Accelerated steady-state electrostatic particle-in-cell simulation of Langmuir probes

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 time steps. 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.

Effects of trapped electrons on the sheath at the boundary of a dusty plasma

“…46,48) One of the basic assumptions is that plasma components obey the Maxwellian distribution, 49) while a significant population of particles may be trapped near the probe, which is non-ideal. 23) So, with the established sheath model, the present results can be helpful to extend the method of calculating parameters from raw probe data, which may lead to a more precise measurement with electric probes.…”

“…On the basis of an unmagnetized collisionless plasma, the simulation of a cylindrical Langmuir probe showed that, due to small fluctuations, a significant population of trapped ions appeared around the probe. 23) In the framework of particle-incell simulations applied to the Enceladus plume, Farrell et al demonstrated that there is a trend for low-energy ions to be adsorbed and trapped within the sheath of negatively charged dust grains. 24) Moreover, the presence of trapped particles is widely discussed in theory.…”

Dispersion and the Speed-Limited Particle-in-Cell Algorithm

“…Potential applications for the SLPIC method include its use in the modeling of plasma thrusters (wherein very small electron/ion mass ratios impose especially demanding numerical constraints) and sheath formation (e.g. near a Langmuir probe 12 ). Collisional lowtemperature plasma discharges are also an area of particular interest; recent efforts have demonstrated that SLPIC can be used in conjunction with standard Monte Carlo collision techniques, in the same manner as is done in collisional PIC discharge modeling (PIC-MCC) 13 .…”

Peculiarities of charged particle kinetics in spherical plasma

“…Second, the electron and ion mass disparity makes our explicit solvers very expensive during the transient process (when 𝑛𝑛 � 𝑒𝑒 ≠ 𝑛𝑛 � 𝑖𝑖 ) due to CFL limitations. This challenge can be resolved using an artificially small mass ratio, which does not substantially affect the steady solution [11]. The method is based on the fact that in steady-state collisionless electrostatic plasma, the solution with a reduced mass ratio can be scaled to the one for the actual mass ratio.…”

“…The method is based on the fact that in steady-state collisionless electrostatic plasma, the solution with a reduced mass ratio can be scaled to the one for the actual mass ratio. It has been successfully used for speed-limited particle-in-cell (SLPIC) simulations [11].…”