Runaway Electron Beam Research Articles

Simulation of DIII-D disruption with argon pellet injection and runaway electron beam

Abstract The next generation of large tokamaks, including ITER, will be equipped with a disruption mitigation system (DMS) that can be activated if a disruption is deemed to be imminent. Introducing impurities by pellet (large or shattered) or massive gas injection has been shown to be an effective mitigation mechanism on many tokamaks. The goal of the mitigation is to lessen the thermal and electromagnetic loads from the disruption without generating enough high-energy (runaway) electrons to damage the device. Variations of this mitigation process with impurity injection are presently being tested on many experiments. We have modeled one such impurity injection experiment on DIII-D using the M3D-C1 nonlinear 3D extended MHD code (Jardin et al 2012 Comput. Sci. Discovery 6 014002), The model includes an argon large pellet injection and ablation model, impurity ionization, recombination, and radiation, and runaway electron formation and subsequent evolution, including both Dreicer and avalanche sources. We obtain reasonable agreement with the experimental results for the timescale of the thermal and current quench and for the magnitude of the runaway electron plateau formed during the mitigation. This is the first 3D full MHD simulation with pellets and REs to simulate the disruption process and it also provides a partial validation of the M3D-C1 DMS model.

Non-linear MHD modelling of transients in tokamaks: a review of recent advances with the JOREK code

Abstract Transient MHD events like edge localized modes (ELMs) or disruptions are a concern for magnetic confinement fusion power plants. Research with the MHD code JOREK towards understanding control of such instabilities is reviewed here. Experimental validation for unmitigated vertical displacement events (VDEs) progressed. The mechanism of vertical force mitigation by impurity injection was identified. Two-way eddy current coupling to CARIDDI was completed. Shattered pellet injection (SPI) was simulated in JET, KSTAR and ASDEX Upgrade (AUG) and ITER. Benign runaway electron (RE) beam termination in JET and ITER was studied. Coupling of kinetic REs to the MHD is ongoing and a virtual RE synchrotron radiation diagnostic was developed. Regarding pedestal physics, regimes devoid of large ELMs in AUG were simulated and predictive JT60-SA simulations are ongoing. For ELM suppression by resonant magnetic perturbations (RMPs), AUG, ITER and EAST simulations were performed. A free boundary RMP model was validated against experiments. Evidence for penetrated magnetic islands at the pedestal top based on AUG experiments and simulations was found. Simulations of the naturally ELM-free quiescent H-mode (QH) in AUG and HL-3 show external kink mode formation prevents pedestal build-up towards an ELM within windows of the edge safety factor. With kinetic neutral particles, high field side high density (HFSHD) formation in ITER was simulated and with kinetic impurities, tungsten transport in AUG RMP plasmas was studied. To capture turbulent transport, electro-static full-f PiC models for ion temperature gradient (ITG) and trapped electron modes (TEM) were established and benchmarked. Application to RMP plasmas shows enhanced turbulence in comparison to unperturbed states. Energetic particle (EP) interactions with MHD were studied. Flux-pumping that prevents the safety factor on axis from dropping below unity was simulated. First non-linear stellarator applications include current relaxation in l=2 stellarators, while verification for advanced stellarators progresses.

Dynamics of JET runaway electron beams in D2-rich shattered pellet injection mitigation experiments

Abstract The publication provide further insights into the dynamics of JET runaway electron (RE) beams mitigated by D2-rich shattered pellet injection (SPI) (Reux et al 2022 Plasma Phys. Control. Fusion 64 034002). Multi-diagnostic analyses show that mechanisms causing continuous RE losses and energy transfer from hot electrons to cold background plasma can act before the SPI. After the SPI, measurements are compatible with a reduction of the maximum energy and pitch angle of the RE distribution while the population of supra-thermal electrons increases. The RE population growth is likely due to electron avalanche. Dark island-like pattern chains, characterised by an integer poloidal mode number and a certain minor radius, are identified in the JET RE beam synchrotron radiation videos. The synchrotron island dynamics is studied via a newly developed computer vision code (Sommariva and Silburn https://c4science.ch/source/pSpiPTV/). The radial motion of synchrotron island chains is found to be consistent with the most plausible time evolution of the radial current density profile compatible with both the RE synchrotron videos and the total RE current time trace. Similarly, correlations are identified between the temporal progression of the synchrotron islands poloidal rotation frequency and sudden MHD relaxation events. Loss-of-RE events probably caused by non-linear interactions between synchrotron islands are observed for the first time. Experimental evidences suggest that synchrotron islands are possibly related to the existence of magnetic islands which may lead to the development of new RE beam mitigation strategies.

Expulsion of runaway electrons using ECRH in the TCV tokamak

Abstract Runaway electrons (REs) are a concern for tokamak fusion reactors from discharge startup to termination. A sudden localized loss of a multi-megaampere RE beam can inflict severe damage to the first wall. Should a disruption occur, the existence of a RE seed may play a significant role in the formation of a RE beam and the magnitude of its current. The application of central electron cyclotron resonance heating (ECRH) in the Tokamak à Configuration Variable (TCV) reduces an existing RE seed population by up to three orders of magnitude within only a few hundred milliseconds. Applying ECRH before a disruption can also prevent the formation of a post-disruption RE beam in TCV where it would otherwise be expected. The RE expulsion rate and consequent RE current reduction are found to increase with applied ECRH power. Whereas central ECRH is effective in expelling REs, off-axis ECRH has a comparatively limited effect. A simple 0-D model for the evolution of the RE population is presented that explains the effective ECRH-induced RE expulsion results from the combined effects of increased electron temperature and enhanced RE transport.

Fast nonlinear scattering of runaway electron beams through resonant interactions with plasma waves

Abstract The resonant interaction between a runaway electron (RE) beam and a reactor-grade background plasma is investigated through two-dimensional particle-in-cell simulations, employing a simplified model of the system. The temporal evolutions of the electron momentum distribution function for two separate initial beam energies (1 and 10 MeV) are tracked, revealing the occurrence of plasma wave growth concomitant with pitch angle scattering or momentum distribution diffusion within the RE beam. Notably, we identify and confirm the dependence of the dominant resonance condition on the initial kinetic energy of the RE beam. Furthermore, we quantify the effect of particle-wave interactions on the RE momentum distribution diffusion by assessing the average kinetic energy flux from the RE distribution function.

Disruption runaway electron generation and mitigation in the Spherical Tokamak for Energy Production (STEP)

Abstract Generation of Runaway Electrons (REs) during plasma disruptions is of great concern for ITER and future reactors based on the tokamak concept. The current STEP (Spherical Tokamak for Energy Production) concept design features a plasma current higher than 20 MA, thus expected to be in a regime of very high avalanche multiplication. This is confirmed by modelling runaway electron generation in unmitigated disruptions using the code DREAM, with hot-tail generation found to be the dominant primary generation mechanism and avalanche confirmed to be extremely high. Varying assumptions for the prescribed thermal quench phase (duration, final electron temperature) as well as the wall time, the plasma-wall distance, and shaping effects, all STEP unmitigated disruptions are found to generate large runaway electron beams (from 10 MA up to full conversion). The possibility of RE avoidance is first studied by idealized, i.e. radially uniform, impurity injection of a mixture of argon and deuterium, with ad-hoc particle transport arising from the stochasticity of the magnetic field during the thermal quench (TQ). Unfortunately, no such injection scenario allows runaways to be avoided while respecting the other constraints of disruption mitigation. STEP disruption mitigation system (DMS) has then been tested with DREAM, by modelling 2-stage Shattered Pellet Injections consisting of pure D2 followed by Ar+D2. Such a scheme is found to reduce the generation of REs by the hot-tail mechanism, reducing the final RE current to about 13 MA, but isn't sufficient by itself. Options for mitigating such a RE beam (benign termination scheme), as well as estimations of required RE losses during the current quench (from a potential passive RE mitigation coil) will also be briefly discussed.

Plasma burn-mind the gap.

The programme to design plasma scenarios for the Spherical Tokamak for Energy Production (STEP), a reactor concept aiming at net electricity production, seeks to exploit the inherent advantages of the spherical tokamak (ST) while making conservative assumptions about plasma performance. This approach is motivated by the large gap between present-day STs and future burning plasmas based on this concept. It is concluded that plasma exhaust in such a device is most likely to be manageable in a double null (DN) configuration, and that high core performance is favoured by positive triangularity (PT) plasmas with an elevated central safety factor. Based on a full technical and physics assessment of external heating and current drive (CD) systems, it was decided that the external CD is provided most effectively by microwaves. Operation with active resistive wall mode (RWM) stabilization as well as high elongation is needed for the most compact solution. The gap between existing devices and STEP is most pronounced in the area of core transport, owing to high normalized plasma pressure in the latter which changes qualitatively the nature of the turbulence controlling transport. Plugging this gap will require dedicated experiments, particularly on high-performance STs, and the development of reduced models that faithfully represent turbulent transport at high normalized pressure. Plasma scenarios in STEP will also need to be such that edge localized modes (ELMs) either do not occur or are small enough to be compatible with material lifetime limits. The high current needed for a power plant-relevant plasma leads to the unavoidable generation of high runaway electron beam current during a disruption, where novel mitigation techniques may be needed. This article is part of the theme issue 'Delivering Fusion Energy - The Spherical Tokamak for Energy Production (STEP)'.

Development of the prototype for the SPARC hard X-ray monitor.

The SPARC tokamak will be equipped with a hard X-ray (HXR) monitor system capable of measuring the bremsstrahlung emission from runaway electrons with photon energies in excess of about 100keV. This diagnostic will detect the formation of runaway electron beams during plasma start-up and inform the plasma control system to terminate the discharge early to protect the machine. In this work, we present a 0D estimate of the HXR emission in SPARC during plasma start-up. Then we discuss the characterization of a prototype of the HXR monitor. The detector mounts a 1 × 1-in.2 LaBr3 inorganic scintillator coupled with a photomultiplier tube and has been tested with γ-ray sources to find its dynamic range. Finally, two possible modes of operation for spectroscopic and current mode measurements on SPARC are proposed.

Runaway electron mitigation by 3D fields application in ASDEX Upgrade, COMPASS, and RFX-mod

Disruption-generated runaway electron (RE) beams represent a potentially severe threat for tokamak plasma-facing components. Application of properly designed 3D fields can act as a mitigation mechanism, as recently investigated in ASDEX Upgrade (AUG) and COMPASS experiments and in the tokamak discharges of RFX-mod. In all of these devices, the dynamics of the disruption are affected by the application of magnetic perturbations (MPs), and the resulting RE beam current and lifetime are significantly reduced. These experiments show, in particular, that the strength of the observed effects strongly depends on the poloidal spectrum of the applied MPs, which has been reconstructed including the plasma response. This paper reports the main findings on RE mitigation from the previously mentioned three devices, highlighting the common physics behind them and their interpretation by using the guiding center code ORBIT.

Assessment of runaway electron beam termination and impact in ITER

The vertical motion and shrinking of the cold plasma column after a tokamak disruption leads to a natural decrease in the edge safety factor when most of the current is carried by runaway electrons (REs). Reaching a low edge safety factor can potentially cause a strong plasma instability. We present magnetohydrodynamic simulations of the termination of a post-disruption plateau-phase RE beam in ITER when the edge safety factor falls close to two. Growth of instabilities is observed to result in stochastization of the magnetic field and a prompt loss of REs. As RE impact must be mitigated in ITER, the effect of parameters that influence the final termination have been assessed. Higher background plasma resistivity is seen to cause larger mode magnitudes and stronger stochastization, leading to less remnant REs after the termination event. Lower ion-densities also project a qualitatively similar behavior although weaker in effect. Using computations from a wall collision model, the ensuing load distribution on the first-wall is also presented.

Characteristics of the Alfvénic activity during the current quench in ASDEX Upgrade

ASDEX Upgrade has developed multiple massive gas injection (MGI) scenarios to investigate runaway electron (RE) dynamics. During the current quench of the MGI induced disruptions, Alfvénic activity is observed in the 300–800 kHz range. With the help of a mode tracing algorithm based on Fourier spectrograms, mode behaviour was classified for 180 discharges. The modes have been identified as global Alfvén eigenmodes using linear gyrokinetic MHD simulations. Changes in the Alfvén continuum during the quench are proposed as explanation for the strong frequency sweep observed. A systematic statistical analysis shows no significant connection of the mode characteristics to the dynamics of the subsequent runaway electron beams. In our studies, the appearance and amplitude of the modes does not seem to affect the potential subsequent runaway beam. Beyond the scope of the 180 investigated dedicated RE experiments, the Alfvénic activity is also observed in natural disruptions with no RE beam forming.

Wall heating by subcritical energetic electrons generated by the runaway electron avalanche source *

Subcritical energetic electrons (SEEs) produced by the runaway electron (RE) avalanche source at energies below the runaway threshold are found to be the primary contributor to surface heating of plasma-facing components (PFCs) during final loss events. This finding is supported by theoretical analysis, computational modeling with the Kinetic Orbit Runaway electrons Code (KORC), and qualitative agreement with DIII-D experimental observations. The avalanche source generates significantly more secondary electrons below the runaway threshold, which thermalize rapidly when well-confined. However, during a final loss event, the RE beam impacts the first wall, and SEEs are deconfined before they can thermalize. Additionally, because the energy deposition length decreases faster than energy, the deposited energy density, and thus the maximum PFC surface temperature change, is larger for SEEs than REs. KORC simulations employ an analytic first wall to model particle deconfinement onto a non-axisymmetric wall composed of individual tiles. PFC surface heating is calculated using a 1D model extended to include an energy-dependent deposition length scale. Simulations of DIII-D qualitatively agree with infrared (IR) imaging only when SEEs from the avalanche source are included. These results demonstrate that SEEs are the dominant contributor to PFC surface heating and indicate that the avalanche source plays a critical role in the PFC damage caused during final loss events. The prominence of SEEs also has important implications for interpreting IR imaging, one of the primary diagnostics for RE-wall interaction diagnosis, despite REs dominating the energy and current density. This result improves predictions of wall damage due to post-disruption REs to estimate material lifetime and design RE mitigation systems for ITER and future reactors.

Simulations of stand-off runaway electron beam termination by tungsten particulates for tokamak disruption mitigation

Stand-off runaway electron termination by injected tungsten particulates offers a plausible option in the toolbox of disruption mitigation. Tungsten is an attractive material choice for this application due to large electron stopping power and high melting point. To assess the feasibility of this scheme, we simulate runaway collisions with tungsten particulates using the MCNP program for incident runaway energies ranging from 1 to 10 MeV. We assess runaway termination from energetics and collisional kinematics perspectives. Energetically, the simulations show that 99% of runaway beam energy is removed by tungsten particulates on a timescale of 4–9 µs. Kinematically, the simulations show that 99% of runaways are terminated by absorption or backscattering on a timescale of 3–4 µs. By either metric, the runaway beam is effectively terminated before the onset of particulate melting. Furthermore, the simulations show that secondary radiation emission by tungsten particulates does not significantly impact the runaway termination efficacy of this scheme. Secondary radiation is emitted at lower particle energies than the incident runaways and with a broad angular distribution such that the majority of secondary electrons emitted will not experience efficient runaway re-acceleration. Overall, the stand-off runaway termination scheme is a promising concept as a last line of defense against runaway damage in ITER, SPARC, and other future burning-plasma tokamaks.

Optimal Conditions for the Generation of Runaway Electrons in High-Pressure Gases

Runaway electron (RAE) generation in high-pressure gases is an important physical phenomenon that significantly influences discharge shapes and properties of initiated plasma. The diffuse discharges formed due to RAEs in the air and other gases at atmospheric pressure find wide applications. In the present review, theoretical and experimental results that explain the reason for RAE occurrence at high pressures are analyzed, and recommendations are given for the implementation of conditions under which the runaway electron beam (RAEB) with the highest current can be obtained at atmospheric pressure. The experimental results were obtained using subnanosecond, nanosecond, and submicrosecond generators, including those specially developed for runaway electron generation. The RAEBs were recorded using oscilloscopes and collectors with picosecond time resolution. To theoretically describe the phenomenon of continuous electron acceleration, the method of physical kinetics was used based on the Boltzmann kinetic equation that takes into account the minimum but sufficient number of elementary processes, including shock gas ionization and elastic electron scattering. The results of modeling allowed the main factors to be established that control the RAE appearance, the most important of which is electron scattering on neutral atoms and/or molecules. Theoretical modeling has allowed the influence of various parameters (including the voltage, pressure, gas type, and geometrical characteristics of the discharge gap) to be taken into account. The results of the research presented here allow RAE accelerators with desirable parameters to be developed and the possibility of obtaining diffuse discharges to be accessed under various conditions. The review consists of the Introduction, five sections, the Conclusion, and the References.

Benign termination of runaway electron beams on ASDEX Upgrade and TCV

This paper discusses the development of a benign termination scenario for runaway electron (RE) beams on ASDEX Upgrade and TCV. A systematic study revealed that a low electron density (n e) companion plasma was required to achieve a large MHD instability, which expelled the confined REs over a large wetted area and allowed for the conversion of magnetic energy to radiation. Control of the companion plasma ne was achieved via neutral pressure regulation and was agnostic to material injection method. The neutral pressure required for recombination was found to be dependent on impurity species, quantity and RE current. On TCV, n e increased at neutral pressures above 1 Pa, indicating that higher collisionality between the REs and neutrals may lead to an upper pressure limit. The conversion of magnetic energy to radiated energy was measured on both machines and a decrease in efficiency was observed at high neutral pressure on TCV. The benign termination technique was able to prevent any significant increase in maximum heat flux on AUG from 200 to 600 kA of RE current, highlighting the ability of this approach to handle fully formed RE beams.

Resistive hose modes in tokamak runaway electron beams

Beams of energetic runaway electrons are generated during disruptions in tokamaks, and fluid models are used to study their effects on macroscale dynamics. Linear computations of a massless, runaway electron beam coupled to MHD plasma show that resistive hose instabilities grow faster than tearing modes at large resistivity. Eigenvalue results with reduced models of the resistive hose instability are compared with results from the full MHD and beam system, showing that the resistive hose decouples from any plasma response. An estimate of plasma temperature at which growth of the resistive hose dominates tearing for post-disruption DIII-D plasma parameters is in a physically relevant regime.

Resonant interaction between runaway electrons and the toroidal magnetic field ripple in TCV

This work explains the anomalously high runaway electron (RE) pitch angles inferred in the flat-top of dedicated Tokamak à Configuration Variable (TCV) experiments. Kinetic modelling shows that the resonant interaction between the gyromotion of the electrons and the toroidal magnetic field ripple will give rise to strong pitch angle scattering in TCV. The resulting increase in synchrotron radiation power losses acts as a RE energy barrier. These observations are tested experimentally by a magnetic field ramp-down, which gradually reduces the resonant parallel momentum at which the REs interact with the ripple. Resulting changes in synchrotron emission geometry and intensity are observed using three multi-spectral camera imaging systems, viewing the RE beam at distinct spatial angles in multiple wavelength ranges. Experimental reconstructions of the RE distribution in momentum- and real-space are consistent with kinetic model predictions.

The mechanism of the global vertical force reduction in disruptions mitigated by massive material injection

Disruptions lead to a rapid loss of thermal and magnetic energy and can cause large heat loads, mechanical forces, and the excitation of a beam of relativistic runaway electrons. The operation of tokamaks at high energy and plasma current requires the use of a mitigation system to limit such detrimental effects. Mitigation techniques rely mainly on the injection of a large amount of impurities to radiate the majority of the thermal and magnetic energies. Heat loads and electro-magnetic (EM) forces as well as their toroidal asymmetries can be greatly reduced by such measures. In this paper, a theory is lined out to explain the reduction of the global vertical force based on large toroidal halo currents that keep the current centroid stationary in the midplane. As a consequence, the vertical current moment, which is linked to the EM-force, is reduced. The theory is backed up by experimental observations in shattered pellet injection mitigated vertical displacement event experiments in ASDEX Upgrade (AUG) and JET as well as by 2D simulations with the extended MHD code JOREK. Scans in the boundary heat flux are carried out to estimate the correct scrape-off layer temperature and the influence of the fraction of conducted energy. Finally, predictive simulations for ITER confirm the reduction of the vertical force by the injection of impurities.

Diffusion–convection model of runaway electrons due to large magnetohydrodynamic perturbations in post-thermal quench plasmas

Systematic test particle tracing simulations for runaway electrons (REs) are performed for six post-thermal quench equilibria from DIII-D and ITER, where large scale, kink-like n = 1 (n is the toroidal mode number) magnetohydrodynamic (MHD) instabilities are found. The modeled particle guiding center orbits allow extraction of the effective diffusion–convection coefficients of REs in the presence of large three-dimensional (3D) perturbations up to 10% of the equilibrium toroidal field. With a fixed spatial distribution of the field perturbation, the RE transport coefficients along the plasma radial coordinate track reasonably well with the surface-averaged perturbation level. A substantial variation in the value of the transport coefficients—by three orders of magnitude in most cases, however, occurs with varying launching location of REs along the plasma radius. Large 3D perturbations almost always lead to comparable diffusion and convection processes, meaning that diffusion alone is insufficient to describe the particle motion. At lower (but still high) level of perturbation, the RE convection is found to be dominant over diffusion. A similar observation is made when the perturbation is too strong. In the presence of large perturbation, the dependence of the RE transport on the particle energy is sensitive to the spatial distribution of the perturbation. Based on numerically obtained RE transport coefficients, an analytic fitting model is proposed to quantify the particle diffusion and convection processes due to large MHD events in post-thermal quench plasmas. The model is shown to reasonably well reproduce the direct test particle tracing results for the RE loss fraction and can, thus, be useful for incorporating into other kinetic RE codes in order to simulate the RE beam evolution in the presence of large 3D perturbations.

Non-linear dynamics of the double tearing mode

3D non-linear magnetohydrodynamics simulations of a double tearing mode with the JOREK code are presented in the context of trying to better understand the benign termination of runaway electron beams observed in some experiments. It is shown that the non-linear behavior qualitatively depends on the resistivity η via its effect on how fast secondary, non-linearly destabilized, tearing modes grow relative to the primary mode. Within a certain range of η, a violent and global relaxation is observed, consistent with the “Kadomtsev-predicted” reconnection region extending from almost the very center up to the edge of the plasma.