Benchmark for two-dimensional large scale coherent structures in partially magnetized ExB plasmas -- Community collaboration & lessons learned

TL;DR

The paper addresses verification of kinetic PIC simulations for low-temperature plasmas by benchmarking a 2D Penning discharge across 17 codes from 19 institutions, focusing on the emergence of rotating spokes and multiscale dynamics. It demonstrates strong cross-code agreement on spoke rotation frequency and key time-averaged diagnostics, while identifying sensitivities to averaging duration, vacuum-region statistics, and solver implementation. It provides actionable lessons for benchmark design and HPC practice, including decomposition strategies and the use of GPU acceleration, to improve future code development. The work lays groundwork for more complex benchmarks, collisional physics, and eventual experimental validation to enhance reliability in plasma simulation software.

Abstract

Low-temperature plasmas are essential to both fundamental scientific research and critical industrial applications. As in many areas of science, numerical simulations have become a vital tool for uncovering new physical phenomena and guiding technological development. Code benchmarking remains crucial for verifying implementations and evaluating performance. This work continues the Landmark benchmark initiative, a series specifically designed to support the verification of low-temperature plasma codes. In this study, seventeen simulation codes from a collaborative community of nineteen international institutions modeled a partially magnetized ExB Penning discharge. The emergence of large scale coherent structures, or rotating plasma spokes, endows this configuration with an enormous range of time scales, making it particularly challenging to simulate. The codes showed excellent agreement on the rotation frequency of the spoke as well as key plasma properties, including time-averaged ion density, plasma potential, and electron temperature profiles. Achieving this level of agreement came with challenges, and we share lessons learned on how to conduct future benchmarking campaigns. Comparing code implementations, computational hardware, and simulation runtimes also revealed interesting trends, which are summarized with the aim of guiding future plasma simulation software development.

Figures (9)

• Figure 1: Illustration of a typical Penning discharge experiment with a beamline source of energetic electrons emitted from the cathode. The outer cylindrical pressure vessel is grounded, with dielectric end-plates. The approximately uniform axial magnetic field (red arrows) is sustained by electromagnets. Dynamics between the magnetized electrons and weakly magnetized ions, which are produced at the center and diffuse outwards, produces a radial ambipolar electric field (blue arrows) in the opposite direction to that of a typical ambipolar field found in un-magnetized plasmas. This results in azimuthal E$\times$B drift (green arrow), with the streaming of electrons against slowly moving ions leading to formation of the rotating spoke.
• Figure 2: Schematic of the Penning discharge benchmark simulation domain, including geometry for the conducting boundaries (thick black lines), injection region (blue circle), and location of the density probe (green dot). The light gray circular boundary is not part of the simulation, but rather indicates the equivalent geometry for a Penning discharge experiment, similar to that shown in Fig. \ref{['fig:experiment']}.
• Figure 3: Plot of ion density at probe location $(x=\frac{1}{2}L_x,y=0)$ against time. Peaks (red dots) are identified via a peak-finding algorithm from the scipy.signal package 2020SciPy-NMeth.
• Figure 4: Contour plots of ion density at four different phases of spoke rotation after the system has reached quasi-steady state. Times are given relative to the left most figure.
• Figure 5: Comparison of time-averaged slices for long-time simulations: (a) ion-density, (b) plasma potential, and (c) electron temperature (Type I).