The reversed magnetic shear (RMS) configuration, a promising candidate for steady-state tokamak operation, facilitates high bootstrap current fractions through internal transport barriers, but also hosts multiple rational surfaces vulnerable to tearing modes. Under high bootstrap current conditions, these modes can trigger explosive bursts via strong positive feedback during magnetic island interactions, posing serious disruption risks. This study numerically investigates the suppression of such explosive phenomena in RMS plasmas using a reduced MHD model that incorporates bootstrap current, electron cyclotron current drive (ECCD) and the radio-frequency current condensation effect (CCE). Numerical findings demonstrate that the CCE fundamentally enhances ECCD efficacy, particularly for large neoclassical tearing mode islands. For moderate bootstrap fractions ($f_b = 0.3$), a counterintuitive control strategy is identified: intentionally delaying ECCD initiation until the island grows larger. This approach exploits the positive correlation between CCE effectiveness and island width, thereby achieving a shorter overall stabilisation time. In high bootstrap scenarios ($f_b = 0.6$), prone to explosive bursts, the CCE introduces a nonlinear positive feedback mechanism that strongly localises current deposition at the O-point of the islands and creates a hysteresis-like response. This enables complete island stabilisation at identical ECCD power and delaying the required onset timing of ECCD by approximately 70 $\%$, substantially extending the control response window. The CCE also effectively mitigates rotation-induced control degradation through enhanced current localisation. This work establishes CCE-enhanced ECCD as a robust mechanism for explosive burst prevention in high-bootstrap-current plasmas. The results provide critical insights for developing advanced stabilisation strategies in future steady-state reactors like ITER, while highlighting the need for future research on integrated control approaches that balance suppression efficiency with disruption risks.

In this work we investigate the landscape of quasi-isodynamic (QI) stellarators using the near-axis expansion of the magnetic field. Building on recent theoretical developments, we construct a database of more than 800 000 stable, approximately QI vacuum magnetic configurations. These configurations span a range of field period numbers and other geometric control parameters, including the magnetic axis shape and plasma elongation. To evaluate each configuration, we use a broad set of measures, including effective ripple, sensitivity of the Shafranov shift to changes in plasma $\beta$, the prevalence of maximum-$\mathcal{J}$ trapped particles and the Rosenbluth–Hinton residual, among others. This enables an exhaustive, thorough and quantitative characterisation of the database. Statistical analysis and modern machine learning techniques are then employed to find correlations and identify key descriptors and heuristics to help understand tendencies that govern the behaviour of numerical optimisation. The database provides baseline configurations for further studies and to serve as tailored initial conditions for optimisation. With this work we initiate a long-term program to complete a systematic exploration of QI stellarator design space.

Strong gradient regions in tokamaks such as the pedestal or internal transport barriers are regions of reduced turbulence where neoclassical transport can play a dominant role. In pedestals, gradient lengths comparable to the ion poloidal gyroradius have been measured. Standard neoclassical theory can miss important strong gradient effects in these regions because it assumes that the gradient length scales of density, temperature and potential are larger than the ion poloidal gyroradius. We extend plateau regime neoclassical theory into regions of gradients of the order of the ion poloidal gyroradius to capture strong gradient effects on transport processes in the pedestal and internal transport barriers. The fundamental idea behind our new framework is to keep a scale separation between the orbit widths and the gradient length scales by performing a large aspect ratio expansion. In the plateau regime, strong gradients cause poloidal variation that is in–out as well as up–down asymmetric. We study two different test cases assuming either radial force balance or the absence of turbulence and show that strong gradient effects can enhance or reduce standard neoclassical theory predictions in the plateau regime in strong gradient regions.

Two-fluid simulations using local Landau-fluid closures derived from linear theory provide an efficient computational framework for plasma modelling, since they bridge the gap between computationally intensive kinetic simulations and fluid descriptions. Their accuracy in representing kinetic effects depends critically on the validity of the linear approximation used in the derivation: the plasma should not be too far from local thermodynamic equilibrium (LTE). However, many of the problems where these models are of particular interest (such as plasma turbulence and instabilities) are in fact quite far from LTE. The question then arises as to whether kinetic-scale processes are still sufficiently well captured outside of the theoretical regime of applicability of the closure. In this paper, we show that two-fluid simulations with Landau-fluid closures can effectively reproduce the energy spectra obtained with fully kinetic Vlasov simulations, used as references, as long as the local closure parameter is appropriately chosen. Our findings validate the usage of two-fluid simulations with a Landau-fluid closure as a possible alternative to fully kinetic simulations of turbulence, in cases where being able to simulate extremely large domains is of particular interest.

Theories of ion-scale microinstabilities in tokamaks and stellarators typically assume that the passing electrons respond adiabatically due to their fast propagation speed. However, when the magnetic shear becomes sufficiently small, ion-scale modes can extend far along the magnetic field and the non-adiabatic response of passing electrons becomes important. We derive a theory of extended modes at low magnetic shear through a multiscale expansion of the gyrokinetic equation. The theory elucidates the physics of the geodesic extended mode, a new type of microinstability. The new mode couples the non-adiabatic physics of both electrons and ions, unlike extended modes at magnetic shear of order unity. The theory is validated against gyrokinetic simulations and the parameter dependences of the new mode are studied.

The effect of the finite ion Larmor radius on the dynamics of two counterstreaming weakly collisional plasma flows in a magnetic field of an arch configuration is considered. Hybrid numerical simulations show that in a system whose dimensions are close to the ion Larmor radius, more intense interaction dynamics is observed and the magnetic arch experiences a significant expansion with the formation of a region with an irregular character of magnetic lines, in which magnetic reconnection processes occur. In this case, the generation of a surface wave of the ion-cyclotron range is observed at the boundaries of the arch. An increase in the scale of the system compared with the ion Larmor radius leads to a transition to the ideal magnetohydrodynamic regime, in which the evolution of the arch occurs much more slowly, and the development of instabilities is not observed.

Quasi-poloidal (QP) magnetic fields have desirable properties for confining plasma: no radial drift of guiding centres (with positive implications for neoclassical transport), zero Pfirsch–Schlüter current and a lower level of damping for poloidal flows. Despite their attractive properties, QP fields are not amenable to the near-axis expansion, a major theoretical tool for understanding toroidal fields. In this paper we provide a novel framework for defining and understanding QP flux surfaces. This framework relies on a simplification that transforms the task of finding a QP flux surface from a three-dimensional problem to a two-dimensional (2D) problem. This simplification also applies to asymmetric magnetic mirrors with desirable properties. We sketch how this 2D problem can form the basis of an efficient optimisation problem for finding QP flux surfaces. We leverage this 2D problem for theoretical understanding: for instance, we identify a route to finding QP flux surfaces that are naturally flat mirrors (Velasco et al. 2023, Nucl. Fusion, 63, 126038). The reduced model is qualitatively checked against numerically optimised QP equilibria. These numerical solutions only satisfy QP approximately, but we predictably find that local discrepancies with the reduced model correspond to significant local QP errors, anomalous parallel currents and field lines deviating from geodesics.

To successfully show that fusion is an attractive energy source, the ARC$^{\scriptstyle \mathrm{TM}}$ fusion power plant will need to operate with a robust, integrated power and particle exhaust solution. To maximise ARC’s fusion power output while avoiding excessive erosion of the plasma-facing components, we will need to radiatively dissipate most of the power crossing the last-closed flux surface, injecting radiating impurities such as argon or neon to access divertor detachment. Divertor detachment will need to be integrated with a high-performance core plasma, and with efficient impurity pumping to prevent the accumulation of helium ash in the core. To access and control detachment in high-performance plasmas, we have designed ARC with up–down-symmetric divertors, with secondary X-points in long, tightly baffled outer legs. Using a core-edge modelling workflow, we predict that with this divertor design, ARC will access detachment with modest argon seeding in the divertor (${c_{Ar,div}}\sim {0.9\,\%}$), which should have minimal impact on the core (${\Delta Z_{\textit{eff},\textit{core}}}\lt {0.5}$) for reasonable argon enrichment (${c_{Ar,div}/c_{Ar,\textit{core}}}={6}$). Due to the high predicted divertor neutral pressure (${p_{\textit{div}}}\sim {20\,\mathrm{Pa}}$), we predict that ARC will sufficiently pump helium to limit ash accumulation in the core (${c_{\textit{He},\textit{core}}}\lt {2\,\%}$) for a helium enrichment of ${c_{\textit{He},\textit{div}}/c_{\textit{He},\textit{core}}}={0.4}$. ARC’s divertor design is expected to increase the stability of a detachment front in the outer divertor leg, helping to prevent divertor reattachment during smaller heat-flux transients such as scrape-off-layer filaments associated with the quasi-continuous exhaust regime. However, this buffering will not be sufficient to prevent divertor reattachment during large type-I edge-localised modes (ELMs), and as such these will need to be avoided on ARC. Experiments on SPARC will be used to select an integrated scenario which avoids or mitigates type-I-ELMs while maintaining access to detachment, good core fusion performance and sufficient impurity exhaust. SPARC experiments will also be used to finalise ARC’s divertor design, by studying the impact of magnetic and first-wall geometry on detachment stability, impurity enrichment and neutral baffling under conditions similar to those expected for ARC. In conclusion, our analysis finds that ARC will have a viable power and particle exhaust solution which is compatible with high-power operations, and this solution will be validated in experiments on SPARC.

In cold weakly ionised plasmas, the Dreicer generation mechanism can be non-diffusive as demonstrated in a recent study. By expanding the previous letter, we present the detailed description of a proper collision operator to precisely account for the non-diffusive electron kinetics. The operator appropriately combines the Fokker–Planck operator and Boltzmann operator where free-bound collision cross-sections are valid in the low-energy region. The proposed operator is envisaged to predict runaway electron generation in cold weakly ionised plasmas, particularly to design a runaway-free reactor tokamak start-up.

The requirement for large-scale global simulations of plasma is an ongoing challenge in both space and laboratory plasma physics. Any simulation based on a fluid model inherently requires a closure relation for the high-order plasma moments. This review compiles and analyses the recent surge of machine learning (ML) approaches developing improved plasma closure models capable of capturing kinetic phenomena within plasma fluid models. We survey two methodological families: neural network surrogates (from multi-layer perceptrons to Fourier neural operators, the latter recently reproducing both linear and nonlinear Landau damping online within a fluid solver) and equation discovery methods such as sparse regression; and organise the studies by whether they are tested offline against reference data or online within a time-evolving solver. We outline the challenges associated with ML closures, including off-diagonal pressure-tensor accuracy, generalisation beyond the training distribution and stable integration into large-scale simulations, and the directions future research might take to address them.

Kinetic theory is one of the fundamental descriptions in plasma physics. Large-scale numerical simulations for kinetic models such as the non-relativistic Vlasov–Poisson system and the Vlasov–Maxwell system are computationally demanding. To save computer resources, this work uses physics-informed neural network (PINN) and its variant separable PINN (SPINN) to approach the Vlasov–Poisson system. We constructed PINN and SPINN solvers for the multi-dimensional Vlasov–Poisson system and implemented the simulation of Landau damping and two-stream instabilities. The SPINN is proved to be effective for approaching high-resolution and high-dimensional solutions because of its fast training and low memory consumption, especially in capturing linear Landau damping in six-dimensional phase space. In this work, these AI solvers show potential in balancing computational cost, effectiveness and efficiency for direct Vlasov simulations. Therefore, they are expected to be useful in kinetic simulation for fusion plasma, astrophysical plasma and related applications.

Magnetospheric twists, that is magnetospheres with a toroidal component, are under scrutiny due to the key role the twist is believed to play in the behaviour of neutron stars. Notably, its dissipation is believed to power magnetar activity, and is an important element of the evolution of these stars. We exhibit a new class of twisted axisymmetric force-free magnetospheric solutions. We solve the Grad–Shafranov equation by introducing an ansatz akin to a multipolar expansion. We obtain a hierarchical system of ordinary differential equations where lower-order multipoles source the higher-order ones. We show that analytical approximations can be obtained, and that in general solutions can be numerically computed using standard ordinary-differential-equation solvers. We obtain a class of solutions with a great flexibility in initial conditions, and show that a subset of these asymptotically tends to vacuum. The twist is not confined to a subset of field lines. The solutions are symmetric about the equator, with a toroidal component that can be reversed. This symmetry is supported by an equatorial current sheet. We provide a first-order approximation of a particular solution that consists of the superposition of a vacuum dipole and a toroidal magnetic field sourced by the dipole, where the toroidal component decays as $1/r^4$, where $r$ is the radial coordinate. As an example of strongly multipolar solution, we also exhibit cases with an additional octupole component.

We report an unanticipated electron dynamics in a classical setting of a uniform magnetic field, a parallel electric field and a right-handed circularly polarised wave (R-wave). The setting admits a natural trajectory that a particle accelerated by the electric field reaches a Doppler–shifted cyclotron resonance and becomes trapped in the resonance space. Remarkably, once it becomes resonantly trapped, the electron undergoes reversal of parallel acceleration together with perpendicular energisation, despite the parallel electric field remaining constant. This counterintuitive behaviour has important implications for particle scattering in various laboratory and space plasmas. Applied to fusion devices, particle-in-cell simulations show that an externally injected R-wave can act as a firewall suppressing further runaway-electron acceleration.

Relativistic magnetic reconnection has been proposed as an important non-thermal particle acceleration (NTPA) mechanism that generates power-law spectra and high-energy emissions. Power-law particle spectra are in general characterised by three parameters: the power-law index, the high-energy cutoff and the low-energy cutoff (i.e. the injection energy). Particle injection into the non-thermal power law, despite also being a critical step in the NTPA chain, has received considerably less attention than the subsequent acceleration to high energies. Open questions on particle injection that are important for both physical understanding and astronomical observations include how the upstream magnetisation $\sigma$ influences the injection energy and the contributions of the known injection mechanisms (i.e. direct acceleration by the reconnection electric field, Fermi kicks and pickup acceleration) to the injected particle population. Using fully kinetic particle-in-cell simulations, we uncover these relationships by systematically measuring the injection energy and calculating the contributions of each acceleration mechanism to the total injected particle population. We also present a theoretical model to explain these results. Additionally, we compare two- and three-dimensional simulations to assess the impact of the flux-rope kink and drift-kink instability on particle injection. We conclude with comparisons with previous work and outlook for future work.

The ARC$^{\textrm {TM}}$ tokamak, a high-field ($B_T$ = 11.4 T) fusion power plant, under development by Commonwealth Fusion Systems, is studied using a suite of integrated modelling tools to predict its fusion power generation ($P_{fus}$), transport and confinement properties. Analysis is based off an ARC operational point scoped first with zero-dimensional (0-D) plasma operational contour (POPCON) modelling to produce 1.13 GW of fusion power. A suite of integrated modelling tools (TRANSP, ASTRA and TORAX) were applied to predict the performance and kinetic profiles of the ARC design point, yielding a range of predicted performance spanning from ${\sim} 900$ to 1300 MW in rough quantitative agreement with POPCON predictions. The sensitivity of these results to uncertain modelling inputs was probed using scans of pedestal boundary conditions around EPED-predicted values (total pressure and temperature ratios), tungsten concentration and seperatrix density around their nominal assumptions. Pedestal pressure and pedestal top $(T_i/T_e)$ play a large role in 1.5-dimensional performance predictions, able to modify the predicted $P_{fus}$ by a factor of 2 within reasonable assumptions. High-fidelity core nonlinear gyrokinetic profile predictions, performed using CGYRO (Candy et al. 2016 J. Comput. Phys., vol. 324, pp. 73–93) coupled with the PORTALS (Rodriguez-Fernandez et al. 2024 Nucl. Fusion, vol. 64, 076034; Phys. Plasmas, vol. 31, 2024, 062501) framework, yield substantially lower performance ($P_{fus} = 677$ MW) compared with 0-D and medium-fidelity modelling for nominal assumptions, showing that there is non-negligible uncertainty between models and that future work on SPARC may help resolve discrepancies. Lower overall performance results from significantly reduced volume-averaged densities and temperatures, along with reduced levels of density and temperature peaking. Turbulence and transport are largely dominated by ion temperature gradient across the profile, confirmed by both linear stability and the response of the nonlinear fluxes to changes in gradients, with some impact of kinetic ballooning modes in the deep core. This work represents one of the most complete scoping of potential fusion power plant conditions performed to date. The extensive integrated modelling provides confidence in ARC performance approaching 1 GW, while nonlinear gyrokinetic modelling results in open questions into the physics of density and temperature peaking in fusion-power-plant-relevant operational space. A discussion of results and the role that the SPARC tokamak (Creely et al. 2020 J. Plasma Phys., vol. 86, 865860502) will play in informing ARC design, performance and operation is presented.

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.

The above question may be answered as follows. A typical longitudinal plasma wave for which the collision frequency, $\nu$, is low relative to the angular wave frequency, $\omega$, only interacts with the degree of freedom, $D$, related to motion parallel to the wave vector. This gives an adiabatic coefficient corresponding to $D = 1$, i.e. 3. At high $\nu /\omega$, relevant to neutral gases, collisions cause even longitudinal sound waves to interact with all active $D$, yielding an adiabatic coefficient of $(D+2)/D$. We present a minimal example illustrating the above transition based on linear analysis of a non-relativistic, isotropic, homogeneous, Maxwellian one-component system with a Bhatnagar–Gross–Krook collision operator. Macroscopic forces, mainly included in plasma physics, are essential for the transition at low $\nu /\omega$. Additionally, the tensor nature of pressure and collision operators satisfying mass, momentum and energy conservation must be invoked to obtain the correct response. Our analysis yields a polytropic index at arbitrary $\omega$ and wavenumbers, which reduces to the adiabatic coefficient in the corresponding limit. An adiabatic wave response is found in two distinct regimes. If the wave phase velocity far exceeds the thermal particle speed, an adiabatic response occurs at any $\nu /\omega$ (plasma wave case). Alternatively, for mean free paths much shorter than the wavelength, an adiabatic response can be obtained even at phase velocities comparable with the thermal particle speed (sound wave case). The analysis finally demonstrates the occurrence of Landau damping in neutral gases with arbitrary $D$ at low $\nu /\omega$.

Plasma equilibrium with a pressure close to the magnetic field pressure ($\beta \sim 1$) are actively studied both in relation to various cosmic phenomena and in the context of more efficient plasma confinement in the magnetic traps. In particular, one of the most promising paths in the development of mirror traps is the transition to the diamagnetic confinement regime. In such a regime, a powerful neutral injection should create an extremely high-pressure plasma with a completely displaced magnetic field (a diamagnetic bubble) in the centre of the trap. The width of the transition layer in this bubble is an important parameter controlling the rate of longitudinal plasma losses. Previously, a model describing the structure of the transition layer in a bubble (Kotelnikov 2020 Plasma Phys. Control Fusion vol. 67, p. 075002) was built on the basis of the collisionless kinetic theory and, using the cold electron approximation, predicted the layer width at the level of ten ion gyroradii. In this paper, the model is generalised to the case of finite electron temperature, requiring us to take into account the electric potential in a self-consistent manner. It is found that, given the comparable temperatures of the ion and electron components, the plasma boundary has a two-scale structure similar to the recently discovered sub-ion magnetic holes. In the inner part of the transition layer, a noticeable jump in the magnetic field is provided exclusively by the electron current on a scale of less than ten electron gyroradii, the remaining part of the jump is created by the diamagnetic ion current on a much longer ion gyroradius scale.