Massive runaway positrons are generated by runaway electrons in tokamaks. The fate of these positrons encodes valuable information about the runaway dynamics. The phase space dynamics of a runaway position is investigated using a Lagrangian that incorporates the tokamak geometry, loop voltage, radiation and collisional effects. It is found numerically that runaway positrons will drift out of the plasma to annihilate on the first wall, with an in-plasma annihilation possibility less than 0.1\%. The dynamics of runaway positrons provides signatures that can be observed as diagnostic tools.
Understanding generation and mitigation of runaway electrons in disruptions is important for the safe operation of future tokamaks. In this paper we investigate runaway dynamics in reactor-scale spherical tokamaks. We study both the severity of runaway generation during unmitigated disruptions, as well as the effect that typical mitigation schemes based on massive material injection have on runaway production. The study is conducted using the numerical framework DREAM (Disruption Runaway Electron Analysis Model). We find that, in many cases, mitigation strategies are necessary to prevent the r…
A kinetic formalism of parametric decay of a large amplitude lower hybrid pump wave into runaway electron mode and a uppersideband mode is investigated. The pump and the sideband exert a ponderomotive force on runaway electrons, driving the runaway mode. The density perturbation associated with the latter beats with the oscillatory velocity due to the pump to produce the sideband. The finite parallel velocity spread of the runaway electrons turns the parametric instability into a stimulated compton scattering process where growth rate scales as the square of the pump amplitude. The large phase…
For ITER-relevant runaway electron studies, such as suppression, mitigation, termination and/or control of runaway beam, obtaining the runaway electrons after the disruption is important. In this paper we report on the first achieved discharges with post-disruptive runaway electron beam, entitled "runaway plateau", in the COMPASS tokamak. The runaway plateau is produced by massive gas injection of argon. Almost all of the disruptions with runaway electron plateaus occurred during the plasma current ramp-up phase. Comparison between the Ar injection discharges with and without plateau has been …
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 perturba…
In this paper, the secular full-orbit simulations of runaway electrons with synchrotron radiation in tokamak fields are carried out using a relativistic volume-preserving algorithm. Detailed phase-space behaviors of runaway electrons are investigated in different dynamical timescales spanning 11 orders. When looking into the small timescale, i.e., the characteristic timescale imposed by Lorentz force, the severely deformed helical trajectory of energetic runaway electron is witnessed. A qualitative analysis of the neoclassical scattering, a kind of collisionless pitch-angle scattering phenomen…
In high-current tokamak devices such as ITER, a runaway avalanche can cause a large amplification of a seed electron population. We show that disruption mitigation by impurity injection may significantly increase the runaway avalanche growth rate in such devices. This effect originates from the increased number of target electrons available for the avalanche process in weakly ionized plasmas, which is only partially compensated by the increased friction force on fast electrons. We derive an expression for the avalanche growth rate in partially ionized plasmas and investigate the effects of imp…
The synchrotron radiation emitted by runaway electrons in a fusion plasma provides information regarding the particle momenta and pitch-angles of the runaway electron population through the strong dependence of the synchrotron spectrum on these parameters. Information about the runaway density and its spatial distribution, as well as the time evolution of the above quantities, can also be deduced. In this paper we present the synchrotron radiation spectra for typical avalanching runaway electron distributions. Spectra obtained for a distribution of electrons are compared to the emission of mon…
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.
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 n…
A new physical mechanism of formation of runaway electron (RE) beams during plasma disruptions in tokamaks is proposed. The plasma disruption is caused by a strong stochastic magnetic field formed due to nonlinearly excited low-mode number magnetohydrodynamic (MHD) modes. It is conjectured that the runaway electron beam is formed in the central plasma region confined inside the intact magnetic surface located between $q=1$ and the closest low--order rational magnetic surfaces [$q=5/4$ or $q=4/3$, \dots]. It results in that runaway electron beam current has a helical nature with a predominant $…
Thermal modeling of runaway electron induced damage in the SPARC tokamak
KTH Royal Institute of Technology（皇家理工学院）；Chalmers Universiy of Technology（查尔姆斯理工大学）；Massachusetts Institute of Technology（麻省理工学院）；Commonwealth Fusion Systems（联邦聚变系统）
Avoidance of the harmful effects of runaway electrons (REs) in plasma-terminating disruptions is pivotal in the design of safety systems for magnetic fusion devices. Here, we describe a computationally efficient numerical tool, that allows for self-consistent simulations of plasma cooling and associated RE dynamics during disruptions. It solves flux-surface averaged transport equations for the plasma density, temperature and poloidal flux, using a bounce-averaged kinetic equation to self-consistently provide the electron current, heat, density and RE evolution, as well as the electron distribu…
Based on the analysis of data from the numerous dedicated experiments on plasma disruptions in the TEXTOR tokamak the mechanisms of the formation of runaway electron beams and their losses are proposed. The plasma disruption is caused by strong stochastic magnetic field formed due to nonlinearly excited low-mode number magnetohydrodynamic (MHD) modes. It is hypothesized that the runaway electron beam is formed in the central plasma region confined by an intact magnetic surface due to the acceleration of electrons by the inductive toroidal electric field. In the case of plasmas with the safety …
The potential formation of multi-mega-ampere beams of relativistic "runaway" electrons (REs) during sudden terminations of tokamak plasmas poses a significant challenge to the tokamak's development as a fusion energy source. Here, we use state-of-the-art modeling of disruption magnetohydrodynamics coupled with a self-consistent evolution of RE generation and transport to show that a non-axisymmetric in-vessel coil will passively prevent RE beam formation during disruptions in the SPARC tokamak, a compact, high-field, high-current device capable of achieving a fusion gain Q > 2 in deuterium-tri…
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 [M. Hoppe et al (2021) Comp. 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 pla…
Steering tokamak plasmas is commonly viewed as a way to avoid disruptions and runaway electrons. Plasma steering sounds as safe as driving to work but will be shown to more closely resemble driving at high speed through a dense fog on an icy road. The long time required to terminate an ITER discharge compared to time over which dangers can be foreseen is analogous to driving in a dense fog. The difficulty of regaining plasma control if it is lost resembles driving on an icy road. Disruptions and runaways are associated with three issues -- a solution to one tends to complicate the solution to …
We propose an asymptotic-preserving (AP), uniformly convergent numerical scheme for the relativistic collisional Drift-Kinetic Equation (rDKE) to simulate runaway electrons in axisymmetric toroidal magnetic field geometries typical of tokamak devices. The approach is derived from an exact Green's function solution with numerical approximations of quantifiable impact, and results in a simple, two-step operator-split algorithm, consisting of a collisional Eulerian step, and a Lagrangian orbit-integration step with analytically prescribed kernels. The AP character of the approach is demonstrated …
For the simulation of disruptions in tokamak fusion plasmas, a fluid model describing the evolution of relativistic runaway electrons and their interaction with the background plasma is presented. The overall aim of the model is to self-consistently describe the nonlinear coupled evolution of runaway electrons (REs) and plasma instabilities during disruptions. In this model, the runaway electrons are considered as a separate fluid species in which the initial seed is generated through the Dreicer source, which eventually grows by the avalanche mechanism (further relevant source mechanisms can …
During disruptions in fusion-grade tokamaks like ITER, large electric fields are induced following the thermal quench (TQ) period which can generate a substantial amount of Runaway Electrons (REs) that can carry up to 10 MA current with energies as high as several tens of MeV [1-3] in current quench phase (CQ). These runaway electrons can cause significant damage to the plasma-facing-components due to their localized energy deposition. To mitigate these effects, impurity injections of high-Z atoms have been proposed [1-3]. In this paper, we use a self-consistent 0D tokamak disruption model as …
Non-thermal electron cyclotron emission during runaway plateau in tokamak disruptions from a highly anisotropic dielectric tensor
Seoul National University（首尔大学）；Nuclear Research Institute for Future Technology and Policy, Seoul National University（首尔大学未来技术与政策核研究所）；POSTECH（浦项工科大学）
In a tokamak, trapped electrons subject to a strong electric field cannot run away immediately, because their parallel velocity does not increase over a bounce period. However, they do pinch towards the tokamak center. As they pinch towards the center, the trapping cone becomes more narrow, so eventually they can be detrapped and run away. When they run away, trapped electrons will have very a different signature from circulating electrons subject to the Dreicer mechanism. The characteristics of what are called trapped-electron runaways are identified and quantified, including their distinguis…
Runaway particles can be produced in plasmas with large electric fields. Here we address the possibility that such runaway ions and electrons excite Alfvénic instabilities. The magnetic perturbation induced by these modes can enhance the loss of runaways. This may have important implications for the runaway electron beam formation in tokamak disruptions.
Runaway electrons (REs) can be generated in tokamak plasmas if the accelerating force from the toroidal electric field exceeds the collisional drag force due to Coulomb collisions with the background plasma. In ITER, disruptions are expected to generate REs mainly through knock-on collisions, 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 REs. Since knock-on runaways are usually scattered off with a significant perpendicular component of the momentum with respect to the local magn…
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 co…
Self-consistent modelling and qualitative comparison of mildly relativistic runaway electron dynamics with a closed flux surface formation model during tokamak startup
Development of a thin-target hard X-ray bremsstrahlung detection system to study confined runaway electrons in Aditya-U Tokamak
Institute for Plasma Research（等离子体研究所）；Homi Bhabha National Institute (HBNI)（霍米·巴巴国立学院）；EPFL（洛桑联邦理工学院）；Indian Space Research Organisation（印度空间研究组织）；Saha Institute for Nuclear Physics（萨哈核物理研究所）
It is discovered that the tokamak field geometry generates a pitch-angle scattering effect for runaway electrons. This neoclassical pitch-angle scattering is much stronger than the collisional scattering and invalidates the gyro-center model for runaway electrons. As a result, the energy limit of runaway electrons is found to be larger than the prediction of the gyro-center model and to depend heavily on the background magnetic field.
Runaway electrons (RE) generated during magnetic disruptions present a major threat to the safe operation of plasma nuclear fusion reactors. A critical aspect of understanding RE dynamics is to calculate the runaway probability, i.e., the probability that an electron in the phase space will runaway on, or before, a prescribed time. Such probability can be obtained by solving the adjoint equation of the underlying Fokker-Planck equation that controls the electron dynamics. In this effort, we present a sparse-grid probabilistic scheme for computing the runaway probability. The key ingredient of …
Synchrotron radiation observed from runaway electrons (REs) in tokamaks depends upon the position and size of the RE beam, the RE energy and pitch distributions, as well as the location of the observer. We show that experimental synchrotron images of a vertically moving runaway electron beam sweeping past the detector in the TCV tokamak agree well with predictions from the synthetic synchrotron diagnostic Soft. This experimental validation lends confidence to the theory underlying the synthetic diagnostics which are used for benchmarking theoretical models of and probing runaway dynamics. We p…
Results from the last FTU campaigns on the deuterium large (wrt FTU volume) pellet REs suppression capability, mainly due to the induced burst MHD activity expelling REs seed are presented for discharges with 0.5 MA and 5.3T. Clear indications of avalanche multiplication of REs following single pellet injection on 0.36 MA flat-top discharges is shown together with quantitative indications of dissipative effects in terms of critical electrical field increase due to fan-like instabilities. Analysis of large fan-like instabilities on post-disruption RE beams, that seem to be correlated with low e…
The effects of kinetic whistler-wave instabilities on the runaway-electron (RE) avalanche is investigated. With parameters from DIII-D experiments, we show that RE scattering from excited whistler waves can explain several poorly understood experimental results seen in a variety of tokamaks. We find an increase of the avalanche growth rate and threshold electric field, bringing the present model much closer to observations than previous results. The excitation of kinetic instabilities and the scattering of resonant electrons are calculated self-consistently using a quasilinear model. We also e…
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 base…
Runaway electrons with strongly anisotropic distributions present in post-disruption tokamak plasmas can destabilize the extraordinary electron (EXEL) wave. The present work investigates the dynamics of the quasi-linear evolution of the EXEL instability for a range of different plasma parameters using a model runaway distribution function valid for highly relativistic runaway electron beams produced primarily by the avalanche process. Simulations show a rapid pitch-angle scattering of the runaway electrons in the high energy tail on the $100-1000\;\rm μs$ time scale. Due to the wave-particle i…
Variability of MHD Instabilities in Benign Termination of High-Current Runaway Electron Beams in the JET and DIII-D Tokamaks
Columbia University（哥伦比亚大学）；CEA-IRFM（法国原子能和替代能源委员会研究部）；Institute of Plasma Physics of the CAS（捷克科学院等离子体物理研究所）；UKAEA（英国原子能管理局）；ITER Organization（国际热核聚变实验堆组织）；General Atomics（通用原子能公司）
Resonant Pitch-Angle Scattering Of Runaway-Electrons by Externally-launched Helicon Waves in the DIII-D Tokamak
Columbia University（哥伦比亚大学）；EPFL, Swiss Plasma Center (SPC)（瑞士联邦理工学院洛桑分校，瑞士等离子体中心）；General Atomics（通用原子能公司）；University of California San Diego（加利福尼亚大学圣地亚哥分校）；University of California, Irvine（加利福尼亚大学尔湾分校）；Oak Ridge National Laboratory（橡树岭国家实验室）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
In the Alcator C-Mod tokamak, runaway electron (RE) experiments have been performed during low density, flattop plasma discharges at three magnetic fields: 2.7, 5.4, and 7.8 T, the last being the highest field to-date at which REs have been generated and measured in a tokamak. Time-evolving synchrotron radiation spectra were measured in the visible wavelength range (~300-1000 nm) by two absolutely-calibrated spectrometers viewing co- and counter-plasma current directions. In this paper, a test particle model is implemented to predict momentum-space and density evolutions of REs on the magnetic…
Runaway electron modelling efforts are motivated by the risk these energetic particles pose to large fusion devices. The sophisticated kinetic models can capture most features of the runaway electron generation but have high computational costs which can be avoided by using computationally cheaper reduced kinetic codes. In this paper, we compare the reduced kinetic and kinetic models to determine when the former solvers, based on analytical calculations assuming quasi-stationarity, can be used. The Dreicer generation rate is calculated by two different solvers in parallel in a workflow develop…
We investigate the effects of runaway electron current on the dispersion relation of resistive magnetohydrodynamic modes in tokamaks. We present a new theoretical model to derive the dispersion relation, which is based on the asymptotic analysis of the resistive layer structure of the modes. It is found that in addition to the conventional resistive layer, a new runaway current layer can emerge whose properties depend on the ratio of the Alfvén velocity to the runaway electron convection speed. Due to the contribution from this layer, both the tearing mode and kink mode will have a real freque…
Self-mediation of runaway electrons via self-excited wave-wave and wave-particle interactions
University of Maryland, College Park（马里兰大学帕克分校）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；School of Nuclear Science and Technology, University of Science and Technology of China（中国科学技术大学核科学技术学院）；School of Computational Science and Engineering, Georgia Institute of Technology（佐治亚理工学院计算科学与工程学院）
Mitigation of runaway electrons is one of the outstanding issues for the reliable operation of ITER and other large tokamaks, and accurate estimates for the expected runaway-electron energies and current are needed. Previously, linearized tools (which assume the runaway population to be small) have been used to study the runaway dynamics, but these tools are not valid in the cases of most interest, i.e. when the runaway population becomes substantial. We study runaway-electron formation in a post-disruption ITER plasma using the newly developed non-linear code NORSE, and describe a feedback me…
