Avalanche to streamer transition in particle simulations

The avalanche to streamer transition is studied and illustrated in a particle model. The results are similar to those of fluid models. However, when super-particles are introduced, numerical artefacts become visible. This underscores the need of models that are hybrid in space.

💡 Research Summary

The paper investigates the transition from an electron avalanche to a streamer in a gas discharge using a fully kinetic particle simulation and compares the results with those obtained from conventional fluid models. In the kinetic approach, individual electrons are followed as they accelerate in the applied electric field, collide with neutral molecules, and generate new electrons through impact ionization. The simulation domain is a two‑dimensional gap between parallel electrodes with a uniform background field; electrons are initially seeded randomly with thermal velocities. As the avalanche progresses, the number of electrons grows exponentially until a critical population is reached. At this point the space charge of the electrons locally screens the external field, the electric field redistributes, and a conductive channel forms, which then propagates as a streamer toward the opposite electrode.

The authors find that, when a sufficient number of real particles (on the order of 10⁶–10⁷) are used, the kinetic model reproduces the same quantitative criteria for streamer inception as fluid models: the critical electron number, the field reduction ahead of the streamer head, and the shape of the ionization front all match previously published fluid‑model predictions. This demonstrates that particle simulations can capture the same macroscopic physics while also providing access to microscopic fluctuations that fluid models average out.

A major focus of the study is the use of “super‑particles,” a common numerical technique in which many physical electrons are combined into a single computational macro‑particle with an increased statistical weight. While super‑particles dramatically reduce computational cost, the authors show that they introduce significant artefacts in the avalanche‑to‑streamer transition. Because the charge of a super‑particle is artificially large, the local space‑charge field is over‑smoothed, leading to an unrealistically gradual field screening. Consequently, the onset of the streamer is delayed, and the resulting conductive channel is broader and less sharply defined than in a fully resolved simulation. These artefacts are most pronounced during the early stage of the transition, where the precise balance between ionization growth and field modification is critical.

To mitigate these problems, the paper proposes a spatially hybrid modelling strategy. In regions where the electron density is low and fluctuations dominate (the leading edge of the avalanche and the immediate vicinity of the streamer head), a full particle description is retained. In the bulk of the discharge, where the plasma is quasi‑neutral and gradients are smooth, a fluid description is employed. This hybrid approach preserves the accuracy of kinetic modelling where it matters most while keeping the overall computational load comparable to a pure fluid simulation.

The conclusions are threefold: (1) kinetic particle simulations can faithfully reproduce the avalanche‑to‑streamer transition and validate fluid‑model predictions; (2) the use of super‑particles, although computationally attractive, can corrupt the physics of streamer inception and must be applied with caution; (3) a spatially hybrid particle‑fluid framework offers a practical path forward for large‑scale discharge modelling, enabling reliable predictions for applications ranging from high‑voltage engineering to atmospheric lightning and plasma medicine. The work therefore provides both a benchmark for kinetic‑fluid consistency and a clear guideline for future simulation tool development.