Istvan Pusztai

Reduced kinetic modelling of shattered pellet injection in ASDEX upgrade – CORRIGENDUM - Volume 92 Issue 5

Electrostatic waves are frequently observed at collisionless shocks and are believed to play a key role in energy dissipation. Recent spacecraft observations have identified a proton‐alpha instability in the Earth's bow shock as a potential mechanism to dissipate the energy associated with a relative drift between protons and alpha particles, . At plasma parameters relevant to this setting, we investigate the dependence of the evolution of this instability on through particle‐in‐cell simulations. We find that the instability produces strong ion heating, increasing ion temperatures by factors of two to five. The electrons, in contrast, experience only minimal heating . The heating is highly anisotropic and is most efficient when the wave vector is at a 45 angle to the alpha flow velocity. To interpret these results, we introduce a geometric model based on Landau resonance interaction bands in velocity space. It explains both the angular dependence and the magnitude of heating through the change in velocity distribution functions. At the same time, the wave properties are consistent with linear theory. Our results demonstrate that the proton‐alpha streaming instability can be an important mechanism to convert the bulk kinetic energy of the alphas into ion heating at collisionless shocks.

Commonwealth Fusion Systems (CFS) plans to operate a tokamak power plant called ARC in the early 2030s. Tokamak plasmas have stability limits that, if crossed, lead to a rapid termination of the plasma, referred to as a disruption. Disruptions pose a melt risk to the first wall resulting from thermal and non-thermal particle heat fluxes, and an electromagnetic loading risk on all metal components within the equilibrium coils. A comprehensive set of models is used herein to provide an assessment of both mitigated and unmitigated ARC disruption loads. A preliminary massive gas injection system is baselined and a runaway electron mitigation coil option is proposed to close possible gaps in the baseline. It is predicted that all ARC disruption loads are within a factor of 2 of the disruption loads in SPARC, a tokamak presently under construction by CFS, and therefore SPARC provides an opportunity to calibrate models, test solutions and inform the design of ARC. The goal for ARC is disruption-free operation, however, the pragmatic design target is to withstand one mitigated disruption per day, and to restart the plasma following mitigation in tens of seconds without interrupting the power output. Unmitigated disruptions must be rare, and experience with unmitigated disruption impacts in SPARC will better define what rare means. The implications of this strategy for plasma disruptivity and disruption prediction are discussed, and operating the ARC scenario on SPARC is expected to refine the ARC final design and operational plan.

Electrostatic waves are frequently observed at collisionless shocks and are believed to play a key role in energy dissipation. Recent spacecraft observations have identified a proton-alpha instability in the Earth’s bow shock as a potential mechanism to dissipate the energy associated with a relative drift between protons and alpha particles, uα. At plasma parameters relevant to this setting, we investigate the dependence of the evolution of this instability on uα through particle-in-cell simulations. We find that the instability produces strong ion heating, increasing ion temperatures by factors of two to five. The electrons, in contrast, experience only minimal heating (~1%). The heating is highly anisotropic and is most efficient when the wave vector is at a 45° angle to the alpha flow velocity. To interpret these results, we introduce a geometric model based on Landau resonance interaction bands in velocity space. It explains both the angular dependence and the magnitude of heating through the change in velocity distribution functions. At the same time, the wave properties are consistent with linear theory. Our results demonstrate that the proton-alpha streaming instability can be an important mechanism to convert the bulk kinetic energy of the alphas into ion heating at collisionless shocks.

This article provides an introduction to kinetic plasma physics through the theory of charged particle motion in prescribed, inhomogeneous, and time-dependent electromagnetic fields. Starting from the exact solution in uniform, static fields, we identify the fundamental spatial and temporal scales of magnetized motion—the Larmor radius and cyclotron frequency—which enable systematic expansions when the electromagnetic fields vary slowly compared with these intrinsic scales. Under this drift (adiabatic) ordering, particle dynamics separates into rapid gyromotion and slower guiding-centre motion. We derive the guiding-centre equations by progressively incorporating spatial and temporal field variations and examine the emergence of adiabatic invariants, including conservation of the magnetic moment and higher-order corrections obtained perturbatively. Applications to tokamak geometry illustrate the implications for magnetic confinement. Finally, we briefly discuss extensions beyond the ideal collisionless picture, including Debye shielding, radiation reaction, and the effects of collisions and turbulence.

A disrupting plasma in a high-performance tokamak such as ITER or SPARC may generate large runaway electron currents that, upon impact with the tokamak wall, can cause serious damage to the device. To quickly identify regions of safe operation in parameter space, it is useful to develop reduced models and analytical criteria that predict when a significant fraction of the Ohmic current is converted into a current of runaway electrons. In deuterium–tritium plasmas, the seed runaway current may have a significant contribution from – or may even be dominated by – tritium beta decay and Compton scattering. In this work, a criterion for significant runaway electron generation that includes tritium beta decay and Compton scattering sources is developed. The avalanche gain factor includes the effects of partial screening of injected noble gases. The result is an analytical model that can predict significant runaway electron generation in the next generation of activated tokamak devices. The model is validated by fluid simulations using Dream (Hoppe et al. 2021 Comput. Phys. Commun. , vol. 268, p. 108098) and is shown to delineate regions in parameter space where significant runaway electron generation may occur.

The dual aims of accuracy and computational efficiency in computational plasma physics lend themselves well to the use of fluid models. The first of these goals, however, is only satisfied for such models insofar as the utilized closure can capture the neglected kinetic physics—something which has proven challenging for multi-scale collisionless processes. In a recent article [Ingelsten et al., J. Plasma Phys. 91, E64 (2025)], we used the data-driven method of sparse regression to discover a novel heat flux closure for electrostatic phenomena. Here, we generalize the six-term closure model found in that work from single- to multi-species modeling. Using data from OSIRIS particle-in-cell simulations over a range of initial conditions, we then demonstrate how the unknown coefficients in front of the three most important terms in the closure can be estimated from box-averaged fluid quantities. Both neural networks and a newly developed framework for nonlinear sparse regression are showcased. The resulting models predict the heat flux for each species with a typical accuracy of 80%–90% and regularly account for 85%–95% of the rate of change in the pressure. The models are also compared with results from multi-species linear collisionless theory.

Using fully kinetic particle-in-cell simulations, we investigate the stability and performance of autoresonant plasma beat-wave excitation in plasmas with tailored density profiles. We show that a prescribed spatial variation of the background density sustains continuous phase locking between the driving laser beat and the excited plasma mode, thereby enabling precise control of the shape and group velocity of the plasma wavepacket and providing an alternative to frequency chirping of the drive lasers. The density-gradient scale is found to govern the nonlinear autoresonant growth, and the attainable saturation amplitude can exceed the classical Rosenbluth–Liu prediction and, for appropriate laser intensities, approach the nonrelativistic wave-breaking limit. We show that a four-laser configuration in a steep parabolic density profile can generate a specially confined two-phase quasi-periodic plasma lattice. The generation of such structures may lead to novel applications in plasma photonics.

Laser wakefield acceleration can generate a femtosecond-scale broadband X-ray betatron radiation pulse from electrons accelerated by an intense laser pulse in a plasma. The micrometer-scale of the source makes wakefield betatron radiation well-suited for advanced imaging techniques, including diffraction and phase-contrast imaging. Recent progress in laser technology can expand these capabilities into the attosecond regime, where the practical applications would significantly benefit from the increased energy contained within the pulse. Here we use numerical simulations combined with batch Bayesian optimization to enhance the radiation produced by an attosecond betatron source. The method enables an efficient exploration of a multi-parameter space and identifies a regime in which a plasma density spike triggers the generation of a high-charge electron beam. This results in an improvement of more than one order of magnitude in the on-axis time-averaged power within the central time containing half of the radiated energy, compared to the reference case without the density spike.