The regulation of electron heat transport in high-$\beta$, weakly collisional, magnetized plasma is investigated. A temperature gradient oriented along a mean magnetic field can induce a kinetic heat-flux-driven whistler instability (HWI), which back-reacts on the transport by scattering electrons and impeding their flow. Previous analytical and numerical studies have shown that the heat flux for the saturated HWI scales as $\beta _e^{-1}$. These numerical studies, however, had limited scale separation and consequently large fluctuation amplitudes, which calls into question their relevance at astrophysical scales. To this end, we perform a series of particle-in-cell simulations of the HWI across a range of $\beta _e$ and temperature-gradient length scales under two different physical set-ups. The saturated heat flux in all of our simulations follows the expected $\beta _e^{-1}$ scaling, supporting the robustness of the result. We also use our simulation results to develop and implement several methods to construct an effective collision operator for whistler turbulence. The results point to an issue with the standard quasi-linear explanation of HWI saturation, which is analogous to the well-known $90^{\circ }$ scattering problem in the cosmic-ray community. Despite this limitation, the methods developed here can serve as a blueprint for future work seeking to characterize the effective collisionality caused by kinetic instabilities.

We construct a description of ion-temperature-gradient (ITG)-driven localised linear modes which retains both wave–particle and magnetic drift resonant effects while capturing the field-line dependence of the electrostatic potential. We exploit the smallness of the magnetic drift and the strong localisation of the mode to resolve the problem with a polynomial–Gaussian expansion in the field-following coordinate. A simple semianalytical formula for the spectrum of the mode is shown to capture long wavelength Landau damping, ion-scale Larmor radius stabilisation, weakening of Larmor radius effects at short wavelengths and magnetic-drift resonant stabilisation. These elements lead to linear spectra with multiple maxima as observed in gyrokinetic simulations in stellarators. Connections to the transition to extended eigenfunctions and those localised by less unfavourable curvature regions (hopping solutions) are also made. The model provides a clear qualitative framework with which to interpret numerically simulated ITG modes’ linear spectra with realistic geometries, despite its limitations for exact quantitative predictions.

We investigate the one-dimensional non-relativistic Weibel instability through the capture of anisotropic pressure tensor dynamics using an implicit 10-moment fluid model that employs the electromagnetic Darwin approximation. The results obtained from the 10-moment model are compared with an implicit particle-in-cell simulation. The linear growth rates obtained from the numerical simulations are in good agreement with the theoretical fluid and kinetic dispersion relations. The fluid dispersion relations are derived using Maxwell’s equations and the Darwin approximation. We also show that the magnetohydrodynamic approximation can be used to model the Weibel instability if one accounts for an anisotropic pressure tensor and unsteady terms in the generalised Ohm’s law. In addition, we develop a preliminary theory for the saturation magnetic field strength of the Weibel instability, showing good agreement with the numerical results.

We study the geometric particle-in-cell methods for an electrostatic hybrid plasma model. In this model, ions are described by the fully kinetic equations, electron density is determined by the Boltzmann relation and space-charge effects are incorporated through the Poisson equation. By discretizing the action integral or the Poisson bracket of the hybrid model, we obtain a finite dimensional Hamiltonian system, for which the Hamiltonian splitting methods or the discrete gradient methods can be used to preserve the geometric structure or energy. The global neutrality condition is conserved under suitable boundary conditions. Moreover, the results are further developed for an electromagnetic hybrid model proposed by Vu (J. Comput. Phys., vol. 124, issue 2, 1996, pp. 417–430). Numerical experiments of finite grid instability, Landau damping and resonantly excited nonlinear ion waves illustrate the behaviour of the numerical methods constructed.

We derive a set of simplified equations that can be used for numerical studies of reduced magnetohydrodynamic turbulence within a small patch of the radially expanding solar wind. We allow the box to be either stationary in the Sun’s frame or to be moving at an arbitrary velocity along the background magnetic-field lines, which we take to be approximately radial. We focus in particular on the case in which the box moves at the same speed as outward-propagating Alfvén waves. To aid in the design and optimization of future numerical simulations, we express the equations in terms of scalar potentials and Clebsch coordinates. The equations we derive will be particularly useful for conducting high-resolution numerical simulations of reflection-driven magnetohydrodynamic turbulence in the solar wind, and may also be useful for studying turbulence within other astrophysical outflows.

This investigation explores the potential formation of a relaxed equilibrium state, specifically the quadruple Beltrami state, in a three-component dusty plasma consisting of electrons, ions and negatively charged dust particles. This equilibrium state is derived by employing momentum-balanced equations along with Ampere's law. The quadruple Beltrami state is a composite of four Beltrami states, each associated with four distinct eigenvalues. Using the variational principle, we obtained the same relaxed state based on the system's constraints, which include magnetofluid energy, and the helicity of electrons, ions and dust particles. The unified flow is also derived. Dynamo action is investigated in two configurations: a rectangular geometry and a rectangular geometry with an internal conductor. Small-scale turbulent dynamo behaviour is observed in the former, while large-scale turbulent dynamo effects are noted in the latter. The magnitude of the magnetic field is found to be greater in the configuration with an internal conductor. Additionally, flow profiles are plotted as functions of Beltrami parameters and density variations of plasma species. This study contributes to the understanding of relaxation theory and the underlying physics of systems with an internal conductor, such as Saturn (planetary rings around a magnetosphere) and Jupiter magnetosphere, Uranus, Neptune, etc.

In this work, we propose a method for optimising stellarator devices to favour the presence of an electron root solution of the radial electric field. Such a solution can help avoid heavy impurity accumulation, improve neoclassical thermal ion confinement and helium ash exhaust, and possibly reduce turbulence. This study shows that an optimisation for such a root is possible in quasi-isodynamic stellarators. Examples are shown for both vacuum and finite plasma pressure configurations.

An analysis of the divertor designs for the Infinity Two fusion pilot plant (FPP) baseline plasma design is presented. The divertor uses an $m=5$, $n=4$ magnetic island chain, where m is the poloidal number and n is the toroidal number. Two divertor designs are presented. A classical divertor that is similar to the Wendelstein 7-X island divertor is analyzed using diffusive field-line following and the fluid code EMC3-Lite. For a baseline $800\text{ MW}$ operating point in Infinity Two, the conditions where the heat flux on the divertor plate remains in the acceptable region are analyzed. In addition a related, but different and novel large island backside divertor (LIBD) design is shown. The LIBD promises improved neutral pumping by closing the divertor through the use of baffling and with a structure inside the island, thus preventing neutralized plasma particles from reente ring the plasma.

The tangential drift of the trapped alpha particles in bounce or transit averaged kinetic treatments of stellarators reverses direction on each flux surface at a particular value of pitch angle. The vanishing of the tangential drift corresponds to a resonance that allows a narrow collisional boundary layer to form due to the presence of pitch angle scattering by the background ions. The alphas in and adjacent to this drift reversal layer are particularly sensitive to collisions because they are in or very close to resonance. As a result, enhanced collisional transport occurs due to the existence of this drift reversal resonance in a nearly quasisymmetric stellarator with a single helicity imperfection. Moreover, the value of the resonant pitch angle for drift reversal on neighbouring flux surfaces varies continuously, with the inner flux surfaces having a larger resonant pitch angle than the outer ones. This pitch angle dependence means phase space ‘tubes’ or ‘pods’ exist that connect the inner flux surfaces to the outer ones. These pods allow collisional radial transport of the alphas to extend over the entire radial cross section. When collisions are finite, but weak, and the single helicity departure from quasisymmetry large enough, the collisionless alpha particle motion remains constrained by collisions as they complete their drift trajectories in phase. In particular, the small radial scales introduced by the radial extent or width of the phase space pods require the retention of the nonlinear radial drift term in the kinetic equation. The associated collisional radial transport is evaluated and found to be significant, but is shown to preferentially remove slower speed alphas without substantially affecting birth alphas.

Turbulence self-organization is studied in the flux-driven regime by means of the reduced model Tokam1D. Derived in the electrostatic and isothermal limit but keeping finite electron and ion temperatures, it features two instabilities that are suspected to dominate turbulent transport at the edge of L-mode tokamak plasmas: interchange (a reduced version of the resistive ballooning modes) and collisional drift waves, governed respectively by an effective gravity parameter $g$ and the adiabaticity parameter $C$. The usual properties of these two instabilities are recovered in the linear regime. The nonlinear study focuses on the self-organization of collisional drift-wave turbulence at $g=0$. It is found that the energy stored in zonal flows (ZFs) decreases smoothly at small $C$ due to the reduction of both electric and diamagnetic stresses. Conversely to gradient-driven simulations, no sharp collapse is observed due to the self-consistent evolution of the equilibrium density profile. The ZFs are found to structure into staircases at small and large $C$. These structures exhibit a rich variety of dynamics but are found to be robust to large perturbations. Their nucleation is found to be critically governed by the phase dynamics. Finally, the staircase structures are lost in the gradient-driven regime, when the system is prevented from storing turbulent energy into the equilibrium density (pressure) profile.

Intermittency as it occurs in fast dynamos in the magnetohydrodynamics (MHD) framework is evaluated through the examination of relations between normalized moments at third order (skewness $S$) and fourth order (kurtosis $K$) for both the velocity and magnetic field, and for their local dissipations. As investigated by several authors in various physical contexts such as fusion plasmas (Krommes 2008 Phys. Plasmas 15, 030703), climate evolution (Sura & Sardeshmukh 2008 J. Phys. Oceano. 38, 639-647), fluid turbulence or rotating stratified flows (Pouquet et al. 2023 Atmosphere 14, 01375), approximate parabolic $K(S)\sim S^\alpha$ laws emerge whose origin may be related to the applicability of intermittency models to their dynamics. The results analyzed herein are obtained through direct numerical simulations of MHD flows for both Taylor–Green and Arnold–Beltrami–Childress forcing at moderate Reynolds numbers, and for up to $3.14 \times 10^5$ turn-over times. We observe for the dissipation $0.2 \lesssim \alpha \lesssim 3.0$, an evaluation that varies with the field, the forcing and when filtering for high-skewness intermittent structures. When using the She & Lévêque (1994) Phys. Rev. Lett. 72, 336-339 intermittency model, one can compute $\alpha$ analytically; we then find $\alpha \approx 2.5$, clearly differing from a (strict) parabolic scaling, a result consistent with the numerical data.

We present two-dimensional global simulations of mitigated and vertically unstable disruptions in ITER in the presence of runaway electrons (REs). An elongated plasma in free-boundary equilibrium is subjected to an artificial thermal quench (TQ) and current profile flattening, followed by one or more massive material injections and a RE avalanche. Scenarios of major disruptions as well as upward and downward vertical displacement events are considered. Results provide important insights into the effects of RE formation, post TQ current profile, injection quantities and timings, and impurity flushout on the overall evolution of disruption and the plasma vertical motion thereof. Interplay between the various effects offers scope for potentially beneficial RE mitigation scenarios.

The linear collisionless plasma response to a zonal-density perturbation in quasisymmetric stellarators is studied, including the geodesic-acoustic-mode oscillations and the Rosenbluth–Hinton residual flow. While the geodesic-acoustic-mode oscillations in quasiaxisymmetric configurations are similar to tokamaks, they become non-existent in quasi-helically symmetric configurations when the effective safety factor in helical-angle coordinates is small. Compared with concentric-circular tokamaks, the Rosenbluth–Hinton residual is also found to be multiplied by a geometric factor $\mathcal {C}$ that arises from the flux-surface-averaged classical polarization. Using the near-axis-expansion framework, we derive an analytic expression for $\mathcal {C}$, which varies significantly among different configurations. These analytic results are compared with numerical simulation results from the global gyrokinetic particle-in-cell code GTC, and good agreement with the theoretical Rosenbluth–Hinton residual level is achieved when the quasisymmetry error is small enough.

In magnetized, stratified environments such as the Sun's corona and solar wind, Alfvénic fluctuations ‘reflect’ from background gradients, enabling nonlinear interactions that allow their energy to dissipate into heat. This process, termed ‘reflection-driven turbulence’, likely plays a key role in coronal heating and solar-wind acceleration, explaining a range of detailed observational correlations and constraints. Building on previous works focused on the inner heliosphere, here we study the basic physics of reflection-driven turbulence using reduced magnetohydrodynamics in an expanding box – the simplest model that can capture local turbulent plasma dynamics in the super-Alfvénic solar wind. Although idealized, our high-resolution simulations and simple theory reveal a rich phenomenology that is consistent with a diverse range of observations. Outwards-propagating fluctuations, which initially have high imbalance (high cross-helicity), decay nonlinearly to heat the plasma, becoming more balanced and magnetically dominated. Despite the high imbalance, the turbulence is strong because Elsässer collisions are suppressed by reflection, leading to ‘anomalous coherence’ between the two Elsässer fields. This coherence, together with linear effects, causes the growth of ‘anastrophy’ (squared magnetic potential) as the turbulence decays, forcing the energy to rush to larger scales and forming a ‘$1/f$-range’ energy spectrum in the process. Eventually, expansion overcomes the nonlinear and Alfvénic physics, forming isolated, magnetically dominated ‘Alfvén vortices’ with minimal nonlinear dissipation. These results can plausibly explain the observed radial and wind-speed dependence of turbulence imbalance (cross-helicity), residual energy, fluctuation amplitudes, plasma heating and fluctuation spectra, as well as making a variety of testable predictions for future observations.

Confinement quality in fusion plasma is influenced significantly by the presence of heavy impurities, which can lead to radiative heat loss and reduced confinement. This study explores the clustering of heavy impurity, i.e. tungsten in edge plasma, using high-resolution direct numerical simulations of the Hasegawa–Wakatani equations. We use the Stokes number to quantify the inertia of impurity particles. It is found that particle inertia will cause spatial intermittency in particle distribution and the formation of large-scale structures, i.e. the clustering of particles. The degrees of clustering are influenced by the Stokes number. To quantify these observations, we apply a modified Voronoi tessellation, which assigns specific volumes to impurity particles. By determining time changes of these volumes, we can calculate the impurity velocity divergence, which allows the clustering dynamics to be assessed. To quantify the clustering statistically, several approaches are applied, such as probability density function (PDF) of impurity velocity divergence and joint PDF of volume and divergence.

The generation of an autoresonantly phase-locked high-amplitude plasma waves to the chirped beat frequency of two driving lasers is studied in two dimensions using particle-in-cell simulations. The two-dimensional plasma and laser parameters correspond to those that optimized the plasma wave amplitude in one-dimensional simulations. Near the start of autoresonant locking, the two-dimensional simulations appear similar to one-dimensional particle-in-cell results (Luo et al., Phys. Rev. Res., vol. 6, 2024, p. 013338) with plasma wave amplitudes above the Rosenbluth–Liu limit. Later, just below wave breaking, the two-dimensional simulation exhibits a Weibel-like instability and eventually laser beam filamentation. These limit the coherence of the plasma oscillation after the peak plasma wave field is obtained. In spite of the reduction of spatial coherence of the accelerating density structure, the acceleration of self-injected electrons in the case studied remains at $70\,\%$ to $80\,\%$ of that observed in one dimension. Other effects such as plasma wave bowing are discussed.

MagNetUS is a network of scientists and research groups that coordinates and advocates for fundamental magnetized plasma research in the USA. Its primary goal is to bring together a broad community of researchers and the experimental and numerical tools they use in order to facilitate the sharing of ideas, resources and common tasks. Discussed here are the motivation and goals for this network and details of its formation, history and structure. An overview of associated experimental facilities and numerical projects is provided, along with examples of scientific topics investigated therein. Finally, a vision for the future of the organization is given.

We solve ‘half’ the problem of finding three-dimensional quasisymmetric magnetic fields that do not necessarily satisfy magnetohydrostatic force balance. This involves determining which hidden symmetries are admissible as quasisymmetries, and then showing explicitly how to construct quasisymmetric magnetic fields given an admissible symmetry. The admissibility conditions take the form of a system of overdetermined nonlinear partial differential equations involving second derivatives of the symmetry's infinitesimal generator.

The Floquet exponents of periodic field lines are studied through the variations of the magnetic action on the magnetic axis, which is assumed to be elliptical. The near-axis formalism developed by Mercier, Solov'ev and Shafranov is combined with a Lagrangian approach. The on-axis Floquet exponent is shown to coincide with the on-axis rotational transform. A discrete solution suitable for numerical implementation is introduced, which gives the Floquet exponents as solutions to an eigenvalue problem. This discrete formalism expresses the exponents as the eigenvalues of a $6\times 6$ matrix.