Runaway Electrons Research Articles

Generation of Runaway Electrons near Micro-Inhomogeneities on the Cathode Surface in Subnanosecond Self-Sustained Discharges in a Wide Range of High Pressures

The results of numerical 3D modeling of the development of an electron avalanche initiated by a field emission electron in a small-sized region of an amplified electric field near the microinhomogeneities at the cathode have been presented. The simulation has been carried out for the discharge gaps with an initially homogeneous distribution of the electric field with a reduced intensity significantly lower than that required by the electron runaway criterion. The possibility of the transition of the field emission electrons initiating avalanches and the electrons in these avalanches into runaway regime has been investigated. The microinhomogeneities in the form of a cone, metal droplets, and boundaries between pores or microcraters have been considered. The calculations were carried out for nitrogen in the pressure range from atmospheric to 40 atm. It has been shown that the initial energy obtained near the microinhomogeneity can significantly facilitate the transition of the electron into the runaway mode. And the electron will continue to run away in a discharge gap electric field weak according to the runaway criterion. It has been shown that this effect is especially noticeable at gas pressures above 10 atm. A comparative analysis of the simulation results with the experimental data obtained by us on the switching characteristics of a discharge gap filled with nitrogen when exposed to voltage pulses with subnanosecond fronts of different steepness has been carried out. This made it possible to divide the ranges of experimental conditions into those when only the amplification of the electric field near the microinhomogeneities is sufficient for the runaway of electrons and when the electric field of an avalanche of critical or close to critical size is additionally necessary for the runaway.

Characterization of early current quench time during massive impurity injection in JT-60SA

Characteristics of the early current quench (CQ) time in mitigated disruptions are studied for a full-current (5.5 MA) scenario in the JT-60SA superconducting tokamak. Self-consistent evolution of the plasma temperature and current density profiles during the early CQ phase before the plasma moves vertically is simulated using the axisymmetric disruption code INDEX for given impurity source profiles. It is shown that the hollow (flat) impurity density profiles peaks (flattens) the current density, and it causes a temporal change in the internal inductance in this phase. However the resultant CQ time is found to be insensitive to the impurity source profile for the same assimilated quantity. The simulation results are interpreted by the L/R model including the temporal change in the internal inductance as well as the effect of a gap between the plasma and the conducting vessel structures and stabilizing plates. This results will improve the accuracy to estimate the amount of impurity assimilated into plasma from the observed CQ rate in the massive gas injection (MGI) experiment planned in JT-60SA. The accessible range in which the CQ time can be scanned as well as the electron densities to suppress runaway electrons is also shown for different injected amounts of neon, argon, and their deuterium mixture under the limitation of the MGI gas amount. Mitigated disruptions in JT-60SA typically lead to the CQ time shorter than the vessel wall time, which is expected to produce relevant contributions to disruption mitigation in ITER and future reactors.

A unified description of atomic physics for electron Fokker–Planck calculations

Most realistic kinetic calculations for tokamak plasmas are now required to incorporate the effect of partially ionized high-Z elements arising either from uncontrolled influxes of metallic impurities, such as tungsten in high input power regimes or from mitigation of runaway electrons generated after possible major disruptions by massive gas injection. The usual electron–ion Fokker–Planck collision operator must therefore be modified, because all plasma atoms are not entirely ionized, as is the case for light elements. This represents a challenge, in order to perform fast but also accurate calculations, regardless of the type of element present in the plasma, but also their local levels of ionization while covering a wide range of electron energies in a consistent way, from a few keV to tens of MeV in plasmas whose electron temperature may itself vary from 10 eV to several keV. In this context, a unified description of the atomic models is proposed, based on a multi-Yukawa representation of the electrostatic potential calibrated against results obtained by advanced quantum calculations. Besides the possibility to improve the description of inner and outer atomic shells in the determination of the atomic form factor, this model allows one to derive analytical formulations for both elastic and inelastic scattering, which can then be easily incorporated in kinetic calculations. The impact of the number of exponentials in the description of the atomic potential is discussed, and a comparison with simple and advanced atomic models is also performed.

Relativistic Runaway Electron Avalanche Development Near the Electric Field Threshold in Inhomogeneous Air

AbstractRelativistic Runaway Electrons Avalanches (RREAs) development depends on the applied electric field and the environment's air density. This dependency controls the RREA exponential growth length scale. The RREA development affects the bremsstrahlung excess occurring due to the passage of charged particles through the thundercloud's electric fields, the gamma‐ray glow. We used Monte Carlo simulations to develop an empirical model showing the RREA behavior in a realistic atmospheric density profile. The new formulation shows how the density variation modulates the electron population under electric field strengths near the RREA electric field threshold. The model limits the initial RREA altitude range as a function of the electric field strength. The new model is valid between ∼0.6 and ∼18 km, covering the relevant heights to investigate the generation of ground‐detected gamma‐ray glows.

Observation of D2 molecule line emission after massive D2 injection into runaway electron plateaus in DIII-D

Molecular deuterium line emission is observed in both the visible and ultraviolet (UV) wavelength ranges after massive (> 100 Torr-L) injection of D2 gas into post-disruption runaway electron (RE) dominated plasmas in the DIII-D tokamak. D2 UV line emission is found to be the dominant source of radiated power, surpassing D Lyα. Interpretive modeling with a collisional-radiative model (CRM) indicates that D2 radiation surpasses D radiation because Lyα is strongly trapped, while D2 UV lines are mostly untrapped. The CRM also indicates that the D2 line emission is completely dominated by RE impact (rather than thermal electron impact), so the D2 line emission can serve as a good diagnostic for the spatial localization of REs. Analysis of D2 visible lines indicates that the D2 molecules in the plasma are thermally equilibrated with the background plasma, with vibrational, rotational, and kinetic temperatures all near 0.3 eV. D2 spectroscopy therefore serves as a convenient diagnostic of background plasma temperature. Measurement of D2 radiated power also appears to serve as a useful diagnostic for constraining neutral transport modeling.

Disk-Shaped Bunch of Runaway Electrons Formed in a Magnetized Air Diode

Disk-Shaped Bunch of Runaway Electrons Formed in a Magnetized Air Diode

Whistler heat flux instability governed interaction of anisotropic beam electrons in electromagnetic Vlasov simulations

The kinetic instability of whistlers in a warm plasma, arising from electron temperature anisotropy with respect to directions parallel and perpendicular to the magnetizing field, is studied. Whistlers resonantly interacting with the electron beams, for example, the fast electrons accelerated by strong parallel electric fields and the so-called runaway electrons in a tokamak, are strong players in the schema of thermalization of stellar winds and mitigation of fast electrons in tokamak disruption events. As an evidence of their role in runaway mitigation, most fusion plasma experiments are found to show a threshold magnetic field strength for the generation of runaways. In many of these examples, the faster primary runaways produce a secondary runaway beam having an avalanche-like non-thermal velocity distribution. The electromagnetic Vlasov simulations presented here self-consistently examine the collisionless interaction of anisotropic electron beams, including an avalanche-like beam distribution, with parallel propagating whistlers and dependence of this process on the magnetic field strength. Analysis of the interaction process includes comparison with the simulations done using more analytically accessible anisotropic bulk and beam electron distributions, namely, the bi-Maxwellian and bi-kappa, for the reference.

TGE Electron Energy Spectra: Comment on “Radar Diagnosis of the Thundercloud Electron Accelerator” by E. Williams et al. (2022)

AbstractE. Williams et al. (2022, commented paper) questioned electron energy spectra derived from thunderstorm ground enhancements (TGEs) measured on Aragats; they concluded that “A more likely origin for any detected electrons at 3.2 km above sea level is Compton scattering and pair production activated by longer‐range bremsstrahlung gamma rays, themselves produced by runaway electron encounters with nuclei in the breakeven field at higher altitude.” In this comment, we show that the selection criteria of “electron” TGEs unambiguously reject the assumption of the origination of TGE electrons measured on Aragats from the Compton and pair production processes. Thus, the strong accelerating electric field above the earth's surface can be significantly lower (25–150 m) than derived in the commented paper 500 m altitude.

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.

VUV lasing in diffuse discharges formed by runaway electrons

The parameters of stimulated emission in diffuse discharges formed in a sharply inhomogeneous electric field by runaway electrons in mixtures of rare gases with the addition of H2 and F2 at pressures up to 10 atm are studied. Efficient VUV lasing was obtained at wavelengths from 148 to 193 nm on the transitions of H2, F2 and exciplex ArF* molecules. It was shown that the addition of He buffer gas increases the pulse duration, while Ne addition improves the output energy of the VUV laser on the H2 Lyman band. A laser pulse duration over 10 ns and an output of 0.12 mJ were obtained. The diffuse discharge in mixtures of He with F2 was found to form as a result of successive ionization waves. It was shown that the laser pulse at 157 nm has three peaks, which correspond to the maxima of the diffuse discharge current. Therewith, the first or second peak of the laser radiation has the maximum intensity, depending on the amplitude of the conduction current in the primary ionization wave. A maximal F2* laser electrical efficiency of η 0 = 0.18% and an output of Q 157 = 3.8 mJ were obtained in a He–F2 gas mixture at pressure of 10 atm, which exceeds the efficiency of lasers of this type pumped by transverse volume discharges with UV preionization. Long-pulse operation of the ArF* laser was achieved in a He–Ne–Ar–F2 gas mixture. Lasing at 193 nm continued during two periods of the diffuse discharge current. The total duration of the laser pulse was as long as 40 ns, and the radiation energy at 193 nm was as high as 2 mJ from an active volume of 20 cm3.

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.

A physics-informed deep learning model of the hot tail runaway electron seed

A challenging aspect of the description of a tokamak disruption is evaluating the hot tail runaway electron seed that emerges during the thermal quench. This problem is made challenging due to the requirement of describing a strongly non-thermal electron distribution, together with the need to incorporate a diverse range of multiphysics processes, including magnetohydrodynamic instabilities, impurity transport, and radiative losses. This work develops a physics-informed neural network (PINN) tailored to the solution of the hot tail seed during an axisymmetric thermal quench. Here, a PINN is developed to identify solutions to the adjoint relativistic Fokker–Planck equation in the presence of a rapid quench of the plasma's thermal energy. It is shown that the PINN is able to accurately predict the hot tail seed across a range of parameters, including the thermal quench timescale, initial plasma temperature, and local current density, in the absence of experimental or simulation data. The hot tail PINN is verified by comparison with direct Monte Carlo simulations, with excellent agreement found across a broad range of thermal quench conditions.

Tokamak plasma equilibrium with relativistic runaway electrons

We consider axisymmetric equilibrium of a tokamak plasma that includes current carried by relativistic runaway electrons (REs). Using a guiding center approach, a qualitative picture of the equilibrium of a pure RE beam is elucidated. In a hot thermal plasma, none of the classical drifts of charged particles contribute to the net field-perpendicular current density, which is purely due to magnetization current. In the case of a runaway beam, however, the curvature drift of REs provides the Lorentz force needed to maintain the centripetal acceleration associated with the relativistic toroidal motion. Two different equilibrium formulations are derived for the general case consisting of a mix of thermal and RE current. At higher RE energies, the shift between flux-surfaces and surfaces of constant generalized angular momentum of REs in such equilibria can exceed the radial extent of a typical magnetohydrodynamic mode such that its stability properties could be altered. Simplified one-dimensional governing equations are derived for the absolute and relative orbit shifts in the case of a circular tokamak, enabling quick estimates of parameter dependencies.

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.

FEATURES OF ELECTRON RUNAWAY IN A GAS GAP WITH A CONICAL CATHODE

The conditions and dynamics of electron runaway in a gas gap with an inhomogeneous distribution of the electric field due to the use of a conical cathode are analyzed. Significant differences in the behavior of electrons at cone opening angles larger and smaller than the threshold value of 98.6 degrees are revealed. For a weakly inhomogeneous field distribution (cones with angles exceeding the threshold), electrons are continuously accelerated throughout the gap. In a strongly inhomogeneous field (cones with relatively small opening angles), electrons can gain maximum energy inside the gap, and begin to decelerate in the near-anode region. Despite this, they reach the anode with high energies comparable to the work of the electric field. This difference leads to the need to use different criteria for the runaway of free electrons in the gas gap.

Specific Features of Electron Runaway in a Gas Gap with a Conical Cathode

Specific Features of Electron Runaway in a Gas Gap with a Conical Cathode

Kinetic modelling of start-up runaway electrons in KSTAR and ITER

Understanding the formation of start-up runaway electrons (REs) is essential to ensure successful plasma initiation in ITER. The design of ITER start-up scenarios requires not only predictive simulations but also a validation of assumptions. The objective of this study is to strengthen the physical background required for predictive simulations aimed at ITER plasma start-up design, by validating the model assumptions. Through kinetic simulations, this study examines the validity of steady-state models for Dreicer generation under slowly-varying time scales relevant to plasma start-up and investigates the finite energy effect, commonly neglected, on the runaway avalanche growth rate. The research findings provide insights into situations where kinetic simulations are necessary. To secure a margin-of-control scheme without kinetic simulation, we suggest a strategy of scanning the Coulomb logarithm in fluid simulations as an alternative to predict runaway current takeover and avoid RE dominant scenarios. Ultimately, this paper seeks to offer a robust physical background, practically supporting the successful design of ITER start-up scenarios.

Self-Consistent Simulation of the Excitation of Compressional Alfvén Eigenmodes and Runaway Electron Diffusion in Tokamak Disruptions.

Alfvénic modes in the current quench (CQ) stage of the tokamak disruption have been observed in experiments. In DIII-D the excitation of these modes is associated with the presence of high-energy runaway electrons (REs), and a strong mode excitation is often associated with the failure of RE plateau formation. In this work we present results of self-consistent kinetic-MHD simulations of RE-driven compressional Alfvén eigenmodes (CAEs) in DIII-D disruption scenarios, providing an explanation of the CQ modes. Simulation results reveal that high energy trapped REs can have resonance with the Alfvén mode through their toroidal precession motion, and the resonance frequency is proportional to the energy of REs. The mode frequencies and their relationship with the RE energy are consistent with experimental observations. The perturbed magnetic fields from the modes can lead to spatial diffusion of REs including the nonresonant passing ones, thus providing the theoretical basis for a potential approach for RE mitigation.

Feasibility of the EDICAM camera for runaway electron detection in JT-60SA disruptions

The visible camera system EDICAM (Event Detection Intelligent Camera), recently installed on JT-60SA, is simulated to assess whether it can be used for measuring synchrotron radiation from relativistic runaway electrons. In this simulation, the SOFT synthetic synchrotron diagnostic framework is used to compute the synthetic synchrotron camera images from a JT-60SA-like disruption modelled with the DREAM disruption simulation code. In the studied scenario, a large amount of argon is added to the plasma, and a disruption is simulated by starting a prescribed exponential temperature drop and finishing with further cooling provided by the argon in a self-consistent simulation of the current quench. The background plasma evolution is calculated by DREAM self-consistently with the fast electron population, which is modelled kinetically. The resulting runaway electron distribution function along with the parameters of the EDICAM visible camera system are used as an input to the SOFT framework to assess the feasibility of the camera for runaway electron detection. We find that the runaway electron beam formed in the disruption can produce synchrotron radiation observable by the EDICAM system, thus enabling the use of the EDICAM for the characterization of runaway electron beams.

Wall cratering upon high velocity normal dust impact

Dust-wall high speed impacts, triggered by the termination of runaway electrons on plasma facing components, constitute a source of erosion. Normal high velocity mechanical impacts of tungsten dust on bulk tungsten plates are reproduced in a controlled manner by light gas gun shooting systems. Post-mortem surface analysis revealed that three erosion regimes are realized; plastic deformation, bonding and partial disintegration. The large impact statistics allowed the extraction of reliable empirical damage laws in the latter regime, which can be employed for erosion estimates in future reactors.