Ola Embréus

Effect of Partially Screened Nuclei on Fast-electron Dynamics

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 subrelativistic 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 fast-electron 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.

Numerical characterization of bump formation in the runaway electron tail

Runaway electrons are generated in a magnetized plasma when the parallel electric field exceeds a critical value. For such electrons with energies typically reaching tens of MeV, the Abraham–Lorentz–Dirac (ALD) radiation force, in reaction to the synchrotron emission, is significant and can be the dominant process limiting electron acceleration. The effect of the ALD force on runaway electron dynamics in a homogeneous plasma is investigated using the relativistic finite-difference Fokker–Planck codes LUKE (Decker and Peysson 2004 Report EUR-CEA-FC-1736, Euratom-CEA), and CODE (Landreman et al 2014 Comput. Phys. Commun. 185 847). The time evolution of the distribution function is analyzed as a function of the relevant parameters: parallel electric field, background magnetic field, and effective charge. Under the action of the ALD force, we find that runaway electrons are subject to an energy limit, and that the electron distribution evolves towards a steady-state. In addition, a bump is formed in the tail of the electron distribution function if the electric field is sufficiently strong. The mechanisms leading to the bump formation and energy limit involve both the parallel and perpendicular momentum dynamics; they are described in detail. An estimate for the bump location in momentum space is derived. We observe that the energy of runaway electrons in the bump increases with the electric field amplitude, while the population increases with the bulk electron temperature. The presence of the bump divides the electron distribution into a runaway beam and a bulk population. This mechanism may give rise to beam-plasma types of instabilities that could, in turn, pump energy from runaway electrons and alter their confinement.

The Gaussian radial basis function method for plasma kinetic theory

Description of a magnetized plasma involves the Vlasov equation supplemented with the non-linear Fokker–Planck collision operator. For non-Maxwellian distributions, the collision operator, however, is difficult to compute. In this Letter, we introduce Gaussian Radial Basis Functions (RBFs) to discretize the velocity space of the entire kinetic system, and give the corresponding analytical expressions for the Vlasov and collision operator. Outlining the general theory, we also highlight the connection to plasma fluid theories, and give 2D and 3D numerical solutions of the non-linear Fokker–Planck equation. Applications are anticipated in both astrophysical and laboratory plasmas.

SOFT: A synthetic synchrotron diagnostic for runaway electrons

Improved understanding of the dynamics of runaway electrons can be obtained by measurement and interpretation of their synchrotron radiation emission. Models for synchrotron radiation emitted by relativistic electrons are well established, but the question of how various geometric effects -- such as magnetic field inhomogeneity and camera placement -- influence the synchrotron measurements and their interpretation remains open. In this paper we address this issue by simulating synchrotron images and spectra using the new synthetic synchrotron diagnostic tool SOFT (Synchrotron-detecting Orbit Following Toolkit). We identify the key parameters influencing the synchrotron radiation spot and present scans in those parameters. Using a runaway electron distribution function obtained by Fokker-Planck simulations for parameters from an Alcator C-Mod discharge, we demonstrate that the corresponding synchrotron image is well-reproduced by SOFT simulations, and we explain how it can be understood in terms of the parameter scans. Geometric effects are shown to significantly influence the synchrotron spectrum, and we show that inherent inconsistencies in a simple emission model (i.e. not modeling detection) can lead to incorrect interpretation of the images.

Kinetic modelling of runaway electrons in dynamic scenarios

Improved understanding of runaway-electron formation and decay processes are of prime interest for the safe operation of large tokamaks, and the dynamics of the runaway electrons during dynamical scenarios such as disruptions are of particular concern. In this paper, we present kinetic modelling of scenarios with time-dependent plasma parameters; in particular, we investigate hot-tail runaway generation during a rapid drop in plasma temperature. With the goal of studying runaway-electron generation with a self-consistent electric-field evolution, we also discuss the implementation of a collision operator that conserves momentum and energy and demonstrate its properties. An operator for avalanche runaway-electron generation, which takes the energy dependence of the scattering cross section and the runaway distribution into account, is investigated. We show that the simplified avalanche model of Rosenbluth & Putvinskii [Nucl. Fusion 1997 37 1355] can give inaccurate results for the avalanche growth rate (either lower or higher) for many parameters, especially when the average runaway energy is modest, such as during the initial phase of the avalanche multiplication. The developments presented pave the way for improved modelling of runaway-electron dynamics during disruptions or other dynamic events.

Effect of bremsstrahlung radiation emission on fast electrons in plasmas

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. We find that electrons accelerated by electric fields can reach significantly higher energies than what is expected from energy-loss considerations. Furthermore, we show that the emission of soft photons can contribute significantly to the dynamics of electrons with an anisotropic distribution.

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

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.

Numerical calculation of ion runaway distributions

Ions accelerated by electric fields (so-called runaway ions) in plasmas may explain observations in solar flares and fusion experiments; however, limitations of previous analytic work have prevented definite conclusions. In this work, we describe a numerical solver of the 2D non-relativistic linearized Fokker-Planck equation for ions. It solves the initial value problem in velocity space with a spectral-Eulerian discretization scheme, allowing arbitrary plasma composition and time-varying electric fields and background plasma parameters. The numerical ion distribution function is then used to consider the conditions for runaway ion acceleration in solar flares and tokamak plasmas. Typical time scales and electric fields required for ion acceleration are determined for various plasma compositions, ion species, and temperatures, and the potential for excitation of toroidal Alfven eigenmodes during tokamak disruptions is considered.

Guiding-centre transformation of the radiation-reaction force in a non-uniform magnetic field

In this paper, we present the guiding-center transformation of the radiation-reaction force of a classical point charge traveling in a nonuniform magnetic field. The transformation is valid as long as the gyroradius of the charged particles is much smaller than the magnetic field nonuniformity length scale, so that the guiding-center 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 [A. J. Brizard, Phys. Plasmas 11 4429 (2004)], 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-center radiation-reaction force include tracing of charged particle orbits in complex magnetic fields as well as 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.

Effect of partially ionized impurities and radiation on the effective critical electric field for runaway generation

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.