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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Nonlinear saturation of whistler modes driven by runaway electrons

Runaway electrons exhibit kinetic instabilities with potentially beneficial consequences. The anomalous Doppler resonance between the electrons and whistler modes is a primary underlying mechanism. These instabilities require a first-principle nonlinear theoretical analysis, which would ultimately enable assessment of their impact on disruption mitigation and diagnostics, especially in ITER-relevant conditions. This paper presents recent progress in developing the required theoretical framework for isolated nonlinear resonances. By employing the generic bump-on-tail model, we predict the wave saturation levels in both near-threshold and strongly driven regimes. Remarkably, for the waves of interest, the parallel component of the wave vector dictates the parallel momentum of the resonant particles. This feature, together with the expected wave saturation level, provides a complete description of the resonance impact on the runaway electron distribution function. We show that the parametric dependence of the nonlinearly saturated mode provides a way to recover certain features of the runaway momentum distribution function.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Measurement of runaway electron energy distribution function during high-Z gas injection into runaway electron plateaus in DIII-D

The evolution of the runaway electron (RE) energy distribution function f{sub ε} during massive gas injection into centered post-disruption runaway electron plateaus has been reconstructed. Overall, f{sub ε} is found to be much more skewed toward low energy than predicted by avalanche theory. The reconstructions also indicate that the RE pitch angle θ is not uniform, but tends to be large at low energies and small θ ∼ 0.1–0.2 at high energies. Overall power loss from the RE plateau appears to be dominated by collisions with background free and bound electrons, leading to line radiation. However, the drag on the plasma current appears to be dominated by collisions with impurity ions in most cases. Synchrotron emission appears not to be significant for overall RE energy dissipation but may be important for limiting the peak RE energy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

On the inward drift of runaway electrons during the plateau phase of runaway current

The well observed inward drift of current carrying runaway electrons during runaway plateau phase after disruption is studied by considering the phase space dynamic of runaways in a large aspect ratio toroidal system. We consider the case where the toroidal field is unperturbed and the toroidal symmetry of the system is preserved. The balance between the change in canonical angular momentum and the input of mechanical angular momentum in such a system requires runaways to drift horizontally in configuration space for any given change in momentum space. The dynamic of this drift can be obtained by integrating the modified Euler-Lagrange equation over one bounce time. It is then found that runaway electrons will always drift inward as long as they are decelerating. This drift motion is essentially non-linear, since the current is carried by runaways themselves, and any runaway drift relative to the magnetic axis will cause further displacement of the axis itself. A simplified analytical model is constructed to describe such inward drift both in the ideal wall case and no wall case, and the runaway current center displacement as a function of parallel momentum variation is obtained. The time scale of such displacement is estimated by considering effective radiation drag, which shows reasonable agreement with the observed displacement time scale. Furthermore, this indicates that the phase space dynamic studied here plays a major role in the horizontal displacement of runaway electrons during plateau phase. (C) 2016 AIP Publishing LLC.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Runaway electrons and magnetic island confinement

The breakup of magnetic surfaces is a central feature of ITER planning for the avoidance of damage due to runaway electrons. Rapid thermal quenches, which lead to large accelerating voltages, are thought to be due to magnetic surface breakup. Impurity injection to avoid and to mitigate both halo and runaway electron currents utilizes massive gas injection or shattered pellets. The actual deposition is away from the plasma center, and the breakup of magnetic surfaces is thought to spread the effects of the impurities across the plasma cross section. The breakup of magnetic surfaces would prevent runaway electrons from reaching relativistic energies were it not for the persistence of non-intercepting flux tubes. These are tubes of magnetic field lines that do not intercept the walls. In simulations and in magnetic field models, non-intercepting flux tubes are found to persist near the magnetic axis and in the cores of magnetic islands even when a large scale magnetic surface breakup occurs. As long as a few magnetic surfaces reform before all of the non-intercepting flux tubes dissipate, energetic electrons confined and accelerated in these flux tubes can serve as the seed electrons for a transfer of the overall plasma current from thermal to relativistic carriers. The acceleration of electrons is particularly strong because of the sudden changes in the poloidal flux that naturally occur in a rapid magnetic relaxation. Furthermore, the physics of magnetic islands as non-intercepting flux tubes is studied. Expressions are derived for (1) the size of islands required to confine energetic runaway electrons, (2) the accelerating electric field in an island, (3) the increase or reduction in the size of an island by the runaway electron current, (4) the approximate magnitude of the runaway current in an island, and (5) the time scale for the evolution of an island.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Quasi-linear analysis of the extraordinary electron wave destabilized by runaway electrons

Runaway electrons with strongly anisotropic distributions present in post-disruption tokamak plasmas can destabilize the extraordinary electron (EXEL) wave. The present work investigates the dynamics of the quasi-linear evolution of the EXEL instability for a range of different plasma parameters using a model runaway distribution function valid for highly relativistic runaway electron beams produced primarily by the avalanche process. Simulations show a rapid pitch-angle scattering of the runaway electrons in the high energy tail on the 100–1000 μs time scale. Due to the wave-particle interaction, a modification to the synchrotron radiation spectrum emitted by the runaway electron population is foreseen, exposing a possible experimental detection method for such an interaction.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

The effects of kinetic instabilities on the electron cyclotron emission from runaway electrons

In this paper we show that the kinetic instabilities associated with runaway electron beams play an essential role for the production of high-level non-thermal electron–cyclotron-emission (ECE) radiation. Most of the non-thermal ECE comes from runaway electrons in the low-energy regime with large pitch angle, which are strongly scattered by the excited whistler waves. The power of ECE from runaway electrons is obtained using a synthetic diagnostic model based on the reciprocity method. The electron distribution function is calculated using a kinetic simulation model including the whistler wave instabilities and the quasilinear diffusion effects. Simulations based on DIII-D low-density discharge reproduces the rapid growth of the ECE signals observed in DIII-D experiments. Unlike the thermal ECE where radiation for a certain frequency is strongly localized inside the resonance region, the non-thermal ECE radiation from runaway electrons is nonlocal, and the emission-absorption ratio is higher than that of thermal electrons. The runaway electron tail is more significant for ECE with higher frequencies, and the ECE spectrum becomes flatter as RE population grows. The nonlinear behavior of the kinetic instabilities is illustrated in the oscillations of the ECE waves. In conclusion, the good agreement with the DIII-D experimental observations after including the kinetic instabilities clearly illustrate the significance of the scattering effects from wave-particle interactions, which can also be important for runaway electrons produced in disruptions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Adjoint Fokker-Planck equation and runaway electron dynamics

The adjoint Fokker-Planck equation method is applied to study the runaway probability function and the expected slowing-down time for highly relativistic runaway electrons, including the loss of energy due to synchrotron radiation. In direct correspondence to Monte Carlo simulation methods, the runaway probability function has a smooth transition across the runaway separatrix, which can be attributed to effect of the pitch angle scattering term in the kinetic equation. However, for the same numerical accuracy, the adjoint method is more efficient than the Monte Carlo method. The expected slowing-down time gives a novel method to estimate the runaway current decay time in experiments. A new result from this work is that the decay rate of high energy electrons is very slow when E is close to the critical electric field. This effect contributes further to a hysteresis previously found in the runaway electron population.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

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

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

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Visible imaging and spectroscopy of disruption runaway electrons in DIII-D

The first visible light images of synchrotron emission from disruption runaway electrons are presented. The forward-detected continuum radiation from runaways is identified as synchrotron emission by comparing two survey spectrometers and two visible fast cameras viewing in opposite toroidal directions. Analysis of the elongation of 2D synchrotron images of oval-shaped runaway beams indicates that the velocity pitch angle v{sub Up-Tack }/v{sub ||} ranges from 0.1 to 0.2 for the detected electrons, with energies above 25 MeV. Analysis of synchrotron intensity from a camera indicates that the tail of the runaway energy distribution reaches energies up to 60 MeV, which agrees with 0D modeling of electron acceleration in the toroidal electric field generated during the current quench. A visible spectrometer provides an independent estimate of the upper limit of runaway electron energy which is roughly consistent with energy determined from camera data. Synchrotron spectra reveal that approximately 1% of the total post-thermal quench plasma current is carried by the detected high-energy runaway population with energies in the range of 25-60 MeV; the bulk of the plasma current thus appears to be carried by relativistic electrons with energy less than 25 MeV. In addition to stable oval shapes, runaway beams with other shapes and internal structure are sometimes observed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

An ITPA joint experiment to study runaway electron generation and suppression

Recent results from an ITPA joint experiment to study the onset, growth, and decay of relativistic electrons (REs) indicate that loss mechanisms other than collisional damping may play a dominant role in the dynamics of the RE population, even during the quiescent I{sub p} flattop. Understanding the physics of RE growth and mitigation is motivated by the theoretical prediction that disruptions of full-current (15 MA) ITER discharges could generate up to 10 MA of REs with 10–20 MeV energies. The ITPA MHD group is conducting a joint experiment to measure the RE detection threshold conditions on a number of tokamaks under quasi-steady-state conditions in which V{sub loop}, n{sub e}, and REs can be well-diagnosed and compared to collisional theory. Data from DIII-D, C-Mod, FTU, KSTAR, and TEXTOR have been obtained so far, and the consensus to date is that the threshold E-field is significantly higher than predicted by relativistic collisional theory, or conversely, the density required to damp REs is significantly less than predicted, which could have significant implications for RE mitigation on ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Numerical simulation of the hot-tail runaway electron production mechanism using CQL3D and comparison with Smith–Verwichte analytical model

Abstract The hot-tail mechanism of runaway electron (RE) production (Harvey et al 2000 Phys. Plasmas 7 4590) is the primary source of RE in the case of rapidly cooling tokamak plasma. Quantifying this mechanism is very important as it can provide most of the post-thermal-quench (TQ) current, or a seed current for the secondary source of RE through the avalanche mechanism. An analytic model which omits pitch-angle scattering is often used in literature for estimating the hot-tail RE density (Smith and Verwichte 2008 Phys. Plasmas 15 072502). In the present study, we use the CQL3D bounce-averaged Fokker–Planck code (Harvey and McCoy 1992 Proc. IAEA Technical Committee Meeting on Advances in Simulation and Modeling of Thermonuclear Plasmas p 527) to test the limits of validity of the model. In particular, we examine the cases of Z = 1 and Z = 18 ions, for sets of different initial temperature, density, electric field and the characteristic time of temperature decay. We show that for Z = 1 plasma, the ratio of RE density computed by CQL3D to that estimated from the model is within 0.6–6.0 in studied cases. For the Z = 18 case, this factor is systematically a much smaller number, typically 0.02–0.6. We suggest a simple correction to the model that narrows down the range of this ratio to 0.3–3.8 in all of the cases, including Z = 1 and Z = 18 plasmas.

Physics↗
DOE OSTI2015

Theory of runaway electrons in ITER: Equations, important parameters, and implications for mitigation

The plasma current in ITER cannot be allowed to transfer from thermal to relativistic electron carriers. The potential for damage is too great. Before the final design is chosen for the mitigation system to prevent such a transfer, it is important that the parameters that control the physics be understood. Equations that determine these parameters and their characteristic values are derived. The mitigation benefits of the injection of impurities with the highest possible atomic number Z and the slowing plasma cooling during halo current mitigation to ≳40 ms in ITER are discussed. The highest possible Z increases the poloidal flux consumption required for each e-fold in the number of relativistic electrons and reduces the number of high energy seed electrons from which exponentiation builds. Slow cooling of the plasma during halo current mitigation also reduces the electron seed. Existing experiments could test physics elements required for mitigation but cannot carry out an integrated demonstration. ITER itself cannot carry out an integrated demonstration without excessive danger of damage unless the probability of successful mitigation is extremely high. The probability of success depends on the reliability of the theory. Equations required for a reliable Monte Carlo simulation are derived.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Runaway electrons in tokamaks

The generation of runaway electrons is a complex and important phenomenon that impacts many areas of plasma physics. Due to the decrease of electron collision frequency with increasing velocity, electrons under strong electric field can experience unlimited “runaway” acceleration. In tokamaks, runaway electrons can be produced in disruptions, due to the strong inductive electric field formed as the thermal energy of plasma gets rapidly lost. This population of runaway electrons can undergo an exponential growth, denoted the runaway electron avalanche, due to hard collisions between relativistic runaway electrons and low energy electrons. It is predicted that in a large tokamak device like the International Thermonuclear Experimental Reactor (ITER), a runway electron beam generated in a disruption event can potentially cause severe damage to the device, which poses a significant challenge for ITER to achieve its mission. It is therefore extremely important to seek an effective mitigation mechanism for runaway electrons. Experimental efforts have been made to study the properties of runaway electrons in tokamaks, including their generation, diffusion, and radiation. In order to understand these experimental results, extensive theoretical and simulation studies of runaway electron physics are required. The main topic of this thesis is to study the wave particle interaction associated with runaway electron beams in tokamaks. The runaway electrons can emit and absorb electromagnetic waves through resonances, and can be diffused in momentum space by the waves. Initially, we address the Cherenkov radiation of runaway electrons, which originates from the polarization of the plasma medium. The energy and momentum loss of the Cherenkov radiation can be modeled by adding a correction to the Coulomb logarithm in the collisional drag force. Subsequently, we address pitch angle scattering caused by normal modes in the plasma, which are driven unstable by the anisotropicity of the runaway electron beam. The fluctuating electromagnetic fields are found to act as a seed for the unstable normal modes. Numerical simulations show that the pitch angle scattering effect from the normal modes, mainly whistler waves, can be significantly larger than that from collisional pitch angle scattering. Finally, we present a synthetic diagnostic tool we developed to calculate the electron cyclotron emission (ECE) from the runaway electrons, and successfully reproduce the prompt growth of the ECE signal observed in DIII-D quiescent runaway electron (QRE) experiments. Within the thesis, we also present the application of the adjoint method to runaway electron research, and show the calculations of the runaway probability function (RPF) and the expected loss time (ELT). These calculations not only help depict the dynamics of runaway electrons in momentum space, but also can be used to efficiently calculate experimentally relevant quantities such as the critical electric field for runaway electron avalanche and the avalanche growth rate.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Models of primary runaway electron distribution in the runaway vortex regime

Generation of runaway electrons (RE) beams can possibly induce the most deleterious effect of tokamak disruptions. A number of recent numerical calculations have confirmed the formation of a RE bump in their energy distribution by taking into account Synchrontron radiational damping force due to RE’s gyromotions. Here, we present a detailed examination on how the bump location changes at different pitch-angle and the characteristics of the RE pitch-angle distribution. Although REs moving along the magnetic field are preferably accelerated and then populate the phase-space of larger pitch-angle mainly through diffusions, an off-axis peak can still form due to the presence of the vortex structure which causes accumulation of REs at low pitch-angle. A simplified Fokker- Planck model and its semi-analytical solutions based on local expansions around the O point is used to illustrate the characteristics of RE distribution around the O point of the runaway vortex in phase-space. The calculated energy location of the O point together with the local energy and pitch-angle distributions agree with the full numerical solution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Self-consistent simulation of resistive kink instabilities with runaway electrons

A new fluid model for runaway electron simulation based on fluid description is introduced and implemented in the magnetohydrodynamics code M3D-C1, which includes self-consistent interactions between plasma and runaway electrons. The model utilizes the method of characteristics to solve the continuity equation for the runaway electron density with large convection speed, and uses a modified Boris algorithm for pseudo particle pushing. The model was employed to simulate magnetohydrodynamics instabilities happening in a runaway electron final loss event in the DIII-D tokamak. Nonlinear simulation reveals that a large fraction of runaway electrons get lost to the wall when kink instabilities are excited and form stochastic field lines in the outer region of the plasma. Plasma current converts from runaway electron current to Ohmic current, and get pinched at the magnetic axis. Here, given the good agreement with experiment, the simulation model provides a reliable tool to study macroscopic plasma instabilities in existence of runaway electron current, and can be used to support future studies of runaway electron mitigation strategies in ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Phase-space dynamics of runaway electrons in magnetic fields

Dynamics of runaway electrons in magnetic fields are governed by the competition of three dominant physics: parallel electric field acceleration, Coulomb collision, and synchrotron radiation. Examination of the energy and pitch-angle flows reveals that the presence of local vortex structure and global circulation is crucial to the saturation of primary runaway electrons. Models for the vortex structure, which has an O-point to X-point connection, and the bump of runaway electron distribution in energy space have been developed and compared against the simulation data. Lastly, identification of these velocity-space structures opens a new venue to re-examine the conventional understanding of runaway electron dynamics in magnetic fields.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗