Generalized collision operator for fast electrons interacting with partially ionized impurities

Abstract

Accurate modelling of the interaction between fast electrons and partially ionized atoms is important for evaluating tokamak disruption mitigation schemes based on material injection. This requires accounting for the effect of screening of the impurity nuclei by the cloud of bound electrons. In this paper, we generalize the Fokker-Planck operator in a fully ionized plasma by accounting for the effect of screening. We detail the derivation of this generalized operator, and calculate the effective ion length-scales, which are needed in the components of the collision operator, for a number of ion species commonly appearing in fusion experiments. We show that for high electric fields, the secondary runaway growth rate can be substantially larger than in a fully ionized plasma with the same effective charge, although the growth rate is significantly reduced at near-critical electric fields. Furthermore, by comparison with the Boltzmann collision operator, we show that the Fokker-Planck formalism is accurate even for large impurity content. † Email address for correspondence: hesslow@chalmers.se

Evaluation of the Dreicer runaway generation rate in the presence of high- impurities using a neural network

“…The Fokker-Planck solver code includes several options for the collision operator. In this work we use the test-particle collision operator given by Braams & Karney (1989) and Pike & Rose (2014), with corrections for partial screening according to Hesslow et al (2018):…”

“…For example, I Ar + = 219.4 eV (Sauer et al 2015), at which temperature argon would already be multiply ionized in equilibrium. Moreover, in our model for partial screening, the enhancement of the slowing-down collision frequency starts to extend into the thermal population at such temperatures (Hesslow et al 2018), and the validity of the screening model starts to become questionable. Rather than using the full set of impurity ion densities as input to the neural network, we use six derived parameters:…”

Impact of a minority relativistic electron tail interacting with a thermal plasma containing high-atomic-number impurities

“…For each ion species in a specific charge state, which is denoted by subscript α, there is a unique mean excitation energy I α and bound electron density n eα . In fact, the standard treatment in runaway modeling is to incorporate the runaway slowing down due to excitation and ionization via a friction in the Fokker-Planck collision operator using the Bethe formula [20,21]. The effect of ion charge state distribution (CSD) on runaway and thermal bulk plasma evolu-tion is through a collisional-radiative (CR) model that deals with only the background Maxwellian population at given temperature.…”

“…The effect of ion charge state distribution (CSD) on runaway and thermal bulk plasma evolu-tion is through a collisional-radiative (CR) model that deals with only the background Maxwellian population at given temperature. In a dilute plasma such as those in tokamak disruption, the aforementioned decoupled treatment of background thermal electrons and runaways [20,21] has a straightforward prediction for the radiative power loss as the bulk electrons are cooled to below a few eV. Namely, the background electron density drops precipitously due to cold thermal electron recombination with ions.…”

“…where Q n is the screened charge [24]. Again using the same form as (4) for the total ionization ICS, we add a relativistic correction [13,34] on top of (7) following the form…”