Neutral atoms recycled from wall interaction interact with confined plasma, thereby refuelling it, most strongly in the region closest to the wall. This occurs near the X-point in diverted configurations, or else near the wall itself in limited configurations. A progression of analytic models is developed for neutral density in the vicinity of a planar or linear source in an ionising domain. First-principles neutral transport simulations with DEGAS2 are used throughout to test the validity and limits of the model when using equivalent sources. The model is further generalised for strong plasma gradients or the inclusion of charge exchange. An important part of the problem of neutral fuelling from recycling is thereby isolated and solved with a closed-form analytic model. A key finding is that charge exchange with the confined plasma can be significantly simplified with a reasonable sacrifice of accuracy by treating it as a loss. The several assumptions inherent to the model (and the simulations with which it is compared) can be adapted according to the particular behaviour of neutrals in the divertor and the manner in which they cross the separatrix.

One of the more interesting features of kinetic descriptions of plasmas are resonant wave particle interactions. These often appear to be collisionless as the collision frequency does not appear in key results even though collisions are actually vital whenever the Coulomb logarithm is large. This deceptive behaviour normally occurs when a resonance is resolved by causality or by inserting a small Krook collision frequency in a linearised kinetic equation to resolve a singularity. However, the actual behaviour of the resonance is more complicated as a narrow collisional boundary layer is responsible for resolving the singular behaviour. The most remarkable example is linear Landau damping, which is normally viewed as a collisionless process. However, an evaluation by Zakharov & Karpman (1963 Sov. Phys. JETP vol. 16, pp. 351-357) proved it to be a collisional process for which collisions can never be ignored for a finite wave amplitude in the collisionless limit. This realisation implies that a small tail bump on a Maxwellian will have a growth or damping rate sensitive to collisions for a finite amplitude monochromatic plasma wave in the very weak collisionality limit. This behaviour is verified here by retaining collisions in both the island dominated limit, as well as the linear, collisional boundary layer dominated regime.

This study investigates the Lagrangian properties of ion turbulent transport driven by drift-type turbulence in tokamak plasmas focusing on the Cyclone Base Case. Despite the compressible and inhomogeneous nature of Eulerian gyrocentre drifts, numerical simulations with the T3ST code reveal approximate ergodicity, stationarity and time-symmetry. These characteristics are attributed to broad initial phase-space distributions that support ergodic mixing. Moreover, relatively minor constraints on the initial distributions are found to have negligible effects on transport levels.

First of a kind comprehensive full-f drift-kinetic (DK) and $\delta$-f gyrokinetic (GK) turbulent simulations are carried out in a linear plasma device. We self-consistently derive an electrostatic model including large-scale slowly varying DK-ordered fields coupled to small-scale rapidly fluctuating GK-ordered fields. By relying on the critical balance ordering, we show that the electrons are described by a drift-reduced Braginskii model while we rely on a Hermite–Laguerre spectral expansion for describing both the DK and GK parts of the ion distribution function. Global simulations are carried out using the parameters of the linear device LAPD, showing that the DK part of the ion distribution function is approximately a bi-Maxwellian. It is observed that the GK fields do not affect the DK fields at the physical LAPD collisionality. Only when the collisionality is reduced and the source term is amplified for the GK fluctuations, an amplification of small-scale turbulent structures is observed. The findings are supported by linear results that show that the simulations are dominated by turbulent fluctuations that are Kelvin–Helmholtz driven. Additionally, a GK Kelvin–Helmholtz-like mode is observed in the low-GK-collisionality regime which can nonlinearly drive small-scale structures.

Cross-field electron transport in partially magnetised plasmas arises from collective, nonlinear instability dynamics that remain only partially understood despite their importance to a wide range of E × B plasma devices. In systems such as Hall thrusters, azimuthal instabilities strongly affect electron confinement and spectral energy distribution, motivating efforts to examine how external modulation may influence these effects. Here, one-and two-dimensional particle-in-cell simulations are employed to investigate how an axially applied oscillatory electric field modifies the instability spectra and the associated cross-field electron transport. The simulations adopt local slab idealisations of an E × B discharge designed to isolate modulation–instability coupling mechanisms and the conclusions should be interpreted within this controlled modelling framework. The simulations show that the plasma response depends sensitively on modulation frequency and amplitude. Notably, modulation near 40 MHz diminishes the amplitude of the electron cyclotron drift instability and reduces axial electron transport by up to 30 %, while modulation near the electron cyclotron frequency leads to spectral broadening and enhanced transport. Bicoherence analysis of the azimuthal electric field fluctuations indicates nonlinear coupling among instability modes, suggesting that modulation reshapes energy pathways, thereby explaining the observed spectral variations. We further show that modulation modifies the phase alignment between azimuthal-electric-field and electron-density fluctuations, in turn directly affecting the observed suppression or amplification of electron transport across modulation regimes. The results provide quantitative evidence of how external modulation can alter instability characteristics in E × B plasmas and point to strategies for controlling electron transport in cross-field plasma technologies, such as Hall thrusters and magnetrons.

Geometrical optics (GO) is widely used for reduced modelling of waves in plasmas, but it fails near reflection points, where it predicts a spurious singularity of the wave amplitude. We show how to avoid this singularity by adopting a different representation of the wave equation. Instead of the physical coordinate $x$ and the wavevector $k$, we use the ray time $\tau$ as the new canonical coordinate and the ray energy $h$ as the associated canonical momentum. To derive the envelope equation in the $\tau$-representation, we construct the Weyl symbol calculus on the $(\tau , h)$ space and show that the corresponding Weyl symbols are related to their $(x, k)$ counterparts by the Airy transform. This allows us to express the coefficients in the envelope equation through the known properties of the original dispersion operator. When necessary, solutions of this equation can be mapped to the $x$-space using a generalised metaplectic transform. However, the field per se might not even be needed in practice. Instead, knowing the corresponding Wigner function usually suffices for linear and quasilinear calculations. As a Weyl symbol itself, the Wigner function can be mapped analytically, using the aforementioned Airy transform. We show that the standard Airy patterns that form in regions where conventional GO fails are successfully reproduced within metaplectic GO (MGO) simply by remapping the field from the $\tau$-space to the $x$-space. An extension to mode-converting waves is also presented. This formulation, which we call generalised MGO, can be particularly useful, for example, for reduced modelling of the O–X conversion in inhomogeneous plasma near the critical density, an effect that is important for fusion applications and also occurs in the ionosphere. Overall, MGO can replace GO for any practical purposes, because it better handles cutoffs and is similar otherwise.

Recently, Alfvénic ion temperature gradient (AITG) modes have been observed in the core plasma on the HL-2A tokamak. Only when electron cyclotron resonance heating (ECRH) and neutral beam injection are simultaneously injected into the deuterium plasma do the AITG modes become unstable. The instability is electromagnetic and localised in the core plasma with an internal transport barrier. Dynamic evolution of AITG modes is greatly affected by the off-axis ECRH. Theoretical analysis suggests that there is a strong dependence of the AITG modes on $\eta _i\simeq \boldsymbol{\nabla }\ln T_i/\boldsymbol{\nabla }\ln n_i$, where $n_i$ is the ion density. It is also found that ECRH can enhances AITG modes by causing a drop of electron density and an increase of $\tau =T_e/T_i$; here $T_e$ and $T_i$ are the electron and ion temperatures, respectively. Besides, high-power ECRH may also change the safety factor or magnetic shear and then contribute to the mitigation of AITG modes. The new findings can not only enrich scientific knowledge for pressure gradient-driven instability, but also be beneficial to active control of core-localised electromagnetic modes in future fusion devices.

The magnetic confinement topologies potentially capable of macro-stability with core plasma pressure greatly exceeding the vacuum magnetic field pressure (or ‘$\beta \rightarrow \infty$’) are discussed. An emphasis is placed on application to magnetic fusion energy (MFE) given the perceived advantages. The particle loss rate from highly diamagnetic plasmas in open-field topologies is quantified, including a generalised model for the gas-dynamic regime. It is concluded that, regardless of the topology type, attractive fusion energy gain from such a system is impossible unless (i) the scrape-off-layer can be made much thinner than one thermal ion gyroradius through ambipolar effects, (ii) sufficient stability exists in the stochastic phase space of certain topologies so as to increase the average number of ion orbits before loss by $\sim$1000 times over the isotropic prediction or (iii) electrostatic or centrifugal effects are used to recover adiabatic confinement. Outside of MFE, high-$\beta$ topologies offer many alternative applications in plasma science. The required magnet bore to limit perpendicular particle loss in a point cusp is estimated. Additionally, the unique spherical multipole topology is reviewed and comments are made on the use of cusp topologies for ‘electromagnetic’ confinement efforts.

The present paper sketches a framework for solving the wave and Fokker–Planck equations in the ion cyclotron resonance frequency domain fully self-consistently. It illustrates that this can be done by first constructing ‘building blocks’ that are commonly needed by the wave and Fokker–Planck equations, allowing us e.g. to account for wave coupling in plasmas containing non-Maxwellian distributions. Up to minor upgrades, the paper exploits known expressions and methods to solve the 2 intimately connected aspects of the description of the wave–particle interaction underlying ion cyclotron resonance heating. Two cases are presented: the case where the guiding centre motion is limited to just following magnetic field lines, and the extended case accounting for drifts away from magnetic surfaces but assuming axisymmetry. A limited set of analytical results is included. As combining wave and Fokker–Planck solutions is the focus, the computation of the dielectric response for arbitrary distribution functions is illustrated as well.

A magnetohydrodynamic (MHD) shock is a discontinuity through which plasma flows, while the mass, momentum and energy are conserved, and the entropy increases. In a collisionless system, the entropy is strictly constant along the phase-space trajectory. The MHD required entropy increase is attributed to dissipative processes causing relaxation to local thermodynamic equilibrium. The search for such dissipative processes in the shock observations usually explores variations of the entropy density or entropy per particle across the shock front. We show that both quantities may increase or decrease across the shock front even when the entropy is strictly conserved. Entropy production should be assessed using the entropy flux density.

Diffuse accretion flows near a supermassive black hole are fundamentally weakly collisional. In such weakly collisional plasmas, the ion and electron distribution functions can deviate significantly from thermal equilibrium, and particle kinetic effects can influence large-scale fluid motion by driving pressure anisotropy, heat conduction and plasma instabilities. Modelling these plasma effects in highly relativistic flows may be important for interpreting horizon-scale observations of black hole images. In this paper, we present a theoretical framework for understanding weakly collisional plasmas in general relativity by deriving the relativistic drift kinetic equations from the Vlasov–Maxwell equations. We present the evolution equations for the moments of the gyroaveraged distribution function and introduce a new analytic Landau fluid closure to capture anisotropic heat flow in relativistic plasmas. Unlike standard (collisional) general relativistic magnetohydrodynamics or extended magnetohydrodynamics, our model does not rely on strong collisions to enforce thermal equilibrium and consistently incorporates Landau damping in a fluid closure. The model introduced in this work provides a complementary approach to fully kinetic simulations in understanding weakly collisional effects in low-luminosity relativistic black hole accretion disks.

A conservative formulation of the drift-reduced fluid plasma model is constructed by analytically inverting the implicit relation defining the polarisation velocity as a function of the time derivative of the electric field. The obtained model satisfies exact conservation laws for energy, mass, charge and momentum, in arbitrary magnetic geometry, also when electromagnetic fluctuations are included.

Vlasov–Poisson–Fokker–Planck (VPFP) simulations of large-amplitude electron plasma waves, where the bounce frequency is much larger than the collision frequency, $\omega _B \gg \nu _{\textit{ee}}$, show that the evolution of these waves exhibits three phases: (i) a short-lived trapping phase during which collisional effects are minimal; (ii) a long-lived detrapping phase during which collisional effects are most influential; (iii) a short-lived Landau damping phase where the effect of collisions becomes minimal again. While the dispersion relation during the trapping and Landau damping phase is well known, the wave behaviour during the detrapping phase is not as well understood. The simulations show that during the detrapping phase, the interplay between weak electron–electron collisions and strong wave–electron interactions results in an increasing frequency shift further from the linear root, $\omega _{\text{EPW}}$. At the conclusion of the detrapping phase, the distribution function is nearly Maxwellian, the frequency shift rapidly diminishes and the wave damps at a larger rate than the Landau damping rate. Empirical fits to the damping rates, frequency shift enhancement rate and the lifetime of the plasma waves are provided as functions of collision frequency, wavenumber and wave amplitude.

This study investigates ion kinetic effects during the parametric decay instability (PDI) of parallel-propagating Alfvén waves under plasma conditions characteristic of the Earth’s ionosphere. By using a series of hybrid particle-in-cell simulations, we examine the evolution of ion velocity distribution functions (VDFs) in ultra-low-beta plasmas. Our numerical campaign systematically explores the dependence on key parameters (plasma beta, pump-wave amplitude and polarisation, and ion composition). To emphasise the role of kinetic effects, we choose to trigger the PDI with a dispersive mother wave with wavelength comparable to the ion characteristic inertial length. Our results reveal pronounced non-thermal VDF modifications, including parallel heating and the formation of secondary ion beams, linked to the nonlinear evolution of parametric decay instability. By varying the plasma beta and the pump-wave amplitude, we identify a critical regime where rapid and complete broadening of the velocity distribution function is observed, triggering bidirectional ion acceleration. Notably, simulations modelling realistic ionospheric conditions demonstrate that even low-amplitude Alfvénic perturbations can induce significant VDF spreading and ion beam generation, with hydrogen ions exhibiting stronger effects than oxygen. These non-thermal microscopic processes offer a plausible mechanism for particle precipitation in space weather events. This work represents the first comprehensive study with hybrid simulations of PDI-driven ion kinetics in ultra-low-beta plasmas, providing quantitative estimates for the time delay between electromagnetic wave impact and ion VDF modification, and new insights into wave–particle interactions that may contribute to ion acceleration, precipitation processes and space plasma dynamics.

The non-resonant divertor (NRD) offers a promising exhaust solution for stellarators, combining topological simplicity with resilience to magnetic field perturbations. To experimentally validate the robustness of NRDs in a quasi-axisymmetric (QA) configuration, we introduce STAR_Lite, a new stellarator experiment at Hampton University. This paper details the design and analysis of the first STAR_Lite coil configuration, STAR_Lite-A. The two-field-period configuration manifests an NRD through X-points with zero rotational transform, at the top and bottom of the device. The divertor legs extruding from the X-points are topologically similar to the poloidal divertors of tokamaks. To expand the experimental range, STAR_Lite-A is optimised for experimental flexibility, producing a wide range of distinct QA configurations by only varying the currents in the modular coils. The NRDs not only persist across these configurations, but numerical strike-line simulations confirm that heat exhaust remains resilient to changes in coil currents, with plasma following the divertor legs and creating a toroidal, discontinuous, strike pattern. We further examine the resilience of the NRD to magnetic perturbations caused by manufacturing errors in the modular coils. We find that quasi-symmetry and the existence of X-points are well preserved under these magnetic field changes, but the rotational transform may vary substantially and displacements of the divertor X-points may lead to one X-point having a dominant effect on edge transport. Overall, our analysis indicates that a compact, modular design can likely generate a resilient NRD structure while satisfying the practical constraints of a university-scale experiment.

We address three two-dimensional magnetohydrodynamics models: reduced magnetohydrodynamics (RMHD), Hazeltine’s model and the Charney–Hasegawa–Mima (CHM) equation. These models are derived to capture the basic features of magnetohydrodynamic turbulence and plasma behaviour. They all possess non-canonical Hamiltonian formulations in terms of Lie–Poisson brackets, which imply an infinite number of conservation laws along with symplecticity of the phase flow. This geometric structure in phase space affects the statistical long-time behaviour. Therefore, to capture the qualitative features in long-time numerical simulations, it is critical to use a discretisation that preserves the rich phase space geometry. Here, we use the matrix hydrodynamics approach to achieve structure-preserving discretisations for each model. We furthermore carry out long-time simulations with randomised initial data and a comparison between the models. The study shows consistent behaviour for the magnetic potential: both RMHD and Hazeltine’s model produce magnetic dipoles (in CHM, the magnetic potential is prescribed). These results suggest an inverse cascade of magnetic energy and of the mean-square magnetic potential, which is empirically verified via spectral scaling diagrams. On the other hand, the vorticity field dynamics differs between the models: RMHD forms sharp vortex filaments with rapidly growing vorticity values, whereas Hazeltine’s model and CHM show only small variation in the vorticity values. Related to this observation, both Hazeltine’s model and CHM give spectral scaling diagrams indicating an inverse cascade of kinetic energy not present in RMHD.

We demonstrate that a localised simple shear in an electrically conducting fluid can generate dynamo action, due to the presence of a distant solid wall with anisotropic electrical conductivity or magnetic permeability. Three cylindrical geometries are considered, depending on the position of the solid wall relative to the shear zone. The wall can be either (a) internal, (b) external, or (c) both internal and external, relative to the shear zone. For each of the three geometries, the dynamo threshold is derived analytically. Results are presented with experimental applications in mind, corresponding to present, past or future dynamo experiments. We also consider an application to the Earth’s core, assuming anisotropic electrical conductivity in the inner core and some shear in the tangent cylinder.

The generation of terahertz (THz) ion acoustic waves (IAWs) via the decay instability of femtosecond laser-driven Langmuir waves in a plasma is investigated theoretically. A high-intensity femtosecond laser pulse incident on a plasma at an oblique angle excites large-amplitude Langmuir waves near the critical layer, which subsequently decay into IAWs and secondary plasma waves. We derive analytical expressions for the laser electric field components, incorporating spatial and temporal Gaussian profiles, and model the energy transfer dynamics between waves and electrons. Landau damping and resonance absorption are identified as critical mechanisms governing the heating of electrons, with the damping rate $\Gamma$ derived in normalised form, revealing an exponential dependence on the normalised wave frequency. The temporal evolution of electron temperature is quantified, showing a direct relationship with the laser field intensity and plasma parameters. Furthermore, the inhomogeneous Airy equation formalism is employed to solve for the electric field structure near resonance layers, highlighting the role of plasma scale length and thermal velocity in wave localisation. Our results demonstrate efficient THz IAW generation under optimised laser and plasma conditions, with the damping rate minimised at specific frequency ratios, enabling sustained wave propagation. This work advances the understanding of laser–plasma interactions for THz wave generation, offering insights for applications in high-frequency radiation sources and plasma diagnostics.

This paper revisits the onset of high-harmonic fast-wave (HHFW) propagation in the scrape-off layer (SOL) plasma of the NSTX/NSTX-U spherical tokamak, motivated by past HHFW heating and current drive experiments and modelling. Previously, the fast-wave propagation in the SOL was correlated with the opening (suppression) of the fast-wave right-hand cutoff layer in front of the antenna. In this work, the SOL propagation is interpreted as a geometric waveguide mode guided by the SOL geometry, whose radial width can be comparable to the wave’s perpendicular wavelength in the HHFW regime. A two-dimensional circular model is first employed using full-wave solvers to characterise the poloidal eigenmode structures and to clarify their relationship to annulus resonance. By progressively adding a tokamak-like magnetic-field configuration, starting from a uniform axial field, the effects of magnetic-field gradients and pitch on the SOL waveguide mode are characterised. The poloidal mode numbers supported by the SOL plasma agree well with analytic estimates, indicating that an anisotropic plasma in a bounded geometry selectively supports and amplifies the resonant poloidal mode number. Additionally, two-dimensional axisymmetric NSTX-U simulations demonstrate that the SOL eigenmode features identified in the circular model persist in the experimentally relevant configurations. A control approach based on lengthening the wave perpendicular wavelength relative to the SOL width, including a higher magnetic (B)-field operation, is discussed. The analysis here shows the key role of a bounded geometry in interpreting HHFW eigenmode coupling and propagation in the NSTX-U SOL plasma.