Plasma terminating disruptions in tokamaks may result in relativistic runaway electron beams with potentially serious consequences for future devices with large plasma currents. In this paper, we investigate the effect of plasma elongation on the coupled dynamics of runaway generation and resistive diffusion of the electric field. We find that elongated plasmas are less likely to produce large runaway currents, partly due to the lower induced electric fields associated with larger plasmas, and partly due to direct shaping effects, which mainly lead to a reduction in the runaway avalanche gain.

The necessity for compact table-top x-ray sources with higher brightness, shorter wavelength and shorter pulse duration has led to the development of complementary sources based on laser-plasma accelerators, in contrast to conventional accelerators. Relativistic interaction of short-pulse lasers with underdense plasmas results in acceleration of electrons and in consequence in the emission of spatially coherent radiation, which is known in the literature as betatron radiation. In this article, we report on our recent results in the rapidly developing field of secondary x-ray radiation generated by high-energy electron pulses. The betatron radiation is characterized with a novel setup allowing to measure the energy, the spatial energy distribution in the far-field of the beam and the source size in a single laser shot. Furthermore, the polarization state is measured for each laser shot. In this way, the emitted betatron x-rays can be used as a non-invasive diagnostic tool to retrieve very subtle information of the electron dynamics within the plasma wave. Parallel to the experimental work, 3D particle-in-cell simulations were performed, proved to be in good agreement with the experimental results.

Experimental evidence supporting the theory of hot tail runaway electron (RE) generation has been identified in TEXTOR disruptions. With higher temperature, more REs are generated during the thermal quench. Increasing the RE generation by increasing the temperature, an obvious RE plateau is observed even with low toroidal magnetic field (1.7 T). These results explain the previously found electron density threshold for RE generation.

In a tokamak, trapped electrons subject to a strong electric field cannot run away immediately, because their parallel velocity does not increase over a bounce period. However, they do pinch toward the tokamak center. As they pinch toward the center, the trapping cone becomes more narrow, so eventually they can be detrapped and run away. When they run away, trapped electrons will have a very different signature from circulating electrons subject to the Dreicer mechanism. The characteristics of what are called trapped-electron runaways are identified and quantified, including their distinguishable perpendicular velocity spectrum and radial extent.

We examine the impact of several factors on electron acceleration by a laser pulse and the resulting electron energy gain. Specifically, we consider the role played by: (1) static longitudinal electric field, (2) static transverse electric field, (3) electron injection into the laser pulse, and (4) static longitudinal magnetic field. It is shown that all of these factors lead, under certain conditions, to a considerable electron energy gain from the laser pulse. In contrast with other mechanisms such as wakefield acceleration, the static electric fields in this case do not directly transfer substantial energy to the electron. Instead, they reduce the longitudinal dephasing between the electron and the laser beam, which then allows the electron to gain extra energy from the beam. The mechanisms discussed here are relevant to experiments with under-dense gas jets, as well as to experiments with solid-density targets involving an extended pre-plasma.

We report the observation of two isolated clouds of positrons inside an active thunderstorm. These observations were made by the Airborne Detector for Energetic Lightning Emissions (ADELE), an array of six gamma-ray detectors, which flew on a Gulfstream V jet aircraft through the top of an active thunderstorm in August 2009. ADELE recorded two 511 keV gamma-ray count rate enhancements, 35 s apart, each lasting approximately 0.2 s. The enhancements, which were approximately a factor of 12 above background, were both accompanied by electrical activity as measured by a flat-plate antenna on the underside of the aircraft. The energy spectra were consistent with a source mostly composed of positron annihilation gamma rays, with a prominent 511 keV line clearly visible in the data. Model fits to the data suggest that the aircraft was briefly immersed in clouds of positrons, more than a kilometre across. It is not clear how the positron clouds were created within the thunderstorm, but it is possible they were caused by the presence of the aircraft in the electrified environment.

Based on the analysis of data from the numerous dedicated experiments on plasma disruptions in the TEXTOR tokamak the mechanisms of the formation of runaway electron (RE) beams and their losses are proposed. The plasma disruption is caused by a strong stochastic magnetic field formed due to nonlinearly excited low-mode-number magneto-hydro-dynamics (MHD) modes. It is hypothesized that the RE beam is formed in the central plasma region confined by an intact magnetic surface due to the acceleration of electrons by the inductive toroidal electric field. In the case of plasmas with the safety factor $q(0)<1$ the most stable RE beams are formed by the outermost intact magnetic surface located between the magnetic surface $q=1$ and the closest low-order rational surface $q=m/n>1~(q=5/4,q=4/3,\dots )$ . The thermal quench (TQ) time caused by the fast electron transport in a stochastic magnetic field is calculated using the collisional transport model. The current quench (CQ) stage is due to the particle transport in a stochastic magnetic field. The RE beam current is modelled as a sum of a toroidally symmetric part and a small-amplitude helical current with a predominant $m/n=1/1$ component. The REs are lost due to two effects: (i) by outward drift of electrons in a toroidal electric field until they touch the wall and (ii) by the formation of a stochastic layer of REs at the beam edge. Such a stochastic layer for high-energy REs is formed in the presence of the $m/n=1/1$ MHD mode. It has a mixed topological structure with a stochastic region open to the wall. The effect of external resonant magnetic perturbations on RE loss is discussed. A possible cause of the sudden MHD signals accompanied by RE bursts is explained by the redistribution of runaway current during the resonant interaction of high-energetic electron orbits with the $m/n=1/1$ MHD mode.

Runaway electrons, which are generated in a plasma where the induced electric field exceeds a certain critical value, can reach very high energies in the MeV range. For such energetic electrons, radiative losses will contribute significantly to the momentum space dynamics. Under certain conditions, due to radiative momentum losses, a non-monotonic feature – a ‘bump’ – can form in the runaway electron tail, creating a potential for bump-on-tail-type instabilities to arise. Here, we study the conditions for the existence of the bump. We derive an analytical threshold condition for bump appearance and give an approximate expression for the minimum energy at which the bump can appear. Numerical calculations are performed to support the analytical derivations.

The transport of energetic electrons is sensitive to magnetic perturbations. By using three-dimensional numerical simulation of test particle drift orbits we show that the transport of untrapped electrons through an open region with magnetic perturbations cannot be described by a diffusive process. Based on our test particle simulations, we propose a model that leads to an exponential loss of particles.

In this paper, we present the guiding-centre transformation of the radiation–reaction force of a classical point charge travelling in a non-uniform magnetic field. The transformation is valid as long as the gyroradius of the charged particles is much smaller than the magnetic field non-uniformity length scale, so that the guiding-centre Lie-transform method is applicable. Elimination of the gyromotion time scale from the radiation–reaction force is obtained with the Poisson-bracket formalism originally introduced by Brizard (Phys. Plasmas, vol. 11, 2004, 4429–4438), where it was used to eliminate the fast gyromotion from the Fokker–Planck collision operator. The formalism presented here is applicable to the motion of charged particles in planetary magnetic fields as well as in magnetic confinement fusion plasmas, where the corresponding so-called synchrotron radiation can be detected. Applications of the guiding-centre radiation–reaction force include tracing of charged particle orbits in complex magnetic fields as well as the kinetic description of plasma when the loss of energy and momentum due to radiation plays an important role, e.g. for runaway-electron dynamics in tokamaks.

High-intensity laser–solid interactions generate relativistic electrons, as well as high-energy (multi-MeV) ions and x-rays. The directionality, spectra and total number of electrons that escape a target-foil is dependent on the absorption, transport and rear-side sheath conditions. Measuring the electrons escaping the target will aid in improving our understanding of these absorption processes and the rear-surface sheath fields that retard the escaping electrons and accelerate ions via the target normal sheath acceleration (TNSA) mechanism. A comprehensive Geant4 study was performed to help analyse measurements made with a wrap-around diagnostic that surrounds the target and uses differential filtering with a FUJI-film image plate detector. The contribution of secondary sources such as x-rays and protons to the measured signal have been taken into account to aid in the retrieval of the electron signal. Angular and spectral data from a high-intensity laser–solid interaction are presented and accompanied by simulations. The total number of emitted electrons has been measured as $2.6\times 10^{13}$ with an estimated total energy of $12\pm 1~\text{J}$ from a $100~{\rm\mu}\text{m}$ Cu target with 140 J of incident laser energy during a $4\times 10^{20}~\text{W}~\text{cm}^{-2}$ interaction.

For ITER-relevant runaway electron studies, such as suppression, mitigation, termination and/or control of a runaway beam, it is important to obtain the runaway electrons after the disruption. In this paper we report on the first discharges achieved with a post-disruptive runaway electron beam, termed a ‘runaway plateau’, in the COMPASS tokamak. The runaway plateau is produced by a massive gas injection of argon. Almost all of the disruptions with runaway electron plateaus occurred during the plasma current ramp-up phase. The Ar injection discharges with and without a runaway plateau were compared for various parameters. Parametrisation of the discharges shows that the COMPASS disruptions fulfil the range of parameters important for runaway plateau occurrence. These parameters include electron density, electric field, disruption speed, effective safety factor, and the maximum current quench electric field. In addition to these typical parameters, the plasma current value just before the massive gas injection proved to be surprisingly important.

Disruptions with runaway electron generation have been deliberately induced by injection of argon using a disruption mitigation valve. A second disruption mitigation valve has been utilised to inject varying amounts of helium after a short time delay. No generation of runaway electrons has been observed when more than a critical amount of helium has been injected no later than 5 ms after the triggering of the first valve. The required amount of helium for suppression of runaway electron generation is up to one order of magnitude lower than the critical density according to Connor & Hastie (1975) and Rosenbluth & Putvinski (1997).

The Sun is a giant particle accelerator. During solar flares, magnetic field energy stored in the corona is suddenly released and transferred to local heating of the coronal plasma, mass motions (e.g. jets) and the generation of energetic particles, i.e. electrons, protons and heavy ions. Basically, a flare occurs as a local enhancement of the emission of electromagnetic radiation from the radio up to the ${\it\gamma}$ -ray range on the Sun. That indicates the production of energetic electrons during flares. NASA’s RHESSI mission has the aim to investigate electron acceleration processes by studying the Sun’s X-ray and ${\it\gamma}$ -ray emission with high spatial, temporal and spectral resolution, i.e. by means of imaging spectroscopy. A substantial part of the energy released during a flare is carried by these energetic electrons. Apart from them, solar energetic particles, i.e. protons and heavy ions, and coronal mass ejections play an important role in the energy budget of a flare. Here, we focus on electron acceleration. The way in which $10^{36}$ electrons are accelerated up to energies beyond 30 keV is one of the open questions in solar physics. A flare is considered as the manifestation of magnetic reconnection in the solar corona. Which mechanisms lead to the production of energetic electrons in the magnetic reconnection region is discussed in this paper. Two of them are described in more detail.

The behaviour of runaway electrons have been investigated in lower hybrid current drive (LHCD) and electron cyclotron current drive (ECCD) plasmas as well as the LHCD only plasmas in the HL-2A tokamak. The fast electrons generated by lower hybrid waves (LHWs) and electron cyclotron waves (ECWs) can act as a seed population for runaway electrons. In the LHCD only discharges, a large number of runaway electrons are produced after the termination of lower hybrid (LH) power by conversion of fast electrons into runaway electrons due to the fast electron tail which extends above the runaway critical energy. However, in contrast to LHCD only discharges, during the simultaneous application of LHCD and ECCD discharges, runaway electrons cannot be created by the termination of LH power when the ECCD is on duty. The runaway production is observed to be enhanced until the EC power termination. The loop voltage increase due to the termination of EC power gives rise to a decline in the critical runaway energy, which leads to some of the energetic fast electrons converting into runaway electrons via the acceleration from the toroidal electric field. That is, the fast electrons created by waves can be accelerated into the runaway regime due to the Dreicer process.

The effects of an imposed, axial magnetic field $B_{z0}$ on hydrodynamics and energetic electrons in inertial confinement fusion indirect-drive hohlraums are studied. We present simulations from the radiation-hydrodynamics code HYDRA of a low-adiabat ignition design for the National Ignition Facility, with and without $B_{z0}=70~\text{T}$ . The field’s main hydrodynamic effect is to significantly reduce electron thermal conduction perpendicular to the field. This results in hotter and less dense plasma on the equator between the capsule and hohlraum wall. The inner laser beams experience less inverse bremsstrahlung absorption before reaching the wall. The X-ray drive is thus stronger from the equator with the imposed field. We study superthermal, or ‘hot’, electron dynamics with the particle-in-cell code ZUMA, using plasma conditions from HYDRA. During the early-time laser picket, hot electrons based on two-plasmon decay in the laser entrance hole (Regan et al., Phys. Plasmas, vol. 17(2), 2010, 020703) are guided to the capsule by a 70 T field. Twelve times more energy deposits in the deuterium–tritium fuel. For plasma conditions early in peak laser power, we present mono-energetic test-case studies with ZUMA  as well as sources based on inner-beam stimulated Raman scattering. The effect of the field on deuterium–tritium deposition depends strongly on the source location, namely whether hot electrons are generated on field lines that connect to the capsule.

Integrated modelling of electron runaway requires computationally expensive kinetic models that are self-consistently coupled to the evolution of the background plasma parameters. The computational expense can be reduced by using parameterized runaway generation rates rather than solving the full kinetic problem. However, currently available generation rates neglect several important effects; in particular, they are not valid in the presence of partially ionized impurities. In this work, we construct a multilayer neural network for the Dreicer runaway generation rate which is trained on data obtained from kinetic simulations performed for a wide range of plasma parameters and impurities. The neural network accurately reproduces the Dreicer runaway generation rate obtained by the kinetic solver. By implementing it in a fluid runaway-electron modelling tool, we show that the improved generation rates lead to significant differences in the self-consistent runaway dynamics as compared to the results using the previously available formulas for the runaway generation rate.

A runaway avalanche can result in a conversion of the initial plasma current into a relativistic electron beam in high-current tokamak disruptions. We investigate the effect of massive material injection of deuterium–noble gas mixtures on the coupled dynamics of runaway generation, resistive diffusion of the electric field and temperature evolution during disruptions in the deuterium–tritium phase of ITER operations. We explore the dynamics over a wide range of injected concentrations and find substantial runaway currents, unless the current quench time is intolerably long. The reason is that the cooling associated with the injected material leads to high induced electric fields that, in combination with a significant recombination of hydrogen isotopes, leads to a large avalanche generation. Balancing Ohmic heating and radiation losses provides qualitative insights into the dynamics; however, an accurate modelling of the temperature evolution based on energy balance appears crucial for quantitative predictions.