ECsim-CYL: Energy Conserving Semi-Implicit particle in cell simulation in axially symmetric cylindrical coordinates

Based on the previously developed Energy Conserving Semi Implicit Method (ECsim) code, we present its cylindrical implementation, called ECsim-CYL, to be used for axially symmetric problems. The main motivation for the development of the cylindrical version is to greatly improve the computational speed by utilizing cylindrical symmetry. The ECsim-CYL discretizes the field equations in two-dimensional cylindrical coordinates using the finite volume method . For the particle mover, it uses a modification of ECsims mover for cylindrical coordinates by keeping track of all three components of velocity vectors, while only keeping radial and axial coordinates of particle positions. In this paper, we describe the details of the algorithm used in the ECsim-CYL and present a series of tests to validate the accuracy of the code including a wave spectrum in a homogeneous plasmas inside a cylindrical waveguide and free expansion of a spherical plasma ball in vacuum. The ECsim-CYL retains the stability properties of ECsim and conserves the energy within machine precision, while accurately describing the plasma behavior in the test cases.

Performance analysis and implementation details of the Energy Conserving Semi-Implicit Method code (ECsim)

We present in this work the implementation of the Energy Conserving Semi-Implicit Method in a parallel code called ECsim. This new code is a three-dimensional, fully electromagnetic particle in cell (PIC) code. It is written in C/C++ and uses MPI to allow massive parallelization. ECsim is unconditionally stable in time, eliminates the finite grid instability, has the same cycle scheme as the explicit code with a computational cost comparable to other semi-implicit PIC codes. All this features make it a very valuable tool to address situations which have not been possible to analyze until now with other PIC codes. In this work, we show the details of the algorithm implementation and we study its performance in different systems. ECsim is compared with another semi-implicit PIC code with different time and spectral resolution, showing its sability to address situations where other codes fail.

Multiple scale kinetic simulations with the energy conserving semi implicit particle in cell (PIC) method

The recently developed energy conserving semi-implicit method (ECsim) for PIC simulation is applied to multiple scale problems where the electron-scale physics needs to be only partially retained and the interest is on the macroscopic or ion-scale processes. Unlike hybrid methods, the ECsim is capable of providing kinetic electron information, such as wave-electron interaction (Landau damping or cyclotron resonance) and non-Maxwellian electron velocity distributions. However, like hybrid, the ECsim does not need to resolve all electron scales, allowing time steps and grid spacing orders of magnitude larger than in explicit PIC schemes. The additional advantage of the ECsim is that the stability at large scale is obtained while conserving energy exactly. Three examples are presented: ion acoustic waves, electron acoustic instability and reconnection processes.