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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.

The electron runaway phenomenon in plasmas depends sensitively on the momentum- space dynamics. However, efficient simulation of the global evolution of systems involving runaway electrons typically requires a reduced fluid description. This is needed, for example, in the design of essential runaway mitigation methods for tokamaks. In this paper, we present a method to include the effect of momentum-dependent spatial transport in the runaway avalanche growth rate. We quantify the reduction of the growth rate in the presence of electron diffusion in stochastic magnetic fields and show that the spatial transport can raise the effective critical electric field. Using a perturbative approach, we derive a set of equations that allows treatment of the effect of spatial transport on runaway dynamics in the presence of radial variation in plasma parameters. This is then used to demonstrate the effect of spatial transport in current quench simulations for ITER-like plasmas with massive material injection. We find that in scenarios with sufficiently slow current quench, owing to moderate impurity and deuterium injection, the presence of magnetic perturbations reduces the final runaway current considerably. Perturbations localised at the edge are not effective in suppressing the runaways, unless the runaway generation is off-axis, in which case they may lead to formation of strong current sheets at the interface of the confined and perturbed regions.

Large-angle Coulomb collisions lead to an avalanching generation of runaway electrons in a plasma. We present the first fully conservative large-angle collision operator, derived from the relativistic Boltzmann operator. The relation to previous models for large-angle collisions is investigated, and their validity assessed. We present a form of the generalized collision operator which is suitable for implementation in a numerical kinetic equation solver, and demonstrate the effect on the runaway-electron growth rate. Finally we consider the reverse avalanche effect, where runaways are slowed down by large-angle collisions, and show that the choice of operator is important if the electric field is close to the avalanche threshold.

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, 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.

Plasma terminating disruptions in tokamaks may result in relativistic runaway electron beams with potentially serious consequences for future devices with large plasma currents. In this paper, we investigate the effect of plasma elongation on the coupled dynamics of runaway generation and resistive diffusion of the electric field. We find that elongated plasmas are less likely to produce large runaway currents, partly due to the lower induced electric fields associated with larger plasmas, and partly due to direct shaping effects, which mainly lead to a reduction in the runaway avalanche gain.

Synchrotron radiation images from runaway electrons (REs) in an ASDEX Upgrade discharge disrupted by argon injection are analysed using the synchrotron diagnostic tool Soft and coupled fluid-kinetic simulations. We show that the evolution of the runaway distribution is well described by an initial hot-tail seed population, which is accelerated to energies between 25–50 MeV during the current quench, together with an avalanche runaway tail which has an exponentially decreasing energy spectrum. We find that, although the avalanche component carries the vast majority of the current, it is the high-energy seed remnant that dominates synchrotron emission. With insights from the fluid-kinetic simulations, an analytic model for the evolution of the runaway seed component is developed and used to reconstruct the radial density profile of the RE beam. The analysis shows that the observed change of the synchrotron pattern from circular to crescent shape is caused by a rapid redistribution of the radial profile of the runaway density.

Massive material injection has been proposed as a way to mitigate the formation of a beam of relativistic runaway electrons that may result from a disruption in tokamak plasmas. In this paper we analyse runaway generation observed in eleven ASDEX Upgrade discharges where disruption was triggered using massive gas injection. We present numerical simulations in scenarios characteristic of on-axis plasma conditions, constrained by experimental observations, using a description of the runaway dynamics with a self-consistent electric field and temperature evolution in two-dimensional momentum space and zero-dimensional real space. We describe the evolution of the electron distribution function during the disruption, and show that the runaway seed generation is dominated by hot-tail in all of the simulated discharges. We reproduce the observed dependence of the current dissipation rate on the amount of injected argon during the runaway plateau phase. Our simulations also indicate that above a threshold amount of injected argon, the current density after the current quench depends strongly on the argon densities. This trend is not observed in the experiments, which suggests that effects not captured by zero-dimensional kinetic modelling – such as runaway seed transport – are also important.

Bremsstrahlung radiation emission is an important energy loss mechanism for energetic electrons in plasmas. In this paper we investigate the effect of spontaneous bremsstrahlung emission on the momentum−space structure of the electron distribution, fully accounting for the emission of finite−energy photons by modeling the bremsstrahlung interactions with a Boltzmann collision operator. We find that electrons accelerated by electric fields can reach significantly higher energies than predicted by the commonly used radiative stopping−power model. Furthermore, we show that the emission of soft photons can contribute significantly to the dynamics of electrons with an anisotropic distribution by causing pitch−angle scattering at a rate that increases with energy.

In this paper, we present the guiding-centre transformation of the radiation–reaction force of a classical point charge travelling in a non-uniform magnetic field. The transformation is valid as long as the gyroradius of the charged particles is much smaller than the magnetic field non-uniformity length scale, so that the guiding-centre Lie-transform method is applicable. Elimination of the gyromotion time scale from the radiation–reaction force is obtained with the Poisson-bracket formalism originally introduced by Brizard (Phys. Plasmas, vol. 11, 2004, 4429–4438), where it was used to eliminate the fast gyromotion from the Fokker–Planck collision operator. The formalism presented here is applicable to the motion of charged particles in planetary magnetic fields as well as in magnetic confinement fusion plasmas, where the corresponding so-called synchrotron radiation can be detected. Applications of the guiding-centre radiation–reaction force include tracing of charged particle orbits in complex magnetic fields as well as the kinetic description of plasma when the loss of energy and momentum due to radiation plays an important role, e.g. for runaway-electron dynamics in tokamaks.

Sufficiently strong electric fields in plasmas can accelerate charged particles to relativistic energies. In this paper we describe the dynamics of positrons accelerated in such electric fields, and calculate the fraction of created positrons that become runaway accelerated, along with the amount of radiation that they emit. We derive an analytical formula that shows the relative importance of the different positron production processes, and show that, above a certain threshold electric field, the pair production by photons is lower than that by collisions. We furthermore present analytical and numerical solutions to the positron kinetic equation; these are applied to calculate the fraction of positrons that become accelerated or thermalized, which enters into rate equations that describe the evolution of the density of the slow and fast positron populations. Finally, to indicate operational parameters required for positron detection during runaway in tokamak discharges, we give expressions for the parameter dependencies of detected annihilation radiation compared to bremsstrahlung detected at an angle perpendicular to the direction of runaway acceleration. Using the full leading-order pair-production cross-section, we demonstrate that previous related work has overestimated the collisional pair production by at least a factor of four.