Free energy, widely used as a measure of turbulence intensity in weakly collisional plasmas, has been recently found to be a suitable basis to describe both linear and nonlinear growth in a wide class gyrokinetic systems. The simplicity afforded by this approach is accompanied by some drawbacks, notably the lack of any explicit treatment of wave–particle effects, which makes the theory unable to describe things like stability thresholds or dependence on the geometry of the background magnetic field. As a step toward overcoming these limitations, we propose an extension of the theory based on a generalization of the free energy. With this, it is demonstrated that resonance effects are recovered, and the bounds on growth are significantly reduced. The simplicity and efficient computation of the associated ‘optimal’ growth rates makes the theory potentially applicable to stellarator optimization.

The OMFIT STEP (Meneghini et al., Nucl. Fusion, vol. 10, 2020, p. 1088) workflow has been used to develop inductive and steady-state H-mode core plasma scenario use cases for a $B_0 = 8 \, {\rm T}$, $R_0 = 4 \, {\rm m}$ machine to help guide and inform future higher-fidelity studies of core transport and confinement in compact tokamak reactors. Both use cases are designed to produce 200 MW or more of net electric power in an up-down symmetric plasma with minor radius $a = 1.4 \, {\rm m}$, elongation $\kappa = 2.0$, triangularity $\delta = 0.5$ and effective charge $Z_{{\rm eff}} \simeq 2$. Additional considerations based on the need for compatibility of the core with reactor-relevant power exhaust solutions and external actuators were used to guide and constrain the use case development. An extensive characterization of core transport in both scenarios is presented, the most important feature of which is the extreme sensitivity of the results to the quantitative stiffness level of the transport model used as well as the predicted critical gradients. This sensitivity is shown to arise from different levels of transport stiffness exhibited by the models, combined with the gyroBohm-normalized fluxes of the predictions being an order of magnitude larger than other H-mode plasmas. Additionally, it is shown that although heating in both plasmas is predominantly to the electrons and collisionality is low, the plasmas remain sufficiently well coupled for the ions to carry a significant fraction of the thermal transport. As neoclassical transport is negligible in these conditions, this situation inherently requires long-wavelength ion gyroradius-scale turbulence to be the dominant transport mechanism in both plasmas. These results are combined with other basic considerations to propose a simple heuristic model of transport in reactor-relevant plasmas, along with simple metrics to quantify coupling and core transport properties across burning and non-burning plasmas.

Pressure anisotropy can strongly influence the dynamics of weakly collisional, high-beta plasmas, but its effects are missed by standard magnetohydrodynamics (MHD). Small changes to the magnetic-field strength generate large pressure-anisotropy forces, heating the plasma, driving instabilities and rearranging flows, even on scales far above the particles’ gyroscales where kinetic effects are traditionally considered most important. Here, we study the influence of pressure anisotropy on turbulent plasmas threaded by a mean magnetic field (Alfvénic turbulence). Extending previous results that were concerned with Braginskii MHD, we consider a wide range of regimes and parameters using a simplified fluid model based on drift kinetics with heat fluxes calculated using a Landau-fluid closure. We show that viscous (pressure-anisotropy) heating dissipates between a quarter (in collisionless regimes) and half (in collisional regimes) of the turbulent-cascade power injected at large scales; this does not depend strongly on either plasma beta or the ion-to-electron temperature ratio. This will in turn influence the plasma's thermodynamics by regulating energy partition between different dissipation channels (e.g. electron and ion heat). Due to the pressure anisotropy's rapid dynamic feedback onto the flows that create it – an effect we term ‘magneto-immutability’ – the viscous heating is confined to a narrow range of scales near the forcing scale, supporting a nearly conservative, MHD-like inertial-range cascade, via which the rest of the energy is transferred to small scales. Despite the simplified model, our results – including the viscous heating rate, distributions and turbulent spectra – compare favourably with recent hybrid-kinetic simulations. This is promising for the more general use of extended-fluid (or even MHD) approaches to model weakly collisional plasmas such as the intracluster medium, hot accretion flows and the solar wind.

In this paper, we summarize our recent work on gyrokinetic applications in electron–positron and non-neutral plasma. The electrostatic stability of electron–positron plasmas was investigated in dipole and slab geometries, with and without ion admixture. The gyrokinetic dispersion relation was derived and, for the slab case, extended to non-neutral plasmas. Here, we further extend the gyrokinetic formulation to the relativistic regime. Electron–positron plasmas are found to be remarkably stable as long as perfect symmetry between the two species prevails, but instabilities appear if this symmetry is broken, for instance by the introduction of impurities or magnetic curvature.

An approximate model for pure electron plasma compression is developed for the case where the rotating wall (RW) electric field couples to the $E\times B$ rotation and axial bounce motion of the electrons. The key assumption in the model is that, throughout the compression, the plasma remains in a slowly evolving thermal equilibrium defined by the plasma temperature and angular momentum. Linearized drift kinetic theory is employed to derive an expression for torque exerted by the RW field on the plasma through coupling to the resonant plasma particles, and averaging is used to find the torque that both compresses and heats the plasma. The evolution equations for the angular velocity and temperature of the plasma include the compression and heating from the torque and cooling from cyclotron radiation.

In typical heliospheric collisionless shocks most of the mass, momentum and energy are carried by ions. Therefore, the shock structure should be most affected by ions. With the increase of the Mach number, ion reflection becomes more and more important, and reflected ions participate in shaping the shock profile. Ion reflection at the collisionless shock is a non-local process: the reflected–transmitted ions re-enter the shock front far from the reflection point. The direction and the magnitude of this shift depend on the shock angle. The distance between the reflection point and the re-entry point is of the order of the upstream ion convective gyroradius and exceeds the shock width. The non-locality of ion reflection may have implications for shock rippling since reflected ions may carry perturbations along the shock front.

This work reports on the development and numerical implementation of the linear electromagnetic gyrokinetic (GK) model in a tokamak flux-tube geometry using a moment approach based on the expansion of the perturbed distribution function on a velocity-space Hermite–Laguerre polynomials basis. A hierarchy of equations of the expansion coefficients, referred to as the gyro-moments (GMs), is derived. We verify the numerical implementation of the GM hierarchy in the collisionless limit by performing a comparison with the continuum GK code GENE, recovering the linear properties of the ion temperature gradient, trapped electron, kinetic ballooning and microtearing modes, as well as the collisionless damping of zonal flows. An analysis of the distribution functions and ballooning eigenmode structures is performed. The present investigation reveals the ability of the GM approach to describe fine velocity-space-scale structures appearing near the trapped and passing boundary and kinetic effects associated with parallel and perpendicular particle drifts. In addition, the effects of collisions are studied using advanced collision operators, including the GK Coulomb collision operator. The main findings are that the number of GMs necessary for convergence decreases with plasma collisionality and is lower for pressure gradient-driven modes, such as in H-mode pedestal regions, compared with instabilities driven by trapped particles and magnetic gradient drifts often found in the core. The accuracy of approximations often used to model collisions (relative to the GK Coulomb operator) is studied in the case of trapped electron modes, showing differences between collision operator models that increase with collisionality and electron temperature gradient, consistent with the results of Pan et al. (Phys. Rev. E, vol. 103, 2021, L051202). Such differences are not observed in other edge microinstabilities, such as microtearing modes. The importance of a proper collision operator model is also confirmed by analysing the collisional damping of geodesic acoustic modes and zonal flows.

It has long been known that the equilibrium of an electron plasma in a stellarator possesses unique properties when compared with other geometries. Previous analyses, both numerical and analytical, as well as experimental results, have indicated that these equilibria are minimum-energy states. Here, it is definitively shown that the equilibrium of an electron plasma on magnetic surfaces with finite rotational transform minimises a constrained physical energy, which has a thermal and an electrostatic contribution. As such, these equilibria are established to be macroscopically stable to all perturbations that do not change the flux-surface average of the density and do not decrease the entropy of the plasma, under the definition of ‘formal stability’ established by Holm et al. (Phys. Rep., vol. 123, no. 1, 1985, 1–116).

Terahertz (THz) field excitation by a rotating relativistic electron beam in a magnetized plasma column is described using numerical analysis and particle-in-cell simulation. A rotating electron beam propagating through a cylindrical plasma column excites plasma wakefields. The plasma wakefields couple with the electron beam to excite transverse currents at THz frequency. As a result, the energy of the wakefield directly converts into the form of electromagnetic radiation in the THz range. The magnetic field supports the transverse modes via electron cyclotron resonance. The strength of the THz field is enhanced due to scattering of the spiralling electron beam on the plasma density perturbation. The THz field amplitude is controllable by the electron beam velocity and beam density. On increasing the beam current, the THz field is enhanced significantly. The analytical results are compared with particle-in-cell simulations and are found to be in reasonable agreement.

To comprehensively study the physical properties of inductively coupled plasma (ICP), a finite element method (FEM) simulation model of ICP is developed using the well-established COMSOL software. To benchmark the validation of the FEM model, two key physical parameters, the electron density and the electron temperature of the ICP plasma, are precisely measured by the state-of-the-art laser Thomson scattering diagnostic approach. For low-pressure plasma such as ICP, the local pressure in the generator tube is difficult to measure directly. The local gas pressure in the ICP tube has been calibrated by comparing the experimental and simulation results of the maximum electron density. And on this basis, the electron density and electron temperature of ICP under the same gas pressure and absorbed power have been compared by experiments and simulations. The good agreement between the experimental and simulation data of these two key physical parameters fully verifies the validity of the ICP FEM simulation model. The experimental verification of the ICP FEM simulation model lays a foundation for further study of the distribution of various physical quantities and their variation with pressure and absorption power, which is beneficial for improving the level of ICP-related processes.

The equations of electrostatic drift kinetics are observed to possess a symmetry associated with their intrinsic scale invariance. Under the assumptions of spatial periodicity, stationarity, and locality, this symmetry implies a particular scaling of the turbulent heat flux with the system's parallel size, from which its scaling with the equilibrium temperature gradient can be deduced under some additional assumptions. This macroscopic transport prediction is then confirmed numerically for a reduced model of electron-temperature-gradient-driven turbulence in slab geometry. The system realises this scaling through a turbulent cascade from large to small perpendicular spatial scales. The route of this cascade through wavenumber space (i.e. the relationship between parallel and perpendicular scales in the inertial range) is shown to be determined by a balance between nonlinear-decorrelation and parallel-dissipation timescales. This type of ‘critically balanced’ cascade, which maintains a constant energy flux despite the presence of parallel dissipation throughout the inertial range (as well as order-unity dissipative losses at the outer scale) is expected to be a generic feature of plasma turbulence. The outer scale of the turbulence, on which the turbulent heat flux depends, is determined by the breaking of drift-kinetic scale invariance due to the existence of large-scale parallel inhomogeneity (the parallel system size).

Both spin and orbital angular momentum can be exchanged between a rotating wave and a rotating magnetized plasma. Through resonances the spin and orbital angular momentum of the wave can be coupled to both the cyclotron rotation and the drift rotation of the particles. It is, however, shown that the Landau and cyclotron resonance conditions which classically describe resonant energy–momentum exchange between waves and particles are no longer valid in a rotating magnetized plasma column. In this case a new resonance condition which involves a resonant matching between the wave frequency, the cyclotron frequency modified by inertial effects and the harmonics of the guiding centre rotation is identified. A new quasilinear equation describing orbital and spin angular momentum exchanges through these new Brillouin resonances is then derived, and used to expose the wave-driven radial current responsible for angular momentum absorption.

This paper discusses thermal equilibrium states of single-species plasmas, such as pure electron plasmas and pure positron plasmas, that are confined in a dipole trap. Thermal equilibrium states for such plasmas are routinely realized in the homogeneous magnetic field of Penning–Malmberg traps. We generalize the theory of these states to include inhomogeneous magnetic dipole fields. The approach to thermal equilibrium takes place in two stages with well separated time scales. On the collision time scale, thermal equilibrium is established along each magnetic field line. On the much longer transport time scale, heat conduction and viscosity bring the plasmas on different flux contours into thermal equilibrium, we call this a state of global thermal equilibrium. We present numerical results for local and global thermal equilibria. These results agree with the analytic predictions for charge collections that are large compared with the Debye length. There is, in principle, no limit to the confinement time of a single-species plasma in a global thermal equilibrium state. Experiments with hot electron–ion plasmas performed in the LDX and RT1 devices give us confidence that, in contrast to a Penning–Malmberg trap, a magnetic dipole field can also confine cold quasi-neutral electron–positron pair plasmas on the time scale of the phenomena of interest. Such pair plasmas are assumed to form in the magnetosphere of neutron stars but have so far not been realized in a laboratory. The creation of an electron–positron pair plasma is the main goal of the APEX collaboration.

In tokamaks and neoclassically optimised stellarators, like Wendelstein 7-X (W7-X) and the Helically Symmetric Experiment, turbulent transport is expected to be the dominant transport mechanism. Among the electrostatic instabilities that drive turbulence, the trapped-electron mode (TEM) has been shown both analytically and in simulations to be absent over large ranges of parameter space in quasi-isodynamic stellarator configurations with the maximum-$J$ property. It has been proposed that the reduction of the linear TEM growth rate in such configurations may lead to the passing-electron-driven universal instability, which is often subdominant to the TEM, becoming the fastest-growing instability over some range of parameter space. Here, we show through gyrokinetic simulations using the Gene code, that the universal instability is dominant in a variety of stellarator geometries over a range of parameter space typically occupied by the TEM, but most consequentially in devices which possess beneficial TEM stability properties like W7-X, which locally satisfies the maximum-$J$ property for deeply trapped particles in the regions of worst curvature. We find that the universal instability exists at long perpendicular wavelengths and, as a result, dominates the potential fluctuation amplitude in nonlinear simulations. In W7-X, universal modes are found to differ in parallel mode structure from trapped-particle modes, which may impact turbulence localisation in experiments.

The construction of kinetic equilibrium states is important for studying stability and wave propagation in collisionless plasmas. Thus, many studies over the past decades have been focused on calculating Vlasov–Maxwell equilibria using analytical and numerical methods. However, the problem of kinetic equilibrium of hybrid models is less studied, and self-consistent treatments often adopt restrictive assumptions ruling out cases with irregular and chaotic behaviour, although such behaviour is observed in spacecraft observations of space plasmas. In this paper, we develop a one-dimensional (1-D), quasineutral, hybrid Vlasov–Maxwell equilibrium model with kinetic ions and massless fluid electrons and derive associated solutions. The model allows for an electrostatic potential that is expressed in terms of the vector potential components through the quasineutrality condition. The equilibrium states are calculated upon solving an inhomogeneous Beltrami equation that determines the magnetic field, where the inhomogeneous term is the current density of the kinetic ions and the homogeneous term represents the electron current density. We show that the corresponding 1-D system is Hamiltonian, with position playing the role of time, and its trajectories have a regular, periodic behaviour for ion distribution functions that are symmetric in the two conserved particle canonical momenta. For asymmetric distribution functions, the system is nonintegrable, resulting in irregular and chaotic behaviour of the fields. The electron current density can modify the magnetic field phase space structure, inducing orbit trapping and the organization of orbits into large islands of stability. Thus, the electron contribution can be responsible for the emergence of localized electric field structures that induce ion trapping. We also provide a paradigm for the analytical construction of hybrid equilibria using a rotating two-dimensional harmonic oscillator Hamiltonian, enabling the calculation of analytic magnetic fields and the construction of the corresponding distribution functions in terms of Hermite polynomials.

We summarize recent attempts to unravel the role of plasma kinetic effects in radiation mediated shocks. Such shocks form in all strong stellar explosions and are responsible for the early electromagnetic emission released from these events. A key issue that has been overlooked in all previous works is the nature of the coupling between the charged leptons, that mediate the radiation force, and the ions, which are the dominant carriers of the shock energy. Our preliminary investigation indicates that in the case of relativistic shocks, as well as Newtonian shocks in multi-ion plasma, this coupling is driven by either, transverse magnetic fields of a sufficiently magnetized upstream medium, or plasma microturbulence if strong enough magnetic fields are absent. We discuss the implications for the shock breakout signal, as well as abundance evolution and kilonova emission in binary neutron star mergers.

We upgrade the three-dimensional linear stability CASTOR3D code by taking into account gyro-viscosity in the momentum equation, as well as pressure and Hall terms in Ohm's law. Making use of the drift approximation, the resulting simplified version of Ohm's law is implemented. The ion and electron diamagnetic drift effects described by these newly implemented terms are investigated for ideal and resistive, low- and medium-$n$ internal modes depending on the ratio of ion and electron pressures, and plasma resistivity. Stability studies are performed for two- and three-dimensional test equilibria. The results confirm previous findings, and provide new insights especially in the case of the three-dimensional equilibrium (e.g. reduction of the coupling of toroidal harmonics).

The oscillating relativistic electrons in the accelerating/focusing wakefields of plasma accelerators emit electromagnetic radiation known as betatron radiation (BR). The proton-driven plasma wakefield acceleration has been demonstrated in the Advanced Wakefield Experiment (AWAKE) at CERN; however, its accompanying radiation emission is less explored compared with those in the laser- and electron beam-driven plasma accelerators. In this paper, a detailed simulation study of BR in the AWAKE is presented. Considering the new set-up of the AWAKE Run 2 (2021–), the radiation emission from both the witness electron beam and the seeding electron beam is investigated using particle-in-cell simulations. The influence of radial size mismatch and misaligned off-axis injection on the witness beam dynamics, as well as the spectral features of the relevant BR are studied. These non-ideal electron injections are likely to occur in experiment. The proton self-modulation stage is also investigated with a close look at the seeding electron beam dynamics and its BR. As a footprint of the emitting particles, BR can provide valuable information about the beam dynamics. Some practical challenges to implement the betatron diagnostic in the AWAKE Run 2 experiment are also addressed.