Enhancing higher-energy spectral resolution for electron particle simulations in air

Abstract

In the presence of an electric field, electrons would theoretically accelerate asymptotically to relativistic energies. However, regular collisions with air molecules limit the increase in electron energy. The stochastic nature of collisions leaves a theoretical probability that an electron elude inelastic collisions thereby accumulating an atypically high energy. Such an electron, under specific criteria, could be called a “thermal” or “cold runaway”. Depending on the electric field, the runaway probability might be too low to be computationally observed without resorting to Monte Carlo importance sampling. This article provides a method for fixing the spectral energy resolution of electrons through the combined methodology of Russian roulette and probabilistic splitting in order to render the study of runaway mechanism amenable to electron swarm simulations in various plasma physics applications. Program summaryProgram title: particle-energy-compaction.pyCPC Library link to program files:https://doi.org/10.17632/k2y2r73t69.1Developer's repository link:https://osf.io/c6wyhLicensing provisions: CC By 4.0Programming language: Python 3Nature of problem: Currently, electron thermal runaway simulations in electric discharges cannot properly resolve the electron energy-spectrum tail. Most codes apply a super-particle restriction algorithm without efficiently or systematically allocating more space for scarcer electrons located at higher-energies. This results in a poor estimation of the thermal runaway rates at electric fields below the critical runaway threshold.Solution method: We provide a methodology based on the Monte-Carlo variance reduction techniques of Russian roulette and splitting, to allocate particles in different energy domains according to a given target super-particle energy density function. The algorithm converts an input set of super-particle energies and weights into another set that matches the desired spectral resolution. To avoid a sudden surge of super-particles in a low-populated spectral region, the algorithm takes also as input a minimum super-particle weight threshold relative to the physical number of particles in the simulation.Additional comments including restrictions and unusual features: A good knowledge of the problem is required in order to design the target spectrum function. An inappropriate selection of the target spectrum can result in a decrease of spectral resolution or also a severe deterioration of the swarm properties due to large stochastic fluctuations. It is recommended that the users first devise the target spectrum based on the physical spectrum obtained from their simulations, and start designing from there.