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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Toroidal modeling of Alfvén eigenmodes excited by runaway electrons in DIII-D and ITER

The non-perturbative MHD-kinetic hybrid code MARS-K (Liu et al 2014 Phys. Plasmas 21 056105) is updated to include relativistic effects for kinetic fast particles, enabling the code to model excitation of Alfvén eigenmodes (AEs) by runaway electrons (REs) in post-disruption tokamak plasmas. Applying the updated code to RE beams in both DIII-D and ITER, a zoo of AE modes triggered by trapped REs due to precessional drift-kinetic resonances is computed while scanning the RE energy. At fixed RE energy, multiple unstable roots are also excited. These AE modes possess radially different eigenmode structures, ranging from global modes to core-localized ones. The computed mode frequency is in the Alfvén frequency range, increasing with the assumed RE energy in a staircase fashion and quantitatively matching the experimental measurement (in DIII-D). At the (more relevant) high-frequency range (above 1 MHz), the modeled eigenmodes are identified as compressional AEs (CAEs) in DIII-D and a mixture of CAE and shear Alfvén waves in ITER.

Alfvén eigenmodes↗
DOE OSTI2025

Measurement of post-disruption runaway electron kinetic energy and pitch angle during final loss instability in DIII-D

Post-disruption runaway electron (RE) kinetic energy K and pitch angle sin$\vartheta$ are critical parameters for determining resulting first wall material damage during wall strikes, but are very challenging to measure experimentally. During the final loss instability, confined RE K and sin$\vartheta$ are reconstructed during center-post wall strikes for both high impurity (high-Z) and low impurity (low-Z) plasmas by combining soft x-ray, hard x-ray, synchrotron emission, and total radiated power measurements. Deconfined (wall impacting) RE sin$\vartheta$ is then reconstructed for these shots by using time-decay analysis of infra-red imaging. Additionally, deconfined RE K and sin$\vartheta$ are reconstructed for a low-Z downward loss shot by analyzing resulting damage to a sacrificial graphite dome limiter. The damage analysis uses multi-step modeling simulating plasma instability, RE loss orbits, energy deposition, and finally material expansion (MARS-F, KORC, GEANT-4, and finally COMSOL). Overall, mean kinetic energies are found to be in the range $\langle$$K$$\rangle$ $≈ 3-4$ MeV for confined REs. KORC simulations indicate that the final loss instability process does not change individual RE kinetic energy K. In conclusion, confined RE pitch angles are found to be fairly low initially pre-instability, $\langle$sin$\vartheta$$\rangle$ $≈ 0.1 – 0.2$, but appear to increase roughly 2x, to $\langle$sin$\vartheta$$\rangle$ $≈ 0.3 – 0.4$ for both confined and deconfined REs during instability onset in the low-Z case; this increase is not observed in the high-Z case.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Toroidal phase of post-disruption runaway electron loss to wall in presence of applied 3-D fields in DIII-D

The toroidal distribution of runaway electrons (REs) striking the centre post in DIII-D post-disruption RE final loss events is simulated utilizing the MARS-F code combined with the REORBIT module, by tracing the guiding-centre drift orbits of test REs in the presence of external (applied) plus internal (intrinsic instability) 3-D fields. To better recover the experimental results, three different equilibria with different safety factor profiles are adopted. Dominant resistive magnetohydrodynamic instabilities are found to be m/n=2/1, 3/2 and 1/1 modes (where m and n are the poloidal and toroidal mode numbers). Externally applied n=1 resonant magnetic perturbations (RMPs), with both even and odd parity configuration, are considered in each equilibrium. Locking of MHD instability to the applied RMPs is simulated by minimizing the total perturbed magnetic energy in the plasma. Here, the simulated toroidal locations, where most REs strike in the presence of an edge m/n= 2/1 instability and the n=1 RMPs in even parity, are found to agree well with experiments. Modeling also captures the measured n = 2 RE loss pattern on the wall for experiments where an edge m/n=3/2 instability is dominant instead of the m/n=2/1 mode. The key overall findings include (a) the measured global RE toroidal impact pattern in experiments can be explained by a locked resistive kink instability, (b) the toroidal phase of the locked mode is well predicted by minimizing the total perturbed magnetic energy, and (c) this edge locked mode determines the toroidal phase of the peak RE wall impact.

Bai, Xue [University of California San Diego, La J↗
DOE OSTI2026

Impact of Resonant Magnetic Perturbations on the Toroidal Location of the Runaway Electron Final Loss Strike Point

It is demonstrated that the peak toroidal impact phase of the post-disruption runaway electrons (REs) can be varied shot-to-shot by means of applied static non-axisymmetric (3D) magnetic fields, or resonant magnetic perturbations (RMPs). In the experiments, high-current (500 kA), purged RE plateaus (i.e. low impurity post-disruption plasmas with current carried completely by REs) were terminated on the DIII-D tokamak center post (CP). The global toroidal impact peak of the REs appears to be dominantly set by the toroidal phase of a wall-locked tearing mode, typically (m/n) = (2/1), but sometimes (m/n) = (3/2). In the absence of external RMP, the locked mode reliably locks close to a preferred toroidal phase Φ ≃ 75◦ probably set by intrinsic error fields. With applied RMP, the locked mode and RE impact phase is pushed to a new location. When the tearing mode is (m/n) = (2/1), the phase is well controlled and tracks the applied RMP phase, but in the case of an (m/n) = (3/2) tearing mode, the new phase location is not well controlled. These results could have application in ITER and other fusion power plant (FPP) - sized tokamaks as a method for spreading disruption first wall damage from REs

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Characterization of runaway electron impact on instrumented sacrificial limiters on DIII-D

Instrumented sacrificial limiter heads, both domed (proud) and flat (flush) are used in DIII-D runaway electron (RE) wall strikes to study the wall impact dynamics with high spatial and time resolution. The approximate structure of the RE wetted area and heating depth on the domed limiter heads were predicted qualitatively using orbit-tracking simulations, although a strong left–right asymmetry (about the magnetic field direction) was not captured well by the simulations. It is hypothesized that this difference is perhaps due to the local 3D magnetic field perturbation of the dome limiter head. The average kinetic energy K and pitch angle θ of REs striking the limiter head were estimated from the spatial distribution of local HXR emission and were estimated to be roughly K ≈ 4 MeV and θ ≈ 0.2 rad. These values are roughly consistent with in-plasma values estimated before the loss event, indicating that RE kinetic energy and pitch angle are not drastically altered when transporting to the wall. Large shot–shot variations (1–10 kJ) in energy deposition into the limiter head were observed and were explained by shot–shot variations in locked magneto-hydrodynamics mode toroidal phase. For the largest deposited energies (10 kJ), graphite material failure and explosive dust release was observed, and the depth of material failure at higher energy deposition was successfully reproduced using modelling of volumetric energy deposition and brittle failure. The presence of energetic (keV) level ion impact during the RE wall strike was confirmed by three different surface analysis techniques. The ratio of energetic ion to RE flux appears to be larger on flat surfaces within the RE wetted area, although the energetic ion flux and total energy flux due to energetic ions have not yet been quantified.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1989

Joule heating and runaway electron acceleration in a solar flare

The hard and soft x ray and microwave emissions from a solar flare (May 14, 1980) were analyzed and interpreted in terms of Joule heating and runaway electron acceleration in one or more current sheets. It is found that all three emissions can be generated with sub-Dreicer electric fields. The soft x ray emitting plasma can only be heated by a single current sheet if the resistivity in the sheet is well above the classical, collisional resistivity of 10(exp 7) K, 10(exp 11)/cu cm plasma. If the hard x ray emission is from thermal electrons, anomalous resistivity or densities exceeding 3 x 10(exp 12)/cu cm are required. If the hard x ray emission is from nonthermal electrons, the emissions can be produced with classical resistivity in the current sheets if the heating rate is approximately 4 times greater than that deduced from the soft x ray data (with a density of 10(exp 10)/cu cm in the soft x ray emitting region), if there are at least 10(exp 4) current sheets, and if the plasma properties in the sheets are characteristic of the superhot plasma observed in some flares by Lin et al., and with Hinotori. Most of the released energy goes directly into bulk heating, rather than accelerated particles.

Holman, Gordon D.↗
NASA NTRS1996

Effects of Spatial Gradients on Electron Runaway Acceleration

The runaway process is known to accelerate electrons in many laboratory plasmas and has been suggested as an acceleration mechanism in some astrophysical plasmas, including solar flares. Current calculations of the electron velocity distributions resulting from the runaway process are greatly restricted because they impose spatial homogeneity on the distribution. We have computed runaway distributions which include consistent development of spatial gradients in the energetic tail. Our solution for the electron velocity distribution is presented as a function of distance along a finite length acceleration region, and is compared with the equivalent distribution for the infinitely long homogenous system (i.e., no spatial gradients), as considered in the existing literature. All these results are for the weak field regime. We also discuss the severe restrictiveness of this weak field assumption.

MacNeice, Peter↗
DOE OSTI2025

Detailed characterization of runaway electron driven whistler waves in low-density DIII-D discharges

RE-driven whistler waves during quiescent DIII-D shots have been investigated further. The waves are confirmed to be mostly perpendicularly propagating and are observed for the first time with frequencies up to 700 MHz. Phase-spectral analysis has been used to infer their toroidal mode numbers, n, which are expected to scale with the wavenumber, k, of the mode. Though we derive a theoretical scaling of k ≈ 4n, the measured mode numbers are found to exhibit a very weak dependence on k. In addition, increases in synchrotron emission have been found to consistently lag whistler wave bursts by roughly 3–5 ms, suggesting the waves are causing pitch-angle scattering, since the emitted synchrotron radiation is a strong function of the REs' perpendicular energy. The stronger the wave bursts, the greater the subsequent increase in synchrotron emission. A predator-prey model is used to describe these nonlinear wave-particle interactions, from which the wave damping rates and the loss parameter can be inferred. The damping rates are found to be of the order of (1.6 ± 0.8) × 10 4 /s, and the unitless loss parameter is found to be approximately 2, suggesting that the loss mechanism is diffusive. These observations will serve to validate models of RE-driven waves in tokamak plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1990

Acceleration of runaway electrons in solar flares

The dc electric field acceleration of electrons out of a thermal plasma and the evolution of the runaway tail are studied numerically, using a relativistic quasi-linear code based on the Ritz-Galerkin method and finite elements. A small field-aligned electric field is turned on at a certain time. The resulting distribution function from the runaway process is used to calculate the synchrotron emission during the evolution of the runaway tail. It is found that, during the runaway tail formation, which lasts a few tens of seconds for typical solar flare conditions, the synchrotron emission level is low, almost ot the same order as the emission from the thermal plasma, at the high-frequency end of the spectrum. However, the emission is enhanced explosively in a few microseconds by several orders of magnitude at the time the runaway tail stops growing along the magnetic field and tends toward isotropy due to the pitch-angle scattering of the fast particles. Results indicate that, in order to account for the observed synchrotron emission spectrum of a typical solar flare, the electric field acceleration phase must be accompanied or preceded by a heating phase which yields an enhanced electron temperature of about 2-15 keV in the flare region if the electric field is 0.1-0.2 times the Dreicer field and cyclotron-to-plasma frequency ratios are of order 1-2.

Moghaddam-Taaheri, E.↗
NASA NTRS1984

Acceleration of runaway electrons and Joule heating in solar flares

The electric field acceleration of electrons out of a thermal plasma and the simultaneous Joule heating of the plasma are studied. Acceleration and heating timescales are derived and compared, and upper limits are obtained on the acceleration volume and the rate at which electrons can be accelerated. These upper limits, determined by the maximum magnetic field strength observed in flaring regions, place stringent restrictions upon the acceleration process. The role of the plasma resistivity in these processes is examined, and possible sources of anomalous resistivity are summarized. The implications of these results for the microwave and hard X-ray emission from solar flares are examined.

Holman, G. D.↗
NASA NTRS1985

Acceleration of runaway electrons and Joule heating in solar flares

The electric field acceleration of electrons out of a thermal plasma and the simultaneous Joule heating of the plasma are studied. Acceleration and heating timescales are derived and compared, and upper limits are obtained on the acceleration volume and the rate at which electrons can be accelerated. These upper limits, determined by the maximum magnetic field strength observed in flaring regions, place stringent restrictions upon the acceleration process. The role of the plasma resistivity in these processes is examined, and possible sources of anomalous resistivity are summarized. The implications of these results for the microwave and hard X-ray emission from solar flares are examined.

Holman, G. D.↗
DOE OSTI2025

Runaway electron-induced plasma facing component damagein tokamaks

This Roadmap article addresses the critical and multifaceted challenge of plasma facing component (PFC) damage caused by runaway electrons (REs) in tokamaks, a phenomenon that poses a significant threat to the viability and longevity of future fusion reactors such as ITER and DEMO. The dramatically increased RE production expected in future high-current tokamaks makes it very difficult to avoid or mitigate REs in such devices when a plasma discharge terminates abnormally. Preventing damage from the intense localised heat loads they can cause requires a holistic approach that considers plasma, REs and PFC damage. Despite decades of progress in understanding the physics of REs and the thermomechanical response of PFCs separately, their complex interplay remains poorly understood. This document aims to initiate a coordinated, interdisciplinary approach to bridge this gap by reviewing experimental evidence, advancing diagnostic capabilities, and improving modelling tools across different scales, dimensionalities, and fidelities. Key topics include RE beam formation and transport, damage mechanisms in both brittle and metallic PFCs, and observed effects in major facilities such as JET, DIII-D, WEST and EAST. The Roadmap emphasises the urgency of predictive, high-fidelity modelling validated against well-diagnosed controlled experiments, particularly in the light of recent changes in ITER’s wall material strategy and the growing importance of private sector fusion initiatives. Each section of the Roadmap article is written to provide a concise overview of one area of this multidisciplinary subject, with an assessment of the status, a look at current and future challenges, and a brief summary. The ultimate goal of this initiative is to guide future mitigation strategies and design resilient components that can withstand the intense localised loads imposed by REs, thus ensuring the safe and sustainable operation of the next generation of fusion power plants.

Ratynskaia, Svetlana [KTH Royal Inst. of Technolog↗
NASA NTRS1992

A hybrid thermal/nonthermal model for the energetic emissions from solar flares

We present an alternative interpretation of the high-resolution solar flare spectra obtained in 1981 by Lin et al. In our interpretation electron heating and acceleration are simultaneous and physically linked, rather than heating being a secondary effect of particle acceleration. We show that the observed properties of solar flare X-ray emission can in general be explained through the Joule heating and electric field acceleration of runaway electrons in current channels. We have fitted a hybrid thermal/nonthermal electron distribution, consisting of hot isothermal electrons with a nonthermal tail of runaway electrons, to representative spectra obtained by Lin et al. The hybrid model relaxes the electron number and energy flux requirements for the hard X-ray emission over those of a purely nonthermal model. The low-energy 'cutoff' to the nonthermal part of the X-ray spectrum is determined by the critical velocity in the electron distribution above which runaway acceleration occurs. We relate the fit parameters to the physical properties (such as the electric field strength in the current channels) of the acceleration region.

Holman, Gordon D.↗
NASA NTRS1992

Direct electric field heating and acceleration of electrons in solar flares

We show that the observed properties of solar flare X-ray and microwave emission can be explained through the Joule heating and electric field acceleration of runaway electrons in current channels. The global properties of the flaring region required for this are presented. We have fit a hybrid thermal/nonthermal electron distribution, consisting of hot, isothermal electrons with a nonthermal tail of runaway electrons, to high-resolution hard X-ray and microwave spectra and have obtained excellent fits to both. The hybrid model relaxes the electron number and energy flux requirements for the hard X-ray emission over those of a purely nonthermal model. The model also provides explanations for several previously unexplained aspects of the high-resolution microwave spectra. The fit parameters can be related to physical properties (such as the electric field strength in the current channels) of the acceleration region.

Holman, Gordon D.↗
NASA NTRS1995

Testing the DC-electric field model in a solar flare observed by Yohkoh and the Compton Gamma-Ray Observatory

We apply a DC-electric field model to the analysis of soft and hard X-ray observations of a solar flare observed by Yohkoh and the Compton Gamma Ray Observatory (CGRO) on 6 September 1992. The flare was observed simultaneously in the soft X-ray Ca XIX line by the Yohkoh Bragg Crystal Spectrometer (BCS) and in hard X-rays (greater than 50 keV) by the CGRO Burst and Transient Spectrometer Experiment (BATSE). A strong stationary component of Ca XIX emission was present at the start of impulsive hard X-ray emission indicating an extended phase of heating prior to the production of energetic nonthermal electrons. We interpret the preflare Ca XIX emission as a signature of Joule heating by field-aligned currents. We relate the temporal variation of impulsive hard X-ray emission to the rate of runaway electron acceleration by the DC-electric field associated with the current. We find that the initial rise in hard X-ray emission is consistent with electron acceleration by a DC-electric field that increased from a preflare value of less than approximately 10(exp -5) V/cm to approximately (9 +/- 1) x 10(exp -5) V/cm at the time of the first hard X-ray peak and then remained constant during the rest of the impulsive phase. We attribute the increase in electric field strength to the formation of a current sheet at the reconnection point of two loop structures. The decrease in hard X-ray emission after flare maximum is consistent with a reduction in the number of runaway electrons due to an increase in coronal density produced by chromospheric evaporation. The increased density quenches the runaway process by enhancing collisional thermalization of electrons. To avoid the generation of an unrealistically large magnetic field, the flaring region must be highly filamented into greater than approximately 10(exp 6) oppositely directed current channels of approximately 30 cm width with an initial preflare current of approximately 3 x 10(exp 10) A per channel.

Zarro, D. M.↗
DOE OSTI2025

Large radiation back-flux from Monte Carlo simulations of fusion neutron–material interactions

Abstract Fusion power reactors will generate intense neutron fluxes into plasma-facing and structural materials (SMs). Radiation back-fluxes, generated from neutron–material interactions under these fluxes, can dramatically impact the plasma dynamics, e.g. by seeding runaway electrons during disruptions via Compton scattering of background electrons by wall-emitted gamma radiation. Here, we quantify these back-fluxes, including neutrons, gamma rays, and electrons, using Monte Carlo calculations for a range of SM candidates and first wall (FW) thicknesses. The radiation back-flux magnitudes are remarkably large, with neutron and gamma radiation back-fluxes on the same order of magnitude as the incident fusion neutron flux. Electron back-fluxes are two orders of magnitudes lower, but are emitted at sufficiently high energies to impact the sheath and boundary plasma dynamics. Material configuration plays a key role in determining back-flux magnitudes. The SM chiefly determines the neutron back-flux magnitude, while the FW thickness principally attenuates the gamma ray and electron back-fluxes. In addition to prompt back-fluxes, which are emitted immediately after fusion neutrons impact the surface, significant delayed gamma ray and electron back-fluxes arise from nuclear decay processes in the activated materials. These delayed back-flux magnitudes range from 2% to 7% of the prompt back-fluxes, and remain present during transients when fusion no longer occurs. During disruptions, build-up of delayed gamma radiation back-flux represents potential runaway electron seeding mechanisms, posing additional challenges for disruption mitigation in a power reactor compared with non-nuclear plasma operations. This work highlights the impact of these radiation back-fluxes plasma performance and demonstrates the importance of considering back-flux generation in materials selection for fusion power reactors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗