Transport Of Runaway Electrons Research Articles

Assessment of the runaway electron load distribution in ITER during 3D MHD induced beam termination

In ITER, disruption-born runaway electrons (REs), unless mitigated, are expected to form a several Mega-Ampere beam that ultimately intercepts the first wall leading to melting of the plasma facing components. Developing a successful mitigation strategy therefore requires modeling that takes into account the coupling between REs and the MHD during the formation and termination of the beam, along with estimates for the wall loads that can be compared to design values. Using the JOREK code, this work aims to provide the latter by presenting a novel model for collisions between REs and the wall and applying it to a beam termination scenario in ITER. To this end, the transport of REs is modeled by tracing particles in the fields calculated by preceding simulations of the disruption event where REs were treated in the fluid picture and self-consistently coupled to the MHD. The resulting heat loads are found to be highly localized in both the poloidal and toroidal directions, with 3D features also playing an important role in the appearance of hot spots. Peak loads were on the order of 107−108Jm2 . The load distribution was found to only be weakly sensitive to the initial phase space distribution of the REs when decoupled from the fields, while modifying properties of the underlying MHD yielded notable differences in wetted area and peak loads, in particular for cases with higher resistivity.

Subdiffusive transport of runaway electrons in presence of small amplitude MHD perturbations in COMPASS

Radial transport of runaway electrons (REs) in tokamaks is affected by the presence of magnetic perturbations, either caused by internal magnetohydrodynamic instabilities or induced by external coils. The magnetic field configuration inside the plasma volume consists in general of intact magnetic surfaces alternated with magnetic islands and stochastic layers, which make the usual diffusive approach, based on the Rechester–Rosenbluth formula, inadequate to the study of transport. Here the fractional diffusion approach is employed to model RE transport in presence of intrinsic magnetic perturbations (magnetic islands) in the flat-top phase of RE-dedicated discharges on COMPASS tokamak. The character of RE transport is found to be subdiffusive. The degree of subdiffusion is evaluated by running simulations with the ORBIT code and a time-fractional diffusion equation is applied to calculate the time evolution of RE particle number. The results are compared with the observed RE losses, estimated from the time integrated neutron signal.

Assessing energy dependence of the transport of relativistic electrons in perturbed magnetic fields with orbit-following simulations

Experimental observations, as well as theoretical predictions, indicate that the transport of energetic electrons decreases with energy. This reduction in transport is attributed to finite orbit width (FOW) effects. Using orbit-following simulations in perturbed tokamak magnetic fields that have an ideal homogeneous stochastic layer at the edge, we quantify the energy dependence of energetic electrons transport and confirm previous theoretical estimates. However, using magnetic configurations characteristic of JET disruptions, we find no reduction in runaway electron transport at higher energies, which we attribute to the mode widths being comparable to the minor radius, making the FOW effects negligible. Instead, the presence of islands and non-uniform magnetic perturbations are found to be more important. The diffusive-advective transport coefficients calculated in this work, based on simulations for electron energies 10 keV–100 MeV, can be used in integrated disruption modelling to account for the transport due to the magnetic field perturbations.

Spatial transport of runaway electrons in axisymmetric tokamak plasmas

An implicit assumption made in the vast majority of studies of runaway electrons is that they are well confined to a given magnetic flux surface, thus allowing the use of slab or bounce averaged formulations that ignore the spatial transport of runaway electrons. While such an assumption is known to break down in the presence of strong 3D magnetic field perturbations, here we show that it can be violated even for an axisymmetric magnetic field under conditions representative of an actively mitigated disrupting plasma. Specifically, the low temperature and large impurity content typical of a post thermal quench plasma are shown to provide a drastic enhancement of the diffusive and convective transport of runaways electrons, where the convective component is found to be dominated by the Ware pinch. This inward convective flux allows runaway electrons to be displaced toward the plasma center, where they are eventually detrapped and reaccelerated, thus focusing populations of runaway electrons in the inner portion of the plasma. The resulting runaway electron distribution is shown to settle into a well-defined spatial eigenmode, whose form is often insensitive to the spatial distribution of the original seed population. The underlying transport processes responsible for determining the width and shape of the spatial runaway electron eigenmode are analyzed under a range of circumstances characteristic of a post thermal quench plasma.

Suppression of runaway electrons by mode locking during disruptions on J-TEXT

The generation of runaway electrons during disruptions poses a serious threat for the operation of ITER. The efficiency of the injection of large amounts of impurities by massive gas injection or shattered pellet injection to achieve runaway suppression might be compromised due to low gas mixture efficiency and the high Rosenbluth density for runaway suppression. The transport of runaway electrons is dominated by magnetic perturbations. The magnetic perturbations have the advantage of expelling the runaway seeds before they reach high energy. Robust runaway suppression has been reached on J-TEXT with mode locking by the application of m/n = 2/1 resonant magnetic perturbations before the thermal quench. The mode locking implemented large magnetic islands inside the plasma which acted as an explosive bomb during disruptions and led to stronger stochasticity in the whole plasma cross section. The NIMROD simulation indicates that this strong stochasticity expels the runaway seeds and results in runaway free disruptions on J-TEXT. This might provide an alternative runaway suppression technique during disruptions for large-scale tokamaks.

Generation and transport of runaway electrons during sawteeth crash in the ADITYA tokamak

Sawteeth oscillations are commonly observed in temporal profiles of temperatures in almost all tokamaks including ADITYA tokamak. In typical discharges of ADITYA, bursts of hard x-ray (HXR) due to interaction of runaway electrons (RE) with limiter, during sawteeth crash are regularly observed in initial period of plasma current flat-top. These HXR bursts are highly correlated with the sawteeth-crash in time, which suggests that sawtooth crash generates these runaway electrons, which then yield the HXR bursts due to their interaction with the limiter. The electric field induced in the toroidal direction due to change in poloidal magnetic field during the sawtooth crash is found to be higher than the critical electric field required for runaway generation. This induced toroidal electric field during each sawtooth crash generates the REs, which then travel to the limiter to give a HXR burst. Furthermore, it is observed that in the later period of the plasma current flat-top of the discharge, no HXR bursts accompany the sawtooth crash. This indicates different transport mechanisms of runaway electrons in the initial and later parts of plasma current flat-top. Further investigation revealed that the overlapping inflated magnetic islands seem to be responsible for loss of sawtooth-crash generated REs and subsequent HXR bursts in the initial phase. Whereas no overlapping of magnetic islands and presence of good magnetic surfaces in-between the islands restricts the transportation of REs leading to absence of correlated HXR bursts in the later phase of plasma current flat-top.

Development of hard X-ray spectrometer with high time resolution on the J-TEXT tokamak

A hard X-ray (HXR) spectrometer has been developed to study the runaway electrons during the sawtooth activities and during the runaway current plateau phase on the J-TEXT tokamak. The spectrometer system contains four NaI scintillator detectors and a multi-channel analyzer (MCA) with 0.5ms time resolution. The dedicated peak detection circuit embedded in the MCA provides a pulse height analysis at count rate up to 1.2 million counts per second (Mcps), which is the key to reach the high time resolution. The accuracy and reliability of the system have been verified by comparing with the hardware integrator of HXR flux. The temporal evolution of HXR flux in different energy ranges can be obtained with high time resolution by this dedicated HXR spectrometer. The response of runaway electron transport with different energy during the sawtooth activities can be studied. The energy evolution of runaway electrons during the plateau phase of runaway current can be obtained.

An advection–diffusion model for cross-field runaway electron transport in perturbed magnetic fields

Disruption-generated runaway electrons (RE) present an outstanding issue for ITER. The predictive computational studies of RE generation rely on orbit-averaged computations and, as such, they lack the effects from the magnetic field stochasticity. Since stochasticity is naturally present in post-disruption plasma, and externally induced stochastization offers a prominent mechanism to mitigate RE avalanche, we present an advection–diffusion model that can be used to couple an orbit-following code to an orbit-averaged tool in order to capture the cross-field transport and to overcome the latter’s limitation. The transport coefficients are evaluated via a Monte Carlo method. We show that the diffusion coefficient differs significantly from the well-known Rechester–Rosenbluth result. We also demonstrate the importance of including the advection: it has a two-fold role both in modelling transport barriers created by magnetic islands and in amplifying losses in regions where the islands are not present.

Measurement of the internal magnetic fluctuation by the transport of runaways on J-TEXT.

The measurement of internal magnetic fluctuation is important for the study of transport in tokamak plasmas. The runaway electron transport induced by the sawtooth crash can be used to obtain the internal magnetic fluctuation. Inversed sawtooth-like activities on hard x-ray (HXR) fluxes following sawtooth activities were observed after the application of electrode biasing on J-TEXT tokamak. The runaway diffusion coefficient Dr is deduced to be about 30 m2/s according to the time delay of HXR flux peaks to the sawtooth crashes. The averaged value of normalized magnetic fluctuation in the discharges with electrode biasing was increased to the order of 1 × 10-4.

Analysis of the experiment on registration of X-rays from the stepped leader of a cloud-to-ground lightning discharge

[1] Using a Monte Carlo technique to simulate the transport of runaway electrons (REs) and X-rays in the atmosphere and through attenuators covering detectors, we have modeled the results of experiments to detect X-rays from triggered lightning and stepped leaders of a natural cloud-to-ground lightning. In the model, bremsstrahlung of high-energy runaway electrons (REs) generated at the leader front is assumed to be the origin of X-rays. Specific fluxes (per one RE) of photons and bremsstrahlung energy at the detectors were calculated. The analysis was executed with monoenergetic and exponential initial energy distributions of REs with different angular distributions. To reproduce the detected radiation energy of ~1–2 MeV, a generation of ~1010–1011 REs per flash is required in the case with the beam angular distribution of monoenergetic REs with the energy in the range 1–10 MeV. The same result was obtained with the exponential energy distribution of REs with the average energy 7 MeV, i.e., with the average energy in the RE avalanche. The electric field amplifies the flux of the radiation energy, and the amplification becoming stronger as the RE source approaches the ground. In the case with an isotropic angular distribution of REs in the bottom hemisphere, with no electric field, (4–5) × 109 REs are required for reproducing ~1–2 MeV of detected X-ray energy. In addition, fluxes of photons and fluxes of their energy at the detectors, energy distributions of photons and their average energy were calculated.

The effect of resonant magnetic perturbations on runaway electron transport in ITER

In this paper the effect of resonant magnetic perturbations (RMPs) on the net radial transport of runaway electrons (REs) is calculated by simulating the RE drift orbits in magnetostatic perturbed fields. Through the transport, RMP influences the time dynamics and preferred loss directions of the REs, which are determined for different magnetic perturbation configurations. The distribution of the field mesh exit points of the REs become more localized compared with the unperturbed case, since the loss pattern depends on the geometric properties of the RMP configuration such as periodicity or helicity. On the other hand, the loss patterns do not depend on the particle energies and starting positions. The particle radial steps are correlated with the local radial magnetic perturbation component, which makes the transport chaotic, but deterministic.

Transport of runaway electrons in sawtooth active plasmas in the HT-7 tokamak

The magnetic fluctuation level is an important parameter in lower hybrid current-drive (LHCD) plasmas because LHCD has been used to improve plasma performance extensively in the HT-7 tokamak. We investigate the transport of runaway electrons in LHCD plasmas with strong sawteeth in the HT-7 tokamak. A delay time was found to exist between the peak of the soft X-ray sawteeth and the peak of the hard X-ray flux. Based on the delay time, we obtained the transport coefficient of the runaway electrons and the averaged magnetic fluctuation level in sawtooth activity of the plasmas. We found that the diffusion coefficient of the runaway electrons was on the order of Dr ∼ 1 m2s−1 and that the magnetic fluctuation level was on the order of b ∼ 10−6.

Runaway electron transport in turbulent and resonantly perturbed magnetic topologies of TEXTOR

The losses of runaway electrons due to magnetic perturbation fields are measured applying a scintillator probe during the flat top phases of purely ohmically heated low density discharges. The effects of well-defined amplitudes of the perturbation on the temporal evolution of the runaway losses and the spectral properties of the runaways are analyzed. The runaway transport towards the plasma edge is described by a model which takes magnetic turbulences and the magnetic perturbation field into account. Using an asymptotic theory, the orbits as well as radially and energy dependent transport coefficients for the runaways are calculated. A diffusion equation, which utilizes the coefficients, is solved delivering the density and the flux of the runaways. The model reproduces the measured enhancement of the runaway losses. Qualitatively different runaway spectra are found inside the plasma and at the edge. The spectra are explained by estimations of the competition between the secondary generation rate of the runaways and their radial diffusion. Thus, a self-consistent understanding of the temporal and spectral properties of the RE transport due to the resonant magnetic perturbation is achieved.

New mechanism of runaway electron diffusion due to microturbulence in tokamaks

Chaotic transport of runaway electrons in a toroidal system in the presence of a weak small-scale magnetic turbulent field with a wide mode spectrum is studied. Using a fast running mapping, the radial profiles of turbulent diffusion coefficients are calculated. It is found that at large Kubo numbers the chaotic transport of the electrons is described by a fractal-like radial dependence of the diffusion coefficients with reduced or zero values near low-order rational drift surfaces which form transport barriers. The latter can be one of the main reasons of the improved confinement of runaway electrons in tokamaks. One can expect that this effect may lead to the formation of the nested beams of runaway electrons.

Asymptotical Theory of Runaway Electron Diffusion Due to Magnetic Turbulence in Tokamak Plasmas

AbstractAsymptotic theory of transport of runaway electrons in a toroidal plasma in the presence of small‐scale magnetic turbulence is proposed. It is based on relativistic Hamiltonian guiding center equations for runaway electrons in toroidal plasmas. Using the asymptotical analysis the explicit relation between the spectral (m, n)‐ components of perturbation Hamiltonian and the corresponding spectrum of the magnetic turbulence is found. This relation depends only on a few parameters of runaway orbits and magnetic surfaces. The radial profiles of runaway diffusion coefficients are found employing two methods, the quasilinear approximation and the direct calculations using a fast running mapping. The dependence of the shielding factor of the runaway electron parameters and the turbulence spectra is discussed (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Spatially distributed scintillator arrays for diagnosing runaway electron transport and energy behavior in tokamaks

We present details of a new bismuth germanate [Bi(4)Ge(3)O(12) (BGO)] scintillator array used to diagnose the transport and energy behavior of runaway electrons (REs) in DIII-D. BGO exhibits important properties for these compact detectors including high light yield which sufficiently excites photodiode detectors (8500 photons/MeV), high density and atomic numbers of constituent materials which maximizes sensitivity, and relative neutron blindness which minimizes complications in data interpretation. The detectors observe primarily hard x-ray radiation emitted in a forward beamed pattern by RE when they strike first wall materials or bulk ions and neutrals in the plasma, although we also address photoneutron signals. The arrangement of the array enables time resolved location of x-ray emission and associated asymmetries which help identify instabilities and confinement properties of RE. By shielding a subset of detectors with different thicknesses of lead, and with interpretative support of the code EGSNRC, we also measure RE energy, although due to the often distributed nature of RE strike points and the forward beamed character of emitted hard x-rays, we restrict interpretation as a lower bound for RE energy.

Runaway electrons as a diagnostic of plasma internal magnetic fluctuations

The transport of runaway electrons in a high-temperature plasma is relatively easy to measure in a steady state experiment and a perturbation experiment, which provides runaway electron diffusion coefficient Dr. This diffusion coefficient is determined by internal magnetic fluctuations, so it can be interpreted in terms of a magnetic fluctuation level. The internal magnetic fluctuation level (r/BT) is estimated to be about (2–4)×−4 in the HL-1M plasma. The results presented here demonstrate the effectiveness of using runaway electron transport techniques to determine internal magnetic fluctuations. A profile of magnetic fluctuation level in the HL-1M plasma can be estimated from Dr.

Internal magnetic fluctuation in the HL-1M tokamak

The transport of runaway electrons in hot plasma can be comparatively easily measured by steady state or perturbation experiments, which provide runaway electron diffusivity Dr. The runaway diffusion coefficient has been obtained using four methods: (1) Dr is deduced from Plasma shift experiment; (2) Dr is deduced from its sawteeth oscillations behaviors of HXR flux and of SXR intensity; (3) Dr is deduced from microwave radiation intensity sawtoothing behaviors; (4) Dr is deduced from hard-X-ray bremsstrahlung spectra. The diffusivity can be interpreted in terms of a magnetic fluctuation level. The internal magnetic fluctuations level (b～r/BT) is estimated to be about (2—4)×10-4 in the HL-1M plasma. The results presented here demonstrate the effectiveness of using runaway transport techniques for determining internal magnetic fluctuations. A profile of the magnetic fluctuation level in the HL-1M can be estimated from Dr.

Edge turbulence in tokamaks, stellarators and reversed field pinches

Characteristics of electrostatic and magnetic turbulence in the edge of tokamaks, stellarators and reversed field pinches are compared and contrasted. Scalings of turbulent fluctuation levels and wave numbers are discussed. Electrostatic turbulence is shown to explain edge density scale lengths in all three device types. Electrostatic fluctuations also determine edge thermal transport in tokamaks and stellarators, while magnetic fluctuations explain edge thermal transport in reversed field pinches and runaway electron transport in tokamaks and stellarators.

Runaway electrons as a diagnostic of magnetic fluctuations (abstract)

The transport of runaway electrons in a hot plasma can be comparatively easily measured by perturbation experiments. The runaway electron diffusion coefficient is determined by intrinsic magnetic fluctuations rather than electrostatic fluctuations because of the high energies involved. The results presented here demonstrate the efficacy of using runaway transport techniques for determining intrinsic magnetic fluctuations. This work was supported in part by U. S. Department of Energy under grant DE-FG05-88ER-53267 and the Texas Advanced Research Program.