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

DIII-D experiments on rapid shutdown runaway electron (RE) beams have improved the understanding of the processes involved in RE beam control and dissipation. Improvements in RE beam feedback control have enabled stable confinement of RE beams out to the volt-second limit of the ohmic coil, as well as enabling a ramp down to zero current. Spectroscopic studies of the RE beam have shown that neutrals tend to be excluded from the RE beam centre. Measurements of the RE energy distribution function indicate a broad distribution with mean energy of order several MeV and peak energies of order 30–40 MeV. The distribution function appears more skewed towards low energies than expected from avalanche theory. The RE pitch angle appears fairly directed (θ ∼ 0.2) at high energies and more isotropic at lower energies (ε < 100 keV). Collisional dissipation of RE beam current has been studied by massive gas injection of different impurities into RE beams; the equilibrium assimilation of these injected impurities appears to be reasonably well described by radial pressure balance between neutrals and ions. RE current dissipation following massive impurity injection is shown to be more rapid than expected from avalanche theory—this anomalous dissipation may be linked to enhanced radial diffusion caused by the significant quantity of high-Z impurities (typically argon) in the plasma. The final loss of RE beams to the wall has been studied: it was found that conversion of magnetic to kinetic energy is small for RE loss times smaller than the background plasma ohmic decay time of order 1–2 ms.

Post-disruption runaway electron (RE) beams in tokamaks with large current can cause deep melting of the vessel and are one of the major concerns for ITER operations. Consequently, a considerable effort is provided by the scientific community in order to test RE mitigation strategies. We present an overview of the results obtained at FTU and TCV controlling the current and position of RE beams to improve safety and repeatability of mitigation studies such as massive gas (MGI) and shattered pellet injections (SPI). We show that the proposed RE beam controller (REB-C) implemented at FTU and TCV is effective and that current reduction of the beam can be performed via the central solenoid reducing the energy of REs, providing an alternative/parallel mitigation strategy to MGI/SPI. Experimental results show that, meanwhile deuterium pellets injected on a fully formed RE beam are ablated but do not improve RE energy dissipation rate, heavy metals injected by a laser blow off system on low-density flat-top discharges with a high level of RE seeding seem to induce disruptions expelling REs. Instabilities during the RE beam plateau phase have shown to enhance losses of REs, expelled from the beam core. Then, with the aim of triggering instabilities to increase RE losses, an oscillating loop voltage has been tested on RE beam plateau phase at TCV revealing, for the first time, what seems to be a full conversion from runaway to ohmic current. We finally report progresses in the design of control strategies at JET in view of the incoming SPI mitigation experiments.

Parameters of the post-disruption runaway electron (RE) beam in the low density background plasma achieved after secondary deuterium injection are investigated in DIII-D. The spatially resolved RE energy distribution function is measured for the first time during the RE plateau stage by inverting hard x-ray bremsstrahlung spectra. It has maximum energy up to 20 MeV and a non-monotonic feature at 5–6 MeV observed only in the core of the beam supporting the possibility of kinetic instabilities. Results of Fokker-Plank modelling qualitatively support the formation of the non-monotonic distribution function. The RE current profile is reconstructed for the first time using the spatially resolved RE energy distribution. It is found to be more peaked than the pre-disruption plasma current, with higher internal inductance, suggesting preferential formation of REs in the core plasma or potentially a radially inward motion of REs. The accessed relatively low current (180 kA) RE beam is found to be MHD stable, likely due to its elevated safety factor profile. From this base stable equilibrium, an internal beam instability is accessed by ramping up the current. The instability leads to a sawtooth-like relaxation of the RE current profile, but drives no RE loss. An internal kink mode proposed as a candidate instability is supported by results of MARS-F modelling. Electron cyclotron emission (ECE) spectrum measured during the low density RE plateau is found to be bifurcated, with a break point at ≈ 100 GHz, suggesting resonant absorption of the ECE at low frequencies.

Numerical studies of the ablation of pellets and shattered pellet injection (SPI) fragments into a runaway electron beam in ITER have been performed using a time-dependent pellet ablation code [Samulyak et al., Nucl. Fusion, 61(4), 046007 (2021)]. The code resolves detailed ablation physics near pellet fragments and large-scale expansion of ablated clouds. The study of a single-fragment ablation quantifies the influence of various factors, in particular, the impact ionization by runaway electrons and cross-field transport models, on the dynamics of ablated plasma and its penetration into the runaway beam. Simulations of SPI performed using different numbers of pellet fragments study the formation and evolution of the ablation clouds and their large-scale dynamics in ITER. The penetration depth of the ablation clouds is found to be of the order of 50 cm.

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 how the effective ECRH-induced RE expulsion results from the combined effects of increased electron temperature and enhanced RE transport.

A drift orbit model for relativistic test electrons has been incorporated into the MARS-F code (Liu et al 2000 Phys. Plasmas 7 3681), in order to study the runaway electron (RE) behavior in the presence of magneto-hydrodynamic perturbations computed by MARS-F. By implementing the model directly into the MARS-F curve-linear magnetic coordinates, maximal accuracy in representing the full field perturbation is preserved. The updated code is utilized to study the high current RE beam loss in a post-disruption DIII-D plasma, revealing that a fast growing, n = 1 (n is the toroidal mode number) resistive kink instability, at ∼100 Gauss level, can induce significant fraction of RE loss, largely by perturbing drift orbits of REs. A ∼1000 Gauss perturbation fully terminates the RE beam, as found in both experiment and modeling. The 3D field induced loss increases with the perturbation amplitude but decreases with the particle energy. The loss fraction is generally not sensitive to the initial particle pitch angle. The particle velocity change, due to electric field acceleration/deceleration, small pitch angle scattering, synchrotron radiation and Bremsstrahlung, further perturbs the RE trajectory but plays a minor role in prompt RE loss within microseconds time scale. Therefore, the dominant dependencies are simply the RE energy and instability strength. For comparison, a resonant magnetic perturbation field, generated by 4 kAt n = 3 even parity I-coil currents in DIII-D and with the plasma response field included, is found to induce almost no loss for the same RE beam.

Full conversion from ohmic to runaway electron (RE) driven current was observed in the tokamak à configuration variable (TCV) following massive injection of neon through a disruption mitigation valve into a low-density limited circular plasma. Following a partial disruption, a stable 200 kA RE beam is maintained for more than 1 s. Controlled ramp-down of the RE beam with adjustable decay rate was demonstrated. Control of the beam vertical position was achieved down to a RE current of 20 kA. RE beam formation is observed in elongated plasma configurations up to κ = 1.5. A reproducible scenario for RE beam generation without loss of circulating current is of particular interest for disruption modelling applications.

We present the first successful simulation of an induced disruption in ASDEX Upgrade from massive material injection (MMI) up to established runaway electron (RE) beam, thus covering pre-thermal quench, thermal quench and current quench (CQ) of the discharge. For future high-current fusion devices such as ITER, the successful suppression of REs, e.g. through MMI, is of critical importance to ensure the structural integrity of the vessel. To computationally study the interplay between MMI, background plasma response, and RE generation, a toolkit based on the 1.5D transport code coupling ASTRA-STRAHL is developed. Electron runaway is described by state-of-the-art reduced kinetic models in the presence of partially ionized impurities. Applied to argon MMI in ASDEX Upgrade discharge #33 108, key plasma parameters measured experimentally, such as temporal evolution of the line averaged electron density, plasma current decay rate and post-CQ RE current, are well reproduced by the simulation presented. Impurity ions are transported into the central plasma by the combined effect of neoclassical processes and additional effects prescribed inside the q = 2 rational surface to explain experimental time scales. Thus, a thermal collapse is induced through strong impurity radiation, giving rise to a substantial RE population as observed experimentally.

A shattered pellet injector based on in situ technology was installed on the HL-2A tokamak, and preliminary experiments were performed recently. In this paper, a fast current shutdown experiment introduces shattered pellet injection (SPI). In comparison with spontaneous disruptions and massive gas injection, SPI has advantages for disruption mitigation. The experimental results show the hard-X-ray radiation intensity (40 to 60 keV) rapidly falling from 20 to 0 when SPI is used. From this, we can infer that runaway electrons are suppressed. This observation indicates that SPI should be a good candidate for current fast shutdown in the future.

This work extends the adjoint-deep learning framework for runaway electron (RE) evolution, developed by McDevitt et al. [Phys. Plasmas 32, 042503 (2025)], to account for large-angle collisions. By incorporating large-angle collisions, the framework allows the avalanche of REs to be captured, an essential component of RE dynamics. This extension is accomplished by using a Rosenbluth–Putvinski approximation to estimate the distribution of secondary electrons generated by large-angle collisions. By evolving both the primary and multiple generations of secondary electrons, the present formulation can capture both the detailed temporal evolution of a RE population beginning from an arbitrary initial momentum space distribution, along with providing approximations to the saturated growth and decay rates of the RE population. Predictions of the adjoint-deep learning framework are verified against a traditional RE solver, with good agreement present across a broad range of parameters.

Runaway electrons (REs) created during tokamak disruptions pose a threat to the reliable operation of future larger machines. Experiments using shattered pellet injection (SPI) have been carried out at the JET tokamak to investigate ways to prevent their generation or suppress them if avoidance is not sufficient. Avoidance is possible if the SPI contains a sufficiently low fraction of high-Z material, or if it is fired early in advance of a disruption prone to runaway generation. These results are consistent with previous similar findings obtained with Massive Gas Injection. Suppression of an already accelerated beam is not efficient using High-Z material, but deuterium leads to harmless terminations without heat loads. This effect is due to the combination of a large magnetohydrodynamic instability scattering REs on a large area and the absence of runaway regeneration during the subsequent current collapse thanks to the flushing of high-Z impurities from the runaway companion plasma. This effect also works in situations where the runaway beam moves upwards and undergoes scraping-off on the wall.

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 experimental synchrotron images of a vertically moving RE beam sweeping past the detector in the Tokamak à Configuration Variable (TCV) tokamak and compare it 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 present a comparison of synchrotron measurements in TCV with predictions of kinetic theory for runaway dynamics in uniform magnetic fields. We find that to explain the detected synchrotron emission, significant non-collisional pitch angle scattering as well as radial transport of REs would be needed. Such effects could be caused by the presence of magnetic perturbations, which should be further investigated in future TCV experiments.

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.

Extremely low density operation free of error eld penetration supports the excitation of trace-level quiescent runaway electron (RE) populations during the at-top of DIII-D Ohmic discharges. Operation in the quiescent regime allows accurate measurement of all key parameters important to RE excitation, including the internal broadband magnetic fluctuation level. RE onset is characterized and found to be consistent with primary (Dreicer) generation rates. Impurity-free collisional suppression of the RE population is investigated by stepping the late-time main-ion density until RE decay is observed. The transition from growth to decay is found to occur 3-5 times above the theoretical critical electric eld for avalanche growth and is thus indicative of anomalous RE loss. Lastly, this suggests that suppression of tokamak RE avalanches can be achieved at lower density than previously expected, though extrapolation requires predictive understanding of the RE loss mechanism and magnitude.

JOREK is a massively parallel fully implicit non-linear extended magneto-hydrodynamic (MHD) code for realistic tokamak X-point plasmas. It has become a widely used versatile simulation code for studying large-scale plasma instabilities and their control and is continuously developed in an international community with strong involvements in the European fusion research programme and ITER organization. This article gives a comprehensive overview of the physics models implemented, numerical methods applied for solving the equations and physics studies performed with the code. A dedicated section highlights some of the verification work done for the code. A hierarchy of different physics models is available including a free boundary and resistive wall extension and hybrid kinetic-fluid models. The code allows for flux-surface aligned iso-parametric finite element grids in single and double X-point plasmas which can be extended to the true physical walls and uses a robust fully implicit time stepping. Particular focus is laid on plasma edge and scrape-off layer (SOL) physics as well as disruption related phenomena. Among the key results obtained with JOREK regarding plasma edge and SOL, are deep insights into the dynamics of edge localized modes (ELMs), ELM cycles, and ELM control by resonant magnetic perturbations, pellet injection, as well as by vertical magnetic kicks. Also ELM free regimes, detachment physics, the generation and transport of impurities during an ELM, and electrostatic turbulence in the pedestal region are investigated. Regarding disruptions, the focus is on the dynamics of the thermal quench (TQ) and current quench triggered by massive gas injection and shattered pellet injection, runaway electron (RE) dynamics as well as the RE interaction with MHD modes, and vertical displacement events. Also the seeding and suppression of tearing modes (TMs), the dynamics of naturally occurring TQs triggered by locked modes, and radiative collapses are being studied.