Session NI3: Disruptions and Energetic Particles

The ins and outs of modelling vertical displacement events

Of the many reasons a plasma discharge disrupts, Vertical Displacement Events (VDEs) lead to the most severe forces and stresses on the vacuum vessel and Plasma Facing Components (PFCs). After loss of positional control, the plasma column drifts across the vacuum vessel and comes in contact with the first wall, at which point the stored magnetic and thermal energy is abruptly released. The vessel forces have been extensively modelled in 2D [1] but, with the constraint of axisymmetry, the fundamental 3D effects that lead to toroidal peaking, sideways forces, field-line stochastisation and halo current rotation have been vastly overlooked. In this work, we present the main results of an intense VDE modelling activity using the implicit 3D extended MHD code M3D­C1 and share our experience with the multi­domain and highly non­linear physics encountered. At the culmination of code development by the M3D­C1 group over the last decade, highlighted by the inclusion of a finite-thickness resistive vacuum vessel within the computational domain [2], a series of fully 3D non-linear simulations are performed using realistic transport coefficients based on the reconstruction of so­called NSTX frozen VDEs, where the feedback control was purposely switched off to trigger a vertical instability. The vertical drift phase, the evolution of the current quench and the onset of 3D halo/eddy currents are diagnosed and investigated in detail. The sensitivity of the current quench to parameter changes is assessed via 2D non­linear runs. The growth of individual toroidal modes is monitored via linear-complex runs. The intricate evolution of the plasma, which is decaying to large extent in force­ balance with induced halo/wall currents, is carefully resolved via 3D non­linear runs. The location, amplitude and rotation of normal currents and wall forces are analysed and compared with experimental traces. [1] Miyamoto, S., et al., Nuclear Fusion 54 (2014) 083002 [2] Ferraro, N., et al., Phys. Plasmas 23 (2016) 056114   

Spatio-Temporally Resolved Measurement of Runaway Electron Momentum Distributions during Controlled Dissipation

We report the first spatially, energetically, and temporally resolved reconstructions of runaway electron (RE) momentum distributions ($f_e$) in tokamaks and their dependence on plasma parameters [1]. These measurements provide unique validation for models of RE evolution and quantify the importance of collisional and synchrotron damping to controlled RE dissipation. Measurements are made with a tangentially viewing pinhole camera where each collimated sightline is equipped with a pulse-height counting hard X-ray (HXR) detector to infer $f_e$. REs are produced in well-diagnosed quiescent Ohmic plasmas, with synchrotron and collisional damping terms actuated by varying the toroidal field and thermal electron density. Comparing experimental and modeled $f_e$ evolution, nearly all qualitative trends are captured: 1) increasing synchrotron damping shifts $f_e$ towards lower energy, 2) increasing collisional damping decreases $f_e$ at all energies, 3) both develop non-monotonic $f_e$ features at consistent energy, 4) $f_e$ are more parallel-directed at high energy. The $f_e$ shape and location of non-monotonic features are thus generally in agreement with modeling as collisional and sychrotron damping terms are varied. Comparing dissipation rates, good agreement with modeling is found at high energy and experimental evidence for a predicted enhancement in the critical electric field for RE decay is shown. A notable disagreement between experiment and theory is found at low energy, where systematically stronger dissipation rates are observed than predicted. The agreement between theory and experiment improves confidence that model-based optimizion of RE mitigation can be achieved, while the identified discrepancies can guide improvements to RE dissipation models. [1] C. Paz-Soldan et al, {\it{Phys. Rev. Lett.}} {\bf{118}} 255002 (2017)   

Physics of the interaction between runaway electrons and the background plasma of the current quench in tokamak disruptions

Runaway electrons are created during disruptions of tokamak plasmas. They can be accelerated in the form of a multi-MA beam at energies up to several 10’s of MeV. Prevention or suppression of runaway electrons during disruptions will be essential to ensure a reliable operation of future tokamaks such as ITER. Recent experiments showed that the suppression of an already accelerated beam with massive gas injection was unsuccessful at JET, conversely to smaller tokamaks. This was attributed to a dense, cold background plasma (up to several $10^{20}$ m$^{-3}$ accompanying the runaway beam. The present contribution reports on the latest experimental results obtained at JET showing that some mitigation efficiency can be restored by changing the features of the background plasma. The density, temperature, position of the plasma and the energy of runaways were characterized using a combined analysis of interferometry, soft X-rays, bolometry, magnetics and hard X-rays. It showed that lower density background plasmas were obtained using smaller amounts of gas to trigger the disruption, leading to an improved penetration of the mitigation gas. Based on the observations, a physical model of the creation of the background plasma and its subsequent evolution is proposed. The plasma characteristics during later stages of the disruption are indeed dependent on the way it was initially created. The sustainment of the plasma during the runaway beam phase is then addressed by making a power balance between ohmic heating, power transfer from runaway electrons, radiation and atomic processes. Finally, a model of the interaction of the plasma with the mitigation gas is proposed to explain why massive gas injection of runaway beams works only in specific situations. This aims at pointing out which parameters bear the most importance if this mitigation scheme is to be used on larger devices like ITER. Acknowledgement: \textit{This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.}   

Full-orbit and backward Monte Carlo simulation of runaway electrons

High-energy relativistic runaway electrons (RE) can be produced during magnetic disruptions due to electric fields generated during the thermal and current quench of the plasma. Understanding this problem is key for the safe operation of ITER because, if not avoided or mitigated, RE can severely damage the plasma facing components. In this presentation we report on RE simulation efforts centered in two complementary approaches: (i) Full orbit (6-D phase space) relativistic numerical simulations in general (integrable or chaotic) 3-D magnetic and electric fields, including radiation damping and collisions, using the recently developed particle-based Kinetic Orbit Runaway electron Code (KORC) and (ii) Backward Monte-Carlo (MC) simulations based on a recently developed efficient backward stochastic differential equations (BSDE) solver. Following a description of the corresponding numerical methods, we present applications to: (i) RE synchrotron radiation (SR) emission using KORC and (ii) Computation of time-dependent runaway probability distributions, RE production rates, and expected slowing-down and runaway times using BSDE. We study the dependence of these statistical observables on the electric and magnetic field, and the ion effective charge. SR is a key energy dissipation mechanism in the high-energy regime, and it is also extensively used as an experimental diagnostic of RE. Using KORC we study full orbit effects on SR and discuss a recently developed SR synthetic diagnostic that incorporates the full angular dependence of SR, and the location and basic optics of the camera. It is shown that oversimplifying the angular dependence of SR and/or ignoring orbit effects can significantly modify the shape and overestimate the amplitude of the spectra. Applications to DIII-D RE experiments are discussed.   

Suppression of Alfv\'{e}nic modes through modification of the fast ion distribution

Experiments on NSTX-U have shown for the first time that small amounts of high pitch-angle, low $\rho_{L}$ beam ions can strongly suppress the counter-propagating Global Alfv\'{e}n Eigenmodes (GAE) [1]. GAE have been implicated in the redistribution of fast ions and modification of the electron power balance in previous experiments on NSTX. The ability to predict the stability of Alfv\'{e}n modes, and development of methods to control them, is important for fusion reactors like ITER, which like NSTX, will be heated with a large population of non-thermal, super-Alfv\'{e}nic ions (unlike the normal operation of conventional tokamaks). The suppression of the GAE by adding a small population of high-pitch resonant fast ions is qualitatively consistent with an analytic model of the Doppler-shifted ion-cyclotron resonance drive responsible for GAE instability [2]. The model predicts that fast ions with $k_{\bot }\rho_{L}$\textless 1.9 are stabilizing, which is in good agreement with the experimental observations. A quantitative analysis was done using the HYM stability code [3] of one of the nearly 100 identified examples of GAE suppression. The simulations find remarkable agreement with the observed mode numbers and frequencies of the unstable GAE prior to suppression. Adding the population of high pitch-angle, low $\rho_{L}$ beam ions to the HYM fast ion distribution function predicts complete suppression of the GAE. TRANSP/NUBEAM calculations for the example analyzed with HYM suggest that the additional beam source increases the population of resonant fast ions with $k_{\bot }\rho_{L}$\textless 1.9 by roughly a factor of four.   

Manipulating Energetic Ion Velocity Space to Control Instabilities and Improve Tokamak Performance

The first-ever demonstration of independent current (I) and voltage (V) control of high power neutral beams in tokamak plasma shots has successfully reduced the prevalence of instabilities and improved energetic ion confinement in experiments at the DIII-D tokamak. Energetic ions drive Alfvén eigenmode (AE) instabilities through a resonant energy exchange that can increase radial diffusion of the ions, thereby reducing beam heating and current drive efficiency. This resonance is incredibly sensitive to the ion velocity and orbit topology, which then allows changes in beam voltage (keeping the injected power constant through compensating changes in current) to remove nearly all instability drive. The implementation of temporal control of beam current and voltage allows for a reduction in the resonant energetic ion velocity space while maintaining the ability to inject maximum power. DIII-D low confinement (L-mode) plasmas demonstrate a nearly complete avoidance of AE activity in plasmas with 55 kV beam injection compared to the many AEs that are observed in plasmas featuring similar total beam power at 70 kV. Across the experimental range of beam settings, resulting increases in beam divergence have been inconsequential. High performance steady-state scenarios featuring equilibria that are conducive to dense arrays of Alfvén waves benefit the most from instability control mechanisms. One such scenario, the so-called high qmin scenario, demonstrates improved confinement and equilibrium evolution when the injected beam voltage begins at lower values (i.e., fewer resonances) and then increases as the plasma reaches its stationary period. These results suggest a future in which plasma confinement and performance is improved through continuous feedback control of auxiliary heating systems such that the energetic ion distribution is constantly adapted to produce an optimal plasma state.