Formation of a high-beta plasma in a mirror magnetic field is studied for the first time using three-dimensional semi-implicit particle-in-cell simulations providing a fully kinetic description of not only ions but also electrons. It is shown that, in addition to the longitudinal jump in electric potential between the centre of the trap and the wall, a radial electric field appears in the plasma. Due to this radial field, almost all of the azimuthal electric current required for equilibrium is created by electrons. It was also found that continuous model injection of plasma into the centre of the trap does not result in reaching the magnetohydrodynamic pressure limit ($\beta =1$) due to the development of the flute instability with an azimuthal number $m=1$. The instability growth rate in such a compact system is found to be comparable to the ion-cyclotron frequency. No stabilising effect is observed either from conducting ends or from the perfectly conducting sidewall. The probable reason for that is fast fluctuations of electric field localised inside the injection region that prevent electrons from being frozen into the field lines.

In situ measurements in space plasmas indicate that the velocity distributions of charged particles are not in thermal equilibrium, deviating from a standard Maxwellian mainly due to anisotropies and suprathermal populations which enhance high-energy tails. Although the standard $\kappa$-distribution (SKD) is well established in modelling these non-equilibrium distributions, its application is often viewed controversially due to certain unphysical implications, in particular divergent velocity moments. To address these issues, the regularised $\kappa$-distribution (RKD) was introduced. Such advanced, in general anisotropic RKDs are invoked here for the first time to investigate oblique firehose instabilities, including those induced by the temperature anisotropy of electrons and protons (the dominant species in space plasmas). In weakly collisional plasmas, both of these instabilities are expected to play significant roles in the self-regulation of the macroscopic properties of space plasmas (such as the expanding solar wind) reported by observations. Is not yet possible to resort to a general dispersion tensor related to RKD plasmas (whose derivation is still a challenge due to the complexity of these models), instead the new generation Arbitrary Linear Plasma Solver (ALPS) is exploited here. The unstable solutions obtained for the already established Maxwellian and SKDs successfully validate the capability of ALPS. For RKDs, the instabilities confirm the stimulating effect of suprathermal populations, with lower $\kappa$ values generally enhancing the firehose growth rates. For the oblique electron firehose instability, RKDs substantially modify the competition between periodic and aperiodic branches only at intermediate angles and can sustain significantly increased growth rates of especially aperiodic modes at highly oblique propagation beyond both the Maxwellian unstable regime and the one that is accessible with SKDs.

We describe the fabrication and operation of a gas puff-injected coaxial plasma gun (CPG) using high-power solid-state switching. Understanding the topological details of the plasma formation and sheath rundown phase are critical for in-space propulsion testing and applications to plasma jet magneto-inertial fusion, for which this CPG is designed. The construction of the CPG electrodes is detailed and used to define the boundary conditions (BCs) for two-dimensional axisymmetric resistive magnetohydrodynamics (MHD) modelling. To the authors’ knowledge, this study represents the first application of the open-source modelling framework of OpenMHD (e.g. Zenitani & Miyoshi 2011 Phys. Plasmas vol. 18, 022105) to an experimental system with physical BCs. Real-time diagnostics of the gas puff injection, plasma sheath ionisation and bulk plasma propagation were synchronised to and referenced against the digital gate signal provided to the custom solid-state switching array. The array is configured to enable reliable and repeatable CPG discharges at 4 kV and 7.7 kA with global shutter camera images taken at digital delay increments throughout the plasma evolution. By tuning the initial conditions (ICs) of OpenMHD modelling, the initial density, velocity and magnetic field profiles, the imaged dynamics could be replicated to a significant degree. While the operation of the CPG deviates from the classic one-dimensional snowplough model, quantifying the multi-dimensional role of blow-by during the rundown phase was the primary result of the resistive MHD modelling. Understanding the plasma profiles through the definition of the ICs will be useful for informing the future placement of diagnostics and enforcing the interaction of the bulk plasma properties with an external magnetic field.

Oscillations and instabilities in $E\!\times\!B$ plasma discharges play a major role in driving turbulence and anomalous transport. The presence of gradients and applied fields that result in a relative drift between the charged species causes the onset of drift-gradient instabilities. This work puts forward a kinetic approach to the low-frequency stability of $E\!\times\!B$, two-species, partially magnetised plasmas. It presents a local linear analysis of electrostatic modes in the long-wavelength limit, assuming wave propagation perpendicular to the magnetic field. Magnetised electrons are described by a drift-kinetic equation, while unmagnetised ions are described as a cold fluid. This allows for a consistent treatment of electron temperature perturbations in an inhomogeneous plasma that takes into account kinetic resonance effects, changing the threshold conditions for drift instabilities previously found in fluid descriptions. The well-known fluid dispersion relation for the collisionless Simon–Hoh instability is recovered by considering the weak magnetic inhomogeneity limit of our kinetic model and, in addition, a perturbative extension of the instability criterion that includes the gradients of the magnetic field and the electron temperature is obtained.

QuickPIC is a quasi-static PIC program for simulating plasma wakefield acceleration. It supports a hybrid parallel simulation on multiple central processing units via OpenMP and message passing interface (MPI). We now present a version of QuickPIC that runs on graphics processing units (GPU), with MPI for communication between different GPUs, based on the UCLA Parallel Partice-In-Cell framework. By rewriting relevant Fortran77 functions with CUDA C, we port the two-dimensional particle and field computations onto GPU platforms. QuickPIC-GPU supports simulation with a single GPU for up to a resolution of $1024^3$ and 25 particles per cell to avoid time spent on cross-processor communications, and simulation with multiple GPUs for larger problem sizes.

Commonwealth Fusion Systems plans to build ARC as the first fusion power plant at a site in Chesterfield County, Virginia, USA by the early 2030s. We present an overview of analysis comprising the physics basis of the ARC V3A design, a high-magnetic-field tokamak with $B_0=11.4 \ \text{T}$, $I_p=12.0 \ \text{MA}$, $R_0=4.62 \, \text{m}$, $a=1.18 \, \text{m}$. ARC V3A is designed to produce $P_{fus} \approx 1.13$ GW DT fusion power and deliver $\geqslant$400 MW net electric power to the grid. This overview includes quantitative analysis of fundamental issues for design of and operational plasma scenarios for a tokamak power plant, and lays out the design targets and strategic choices for ARC, including empirical fusion performance projections, assessment of H-mode access, ion cyclotron resonance heating simulations, alpha particle physics and time-dependent full-pulse simulations. This is complemented by topical papers on fusion performance and transport, disruption physics, boundary physics and magnetohydrodynamic stability. Critically, these studies identify key model uncertainties and physics risks to be retired through SPARC operation. Due to the modular nature of ARC, early results from SPARC can be incorporated into the design of the first ARC as well as subsequent replacements of the ARC vacuum vessel.

Experimental analysis and simulations with the BOUT++ code show that small edge-localised modes (ELMs) in reactor-relevant high-density regimes originate in a region close to the separatrix and only marginally perturb the pedestal structure. The measured divertor peak parallel energy fluence (ε∥,peak) for a database of small ELM scenarios in DIII-D and ASDEX Upgrade can be reproduced, within 40 % accuracy on average, if an ad hoc modification of the Eich peak parallel ELM energy fluence model is applied to account for the small ELM pedestal birth location. This allows for first-order extrapolation of small-ELM divertor ε∥,peak to ITER and SPARC, resulting in values that satisfy the nominal melting threshold of tungsten monoblocks of 12 MJ m−2. The findings reported in this study, both via modelling and direct measurements, constitute a step forward in assessing small ELMs in high edge-collisionality scenarios as a viable plasma regime for the operation of next-generation fusion machines.

An adjoint formulation of energetic particle confinement in axisymmetric tokamak geometry is derived and evaluated using a physics-informed neural network (PINN). The PINN estimates the mean escape time of energetic ions by solving an inhomogeneous adjoint of the drift kinetic equation with a Lorentz collision operator, yielding predictions of fast ion loss in tokamak geometry due to direct ion orbit loss and collisional transport. To our knowledge, this is the first time a PINN has been used to solve the drift kinetic equation in tokamak geometry, a challenging problem due to the large time scale separation between the rapid transit time of energetic ions and their slow collisional time scale. It is shown that a careful and intentional design of a PINN is able to learn the mean escape time across the majority of the plasma volume, suggesting a path towards constructing a rapid surrogate for use within a broader optimisation framework.

In this work, we investigate prompt ion drift orbit losses caused by shear-Alfvén waves (SAWs) in quasi-symmetric and quasi-isodynamic (QI) stellarators optimised for equilibrium confinement of energetic particles (EPs). We use the ideal reduced magnetohydrodynamic (MHD) model for SAW perturbations and study their impact on the collisionless EP drift dynamics. We present a semi-analytical model for resonance between the passing EP and SAW, generalised to arbitrary quasi-symmetric configurations including the quasi-poloidal case relevant to QI equilibria. Analysis reveals that an increase in the number of field periods $N_{\mathrm{fp}}$ suppresses stochasticity in quasi-helical (QH) and quasi-isodynamic, but not quasi-axisymmetric (QA) stellarators. We show that wave-induced transitions between passing and trapped orbits cause significant losses in QA and QH, but not in QI configurations. For the considered equilibria at scales relevant to fusion power plants, we numerically determine the SAW amplitudes needed to induce prompt loss of fusion-born alpha particles. Using the weighted Birkhoff averaging technique, we confirm that the onset of prompt losses across all orbit classes occurs with the onset of stochasticity in ion motion. This motivates extending the stochasticity-onset criterion beyond passing orbits in future work.

We study the interaction of an ion with a fluctuation in the electromagnetic fields that is localised in both space and time. We study the scale dependence of the interaction in both space and time, deriving a generic form for the ion’s energy change, which involves an exponential cutoff based on the characteristic time scale of the electromagnetic fluctuation. This leads to diffusion in energy in both $v_\perp$ and $v_\parallel$. We show how to apply our results to general plasma physics phenomena, and specifically to Alfvénic turbulence and to reconnection. Our theory can be viewed as a unification of previous models of stochastic ion heating, cyclotron heating and reconnection heating in a single theoretical framework.

We revisit the double-adiabatic evolution equations and extend them to the relativistic and ultrarelativistic regimes. We analytically solve the relativistic, time-dependent drift kinetic equation for a homogeneous, magnetised, collisionless plasma and obtain a solution explicitly dependent on the magnetic field and density variations. In the case of an initial relativistic Maxwellian distribution, a natural extension to an anisotropic Maxwell–Jüttner distribution is obtained. We calculate the moments of this time-dependent solution and obtain analytical expressions for the evolution of the perpendicular and parallel pressures in the ultrarelativistic case. We numerically solve the moment equations in the relativistic case and obtain general expressions for the double-adiabatic equations in this regime. We confirm our results using fully kinetic particle-in-cell simulations of shearing and compressing boxes. Our findings can be readily applied to relativistic species including cosmic rays and electron–positron pairs, present in astrophysical plasmas like pulsar wind nebulae, astrophysical jets, black hole accretion flows and Van Allen radiation belts.

We present a novel mechanism in which plasma electrons and ions optically acquire angular momentum during local pump depletion of an azimuthally polarised laser, despite the laser carrying none. Using theoretical considerations and multi-dimensional particle-in-cell simulations, we find that this process is enabled by a strong frequency downshift at the gradually eroding laser pulse front. We further show that the angular momentum gained by the plasma electrons is compensated by the ions and by the combined electromagnetic fields of the laser and nonlinear plasma wave. By varying key laser parameters such as phase, frequency and polarisation, we demonstrate that the transverse momentum of high-energy electrons can be effectively controlled.

Results from one- and two-dimensional particle-in-cell simulations – both of nonlinear electron plasma waves (EPWs) and of self-consistent stimulated Raman scattering (SRS) – are shown that explore effects of small magnetic fields ($\omega _c / \omega _p \ll 1$) oriented perpendicular to the direction of laser propagation on SRS across a range of laser intensities of relevance to inertial fusion energy. The magnetic field effect is strongly intensity dependent. The magnetic field raises the threshold for kinetic inflation and can suppress SRS entirely at intensities just above the unmagnetised threshold. At intermediate intensities, it reduces time-averaged reflectivity by factors of approximately two to three in one dimension. Far above threshold the suppressive effect largely disappears, and the reflectivity becomes comparable to, or modestly greater than, its unmagnetised value. Nevertheless, the instability retains distinct signatures in the presence of the magnetic field. The magnetic field promotes the detrapping of resonant electrons, enhances EPW damping, limits distribution-function flattening and the associated nonlinear frequency shift, and thereby produces a more regular recurrence of SRS bursts. Multi-dimensional effects weaken the contrast in EPW damping through transverse localisation and wavefront effects, but preserve the same qualitative intensity dependence and changes in recurrence behaviour. These results delimit the regime in which small transverse magnetic fields mitigate kinetic SRS and show that time-averaged reflectivity alone does not fully characterise their influence on the instability.

The influence of Tsallis q-entropy on the electron-impact excitation process is derived for a non-extensive plasma. The ionisation probability is obtained as a function of the impact parameter using a semiclassical trajectory analysis. Results indicate that Tsallis q-entropy suppresses the electron-impact ionisation cross-section in a non-extensive plasma. Additionally, the influence of Tsallis q-entropy diminishes as the ratio of the electron temperature to the ion temperature increases. In addition, the influence of Tsallis q-entropy amplifies with increasing projectile electron energy. Furthermore, it is shown that the position of maximum ionisation probability is recessed from the target centre as the q-entropy increases.

The adiabatic equation of state $P \propto n^{\varGamma }$ describes the pressure evolution of highly collisional, isotropic plasmas in terms of their density, providing a possible closure of the fluid moment hierarchy in the absence of heat fluxes and dissipation. An analogous closure exists for collisionless, magnetised plasmas, whose pressure tensor is anisotropic with respect to the magnetic field, and the closure is therefore double adiabatic, prescribing the evolution of the parallel and perpendicular pressures in terms of the magnetic-field strength and density. Here, we present a general first-principles formalism to derive adiabatic laws using symmetries and phase-space conservation properties of the distribution function. With this theory we recover the adiabatic equation of state $P \propto n^{\varGamma }$ for isotropic plasmas and the double-adiabatic equations of state for collisionless, magnetised plasmas. We extend the latter to the relativistic regime, finding that their exact functional form depends on the pressure anisotropy and is not a simple power law. Our double-adiabatic equations of state describe simple geometries, like magnetic mirrors or compressed homogeneous plasmas, as well as complex high-energy astrophysical processes, such as the evolution of plasmoid structures formed during magnetic reconnection.

In this work, the geometric electromagnetic particle-in-cell (PIC) framework, GEMPICX, is extended to solve the quasineutral, fully kinetic Vlasov–Maxwell equations on dual grids using mimetic finite differences. The discrete action principle is derived, taking into account the duality between the grids. The temporal derivative of the electric field does not directly appear in the dynamical system for the quasineutral model. Hence, a discretised curl–curl equation is used to implicitly obtain the electric field at every time-step. This also circumvents the need to obtain electric potentials. A Lagrange multiplier is used to maintain the discretised divergence of the current density at machine zero.

The paper presents a fusion plant concept called VOYAGER developed by leading groups in fusion research (BINP SB RAS) and high-temperature superconductivity (SuperOx LLC). This plant has an open trap configuration with high-temperature superconducting (HTS) vortex (helical) magnets for plasma confinement. The plant is designed with deuterium–deuterium fusion in the ignited regime (without external plasma heating) providing an unlimited supply of reactor fuel, using already proven technologies, and thus maximising the plant’s electrical power output and revenue. The costs for construction and operation of the power plant, as well as levelised cost of electricity (LCOE) for the plant, are calculated. The VOYAGER plant has comparable construction and operating costs with existing fusion plant projects; however, VOYAGER, due to the high electrical power output, has the lowest LCOE. The low LCOE value for the proposed plant makes it competitive with conventional electricity sources. Reduced research and development costs due to the use of proven technologies and modular nature of open trap confinement make VOYAGER an even more attractable preposition among fusion plant concepts.

Stellarator boundary optimisation faces a fundamental numerical challenge: the extreme disparity between low- and high-mode amplitudes creates an optimisation landscape in which direct full-spectrum approaches typically converge to poor local minima. Traditionally, this challenge has been addressed through a computationally expensive, multi-step Fourier continuation, in which low Fourier modes are optimised first, followed by the gradual incorporation of higher modes. We present exponential spectral scaling (ESS), a technique that applies a mode-dependent exponential scaling factor to each Fourier mode. Our primary implementation uses the $L_{\infty }$ norm to determine the scaling pattern, creating a square spectral decay profile that effectively reduces the dynamic range of optimisation variables from 6–7 orders of magnitude to 2–3. This scaling aligns with the natural spectral decay of physically meaningful configurations and enables direct single-step optimisation using the full spectrum of boundary Fourier modes. ESS eliminates arbitrary staging decisions and reduces computation time by a factor of ${\sim}2{-}5$ in benchmark cases. In addition to accelerating optimisation, ESS improves robustness, reducing sensitivity to initial conditions and increasing confidence in avoiding local optima. We demonstrate the effectiveness of ESS across both quasi-axisymmetric (QA) and quasi-helically symmetric (QH) configurations, using two distinct optimisation toolkits: simsopt and desc.

This paper presents experimental investigations of a non-resonant photon trap featuring adiabatic radiation confinement, designed for the photoneutralisation of negative hydrogen (H−/D−) ion beams in fusion plasma injection heating systems. The trap is formed by two monolithic dielectric mirrors with high reflectivity. The study focuses on the methodology and results of measuring the confinement time and integral optical losses. The diagnostic approach is based on analysing the decay rate of radiation within the optical cavity following abrupt interruption of the pump source, utilising wire attenuators for signal reduction. The influence of the laser beam angular divergence on the accumulation efficiency is examined. The obtained data confirm the adiabatic nature of the photon confinement, demonstrate consistency between the measured losses and the specified mirror coating parameters and validate the feasibility of controlling the density of the photon ensemble within the trap. This work confirms the technical feasibility and potential of this approach for the development of high-efficiency photoneutralisation systems.