Runaway Electrons Research Articles

Cross-calibration and first Vertical ECE measurement of electron energy distribution in the TCV Tokamak

Abstract This paper describes the first Vertical Electron Cyclotron Emission (V-ECE) measurement of non-thermal electron distributions in the Tokamak à Configuration Variable, TCV. These measurements were conducted in runaway electron scenarios and in the presence of Electron Cyclotron Current Drive. Measured intensities of linearly polarised X- and O-mode radiation from fast electrons allow the analysis of the energy distribution. The measurements were made possible through the creation of an operational regime for the diagnostic that is free of thermal background radiation, in relaxed electron density operations. This operational regime notably enables the cross-calibration of the diagnostic system, relying on thermal plasma measurements and modeling with the ray-tracing code SPECE.

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.

Experimental investigation of kinetic instabilities driven by runaway electrons in the EXL-50 spherical torus

Abstract In this study, high-frequency instabilities driven by runaway electrons in the EXL-50 spherical torus have been reported using a high-frequency magnetic pickup coil. The frequency of these instabilities is found to be power function dependent on the plasma density, similar to the dispersion relation of the whistler wave. The observed instability seems to exhibit a fluctuating pattern, resembling frequency chirping behavior, which appears to align with the expected outcomes predicted by the Berk-Breizman model. Theoretically, the excitation threshold of the instability driven by runaway electrons is related to the ratio of the runaway electron density to the background plasma density, and the stability criterion is first demonstrated qualitatively in this work. The instability can be stabilized by the spontaneous rise of plasma density, consistent with the wave-particle resonance mechanism. This investigation demonstrates the excitation characteristic of chirping instabilities in a tokamak plasma and reveals new features of these instabilities, thereby advancing the understanding of the mechanisms for controlling and mitigating runaway electrons.

Reduction of the Downward Energy Flux of Nonthermal Electrons in the Solar Flare Corona due to Cospatial Return-current Losses

High-energy electrons carry much of a solar flare’s energy. Therefore, understanding changes in electron beam distributions during their propagation is crucial. A key focus of this paper is how the cospatial return current reduces the energy flux carried by these accelerated electrons. We systematically compute this reduction for various beam and plasma parameters relevant to solar flares. Our 1D model accounts for collisions between beam and plasma electrons, return-current electric-field deceleration, thermalization in a warm target approximation, and runaway electron contributions. The results focus on the classical (Spitzer) regime, offering a valuable benchmark for energy flux reduction and its extent. Return-current losses are only negligible for the lowest nonthermal fluxes. We calculate the conditions for return-current losses to become significant and estimate the extent of the modification to the beam’s energy flux density. We also calculate two additional conditions that occur for higher injected fluxes: (1) where runaway electrons become significant, and (2) where current-driven instabilities might become significant, requiring a model that self-consistently accounts for them. Condition 2 is relaxed and the energy flux losses are reduced in the presence of runaway electrons. All results are dependent on beam and cospatial plasma parameters. We also examine the importance of the reflection of beam electrons by the return-current electric field. We show that the interpretation of a number of flares needs to be reviewed to account for the effects of return currents.

Designing tungsten armoured plasma facing components to pulsed heat loads in magnetic fusion machines

A possible design rule for preventing surface damage from thermal transients to solid tungsten armour is proposed and formulated for the plasma facing components (divertor, first wall) of magnetic fusion machines. The rule is based on combined results from laboratory experiments and operating fusion machines, and fundamental engineering principles such as the heat flux factor (FHF) and fatigue usage fraction (FUF). As an example, the rule would allow 2.104 transient heat loads cycles at a FHF of 10MJm-2s-½ before the lifetime is considered exhausted. The formulation of the rule using engineering principles allows combining loads of different magnitudes and various number of cycles. A practical example of the rule usage is provided, illustrating loads combination and how the rule may contribute to the component geometrical design. The proposed rule is only valid for surface loading conditions, hence is not usable for volumetric loading conditions such as runaway electrons. Setting a budget lifetime and a design rule does not preclude actual plasma operation beyond the design lifetime. It is actually normal that experimental devices explore a larger domain than the one defined at the time of the design.

Local and nonlocal conditions for electron runaway in a gas gap with a conical cathode with a variable opening angle

The conditions for the generation of runaway electrons in an air gap are compared at different degrees of inhomogeneity of the electric field distribution provided by varying the opening angle of the conical cathode: in the range 40°–120° in experiments and 0°–180° in calculations. It is demonstrated that, in a weakly inhomogeneous electric field (according to the proposed classification, this corresponds to cones with angles greater than the Taylor angle of 98.6°), the runaway condition has a local character. The transition of free electrons into the runaway mode is determined by the local distribution of the electric field near their starting point—the tip of the cone. The local electric field strength must exceed a threshold value comparable to the strength critical for the runaway of electrons in a uniform field. In a strongly inhomogeneous field (cones with angles less than 98.6°), this condition is not sufficient for electrons to run away throughout the gap. Electrons accelerating in the near-cathode region may begin to slow down in a weak field at a distance from the cathode. In this case, the runaway condition becomes nonlocal. It is determined by the dynamics of electrons in the entire gap, primarily in the near-anode region, and reduces to the requirement that the potential difference applied to the gap exceeds a certain threshold value.

Electron kinetics near the minimum of Paschen's curves of pulsed breakdown

The main objective of the present paper is the detailed analysis of the electron kinetics near the Paschen's curve minimum of pulsed breakdown of nitrogen gas. Three main questions are to be answered. First, whether the breakdown curve minimum corresponds to the threshold electric field necessary for the runaway electron generation. Second, what is the role of these electrons in the vicinity of the Paschen's curve minimum. Third, what is the ionization cost near the minimum. To answer these questions, the one-dimensional model is used in which electrons are modeled using the Particle-in-Cell approach, while ions are modeled in the drift-diffusion approximation.

First results of a newly-built hard-X-ray/soft-Gamma spectrometer imaging system: on the aspect of plasma disruptions

Abstract A new Hard X-ray and soft gamma-ray spectrometer imaging System (HXS) has been built for the 2-Dimensional measurements of plasma emitted photons on the Experimental Advanced Superconducting Tokamak (EAST). The system uses a 2-D Cadmium Zinc Telluride (CZT) detector and an integrated electronics, which is as a whole shielded by a tungsten box with a pinhole and is tangential to the toroidal field. Three classes of typical energy spectra have been summarized in differently experimental scenarios over the past campaigns. After performing tomography calculations, the local emissivity contours have been obtained in different energy ranges which obviously show the asymmetry on the plasma cross section. The spatial perturbation structure is similar to the magnetohydrodynamics (MHD) modes with low mode numbers. In particular, the runaway island found by an infrared camera [R. Jaspers et al, Phys. Rev. Lett. 72, 4093 (1994)] is also measured by the HXS. There exists a reversal population on the energy spectra in both slide-away and strong neutral beam injection (NBI) shots. It is consistently observed that the count rate is increased in the low energy range before the plasma disruptions. Calculations in phase space indicate that the accelerated momentum flux can be deflected back to the low energy region by the large pitch-angle scattering. In the post-disruption phase the plasma current is not replaced by runaway electrons due to tearing modes or transiently bursting instabilities. This paper constructs the basics for the proper use of HXS for Hard X-ray and Soft Gamma-ray measurements in future investigations of plasma disruptions.

Normal high velocity solid dust impacts on tiles of tokamak-relevant temperature

Runaway electron incidence on plasma facing components triggers explosive events that are accompanied by the expulsion of fast solid debris. Subsequent dust-wall high speed impacts constitute a mechanism of wall damage and dust destruction. Empirical damage laws that can be employed for erosion estimates are based on room-temperature impact experiments. We use light-gas gun shooting systems to accelerate solid tungsten dust to near-supersonic speeds towards bulk tungsten targets that are maintained at different temperatures. This concerns targets cooled down to −100°C with liquid nitrogen and targets resistively heated up to 400 °C. Post-mortem surface analysis reveals that the three erosion regimes (plastic deformation, bonding, partial disintegration) weakly depend on the target temperature within the investigated range. It is concluded that empirical damage laws based on room-temperature measurements can be safely employed for predictions.

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.

Overview of damage to beryllium limiters by unmitigated disruptions and runaway electrons in the JET tokamak with metal walls

Abstract The Joint European Torus (JET) fusion reactor was upgraded to the metallic wall configuration in 2011 which consisted of bulk beryllium (Be) tiles in the main chamber and bulk tungsten (W) and W-coated CFC tiles in the divertor [1]. During each campaign, a series of wall damages were observed; on the upper dump plates (UDP) positioned to the top part of the vessel walls and on the inner wall - mainly affecting the inner wall guard limiters (IWGL). In both cases, it was concluded that the causes of these damages were unmitigated plasma disruptions. In the case of JET with the metallic wall configuration, most of these plasma disruptions were intentionally provoked. The overall objective was to study the behaviour of these phenomena, in order to assess their impact on the wall, improve understanding of morphological material changes, and – based on that - to develop, implement and test mitigation techniques for their prospective use on ITER. The current results bring additional information on the effects of the unmitigated plasma disruptions on the UDPs and are a significant extension of work presented in [2] where the scale of the damage after three operational campaigns on the Be top limiters of JET was highlighted. In addition, new data is presented on the damaging effect that the high energetic runaway electrons had on the Be IWGL in JET.

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.

Formation of directed wide-aperture flows of runaway electrons in air-filled magnetized diodes.

This paper presents the results of research, development, and testing of magnetically insulated air diodes with replaceable graphite and stainless-steel tubular and coaxial cathodes of various configurations capable of generating directed bunches of runaway electrons. At the anode, the bunches have cross sections shaped as circles or rings with an outer diameter of 1-2cm. The durations of the bunches, which carry currents of a few to tens of amperes, range from tens of picoseconds to 100ps, and their charges range from tenths of a nanocoulomb to a few nanocoulombs. The kinetic energy of the bunch electrons at the peak of the current pulse is typically of the order of 150keV. The bunch parameters are set (and varied) by varying the amplitude and duration of the subnanosecond high-voltage pulse driving the diode; they depend on the cathode material and on the strength and profile of the applied external magnetic field. The bunches, retaining their cross-sectional structure, are brought out from the diode, along the field lines, through a thin foil or mesh anode into the open space with a quasi-uniform magnetic field between two Helmholtz coils. In this space, the samples to be irradiated with electrons, similarly to objects exposed to radiation in various experiments and technological applications, can be placed.

SPARC x-ray diagnostics: Technical and functional overview.

An overview is given of SPARC's three main x-ray diagnostics, with a focus on the functions they fulfill with respect to tokamak operation. The first is an in-vessel soft x-ray tomography diagnostic, aimed at providing early campaign information on plasma position, MHD activity, and impurity content. The second is an ex-vessel set of hard x-ray scintillators aimed at detecting the presence of runaway electrons, in particular during plasma startup phases. The third is a set of x-ray Bragg spectrometers, located outside of the tokamak hall, aimed at informing on the ion temperature as an indirect constraint to reduce uncertainties on the fusion power, on providing plasma rotation velocity estimates, and on observing impurity emission. Finally, more technical details are given on the beamlines at the end of which the spectrometers are located. It explains how their design allows us to ensure tritium containment and limit neutron radiation while providing a straight view into the plasma that can also be used for testing new innovative sensors.

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.

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.

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.

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)'.

Overview of physics results from the ADITYA-U tokamak and future experiments

The ADITYA upgrade (ADITYA-U), a medium-sized (R0=75 cm,a=25 cm) conventional tokamak facility in India, has been consistently producing experiments findings by using circular and shaped-plasmas. Recognizing the plasma parameters aligning closely with the design parameters of circular limited plasmas, ADITYA-U shifted its focus toward exploring the operational regime for experimentation on saw-tooth and MHD phenomena. Moreover, ADITYA-U has made consistent advancements toward conducting preliminary plasma shaping experiments through the activation of top and bottom divertor coils utilizing hydrogen as well as deuterium fuels. Confinement is improved by a factor of ∼1.5 in D2 plasmas when compared to H 2 plasmas of ADITYA-U. Further, ADITYA-U operations emphasize preventing disruptions and runaway electrons (REs) to ensure safe operations for future fusion devices. Significant suppression of REs has been achieved in ADITYA-U with the application of pulsed localized vertical magnetic field (LVF) perturbation, thereby establishing the technique’s independence from the tokamak device. The successful RE mitigation requires a critical threshold of LVF pulse magnitude, which is approximately 1% of the toroidal magnetic field, and a minimum duration of ∼5 ms. Apart from this, several novel findings have been achieved in the ADITYA-U experiments, including the modification of sawtooth duration through gas-puff, the emergence of MHD-induced geodesic acoustic mode-like oscillations, the propagation of fast heat pulses induced by MHD activity, the control of RE dynamics through Gas-puffs, the propagation of pinch-driven cold-pulses, the transport and core accumulations of argon impurities, the mass dependency of plasma toroidal rotation and the detection of ‘RICE’ scaling, as well as the characterization of edge plasma using wall conditioning methods, such as glow discharge cleaning using a combination of Ar-H 2 mixture, localized wall cleaning by electron cyclotron resonant plasma, and the development of machine learning-based disruption predictions, will be discussed in this paper.

NSTX-U research advancing the physics of spherical tokamaks

The objectives of NSTX-U research are to reinforce the advantages of STs while addressing the challenges. To extend confinement physics of low-A, high beta plasmas to lower collisionality levels, understanding of the transport mechanisms that set confinement performance and pedestal profiles is being advanced through gyrokinetic simulations, reduced model development, and comparison to NSTX experiment, as well as improved simulation of RF heating. To develop stable non-inductive scenarios needed for steady-state operation, various performance-limiting modes of instability were studied, including MHD, tearing modes, and energetic particle instabilities. Predictive tools were developed, covering disruptions, runaway electrons, equilibrium reconstruction, and control tools. To develop power and particle handling techniques to optimize plasma exhaust in high performance scenarios, innovative lithium-based solutions are being developed to handle the very high heat flux levels that the increased heating power and compact geometry of NSTX-U will produce, and will be seen in future STs. Predictive capabilities accounting for plasma phenomena, like edge harmonic oscillations, ELMs, and blobs, are being tested and improved. In these ways, NSTX-U researchers are advancing the physics understanding of ST plasmas to maximize the benefit that will be gained from further NSTX-U experiments and to increase confidence in projections to future devices.