A runaway avalanche can result in a conversion of the initial plasma current into a relativistic electron beam in high-current tokamak disruptions. We investigate the effect of massive material injection of deuterium–noble gas mixtures on the coupled dynamics of runaway generation, resistive diffusion of the electric field and temperature evolution during disruptions in the deuterium–tritium phase of ITER operations. We explore the dynamics over a wide range of injected concentrations and find substantial runaway currents, unless the current quench time is intolerably long. The reason is that the cooling associated with the injected material leads to high induced electric fields that, in combination with a significant recombination of hydrogen isotopes, leads to a large avalanche generation. Balancing Ohmic heating and radiation losses provides qualitative insights into the dynamics; however, an accurate modelling of the temperature evolution based on energy balance appears crucial for quantitative predictions.

We analyze the dynamics of fast electrons in plasmas containing partially ionized impurity atoms, where the screening effect of bound electrons must be included. We derive analytical expressions for the deflection and slowing-down frequencies, and show that they are increased significantly compared to the results obtained with complete screening, already at sub-relativistic electron energies. Furthermore, we show that the modifications to the deflection and slowing down frequencies are of equal importance in describing the runaway current evolution. Our results greatly affect fastelectron dynamics and have important implications, e.g. for the efficacy of mitigation strategies for runaway electrons in tokamak devices, and energy loss during relativistic breakdown in atmospheric discharges.Introduction.-Fast electrons, having speeds well above the thermal speed of the bulk plasma population, are ubiquitous in space and laboratory plasmas. An important process leading to such high-energy electrons is the runaway mechanism. Runaway electrons can be produced in the presence of an accelerating electric field if it exceeds the critical value E c = n e e 3 ln Λ 0 /4πǫ

In high-current tokamak devices such as ITER, a runaway avalanche can cause a large amplification of a seed electron population. We show that disruption mitigation by impurity injection may significantly increase the runaway avalanche growth rate in such devices. This effect originates from the increased number of target electrons available for the avalanche process in weakly ionized plasmas, which is only partially compensated by the increased friction force on fast electrons. We derive an expression for the avalanche growth rate in partially ionized plasmas and investigate the effects of impurity injection on the avalanche multiplication factor and on the final runaway current for ITERlike parameters. For impurity densities relevant for disruption mitigation, the maximum amplification of a runaway seed can be increased by tens of orders of magnitude compared to previous predictions. This motivates careful studies to determine the required densities and impurity species to obtain tolerable current quench parameters, as well as more detailed modeling of the runaway dynamics including transport effects.

We derive a formula for the effective critical electric field for runaway generation and decay that accounts for the presence of partially ionized impurities in combination with synchrotron and bremsstrahlung radiation losses. We show that the effective critical field is drastically larger than the classical Connor-Hastie field, and even exceeds the value obtained by replacing the free electron density by the total electron density (including both free and bound electrons). Using a kinetic equation solver with an inductive electric field, we show that the runaway current decay after an impurity injection is expected to be linear in time and proportional to the effective critical electric field in highly inductive tokamak devices. This is relevant for the efficacy of mitigation strategies for runaway electrons since it reduces the required amount of injected impurities to achieve a certain current decay rate.

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