Accelerated Steady-State Electrostatic Particle-in-Cell Simulation of Langmuir Probes

TL;DR

This paper introduces a scaled-mass PIC simulation method that significantly accelerates steady-state electrostatic plasma simulations by a factor of the square root of the mass ratio, enabling faster and more comprehensive Langmuir probe analysis.

Contribution

The paper presents a scaled-mass approach and its relation to numerical timestepping and SLPIC, extending efficient PIC simulations to include additional physical effects.

Findings

Simulation speed increased by two orders of magnitude.

Method accurately reproduces steady-state solutions with reduced computational cost.

Applicable to complex plasma phenomena including collisions and geometric effects.

Abstract

First-principles particle-in-cell (PIC) simulation is a powerful tool for understanding plasma behavior, but this power often comes at great computational expense. Artificially reducing the ion/electron mass ratio is a time-honored practice to reduce simulation costs. Usually, this is a severe approximation. However, for steady-state collisionless, electrostatic (Vlasov-Poisson) systems, the solution with reduced mass ratio can be scaled to the solution for the real mass ratio, with no approximation. This 'scaled mass' method, which works with already-existing PIC codes, can reduce the computation time for a large class of electrostatic PIC simulations by the square root of the mass ratio. The particle distributions of the resulting steady state must be trivially rescaled to yield the true distributions, but the self-consistent electrostatic field is independent of the mass ratio. This method is equivalent to 'numerical timestepping,' an approach that evolves electron and ion populations with different timesteps. Numerical timestepping can be viewed as a special case of the speed-limited PIC (SLPIC) method, which is not restricted to steady-state phenomena. Although the scaled-mass approach is simplest, numerical timestepping and SLPIC more easily generalize to include other effects, such as collisions. The equivalence of these new approaches is demonstrated by applying them to simulate a cylindrical Langmuir probe in electron-argon plasma, speeding up simulation by two orders of magnitude. Methods such as SLPIC can therefore play an invaluable role in interpreting probe measurements by including geometric effects, collisions, secondary emission, and non-Maxwellian distributions.