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.

Townsend 放电理论通常用于描述和近似通过欧姆击穿在托卡马克装置中等离子体引发的非常早期阶段的电离分数增长率。电离分数增长率的预测最常使用连续介质或动力学模型进行，这些模型又归结为第一个汤森系数α、压力p和电场强度E（即α / p和E / p）。迄今为止，很少有计算模型试图通过电子-中性碰撞对每个电离事件进行显式建模来模拟电离分数增长率。这主要是由于解决电离过程中带电粒子指数增长的挑战，以及N体模拟的高计算成本。在这项工作中，展示了一种新的全三维、第一性原理的汤森氢气排放模型，并与之前的实验结果进行了对比。这些测试还包括比较三个独立模型的散射角及其对获得的α / p 的影响和平均电子漂移速度。发现与实验测量相比，各向同性散射与在电离事件期间沿入射电子的速度矢量限制自由电子的散射角相结合给出了最接近的α / p一致性。