The Magnetic Recoil Spectrometer (MRS) at the National Ignition Facility is used to measure the neutron spectrum from deuterium–tritium-fuelled inertial confinement fusion implosions via neutron–deuteron elastic scattering and magnetic dispersion of recoil deuterons. From the MRS-determined neutron spectrum, the yield ($Y_n$), apparent ion temperature ($T_i$) and areal density ($\rho R$) are determined. However, anomalous energy modulations in recoil deuterons have been observed in several high-yield indirect drive experiments ($Y_n\sim 10^{16}{-}10^{18}$). These observations raise concerns about their potential impact on the MRS-inferred performance metrics. Analytic calculations and particle-in-cell simulations are used to examine the possible beam–plasma instabilities, which indicate the two-stream instability as a plausible mechanism behind energy modulations. Based on a statistical analysis of synthetic deuteron spectra, the modulation-induced errors are found to be within the errors of the determined $Y_n$, $T_i$ and $\rho R$ values and thus do not have a significant impact on the MRS measurement.

We present a fast, spectrally (exponentially) accurate, automatically differentiable bounce-averaging algorithm that is used to simplify kinetic models. Using this algorithm, implemented in the DESC stellarator optimisation suite, we can perform efficient optimisation of many objectives to improve stellarator performance, such as the effective ripple $\epsilon _{\mathrm{eff}}$ metric for the neoclassical transport coefficient in the low collisionality regime and proxies for energetic particle confinement. For the first time, we optimise a finite-beta stellarator to directly reduce neoclassical ripple transport using reverse-mode differentiation. This ensures the computational cost of differentiation is independent of the number of controllable parameters.

Hosking & Schekochihin (Phys. Rev. X, 2021, vol. 11, 041005) have proposed that statistically isotropic decaying magnetohydrodynamic turbulence without net magnetic helicity conserves the mean square fluctuation level of magnetic helicity in large volumes – or, equivalently, the integral over space of the two-point correlation function of the magnetic-helicity density, denoted $I_{\!H}$. Formally, the conservation and gauge invariance of $I_{\!H}$ require the vanishing of certain boundary terms related to the strength of long-range spatial correlations. These boundary terms represent the ability (or otherwise) of the turbulence to organise fluxes over arbitrarily large distances to deplete or enhance fluctuations of magnetic helicity. In this work, we present a theory of these boundary terms, employing a methodology analogous to that of Batchelor & Proudman (Philos. Trans. R. Soc. A, 1956, vol. 248, p. 369) to determine the relevant asymptotic forms of correlation functions. We find that long-range correlations of sufficient strength to violate the conservation of $I_{\!H}$ cannot develop dynamically if the evolution equation for the magnetic vector potential is chosen to be local in space. Likewise, we find that such correlations cannot develop for a wide class of gauge choices that make this equation non-local (including the Coulomb gauge). Nonetheless, we also identify a class of non-local gauge choices for which correlations that are sufficiently strong to violate the conservation of $I_{\!H}$ do appear possible. We verify our theoretical predictions for the case of the Coulomb gauge with measurements of correlation functions in a high-resolution numerical simulation.

Within the gyrokinetic formalism, we present and analytically study the equations for an explicit treatment of the trapped-electron-modified kinetic ballooning mode (KBM) and the electromagnetic version of the trapped-electron mode, in general geometry. The gradient of the plasma $\beta =8\pi p /B^2,$ the ratio of kinetic to magnetic pressure, is taken to be small enough to avoid including perturbations of the magnetic field strength. Trapped-electron-modified KBMs are first described close to ideal magnetohydrodynamic marginality, retaining the explicit resonant contribution of both ions and trapped electrons, and then in a strongly driven fluid limit. We show that maximum-$\mathcal J$ devices (where $\mathcal J$ is the second adiabatic invariant) enjoy relatively good stability properties at finite $\beta ,$ but the coupling of trapped electron and KBMs might induce modes rotating in the ion direction, thus eluding good maximum-$\mathcal J$ properties. An eigenvalue equation for the finite$\hbox{-}\beta$ trapped-electron-mode is derived and studied. We highlight the possibility of having an electron-temperature-gradient driven electromagnetic instability in regions of bad magnetic curvature. A mechanism for the destabilisation of the trapped-particle-enabled collisionless microtearing mode also is proposed. Our results are general and provide new theoretical ground for the characterisation of several magnetic confinement concepts, such as tokamaks, quasisymmetric and quasi-isodynamic stellarators.

In collisionless astrophysical plasmas, turbulence mediates the partitioning of free energy among cascade channels, and its dissipation into ion and electron heat. The resulting ion heating is often anisotropic, with ions observed to be preferentially heated perpendicular to the local magnetic field; understanding the mechanisms responsible for this heating is a key step in understanding the evolution of such plasmas. In this paper, we use the framework of quasi-linear theory to compute analytically the heating rates of ions interacting with turbulent, large-scale Alfvénic fluctuations. We show how the imbalance of the turbulence (the difference in energies between Alfvénic fluctuations travelling parallel and antiparallel to the magnetic field) modifies the spatiotemporal spectrum of these fluctuations, allowing the heating mechanism to smoothly transition between stochastic heating in balanced turbulence and cyclotron-resonant heating in imbalanced turbulence. The resultant heating rate is found to have a general form regardless of the level of imbalance, exhibiting a suppression related to the conservation of the ions’ magnetic moment at small turbulent amplitudes and recovering previous empirical results in a formal calculation. The results of this work help to consolidate our qualitative understanding of ion heating within astrophysical plasmas, as well as yielding specific quantitative predictions to analyse simulations and observations.

A flexible laboratory configuration on the Big Red Ball device has been created for studying the physics of parallel shock formation by firing a coaxial plasma gun into a pre-existing plasma along the direction of the background magnetic field. At Alfvén Mach numbers near $M_A \sim 2.4$, we observe this plasma gun piston initiate a dispersive whistler pulse and reflect ions that are collisionless against the background. These reflected ions are focused into an on-axis bunch by a concave-forward potential structure specific to the cylindrical geometry. Resonance of these reflected ions with the dispersive whistler waves, though not observed in the experiment, is a potential mechanism for collisionless shock formation.

This paper proposes a novel approach for creating an inverse electron distribution function (EDF). The results of numerical modelling and theoretical analysis are used to present reliable criteria and scaling for the evaluation of the possible inversion of the EDF under specific conditions. By solving the non-local Boltzmann kinetic equation in energy and coordinate variables, it is shown that the simplest way to implement the inversion of the EDF is a glow discharge with a hollow cathode. For such discharges, practical recommendations are developed and specific conditions for the experimental detection of an inverse EDF are identified.

We present a method for imposing quasineutrality and, more generally, charge density conservation in the Vlasov–Poisson (VP) and Vlasov–Ampère (VA) systems, which describe electrostatic plasma dynamics, by applying the Dirac theory of constraints. Leveraging the Hamiltonian field formulations of the VP and VA models, we construct generalised Dirac brackets using the Dirac algorithm. The resulting constrained systems enforce charge density conservation, and consequently quasineutrality, given that the initial charge density is zero, through new advection terms in the Vlasov equations involving generalised-force terms, while the electric field is eliminated from the constrained Vlasov dynamics. To verify charge density conservation we conduct one-dimensional numerical experiments using a semi-Lagrangian method, demonstrating that the enforcement of the quasineutrality constraint significantly modifies the dynamics. This approach enables us to identify the forces required to enforce quasineutrality, offering a systematic way to assess the validity of the quasineutral approximation across different kinetic scales.

In magnetically confined fusion plasmas, the role played by zonal $E \times B$ flow shear layers in the suppression of turbulent transport is relatively well understood. However, less is understood about the role played by the weak shear regions that arise in the non-monotonic radial electric field profiles often associated with these shear layers. In electrostatic simulations from the global total-$f$ gyrokinetic particle-in-cell code XGC, we demonstrate how shearless regions with non-zero flow curvature form zonal ‘jets’ that, in conjunction with neighbouring regions of shear, can act as robust barriers to particle transport and turbulence spreading. By isolating quasi-coherent fluctuations radially localised to the zonal jets, we construct a map model for the Lagrangian dynamics of gyrokinetic test particles in the presence of drift waves. We identify the presence of shearless invariant tori in this model and verify that these tori act as partial phase-space transport barriers in the simulations. We also demonstrate how avalanches impinging on these shearless tori cause eddy detachment events that form ‘cold/warm core ring’ structures analogous to those found in oceanic jets, facilitating transport across the barriers without destroying them completely. We discuss how shearless tori may generically arise from tertiary instabilities or other types of discrete eigenmodes, suggesting their potential relevance to broader classes of turbulent fluctuations.

Structures in tokamak plasmas are elongated along the direction of the magnetic field and short in the directions perpendicular to the magnetic field. Many tokamak simulation codes take advantage of this by using a field-aligned coordinate system. However, field-aligned coordinate systems have a coordinate singularity at magnetic X-points where the poloidal magnetic field vanishes, which makes it difficult to use field-aligned coordinate systems when simulating the core and scrape-off layer simultaneously. Here, we present an algorithm for grid generation and computing geometric quantities in a standard field-aligned coordinate system that avoids the singularity and allows one to conduct two-dimensional gyrokinetic axisymmetric simulations in X-point geometries. Convergence tests of advection, boundary value problems and geometric quantities all show greater than first-order convergence even in the vicinity of the X-point. We also demonstrate the geometric consistency of our algorithm with an example simulation of the spherical tokamak for energy production, which shows machine-precision particle conservation.

The present paper originates from the need to understand nonlinear wave behaviour in dusty plasmas, aiming to explore stable envelope wave propagation and interactions beyond traditional theoretical models. By using nonlinear Schrödinger equation (NLSE) analysis and molecular dynamics (MD) simulations, the study verifies the existence and stable propagation of non-standard envelope waves. It demonstrates elastic like collisions, introduces tuneable parameters for wave shaping and quantifies error trends with nonlinearity. A key breakthrough is confirming that even analytically invalid waveforms remain stable, challenging NLSE constraints. Present results enhance nonlinear wave theory and support precise, tuneable signal transmission in plasma diagnostics and microgravity experiments.

Turbulent transport in magnetic confinement fusion devices governs the overall plasma confinement properties and regulates the plasma–material interaction at the first wall. At the plasma boundary, turbulence is typically investigated through three-dimensional two-fluid flux-driven turbulence simulations. In this work, the GBS boundary turbulence code is extended to enable turbulence simulations in reversed field pinch configurations, encompassing the reversal surface and an arbitrary level of magnetic chaos. The differential operators implemented in the code are modified to avoid the approximations of large aspect ratio and weak poloidal magnetic field. Three-dimensional Poisson and Ampère solvers are implemented to allow for turbulence simulations in conditions of partially or fully disrupted magnetic flux surfaces. This modified version of the GBS code is then applied to simulate turbulence in the boundary of RFX-mod reversed field pinch plasmas. Turbulent eddies across the reversal surface show properties similar to those typically found in tokamak boundary turbulence simulations. Despite the good agreement found with experimental measurements, these simulations reveal a significant limitation of the fluid-based turbulence modelling of the edge region in reversed field pinch plasmas, which arises from the intrinsically short parallel connection length. This conclusion is also supported by a linear gyrokinetic analysis that identifies trapped electron modes as the dominant microinstability in this region.

This work investigates a complex plasma in a capacitively coupled discharge operated in push–pull mode. Experiments are combined with particle-in-cell/Monte Carlo collisions (PIC/MCC) simulations under single-frequency (27.12 MHz) and dual-frequency (2 and 27.12 MHz) excitation. In argon at 20 Pa, non-intrusive measurements of electron density and electron temperature are performed using optical-emission spectroscopy coupled with a collisional–radiative model. Under single-frequency 27.12 MHz excitation, both electron density and electron temperature exhibit a symmetric double-peaked distribution. Under dual-frequency excitation, with the 27.12 MHz voltage amplitude held constant, increasing the 2 MHz voltage amplitude promotes electron transport toward the bulk-plasma centre, and the electron-density profile gradually evolves toward an approximately bulk-uniform distribution. These experimental trends are consistent with the PIC/MCC results. The solid SiO2 particles of 3.9 µm in diameter are dispensed, which levitate in the sheath above the lower electrode. The levitation height of the bottom of the particle cloud remains stable under single-frequency excitation, the dust layer compresses with increasing voltage and void formation exhibits a clear threshold. Under dual-frequency excitation, the void appears at lower voltages, the overall levitation height increases and rises with the 2 MHz voltage amplitude and the void undergoes stepwise growth. These findings show how discharge parameters shape two-dimensional plasma distributions and dust-cloud structure, providing experimental evidence for controlling complex plasmas in dual-frequency push–pull mode.

The near-axis theory for quasi-isodynamic stellarator equilibria is reformulated in terms of geometric inputs to allow greater control of the ‘direct construction’ of quasi-isodynamic configurations and to facilitate understanding of the space of such equilibria. This includes a method to construct suitable magnetic axis curves by solving Frenet–Serret equations and an approach to controlling magnetic surface shaping at first order (plasma elongation), which previously has required careful parameter selection or additional optimisation steps. The approach is suitable for studying different classes of quasi-isodynamic stellarators including different axis ‘helicities’ and topologies (e.g. knotted solutions), and as the basis for future systematic surveys using higher order near-axis theory. As an example application, we explore a family of configurations with per-field-period axis helicity equal to one half, demonstrating an approximate scaling symmetry relating different field period numbers.

We present two-dimensional particle-in-cell simulations of a magnetised, collisionless, relativistic pair plasma subjected to combined velocity and magnetic field shear, a scenario typical at intermittent structures in plasma turbulence. We create conditions where only the Kelvin–Helmholtz instability (KHI) and drift–kink instability (DKI) can develop, while tearing modes are forbidden. The interaction of DKI and KHI generates qualitatively new structures, marked by a thickened shear layer with very weak electromagnetic field, modulated by KH vortices. Over a range of moderately strong velocity shears explored, the interaction of DKI and KHI results in a significant enhancement of dissipation over cases with only velocity shear or only magnetic shear. Moreover, we observe a new and efficient way of particle acceleration where particles are stochastically accelerated by the motional electric field exterior to the shear layer as they meander in an S-shaped pattern in and out of it. This process takes advantage of the bent geometry of the shear layer caused by the DKI–KHI interaction and is responsible for most of the highest-energy particles produced in our simulations. These results further our understanding of dissipation and particle acceleration at intermittent structures, which are present in plasma turbulence across a wide range of astrophysical contexts such as in active galactic nucleus jet sheaths, potentially relevant to limb-brightened emission, etc., and highlight the sensitivity of dissipation to multiple interacting instabilities, thus providing a strong motivation for further studies of their nonlinear interaction at the kinetic level.

This work presents an integrated modelling study of fast-proton distributions generated by ion cyclotron range of frequency (ICRF) minority heating in the Experimental Advanced Superconducting Tokamak (EAST). Using a series of high-confinement (H-mode) discharges with increasing ICRF power levels from 0.8 to 2.4 MW, fast protons were produced via minority heating mechanisms and analysed through simulations using the ASCOT code. The results reveal that the fast protons are primarily concentrated near the fundamental cyclotron resonance layer and exhibit strong power-dependent behaviour in both real-space (R–Z) distribution and velocity space, where R is the major radius and Z is the vertical coordinate. As the ICRF power increases, the energetic proton population shows significant spatial broadening and energy enhancement, reaching up to 1 MeV. The fast-ion pitch-angle distribution becomes increasingly anisotropic, with high-energy ions concentrated around $|\textit{v}_{\|}/\textit{v}| \lt 0.5$, where $\nu$ is the magnitude (speed) of the full velocity vector of the particle. Furthermore, the energy density of fast ions aligns well with the ICRF power deposition profile, confirming efficient central-core heating. These findings, which provide insight into fast-ion behaviour and ICRF heating characteristics in EAST plasmas, also support future fast-ion diagnostics and performance control strategies in EAST and similar experimental conditions.

This paper describes the generation of a target plasma and first experiments on neutral beam injection into the Compact Axisymmetric Toroid (CAT) device. The target plasma produced by a washer-stack gun captures 20 % of a 1.7 MW hydrogen beam injected into a main fast-ion confinement region. The work provides a foundation for future experiments with higher injection power and additional diagnostics to investigate the accumulation of large-orbit fast ions, high plasma beta effects and possible magnetic field reversal.

The phase-space Lagrangian model of Dewar et al. (Phys. Plasmas 27, 062507, 2020) provides a model for incorporating cross-field flow into relaxed equilibria while retaining ideal magnetohydrodynamics force balance. Here, we characterise the steady-state solution space and identify a solvability condition that couples the prescribed constrained flow to the geometry through the metric tensor. Using this condition, we construct equilibria in slab, cylindrical and toroidal geometries. In toroidal geometry, the cross-field flow strongly correlates with magnetic-island structure: varying the angular frequency modifies the dominant Fourier harmonic of the radial component of the magnetic field and can drive a transition from a primary ($m=1$) island to secondary ($m=2$) islands. In slab and cylindrical geometries, flow parameters weakly affect island width but strongly modify equilibrium profiles.

We propose a methodology to infer collision operators from phase space data of plasma dynamics. Our approach combines a differentiable kinetic simulator, whose core component in this work is a differentiable Fokker–Planck solver, with a gradient-based optimisation method to learn the collisional operators that best describe the phase space dynamics. We test our method using data from two-dimensional particle-in-cell simulations of spatially uniform thermal plasmas, and learn the collision operator that captures the self-consistent electromagnetic interaction between finite-size charged particles over a wide variety of simulation parameters. We demonstrate that the learned operators are more accurate than alternative estimates based on particle tracks, while making no prior assumptions about the relevant time scales of the processes and significantly reducing memory requirements. We find that the retrieved operators, obtained in the non-relativistic regime, are in excellent agreement with theoretical predictions derived for electrostatic scenarios. Our results show that differentiable simulators offer a powerful and computational efficient approach to infer novel operators for a wide range of problems, such as electromagnetically dominated collisional dynamics and stochastic wave–particle interactions.