A disrupting plasma in a high-performance tokamak such as ITER or SPARC may generate large runaway electron currents that, upon impact with the tokamak wall, can cause serious damage to the device. To quickly identify regions of safe operation in parameter space, it is useful to develop reduced models and analytical criteria that predict when a significant fraction of the Ohmic current is converted into a current of runaway electrons. In deuterium–tritium plasmas, the seed runaway current may have a significant contribution from – or may even be dominated by – tritium beta decay and Compton scattering. In this work, a criterion for significant runaway electron generation that includes tritium beta decay and Compton scattering sources is developed. The avalanche gain factor includes the effects of partial screening of injected noble gases. The result is an analytical model that can predict significant runaway electron generation in the next generation of activated tokamak devices. The model is validated by fluid simulations using Dream (Hoppe et al. 2021 Comput. Phys. Commun., vol. 268, p. 108098) and is shown to delineate regions in parameter space where significant runaway electron generation may occur.

In toroidal confinement systems, the scrape-off layer (SOL) magnetic field exhibits characteristics analogous to those of a magnetic mirror configuration, particularly in the edge plasma region. Therefore, linear plasma devices have advanced divertor simulation studies. To further promote divertor simulation studies, a new divertor simulator, ‘Pilot GAMMA PDX-SC (PGX-SC)’ has been developed, incorporating a pair of superconducting coils that generate a simple magnetic mirror configuration. An electrode-biasing system was installed on the PGX-SC to regulate the plasma potential. The system comprises three concentric basing plates installed at the east end of the main chamber of PGX-SC, in conjunction with a DC-stabilised power supplies for each basing plate. This system can also measure the floating potentials and electrode currents by connecting a resistor to each plate in the absence of an external power supply. Preliminary experiments were conducted to investigate the effect of plasma by applying a bias to the electrode plates. Applying a voltage to the inner electrode increased the plasma potential at the outer electrode. This result suggests the feasibility of controlling the peripheral plasma potential using concentric biasing plates. When voltage was applied to the outer electrode, the amplitude of the fluctuating current decreased. These results collectively indicate the capability of plasma control employing concentric biasing plates.

Phase-space electron holes, recognised as fundamental nonlinear electrostatic structures in space plasmas, have recently been detected near the mantle boundary of the Venusian magnetosheath by both the Parker Solar Probe (PSP) and the Pioneer Venus Orbiter (PVO). To understand their origin and characteristics, we develop a hydrodynamic model coupled with reductive perturbation theory that incorporates a small population of non-isothermal trapped electrons together with the dynamical effects of solar-wind ions and electrons. This formulation yields a generalised Schamel–Korteweg de Vries equation supporting two distinct classes of nonlinear electrostatic modes: solitary waves and double layers. Using parameter ranges constrained by in situ measurements – including relative densities, drift velocities and temperature ratios – we conduct a detailed parametric investigation of both structures. For the solitary-wave solutions, the model predicts electric field amplitudes of ${\sim} 20$ mV m–1, temporal scales of ${\sim} (2.5{-}4.5)\,$ms and characteristic frequencies of ${\sim} (0.31{-}5.6)$ kHz. The double-layer solutions exhibit fields of ${\sim} 18$ mV m–1, durations of ${\sim} 4.5\,$ms and frequencies of ${\sim} (0.63{-}1.6)$ kHz. These results are in strong agreement with PSP and PVO observations, which report electrostatic fluctuations near 5.4 kHz with amplitudes of ${\sim} 20$ mV m–1. The present analysis therefore provides a consistent physical interpretation of electron-hole structures in the Venusian magnetosheath and highlights their role in mediating kinetic processes at unmagnetised planetary boundaries.

We investigate the linear growth rate of tearing instability in a resistive force-free current sheet using the linearised fully compressible magnetohydrodynamics (MHD) equations. Our results show that, as the plasma beta ($\beta$), which is proportional to the ratio of thermal pressure to magnetic pressure, increases, the dispersion relation approaches that of the incompressible tearing mode. As $\beta$ decreases, the growth rate increases, but this increase remains finite even in the limit $\beta \rightarrow 0$. The relative increase in the growth rate from $\beta = +\infty$ to $\beta =0$ depends on the Lundquist number, with lower Lundquist numbers showing a more pronounced increase. These findings indicate that, while compressibility has a negligible effect on the growth rate of tearing instability in high-Lundquist-number regimes, its effect becomes significant at low Lundquist numbers. This suggests that compressibility may influence the critical Lundquist number for the transition from laminar to plasmoid-dominated magnetic reconnection. Moreover, in low-$\beta$ regimes ($\beta \lt 1$), the generated density perturbation can be substantial, comparable to or even larger than the magnetic field perturbation, even though the growth rate is only slightly modified by the compressibility.

Predictions of the pedestal temperature profile calculated using a model for electron-temperature-gradient (ETG) turbulent electron heat transport Field et al. (2023 Philos. Trans. R. Soc. A, vol. 381, p. 20210228) are compared with the pedestal structure of H-mode plasmas in JET-Be/W (with Be wall and W divertor) over scans of the deuterium–tritium (D:T) isotope mix and hydrogenic gas fuelling rate Frassinetti et al. (2023 Nucl. Fusion, vol. 63, p. 112009). Predictions for the electron temperature at the location of the density pedestal top $T_e(\psi _N^{n_{e,top}})$ (where $\psi_N$, is the normalised poloidal flux) are found to agree well with measured values over both scans across the full range of D:T ratio. However, the pedestal top temperature $T_{e,ped}$, typically located somewhat inside the density pedestal top, is under-predicted by as much as a factor ${\sim} 2$. This implies that the ETG heat flux scaling appropriate for the steep-density gradient region, on which the model is based, is not applicable where the density gradient is weak. This difference might be attributed to a difference between the physics of the ETG turbulence in regimes where the density gradient is either strong or weak, which are thought to be dominated by either the ‘slab’ or ‘toroidal’ branches of ETG turbulence. Other branches of turbulence might also play a role in the electron heat transport, particularly in regions of weak-density gradient. As in the experiment, the predicted $T_e$ across the pedestal decreases with the ratio of separatrix to pedestal density $n_{e,sep}/n_{e,ped}$, which increases with the gas fuelling rate. Results from three models combining the ETG heat flux model with the EPED1 pedestal (EPED) model (Snyder et al., Phys. Plasmas, 2009, vol. 16, p. 056118) are also presented, including one which also incorporates the density pedestal prediction mode of Saarelma et al. (Nucl. Fusion, 2023, vol. 63, p. 052002), this model providing a complete prediction of the pedestal profiles.

The present study investigates the propagation of power carried by fast magnetosonic waves transmitted beyond the cutoff, utilising a slab model that incorporates non-zero wave poloidal wavenumbers. The plasma density profile is assumed to be an exponential one. The fraction of the transmitted power is analysed as a function of the plasma density decay length, subject to toroidal and poloidal refractive indices, plasma density at the antenna and operating frequency. The numerical analysis of the analytical expressions reveals a substantial sensitivity of the fraction of the transmitted power to the plasma density decay length and poloidal refractive index sign.

We investigate plasma wake generation via Compton scattering from photon bursts in the Thomson regime, a non-ponderomotive process relevant when the photon wavelength is shorter than the interparticle distance. In this regime, electrons can reach relativistic velocities. We extend linear theory to the nonlinear regime, showing that plasma waves can reach the wave-breaking limit. Perfectly collimated drivers produce wakes propagating at the speed of light, allowing electron phase-locking (limited by driver depletion). Non-collimated drivers induce subluminal phase velocities, limiting acceleration via dephasing. Two-dimensional simulations reveal unique transverse fields compared with laser wakefields, with a DC magnetic field leading to consistent focusing. The work considers observational prospects in laboratory and astrophysical scenarios such as around highly luminous compact objects (e.g. pulsars, gamma-ray bursts) interacting with tenuous interstellar or intergalactic plasmas, where conditions favour Compton-dominated wakefield acceleration.

Fully kinetic, energy-conserving electrostatic particle-in-cell (PIC) simulations are employed to quantify how geometry and two-dimensional (2-D-$rz$) and three-dimensional (3-D) effects modify confinement, acceleration and cross-field transport by comparing our results with previous 1-D simulations in an open magnetic mirror. The bulk of the simulations are performed using an explicit scheme at a plasma density of approximately $10^{16}\,\mathrm{m}^{-3}$. In addition to being computationally accessible to explicit PIC, this regime has a relatively large Debye length and therefore emphasises charge-separation effects important in 2-D and 3-D simulations. Starting from a 2-D axisymmetric (2-D-$rz$) model and extending to three dimensions, we isolate finite-ion-Larmor-radius (FLR) effects and azimuthal instabilities. In the 2-D-$rz$ case, FLR effects partially decouple ions from magnetised electrons, producing charge separation near the plasma edge and modest radial ion leakage to the wall, while the near-axis density, potential and acceleration profiles remain close to those in the reduced 1-D model. Full 3-D simulations demonstrate azimuthal modes that induce radial currents, broaden radial density profiles and reduce the confining potential and the total axial potential drop. At low ion temperature, a coherent azimuthal mode of low frequency and low mode number $m=2$ is observed. At high ion temperature, fluctuations shift toward higher mode numbers $m\simeq 4$–$5$ and higher frequencies, with a broadband turbulent spectrum. The particle and energy (for ions and electrons) radial and axial losses are studied in detail. We show that for 3-D cases, radial ion losses account for approximately $30\,\%$ of the flux injected from the source region. The radial electric field produced by the endplate biasing introduces azimuthal shear that weakens coherent structures and reduces radial losses. Finally, additional simulations at densities of the order $10^{18}\,\mathrm{m}^{-3}$ have been performed with a semi-implicit electrostatic PIC algorithm.

Energy transfer across scales is essential for understanding the dissipation and heating of plasma turbulence. In the energy cascade scenario, the energy transfer rate can be assessed through the third-order law in the inertial range, and it is directly related to the rate of dissipation occurring at the small scale. To investigate the local properties of the energy transfer process, here, we employ three main diagnostics: the locally averaged dissipation rate $\varepsilon _r$ at different scales $r$, the local energy transfer (LET) rate and the scale-filtered energy flux. The analyses are performed on direct numerical simulations of three-dimensional (3-D) incompressible magnetohydrodynamic (MHD) turbulence to evaluate these diagnostics. The outcomes of our study include: (i) an assessment of the spatial distribution of energy transfer rates across scales to determine which diagnostic best captures the features of energy transfer in different ranges; and (ii) a comparison of the outputs of the different diagnostics at significant scales, including a quantitative evaluation of their correlation using appropriate correlation coefficients. The latter shows that the energy dissipation rate, the LET and the scale-filtered energy flux have regional correlation, that is, although not exactly co-located, the intense regions of these three diagnostics occur in spatial proximity. Our results provide insights into understanding the energy transfer process in MHD and plasma turbulence, which shall be extended to more realistic systems.

Wave interactions with magnetised particles underlie many plasma heating and current drive technologies. Typically, these interactions are modelled by bounce averaging the quasilinear Kennel–Engelmann diffusion tensor over the particle orbit. However, as an object derived in a two-dimensional space, the Kennel–Engelmann tensor does not fully respect the conservation of four-momentum required by the action conservation theorem, since it neglects the absorption of perpendicular momentum. This defect leads to incorrect predictions for the wave-induced cross-field particle transport. Here, we show how this defect can easily be fixed, by extending the tensor from two to four dimensions and matching the form required by four-momentum conservation. The resulting extended tensor, when bounce averaged, recovers the form of the diffusion paths required by action-angle Hamiltonian theory. Importantly, the extended tensor should be easily implementable in Fokker–Planck codes through a mild modification of the existing Kennel–Engelmann tensor.

Electron hole treatments normally match collisionless distribution functions associated with spatially varying electrostatic potential wells containing bound or reflecting electrons to unbound or non-reflecting electrons. When the matching is piecewise continuous at the separatrix between the bound and unbound, the second derivative in velocity space normally diverges, indicating collisions should be retained to remove the singular behaviour. The solubility constraint introduced by the collision operator severely restricts the allowed bound and unbound solutions, as illustrated by solving a model problem for a solitary electron depleted hole. As a result, a narrow collisional boundary layer encloses the separatrix between the bound and barely unbound electrons most sensitive to collisions. The procedure employed does not require resolving the collisional boundary layer, yet self-consistently accounts for the discontinuous behaviour to demonstrate an electron hole can last a long time when collisions are very weak.

We ask how a stationary cylindrical magnetic flux rope can sustain a field-aligned electric field while satisfying Maxwell’s equations, and what this implies for its helical structure and magnetic helicity. Since $\boldsymbol E\boldsymbol{\cdot }\boldsymbol B\neq 0$, the electromagnetic field is algebraically non-degenerate and separates locally into two mutually orthogonal rank-two contributions. For stationary, axisymmetric profiles on a finite annulus, the homogeneous Maxwell equations lock these contributions: the observable magnetic pitch, the azimuthal electromotive period and the axial electric drive determine the complementary-sector amplitude and radial–temporal mixing pointwise. On every regular Lorentzian branch, the principal variables can be reconstructed locally from the two observable magnetic components and the two drive constants. The resulting field carries a helical electric current, and requires material force support, a parallel non-ideal response and external power. A constant-conductivity example demonstrates a smooth regular branch supported by a non-negative isotropic pressure. Only after an additional periodic axial identification do the fixed-radius surfaces become tori and the principal magnetic directions acquire winding classes. On this periodic annulus, the generalised magnetic helicity is the oriented area traced by the accumulated axial and azimuthal fluxes. Its principal-sector contributions are flux-weighted integrals of radial pitch shear, while their mutual contribution reduces, in a formal localised-shell limit, to the torus intersection pairing. Because the magnetic field is stationary, the generalised helicity is time independent; the variation of the raw Chern–Simons integral is compensated by the evolving harmonic periods. This is a balance specific to the periodic annulus, not a general helicity-conservation theorem for fields with $\boldsymbol E\boldsymbol{\cdot }\boldsymbol B\neq 0$.

Axisymmetric cylindrical configurations of the magnetic field are used to confine and guide plasmas in fusion and electric propulsion devices, where plasma equilibria are established as a balance between plasma pressure, magnetic stress (pressure) and inertial forces due to azimuthal plasma rotation and axial flow rotation. Most generally, in an axially inhomogeneous case, plasma rotation and azimuthal magnetic field are related via Alfvén wave type coupling. We show that, for a special case of a current-free nozzle and, therefore, absence of the azimuthal plasma rotation, the plasma flow along the magnetic surface can be analysed independently of the exact shape of the magnetic surface. The velocity of the transonic plasma flow is determined by the magnitude of the magnetic field on the magnetic surface, while the actual shape of the magnetic surface is determined by the solution of the generalised Grad–Shafranov equation that includes the inertial forces. These analytical results are confirmed with numerical simulations that highlight the contribution of the inertial forces to plasma acceleration and equilibrium. Implications for the flows in the magnetic nozzle for the electric propulsion and open mirrors for fusion are discussed.

ARC is designed to produce ${400}\,\textrm {MW}$ of net electricity and prove the commercial feasibility of a fusion power plant. In order to achieve this goal ARC has to operate with optimal core performance in a stationary scenario that minimises wear on the first wall and divertor. This requires avoiding or mitigating magnetohydrodynamic (MHD) instabilities which have the potential to not only degrade the plasma core but also lead to deleterious transient heat loads on plasma facing components. Therefore, this work aims at characterising the MHD stability of the high performance ARC scenario and inform the design of error field correction coils. Firstly, simulations of vertical displacement events show that an in-vessel coil is not needed and instead the poloidal shaping coils can be used to control vertical stability. These simulations also inform the demands on the corresponding coil power supplies. Stability analysis of the ideal kink mode with or without a conducting wall and kinetic effects suggests that the ARC baseline scenario operates deeply in the stable region. Using RDCON, tearing modes at the $m/n=2/1$ and $3/2$ surfaces (with poloidal mode number $m$, and toroidal mode number $n$) are shown to be linearly stable, and including thermal transport effects in the rational surfaces lead to further stabilisation. However, other transient plasma instabilities can seed neoclassical tearing modes (NTMs). The marginally stable width of NTMs in ARC strongly depends on the internal inductance and can fall below ${0.1}{\,\,\%}$ of the normalised poloidal flux. Furthermore, an empirical cross-machine model of the $n=1$ error field leading to a disruption predicts a critical error field larger than SPARC but smaller than ITER. Three-dimensional coils can be designed with the Generalised Purturbed Equilbium Code based on a simple model that calculates the maximum correctable error field that is limited by the neoclassical toroidal viscosity torque. Broad scans of different coil geometries identify a set of 2 rows of off-midplane coils to be a suitable solution. It is also determined that such a set of three-dimensional coils is capable of correcting $n=2$ error fields to some degree and creating strong enough $n=2$ or $n=3$ edge resonant perturbation fields for the suppression of edge-localised modes at reasonable coil currents. The final design of the first ARC will be further informed by results from SPARC.

Compared with contemporary experimental parameters, a burning plasma device operates at significantly higher densities and temperatures. Furthermore, the magnetic field and device size are several times larger than those of existing tokamaks. Discrepancies of these parameters may influence the linear stability of Alfvén eigenmodes; thus, the extrapolation of energetic particle-driven instabilities in present experiments to burning plasma conditions requires rigorous validation. Starting from a quadratic form of the momentum equation, we employ a perturbative approach to evaluate kinetic effects, specifically the drive from alpha particles and the Landau damping from bulk ions. This framework allows for the determination of the linear growth rate, while including radiative damping and trapped electron collisional damping from analytic formulations. For the core-localised toroidal Alfvén eigenmodes (TAE) and global TAEs, we find that the alpha beta thresholds for TAE instabilities are approximately $1.0\,\%$. By maintaining a constant bulk plasma beta or fusion triple product, we conduct systematic parameter scans to identify the key dependences of the linear stability of TAEs. With increases of background temperature and magnetic field strength, the density and beta of alpha particles increase correspondingly from the consistent parameter variations at a fixed plasma beta or fusion triple product, resulting in enhancement of TAE instabilities. However, other types of parameter scaling with magnetic field may induce the stabilisation of TAEs.

In this study, a radiative divertor simulator was developed using the linear magnetic mirror device KAIMIR, considering the center chamber as the upstream scrape-off layer and the expander chamber as the downstream region. To achieve divertor-relevant conditions, the gas feed system of the KAIMIR device was upgraded to increase the particle flux at the downstream region. In addition, a differential pumping system using a skimmer structure was implemented to enable independent control of the neutral pressure between the upstream and downstream regions by reducing the vacuum conductance between the chambers. With this system, a neutral pressure up to 70 mTorr was achieved in the expander chamber while maintaining plasma characteristics in the center chamber. Simulations were then conducted, where non-monotonic behaviour of the ion saturation current and line-integrated density was observed with increasing neutral pressure in the expander chamber, suggesting a transition from attached to detached plasma regimes. Visible emission profiles from fast camera measurements revealed enhanced recombination emission and the formation of localised low-temperature plasma near the downstream region. These results demonstrate that the upgraded KAIMIR device provides a controllable linear divertor simulator suitable for the investigation of radiative and detached divertor plasma physics in a linear configuration.

We investigate the appearance of a low-frequency $1/f$ magnetic spectrum in three-dimensional incompressible magnetohydrodynamic turbulence using direct numerical simulations and virtual spacecraft sampling. Our goal is to determine how the measured temporal spectra depend on the mean magnetic guide field, the probe velocity relative to the Alfvén speed and the sampling angle with respect to the guide field. We find that the clearest $1/f$ ranges are obtained for stronger guide fields and are favoured by faster sampler trajectories oriented more nearly perpendicular to the mean magnetic field. To characterise this behaviour, we introduce a quantitative score that measures the quality and spectral coverage of the detected $1/f$ interval. We further show that, as the probe speed increases, the measured temporal spectra become progressively more consistent with the corresponding Eulerian spectra at intermediate and high wavenumbers for both parallel and perpendicular sampling directions, particularly in the strong guide field case. These results indicate that the presence and clarity of a temporal $1/f$ range depend not only on the underlying turbulent dynamics, but also on the geometry and speed of the sampling process, with implications for the interpretation of low-frequency in situ measurements in the solar wind.

Numerical computation of the ideal magnetohydrodynamic (MHD) equilibrium magnetic field is at the base of stellarator optimisation and provides the starting point for solving more sophisticated partial differential equations like transport or turbulence models. Conventional approaches solve for a single stationary point of the ideal MHD equations, which is fully defined by three invariants and the numerical scheme employed by the solver. We present the first numerical approach that can solve for a continuous distribution of equilibria with fixed boundary and rotational transform, varying only the pressure invariant. This approach minimises the force residual by optimising parameters of multilayer perceptrons that map from a scalar pressure multiplier to the Fourier Zernike basis as implemented in the modern stellarator equilibrium solver DESC.

We derive the hot-electron-limit (HEL) closure for the moment hierarchy used to solve the gyrokinetic equations, known as the gyromoment (GM) approach. By expanding the gyroaveraging kernels in the small ion-to-electron temperature ratio limit, $\tau \ll 1$, and retaining only the essential $\mathcal{O}(\tau )$ terms, we obtain a closed system for the density, parallel velocity and parallel and perpendicular temperatures. In a Z-pinch geometry, the GM system with the HEL closure is analytically equivalent to the one developed by Ivanov et al. (2022 J. Plasma Phys., vol. 88, no. 5, p. 905880506). Numerical benchmarks confirm the closure’s accuracy, reproducing established linear growth rates, nonlinear heat transport and low collisionality dynamics. An extension to the tokamak-relevant $s{-}\alpha$ geometry and a comparison with gyrokinetic simulations reveal the capabilities and limitations of the HEL-closed GM model: while transport levels and the temporal dynamics are qualitatively preserved even at $\tau =1$, the absence of higher-order kinetic moments prevents an accurate prediction of the Dimits shift and of transport suppression.