Kinetic modelling of runaways in plasmas

The phenomenon of runaway occurs in plasmas in the presence of a strong electric field, when the accelerating force overcomes the collisional friction acting on the charged particles moving through the plasma. Electron runaway is observed in both laboratory and space plasmas, and is of great importance in fusion-energy research, where the energetic electrons can damage the plasma-facing components of fusion reactors.In this thesis, we present a series of papers which investigate various aspects of runaway dynamics. We advance the kinetic description of electron runaway by deriving and analyzing a fully conservative large-angle collision operator suitable for studying runaway dynamics, and explore its impact on runaway generation and decay. We also present a generalization of the Landau-Fokker-Planck equation to describe screening effects in partially ionized plasmas, providing improved capability of modelling the effect of runaway mitigation schemes in fusion devices.The emission of synchrotron and bremsstrahlung radiation are important energy-loss mechanisms for relativistic runaway electrons, and they also provide essential diagnostic tools. We demonstrate the need for a stochastic description in order to accurately describe the effect of bremsstrahlung radiation losses on the electron motion. Synchrotron radiation is often emitted at visible and infrared wavelengths in tokamaks, allowing the emission to be readily observed. We have developed a synthetic synchrotron diagnostic tool, SOFT, which provides new insight into how features of the runaway distribution can affect the observed emission patterns.Finally, we have investigated the runaway dynamics of ions and of positrons which are generated during runaway. The runaway description in these cases differs from regular electron runaway due to the high mass of the ions, and the fact that positrons are created with a large momentum antiparallel to their direction of acceleration

Effects of magnetic perturbations and radiation on the runaway avalanche

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

Modelling of runaway electron dynamics during argon-induced disruptions in ASDEX Upgrade and JET

Disruptions in tokamak plasmas may lead to the generation of runaway electrons that have the potential to damage plasma-facing components. Improved understanding of the runaway generation process requires interpretative modelling of experiments. In this work we simulate eight discharges in the ASDEX Upgrade and JET tokamaks, where argon gas was injected to trigger the disruption. We use a fluid modelling framework with the capability to model the generation of runaway electrons through the hot-tail, Dreicer and avalanche mechanisms, as well as runaway electron losses. Using experimentally based initial values of plasma current and electron temperature and density, we can reproduce the plasma current evolution using realistic assumptions about temperature evolution and assimilation of the injected argon in the plasma. The assumptions and results are similar for the modelled discharges in ASDEX Upgrade and JET. For the modelled discharges in ASDEX Upgrade, where the initial temperature was comparatively high, we had to assume that a large fraction of the hot-tail runaway electrons were lost in order to reproduce the measured current evolution

Effect of plasma elongation on current dynamics during tokamak disruptions

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. \ua9 Cambridge University Press 2020

Estimate of pre-thermal quench non-thermal electron density profile during Ar pellet shutdowns of low-density target plasmas in DIII-D

The radial density profile of pre-thermal quench (pre-TQ) early-time non-thermal (hot) electrons is estimated by combining electron cyclotron emission and soft x-ray data during the rapid shutdown of low-density (ne≲1019m−3) DIII-D target plasmas with cryogenic argon pellet injection. This technique is mostly limited in these experiments to the pre-TQ phase and quickly loses validity during the TQ. Two different cases are studied: a high (10 keV) temperature target and a low (4 keV) temperature target. The results indicate that early-time, low-energy (∼10 keV) hot electrons form ahead of the argon pellet as it enters the plasma, affecting the pellet ablation rate; it is hypothesized that this may be caused by rapid cross field transport of argon ions ahead of the pellet or by rapid cross field transport of hot electrons. Fokker-Planck modeling of the two shots suggests that the hot electron current is quite significant during the pre-TQ phase (up to 50% of the total current). Comparison between modeled pre-TQ hot electron current and post-TQ hot electron current inferred from avalanche theory suggests that hot electron current increases during the high-temperature target TQ but decreases during the low-temperature target TQ. The uncertainties in this estimate are large; however, if true, this suggests that TQ radial loss of hot electron current could be larger than previously estimated in DIII-D

Kinetic modelling of runaway in plasmas

The phenomenon of runaway occurs in plasmas in the presence of a strong electric field, which overcomes the collisional friction acting on the charged particles moving through the plasma. A subpopulation of particles can then be accelerated to energies significantly higher than the thermal energy. Such events are observed in both laboratory and space plasmas, and are of great importance in fusion-energy research, where highly energetic runaway electrons can damage the plasma-facing components of the reactor.In this thesis, a series of papers are presented which investigate various aspects of runaway dynamics. The emission of synchrotron and bremsstrahlung radiation are important energy-loss mechanisms for relativistic runaway electrons. Photons emitted in bremsstrahlung radiation often have energy comparable to the energetic electrons, and we therefore use a Boltzmann transport equation in order to describe their effect on the electron motion. This treatment reveals that electrons can reach significantly higher energies than previously thought. In comparison, synchrotron radiation has lower frequency, and is well described by the classical electromagnetic radiation-reaction force. This loss mechanism, often dominant in laboratory plasmas, significantly alters the electron dynamics, and is found to produce non-monotonic features in the runaway tail.A study is also presented of the related phenomenon of ion runaway acceleration, which differs from electron runaway due to their larger mass. Renewed interest in this topic has been sparked after recent observations of fast ions in various experiments. Finally a new method is explored to treat the non-linear Fokker-Planck equation which is commonly used to describe the collisional dynamics in a plasma. The new method is appealing for its physically intuitive description and analytic simplicity

Kinetic modelling of runaway in plasmas

The phenomenon of runaway occurs in plasmas in the presence of a strong electric field, which overcomes the collisional friction acting on the charged particles moving through the plasma. A subpopulation of particles can then be accelerated to energies significantly higher than the thermal energy. Such events are observed in both laboratory and space plasmas, and are of great importance in fusion-energy research, where highly energetic runaway electrons can damage the plasma-facing components of the reactor.In this thesis, a series of papers are presented which investigate various aspects of runaway dynamics. The emission of synchrotron and bremsstrahlung radiation are important energy-loss mechanisms for relativistic runaway electrons. Photons emitted in bremsstrahlung radiation often have energy comparable to the energetic electrons, and we therefore use a Boltzmann transport equation in order to describe their effect on the electron motion. This treatment reveals that electrons can reach significantly higher energies than previously thought. In comparison, synchrotron radiation has lower frequency, and is well described by the classical electromagnetic radiation-reaction force. This loss mechanism, often dominant in laboratory plasmas, significantly alters the electron dynamics, and is found to produce non-monotonic features in the runaway tail.A study is also presented of the related phenomenon of ion runaway acceleration, which differs from electron runaway due to their larger mass. Renewed interest in this topic has been sparked after recent observations of fast ions in various experiments. Finally a new method is explored to treat the non-linear Fokker-Planck equation which is commonly used to describe the collisional dynamics in a plasma. The new method is appealing for its physically intuitive description and analytic simplicity

Gaussian radial basis functions for plasma physics: Numerical aspects

A magnetized plasma is described by the Vlasov equation and the non-linear Fokker-Planck collision operator [1]. The Vlasov part describes phase-space advection and the collision operator adds dissipation due to collisional energy and momentum exchange. Numerical discretization of the collision operator, however, is far from trivial. Recently, we have developed a new approach [2] to address this issue. The new approach is based on an expansion in Gaussian Radial Basis Functions (RBFs), a method widely used in neural network calculations [3]. In this paper, we discusss useful details regarding the numerical implementation of the RBF method

Gaussian radial basis functions for plasma physics: Numerical aspects

A magnetized plasma is described by the Vlasov equation and the non-linear Fokker-Planck collision operator [1]. The Vlasov part describes phase-space advection and the collision operator adds dissipation due to collisional energy and momentum exchange. Numerical discretization of the collision operator, however, is far from trivial. Recently, we have developed a new approach [2] to address this issue. The new approach is based on an expansion in Gaussian Radial Basis Functions (RBFs), a method widely used in neural network calculations [3]. In this paper, we discusss useful details regarding the numerical implementation of the RBF method

Conservative large-angle collision operator for runaway avalanches

Avalanche runaway generation is the phenomenon whereby runaway electrons (REs) are generated due to large-angle collisions of thermal electrons with existing REs, leading to an exponential growth of the runaway current. These large-angle collisions are not described by the Fokker-Planck operator commonly employed to model collisions in plasmas, and have previously been accounted for by the addition of a particle source term in the kinetic equation [M. Rosenbluth et al., 1997, Nucl. Fusion 37, 1355; S. C. Chiu et al. 1998, Nucl. Fusion 38, 1711]. In this contribution we describe a new large-angle collision operator, derived as the high-energy limit of the linearized relativistic Boltzmann collision integral. This operator generalizes previous models of large-angle collisions to account for the full momentum dependence of the primary distribution and conserves particle number, momentum and energy, while also avoiding double counting of small- and large-angle collisions. The new operator is implemented in the 2D Fokker-Planck solver CODE [M. Landreman et al. 2014, Comp. Phys. Comm. 185, 847], with which we investigate its effect on the evolution of the runaway distribution