Development of a 1-D Electrostatic Particle-in-Cell Code

Abstract

In this article, a 1-D electrostatic particle-in-cell (PIC) code is developed in an object-oriented paradigm with a computationally improved Poisson Solver. The performance of a Poisson solver plays a vital role in the computational cost of an electrostatic PIC. Therefore, to reduce the overall cost of the system, the Gauss–Seidel with a modified Chebyshev acceleration scheme is implemented as a Poisson solver. This method is designed by altering the standard Chebyshev acceleration scheme and executed with the optimal spectral radius. A separate program is written to optimize the spectral radius and to investigate its impact on the rate of convergence. Subsequently, a comparative analysis of this solver with the Gauss–Seidel, Gauss–Seidel with successive over-relaxation, and Gauss–Seidel with the Chebyshev acceleration factor is carried out, which implies that the modified solver converges fast. This article also provides the object-oriented architecture, including some key features of C++. The developed code is benchmarked with the two-stream instability, which evolved self-consistently. The performance of the overall code is evaluated by considering up to two million particles on two different CPUs and it is observed that the standard CPU is capable to solve the 1-D PIC problem. This code is implemented to study various characteristics of a finite-size photoplasma like plasma sheath formation, ion phase response, and electron dynamics when it is subjected to a uniform electric field.