Three-dimensional first principles simulation of a hydrogen discharge

Abstract

Townsend discharge theory is commonly used to describe and approximate the ionisation fraction growth rate in the very early phase of plasma initiation in tokamak devices via ohmic breakdown. The prediction of the ionisation fraction growth rate is done most commonly with continuum or kinetic models, which in turn boil down to the relation between the first Townsend's coefficient α, pressure p and electric field strength E (namely, α/p and E/p). To date there are few computational models that attempt to simulate the ionisation fraction growth rate via explicit modelling of each ionisation event through electron-neutral collisions. This is largely due to the challenge of addressing the exponential growth of charged particles from ionisation processes, combined with the high computational cost of N-body simulation. In this work, a new fully three-dimensional, first-principles model of a Townsend hydrogen discharge is demonstrated and benchmarked against prior experimental findings. These tests also include comparisons of three separate models for the scattering angle and their impact on the obtained α/p and mean electron drift velocity. It is found that isotropic scattering combined with restricting the freed electron's scattering angle along the incident electron's velocity vector during ionisation events gives the closest agreement of α/p compared to experimental measurements.

A tutorial overview of the angular scattering models of electron–neutral, ion–neutral, neutral–neutral, and Coulomb collisions in Monte Carlo collision modeling on low-temperature plasma

“…The second reason is the lack of analytically simpleto-use models of DCS, through which scattering angles can be randomly sampled by easy inversion instead of the timeconsuming accept-reject method. During the last two decades, different angular scattering models have been compared in various scenarios, such as electron transport study, ionization source terms in glow discharge, thermal runaway electrons in streamer discharge, and interstellar neutral atoms in the outer heliosheath [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. It was found that the angular scattering model is a non-trivial topic.…”

Simulation of the statistical and formative time delay of Townsend‐mechanism‐governed breakdown in argon at low pressure

“…Electric breakdown of gases, in general, has been widely studied in the literature. [14][15][16][17][18][19][20][21][22][23][24] For instance, the Monte Carlo method of electron transport has been used to determine the breakdown criterion for the low-pressure Townsend breakdown in helium and investigate electron bursts under the homogeneous electric field. [14] The radio-frequency breakdown in low-pressure argon has been studied in Reference [15], while low-pressure Townsend discharge in hydrogen has been modelled in Reference [16].…”

“…[14][15][16][17][18][19][20][21][22][23][24] For instance, the Monte Carlo method of electron transport has been used to determine the breakdown criterion for the low-pressure Townsend breakdown in helium and investigate electron bursts under the homogeneous electric field. [14] The radio-frequency breakdown in low-pressure argon has been studied in Reference [15], while low-pressure Townsend discharge in hydrogen has been modelled in Reference [16]. Besides low pressure, particle models have also been used for modelling an atmospheric-pressure streamer breakdown in References [17][18][19].…”

Simulation study of the influences of beryllium on the tokamak start-up process

“…Chew's work presented a three-dimensional simulation of a hydrogen discharge to expand to the tokamak ohmic breakdown (Chew et al. 2021) and compared different scatter models for electron–neural collisions.…”