Kinetic modelling of runaway electron avalanches in tokamak plasmas

Abstract

Runaway electrons can be generated in tokamak plasmas if the accelerating force from the toroidal electric field exceeds the collisional drag force owing to Coulomb collisions with the background plasma. In ITER, disruptions are expected to generate runaway electrons mainly through knock-on collisions [1], where enough momentum can be transferred from existing runaways to slow electrons to transport the latter beyond a critical momentum, setting off an avalanche of runaway electrons. Since knock-on runaways are usually scattered off with a significant perpendicular component of the momentum with respect to the local magnetic field direction, these particles are highly magnetized. Consequently, the momentum dynamics require a full 3-D kinetic description, since these electrons are highly sensitive to the magnetic non-uniformity of a toroidal configuration. For this purpose, a bounce-averaged knockon source term is derived. The generation of runaway electrons from the combined effect of Dreicer mechanism and knock-on collision process is studied with the code LUKE, a solver of the 3-D linearized bounce-averaged relativistic electron Fokker-Planck equation [2], through the calculation of the response of the electron distribution function to a constant parallel electric field. The model, which has been successfully benchmarked against the standard Dreicer runaway theory now describes the runaway generation by knock-on collisions as proposed by Rosenbluth [3]. This paper shows that the avalanche effect can be important even in non-disruptive scenarios. Runaway formation through knock-on collisions is found to be strongly reduced when taking place off the magnetic axis, since trapped electrons can not contribute to the runaway electron population. Finally, the relative importance of the avalanche mechanism is investigated as a function of the key parameters for runaway electron formation, namely the plasma temperature and the electric field strength. In agreement with theoretical predictions, the LUKE simulations show that in low temperature and electric field the knock-on collisions becomes the dominant source of runaway electrons and can play a significant role for runaway electron generation, including in non-disruptive tokamak scenarios.

On the relativistic large-angle electron collision operator for runaway avalanches in plasmas

“…For the Rosenbluth-Putvinski operator, this behavior was also observed by Nilsson et al (2015). When the test-particle operator is added, but the Coulomb logarithm ln Λ is left unmodified, the growth rate is decreased.…”

“…In the non-relativistic limit, p m e c, secondaries are born at perpendicular angles, p ∼ 0, and are prone to trapping in an inhomogeneous magnetic field. Away from the magnetic axis of a tokamak, this can lead to a strong reduction in the avalanche growth rate, as recently shown by Nilsson et al (2015). A more general model was later described by Chiu et al (1998) (from now on referred to as the Chiu-Harvey operator), which has also been used in runaway studies (Chiu et al 1998;Harvey et al 2000;Stahl et al 2016).…”

Physics of runaway electrons in tokamaks

“…A more recent work [102] reports a much stronger reduction with a numerical factor 1.2 rather than 0.5, but it does not offer any comments on such disagreement with the previous results. Incidentally, Ref.…”

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

“…For the remainder of this work, we therefore neglect the effect of radiation reaction on the Dreicer generation rate. We also disregard the effect of toroidicity, which may have an appreciable effect on Dreicer generation off the magnetic axis: if the bounce time is much shorter than the detrapping time, the generation rate is reduced due to magnetic trapping (Nilsson et al 2015). Conversely, at high densities and electric fields E E c , which can be present during tokamak disruptions, the Dreicer generation is approximately local (as in this work), but will be spatially non-uniform since the induced electric field decreases in magnitude with major radius (McDevitt & Tang 2019).…”