Runaway-electron model development and validation in tokamaks

Magnetic confinement fusion (MCF), in which a hot plasma at more than 100 million kelvin is confined using magnetic fields, is the most successful fusion energy concept developed to date. After decades of research, MCF devices designed to demonstrate a positive net energy output are being constructed, completing a crucial milestone on the path to making fusion a commercially viable energy source. Several hurdles remain on this path, however, and one of the most pressing issues concerns the sudden and rapid loss of confinement of the fusion plasma, known as a disruption. An undesirable consequence of disruptions is the acceleration of a fraction of the plasma electrons to relativistic energies which---if the electrons were to strike the device wall---could deposit a significant portion of the plasma energy on a small area, causing severe and potentially irreparable damage.The aim of this thesis is to develop a robust simulation tool capable of accurately predicting the number of runaway electrons produced in different disruption scenarios. Since the evolution of the runaway electrons affects the background plasma, it is important to also allow quantities such as electron temperature, ion density, and electric field to evolve self-consistently in the simulation. This leads to a tightly coupled system of non-linear equations, and to solve it we have developed the numerical tool DREAM.The complexity of the models used to simulate runaway electrons demands that the validity of the models is carefully evaluated by comparing predictions with existing experimental data. One of the most informative techniques for studying the dynamics of runaway electrons in MCF experiments utilises synchrotron radiation, and to facilitate direct comparison of runaway electron simulations with experiments we have developed the synthetic diagnostic framework SOFT. Using SOFT, we study runaway electrons in the ASDEX Upgrade and TCV fusion devices, and develop powerful techniques for\ua0 accurately extracting information about the location and momentum of runaway electrons

Dynamics of positrons during relativistic electron runaway

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

Runaway dynamics in tokamak disruptions with current relaxation

The safe operation of tokamak reactors requires a reliable modelling capability of disruptions, and in particular the spatio-temporal dynamics of associated runaway electron currents. In a disruption, instabilities can break up magnetic surfaces into chaotic field line regions, causing current profile relaxation, as well as a rapid radial transport of heat and particles. Using a mean-field helicity transport model implemented in the disruption runaway modelling framework Dream, we calculate the dynamics of runaway electrons in the presence of current relaxation events. In scenarios where flux surfaces remain intact in parts of the plasma, a skin current is induced at the boundary of the intact magnetic field region. This skin current region becomes an important centre concerning the subsequent dynamics: it may turn into a hot ohmic current channel, or a sizeable radially localized runaway beam, depending on the heat transport. If the intact region is in the plasma edge, runaway generation in the countercurrent direction can occur, which may develop into a sizeable reverse runaway beam. Even when the current relaxation extends to the entire plasma, the final runaway current density profile can be significantly affected, as the induced electric field is reduced in the core and increased in the edge, thereby shifting the centre of runaway generation towards the edge

Simulation and analysis of radiation from runaway electrons

Electron runaway constitutes one of the primary threats to future tokamak fusion reactors such as ITER. Successful prevention and mitigation of runaways relies on the development of theoretical models which accurately describe the dynamics of runaway electrons, and these models must in turn be validated in experiments. Experimental validation of models is however often made difficult by the fact that the diagnostic signals obtained in experiments only depend indirectly on the particle dynamics. In this thesis, a synthetic diagnostic model is presented which has been implemented in the Synchrotron-detecting Orbit Following Toolkit (SOFT), and which bridges this divide between theory and experiment. The synthetic diagnostic calculates the bremsstrahlung and synchrotron radiation diagnostic signals corresponding to a given runaway electron population, which can be directly compared to camera images and radiation spectra obtained in experiments. Bremsstrahlung and synchrotron radiation from runaway electrons are particularly sensitive to the runaway dynamics and, as is shown in this thesis, they provide insight into the runaway electron distribution function.This thesis focuses on geometric effects observed in the detected radiation when magnetic field inhomogeneities and detector properties aretaken into account, something which previous studies have neglected. The dependence of the observed radiation on magnetic field geometry, detector properties and runaway parameters is characterised, and it is explained how geometric effects limit the otherwise monotonic growth of the diagnostic response function with the runaway pitch angle. The synthetic diagnostic model is applied to experiments in the Alcator C-Mod and the DIII-D tokamaks and is used to validate kinetic theory predictions of the electron distribution function. It is found that the kinetic model agrees well in certain scenarios and fails in others. In the scenarios where it fails, the synthetic diagnostic model suggests that a mechanism causing a larger spread in pitch angle may be missing from the kinetic model

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.Comment: 24 pages, 12 figure

The hot-tail runaway seed landscape during the thermal quench in tokamaks

Runaway electron populations seeded from the hot-tail generated by the rapid cooling in plasma-terminating disruptions are a serious concern for next-step tokamak devices such as ITER. Here, we present a comprehensive treatment of the thermal quench, including the superthermal electron dynamics, heat and particle transport, atomic physics, and radial losses due to magnetic perturbations: processes that are strongly linked and essential for the evaluation of the runaway seed in disruptions mitigated by material injection. We identify limits on the injected impurity density and magnetic perturbation level for which the runaway seed current is acceptable without excessive thermal energy being lost to the wall via particle impact. The consistent modelling of generation and losses shows that runaway beams tend to form near the edge of the plasma, where they could be deconfined via external perturbations.Comment: 6 pages, 3 figure

Angiotensin converting enzyme intron 16 insertion/deletion genotype is associated with plasma C-reactive protein concentration in uteroplacental dysfunction

Introduction: Disturbance of the uteroplacental circulation (UPC) and the renin-angiotensin system are involved in the pathogenesis of preeclampsia. In women with history of preeclampsia persistently elevated C-reactive protein (CRP) levels have been described. The angiotensin-converting enzyme (ACE) intron 16 insertion/deletion (I/D) genotype is associated with ACE activity and assumed to be a risk factor for preeclampsia. As ACE generates proinflammatory angiotensin II, we analysed, whether ACE intron 16 I/D genotype is associated with CRP and whether this association exhibited a relation to uteroplacental dysfunction. Materials and methods: A total of 639 women have been followed during pregnancy with repeated measurements of CRP levels (observations: n=2333). ACE intron 16 I/D genotype was determined, and its association with CRP was assessed with adjustment for non-independent observations. Results: CRP levels of ACE D allele carriers were significantly higher than those of the ACE II (wild-type) genotype (p=0.0003, p adj=0.04). This relation was allele-dose dependent (p<10−4, p adj<0.02). Association between ACE I/D and CRP was significantly restricted to patients presenting with impaired UPC in univariate (p<0.04) and multivariate analyses (p=0.01). Conclusions: The ACE I/D genotype is significantly associated with CRP elevations during pregnancies complicated by disturbed UPC. Whether this effect on CRP is involved in pathogenesis of preeclampsia has to be elucidated

Runaway electron generation during tokamak start-up

Tokamak start-up is characterized by low electron densities and strong electric fields, in order to quickly raise the plasma current and temperature, allowing the plasma to fully ionize and magnetic flux surfaces to form. Such conditions are ideal for the formation of superthermal electrons, which may reduce the efficiency of ohmic heating and prevent the formation of a healthy thermal fusion plasma. This is of particular concern in ITER where engineering limitations put restrictions on the allowable electric fields and limit the prefill densities during start-up. In this study, we present a new 0D burn-through simulation tool called STREAM (STart-up Runaway Electron Analysis Model), which self-consistently evolves the plasma density, temperature and electric field, while accounting for the generation and loss of relativistic runaway electrons. After verifying the burn-through model, we investigate conditions under which runaway electrons can form during tokamak start-up as well as their effects on the plasma initiation. We find that Dreicer generation plays a crucial role in determining whether a discharge becomes runaway-dominated or not, and that a large number of runaway electrons could limit the ohmic heating of the plasma, thus preventing successful burn-through or further ramp-up of the plasma current. The runaway generation can be suppressed by raising the density via gas fuelling, but only if done sufficiently early. Otherwise a large runaway seed may have already been built up, which can avalanche even at relatively low electric fields and high densities

Effect of two-stage shattered pellet injection on tokamak disruptions

An effective disruption mitigation system in a tokamak reactor should limit the exposure of the wall to localized heat losses and to the impact of high current runaway electron beams, and avoid excessive forces on the structure. We evaluate with respect to these aspects a two-stage deuterium-neon shattered pellet injection in an ITER-like plasma, using simulations with the DREAM framework (Hoppe et al 2021 Comput. Phys. Commun. 268 108098). To minimize the obtained runaway currents an optimal range of injected deuterium quantities is found. This range is sensitive to the opacity of the plasma to Lyman radiation, which affects the ionization degree of deuterium, and thus avalanche runaway generation. The two-stage injection scheme, where dilution cooling is produced by deuterium before a radiative thermal quench caused by neon, reduces both the hot-tail seed and the localized transported heat load on the wall. However, during nuclear operation, additional runaway seed sources from the activated wall and tritium make it difficult to reach tolerably low runaway currents