tested.