Kinetic modelling of runaway electron generation in argon-induced disruptions in ASDEX Upgrade

Abstract

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.

Spatiotemporal analysis of the runaway distribution function from synchrotron images in an ASDEX Upgrade disruption

“…Furthermore, even though the temperature evolution affects the self-consistent electric field evolution during the CQ, the final runaway current is mainly sensitive to the time-integrated electric field, which is independent of temperature evolution. The post-disruption temperature is therefore taken to be T = 5 eV throughout the plasma, which is largely consistent with simulated values during the CQ of ASDEX Upgrade disruptions induced by argon gas injection (Insulander et al 2020). Although the temperature is expected to drop to a significantly lower value during the runaway plateau, it only weakly impacts the runaway dynamics and consequently we neglect this effect here.…”

“…The post-disruption temperature is therefore taken to be throughout the plasma, which is largely consistent with simulated values during the CQ of ASDEX Upgrade disruptions induced by argon gas injection (Insulander et al. 2020). Although the temperature is expected to drop to a significantly lower value during the runaway plateau, it only weakly impacts the runaway dynamics and consequently we neglect this effect here. We assume that neutral argon atoms with density (corresponding to 20 % of the injected atoms Pautasso et al.…”

“…Runaway electrons in ASDEX Upgrade disruptions, such as #35628, are typically generated through a combination of the hot-tail and avalanche mechanisms (Insulander et al. 2020). The avalanche exponentiation factor is robust and depends mainly on the change in the poloidal flux profile.…”

“…2020; Insulander et al. 2020) are uniformly distributed in radius at the beginning of the simulation, and neglect their radial transport throughout the simulation. The densities of the various ionization states, and the corresponding electron density, are calculated assuming an equilibrium between ionization and recombination; that is, are computed from where is the total density of species .…”

“…Although the temperature is expected to drop to a significantly lower value during the runaway plateau, it only weakly impacts the runaway dynamics and consequently we neglect this effect here. (iii) We assume that neutral argon atoms with density n Ar = 0.83 × 10 20 m −3 (corresponding to 20 % of the injected atoms Pautasso et al 2020;Insulander et al 2020) are uniformly distributed in radius at the beginning of the simulation, and neglect their radial transport throughout the simulation. The densities of the various ionization states, and the corresponding electron density, are calculated assuming an equilibrium between ionization and recombination; that is, n i k are computed from…”