The safe operation of tokamak reactors requires a reliable modelling capability of disruptions, and in particular the spatio-temporal dynamics of associated runaway electron currents. In a disruption, instabilities can break up magnetic surfaces into chaotic field line regions, causing current profile relaxation, as well as a rapid radial transport of heat and particles. Using a mean-field helicity transport model implemented in the disruption runaway modelling framework Dream, we calculate the dynamics of runaway electrons in the presence of current relaxation events. In scenarios where flux surfaces remain intact in parts of the plasma, a skin current is induced at the boundary of the intact magnetic field region. This skin current region becomes an important centre concerning the subsequent dynamics: it may turn into a hot ohmic current channel, or a sizeable radially localized runaway beam, depending on the heat transport. If the intact region is in the plasma edge, runaway generation in the countercurrent direction can occur, which may develop into a sizeable reverse runaway beam. Even when the current relaxation extends to the entire plasma, the final runaway current density profile can be significantly affected, as the induced electric field is reduced in the core and increased in the edge, thereby shifting the centre of runaway generation towards the edge.

Three machine learning techniques (multilayer perceptron, random forest and Gaussian process) provide fast surrogate models for lower hybrid current drive (LHCD) simulations. A single GENRAY/CQL3D simulation without radial diffusion of fast electrons requires several minutes of wall-clock time to complete, which is acceptable for many purposes, but too slow for integrated modelling and real-time control applications. The machine learning models use a database of more than 16 000 GENRAY/CQL3D simulations for training, validation and testing. Latin hypercube sampling methods ensure that the database covers the range of nine input parameters ($n_{e0}$, $T_{e0}$, $I_p$, $B_t$, $R_0$, $n_{\|}$, $Z_{{\rm eff}}$, $V_{{\rm loop}}$ and $P_{{\rm LHCD}}$) with sufficient density in all regions of parameter space. The surrogate models reduce the inference time from minutes to $\sim$ms with high accuracy across the input parameter space.

A fluid dispersion theory in partially magnetised plasmas is analysed to examine the conditions under which large-wavelength modes develop in Penning-type configurations, that is, where an electric field is imposed perpendicular to a homogeneous magnetic field. The fluid dispersion relation assuming a slab geometry shows that two types of low-frequency, gradient drift instabilities occur in the direction of the $\boldsymbol {E} \times \boldsymbol {B}$ and diamagnetic drifts. One type of instability, observed when the equilibrium electric field and plasma density gradient are in the same direction, is similar to the classic modified Simon–Hoh instability. A second instability is found for conditions in which (i) the diamagnetic drift is in the direction opposite to the $\boldsymbol {E} \times \boldsymbol {B}$ drift and (ii) the magnitude of the diamagnetic drift is sufficiently larger than the electron thermal speed. The present fluid dispersion theory suggests that the rotating spokes driven by such fluid instabilities propagate in the same direction as the diamagnetic drift, which can be in the same direction as or opposite to the $\boldsymbol {E} \times \boldsymbol {B}$ drift, depending on the plasma conditions. This finding may account for the observation, in some plasma devices, of the rotation of large-scale structures in both the $\boldsymbol {E} \times \boldsymbol {B}$ and $-\boldsymbol {E} \times \boldsymbol {B}$ directions.

The ideal Chew–Goldberger–Low (CGL) plasma equations, including the double adiabatic conservation laws for the parallel ($p_\parallel$) and perpendicular pressure ($p_\perp$), are investigated using a Lagrangian variational principle. An Euler–Poincaré variational principle is developed and the non-canonical Poisson bracket is obtained, in which the non-canonical variables consist of the mass flux ${\boldsymbol {M}}$, the density $\rho$, the entropy variable $\sigma =\rho S$ and the magnetic induction ${\boldsymbol {B}}$. Conservation laws of the CGL plasma equations are derived via Noether's theorem. The Galilean group leads to conservation of energy, momentum, centre of mass and angular momentum. Cross-helicity conservation arises from a fluid relabelling symmetry, and is local or non-local depending on whether the gradient of $S$ is perpendicular to ${\boldsymbol {B}}$ or otherwise. The point Lie symmetries of the CGL system are shown to comprise the Galilean transformations and scalings.

This paper presents quasilinear theory (QLT) for a classical plasma interacting with inhomogeneous turbulence. The particle Hamiltonian is kept general; for example, relativistic, electromagnetic and gravitational effects are subsumed. A Fokker–Planck equation for the dressed ‘oscillation-centre’ distribution is derived from the Klimontovich equation and captures quasilinear diffusion, interaction with the background fields and ponderomotive effects simultaneously. The local diffusion coefficient is manifestly positive-semidefinite. Waves are allowed to be off-shell (i.e. not constrained by a dispersion relation), and a collision integral of the Balescu–Lenard type emerges in a form that is not restricted to any particular Hamiltonian. This operator conserves particles, momentum and energy, and it also satisfies the $\smash {H}$-theorem, as usual. As a spin-off, a general expression for the spectrum of microscopic fluctuations is derived. For on-shell waves, which satisfy a quasilinear wave-kinetic equation, the theory conserves the momentum and energy of the wave–plasma system. The action of non-resonant waves is also conserved, unlike in the standard version of QLT. Dewar's oscillation-centre QLT of electrostatic turbulence (Phys. Fluids, vol. 16, 1973, p. 1102) is proven formally as a particular case and given a concise formulation. Also discussed as examples are relativistic electromagnetic and gravitational interactions, and QLT for gravitational waves is proposed.

In this study, we experimentally evaluate the ion transportation through a cone guide target, which accelerates ions up to MeV energies via target normal sheath acceleration, and transports them onto the position of imploding fuel in the fast ignition scenario of nuclear fusion. We measured the electric and magnetic fields (EM-fields) induced by return current streaming along the cone wall by proton radiography, and we report that the EM-fields are predominantly induced within a temporal window up to 30 ps after the laser injection. The magnitude of the electric field is maximized around 13 ps, reaching $4.0\times 10^{10} \mathrm {V}\ \mathrm {m}^{-1}$, when the magnetic field is below 200 T. The present scheme provides insights on the EM-fields evaluation in the time region that is difficult to treat with simulations due to the computing resources.

The Dimits shift, an upshift in the onset of turbulence from the linear instability threshold, caused by self-generated zonal flows, can greatly enhance the performance of magnetic confinement plasma devices. Except in simple cases, using fluid approximations and model magnetic geometries, this phenomenon has proved difficult to understand and quantitatively predict. To bridge the large gap in complexity between simple models and realistic treatment in toroidal magnetic geometries (e.g. tokamaks or stellarators), the present work uses fully gyrokinetic simulations in a Z-pinch geometry to investigate the Dimits shift through the lens of tertiary instability analysis, which describes the emergence of drift waves from a zonally dominated state. Several features of the tertiary instability, previously observed in fluid models, are confirmed to remain. Most significantly, an efficient reduced-mode tertiary model, which previously proved successful in predicting the Dimits shift in a gyrofluid limit (Hallenbert & Plunk, J. Plasma Phys., vol. 87, issue 05, 2021, 905870508), is found to be accurate here, with only slight modifications to account for kinetic effects.

We study the stability problem of a magnetohydrodynamic current sheet with the presence of a plasma jet. The flow direction is perpendicular to the normal of the current sheet and we analyse two cases: (1) the flow is along the antiparallel component of the magnetic field; (2) the flow is perpendicular to the antiparallel component of the magnetic field. A generalized equation set with the condition of incompressibility is derived and solved as a boundary value problem. For the first case we show that the streaming kink mode is stabilized by the magnetic field at $V_0/B_0 \lesssim 2$, where $V_0$ and $B_0$ are the jet speed and upstream Alfvén speed, and it is not affected by resistivity significantly. The streaming sausage mode is stabilized at $V_0/B_0 \lesssim 1$, and it can transit to the streaming tearing mode with a finite resistivity. The streaming tearing mode has larger growth rate than the pure tearing mode, though the scaling relation between the maximum growth rate and the Lundquist number remains unchanged. When the jet is perpendicular to the antiparallel component of the magnetic field, the most unstable sausage mode is usually perpendicular (wavevector along the jet) without a guide field. But with a finite guide field, the most unstable sausage mode can be oblique, depending on the jet speed and guide field strength.

Many linear stability aspects in plasmas are heavily influenced by non-ideal effects beyond the basic ideal magnetohydrodynamics (MHD) description. Here, the extension of the modern open-source MHD spectroscopy code Legolas with viscosity and the Hall current is highlighted and benchmarked on a stringent set of historic and recent findings. The viscosity extension is demonstrated in a cylindrical set-up featuring Taylor–Couette flow and in a viscoresistive plasma slab with a tearing mode. For the Hall extension, we show how the full eigenmode spectrum relates to the analytic dispersion relation in an infinite homogeneous medium. We quantify the Hall term influence on the resistive tearing mode in a Harris current sheet, including the effect of compressibility, which is absent in earlier studies. Furthermore, we illustrate how Legolas mimics the incompressible limit easily to compare with literature results. Going beyond published findings, we emphasise the importance of computing the full eigenmode spectrum, and how elements of the spectrum are modified by compressibility. These extensions allow for future stability studies with Legolas that are relevant to ongoing dynamo experiments, protoplanetary disks or magnetic reconnection.

We derive a model equation describing electrostatic plasma turbulence in general (inhomogeneous and curved) magnetic fields by analysing the effect of curved geometry on the ion fluid polarization drift velocity. The derived nonlinear equation generalizes the Hasegawa–Mima equation governing drift wave turbulence in a straight homogeneous magnetic field, and may serve as a toy model for the description of turbulent plasmas. The equation is most appropriate for configurations with a small $\boldsymbol {E}\times \boldsymbol {B}$ drift velocity divergence, or a mild spatial change in $\boldsymbol {E}\times \boldsymbol {B}$ drift velocity. We identify the conserved energy of the system, and obtain conditions on magnetic field topology for conservation of generalized enstrophy. Through numerical examples, we further show how the curvature of the magnetic field reshapes self-organized steady turbulent states.

Tokamak start-up is characterized by low electron densities and strong electric fields, in order to quickly raise the plasma current and temperature, allowing the plasma to fully ionize and magnetic flux surfaces to form. Such conditions are ideal for the formation of superthermal electrons, which may reduce the efficiency of ohmic heating and prevent the formation of a healthy thermal fusion plasma. This is of particular concern in ITER where engineering limitations put restrictions on the allowable electric fields and limit the prefill densities during start-up. In this study, we present a new 0D burn-through simulation tool called STREAM (STart-up Runaway Electron Analysis Model), which self-consistently evolves the plasma density, temperature and electric field, while accounting for the generation and loss of relativistic runaway electrons. After verifying the burn-through model, we investigate conditions under which runaway electrons can form during tokamak start-up as well as their effects on the plasma initiation. We find that Dreicer generation plays a crucial role in determining whether a discharge becomes runaway-dominated or not, and that a large number of runaway electrons could limit the ohmic heating of the plasma, thus preventing successful burn-through or further ramp-up of the plasma current. The runaway generation can be suppressed by raising the density via gas fuelling, but only if done sufficiently early. Otherwise a large runaway seed may have already been built up, which can avalanche even at relatively low electric fields and high densities.

This paper focuses on utilizing several different optical diagnostics to experimentally characterize a pure helium atmospheric pressure plasma jet. Axial electric field measurements were carried out along the plasma plume through the use of a non-perturbing method based on polarization-dependent Stark spectroscopy of the helium $492.2$ nm line. The electric field is shown to increase with distance along the plume length, reaching values as high as $24.5$ kV cm$^{-1}$. The rate of increase of the electric field is dependent on the helium gas flow rate, with lower gas flows rising quicker with distance in comparison with larger flow rates, with the typical values remaining within the same range. This sensitivity is linked to gas mixing between the helium and surrounding ambient air. Schlieren imaging of the gas flow is included to support this. The addition of a target is shown to further increase the measured electric field in close range to the target, with the magnitude of this increase being strongly dependent on the distance between the tube exit and target. The relative increase in the electric field is shown to be on average greater for a conducting target of water in comparison with plastic. A minimal equipment optical configuration, which is here referred to as fast two-dimensional monochromatic imaging, is introduced as an approach for estimating excited state densities within the plasma. Densities of the upper helium states for transitions, $1s3s$ $^{3}S_{1}$ $\rightarrow$ $1s2p$ $^{3}P^{0}_{0,1,2}$ at $706.5$ nm and $1s3s$ $^{1}S_{0}$ $\rightarrow$ $1s2p$ $^{1}P^{0}_{1}$ at $728.1$ nm, were estimated using this approach and found to be of the order of $10^{10}$–$10^{11}$ cm$^{-3}$.

Understanding edge-localised-mode (ELM)-free high-confinement (H-)mode scenarios is vital for developing practical future demonstration reactor scenarios. An argon-seeded EDA H-mode discharge performed in ASDEX Upgrade is computationally studied in detail for the first time with the gyrokinetic GENE code using experimental profiles and magnetic equilibrium as direct code inputs. Linear scans outline dominant instabilities in the regime and reveal distinct ion- and electron-scale wavenumber growth-rate peaks for two local core and two local pedestal top scenarios. Linear ion-scale growth rates are found to be relatively insensitive to the addition of argon, and collisionality scans demonstrate increased sensitivity in the pedestal top. The addition of an argon impurity profile while keeping the input main ion temperature gradient (ITG) largely unchanged is found to reduce ITG-driven turbulence in the outer core. Nonlinear electromagnetic simulations reveal close agreement with experimentally predicted heat fluxes in the core, outline key sensitivities to electron $\beta$ and background $\boldsymbol{E\times B}$ shearing, and reveal gyrokinetic challenges in analysing the quasicoherent mode. Global electrostatic nonlinear simulations reduce local simulated heat transport overpredictions at the pedestal top. A quasilinear analysis finds that there is good core agreement but poor agreement in the pedestal between linear and nonlinear temperature and density fluctuation cross-phases. Local simulation limitations are elucidated and paths forward for future computation are suggested.

Following indirect-drive experiments which demonstrated promising performance for low convergence ratios (below 17), previous direct-drive simulations identified a fusion-relevant regime which is expected to be robust to hydrodynamic instability growth. This paper expands these results with simulated implosions at lower energies of 100 and 270 kJ, and ‘hydrodynamic equivalent’ capsules which demonstrate comparable convergence ratio, implosion velocity and in-flight aspect ratio without the need for cryogenic cooling, which would allow the assumptions of one-dimensional-like performance to be tested on current facilities. A range of techniques to improve performance within this regime are then investigated, including the use of two-colour and deep ultraviolet laser pulses. Finally, further simulations demonstrate that the deposition of electron energy into the hotspot of a low convergence ratio implosion through auxiliary heating also leads to significant increases in yield. Results include break even for 1.1 MJ of total energy input (including an estimated 370 kJ of short-pulse laser energy to produce electron beams for the auxiliary heating), but are found to be highly dependent upon the efficiency with which electron beams can be created and transported to the hotspot to drive the heating mechanism.

We introduce modes of instantaneous optimal growth of free energy for the fully electromagnetic gyrokinetic equations. We demonstrate how these ‘optimal modes’ arise naturally from the free energy balance equation, allowing its convenient decomposition, and yielding a simple picture of energy flows. Optimal modes have a number of other favourable features, such as their low dimensionality, efficiency of computation and the fact that their growth rates provide a rigorous and ‘tight’ upper bound on both the nonlinear growth rate of energy, and the linear growth rate of traditional gyrokinetic (normal mode) instabilities. We provide simple closed-form solutions for the optimal growth rates in a number of asymptotic limits, and compare these with our previous bounds.

The theory of magnetohydrodynamic (MHD) turbulence predicts that Alfvénic and slow-mode-like compressive fluctuations are energetically decoupled at small scales in the inertial range. The partition of energy between these fluctuations determines the nature of dissipation, which, in many astrophysical systems, happens on scales where plasma is collisionless. However, when the magnetorotational instability (MRI) drives the turbulence, it is difficult to resolve numerically the scale at which both types of fluctuations start to be decoupled because the MRI energy injection occurs in a broad range of wavenumbers, and both types of fluctuations are usually expected to be coupled even at relatively small scales. In this study, we focus on collisional MRI turbulence threaded by a near-azimuthal mean magnetic field, which is naturally produced by the differential rotation of a disc. We show that, in such a case, the decoupling scales are reachable using a reduced MHD model that includes differential-rotation effects. In our reduced MHD model, the Alfvénic and compressive fluctuations are coupled only through the linear terms that are proportional to the angular velocity of the accretion disc. We numerically solve for the turbulence in this model and show that the Alfvénic and compressive fluctuations are decoupled at the small scales of our simulations as the nonlinear energy transfer dominates the linear coupling below the MRI-injection scale. In the decoupling scales, the energy flux of compressive fluctuations contained in the small scales is almost double that of Alfvénic fluctuations. Finally, we discuss the application of this result to prescriptions of ion-to-electron heating ratio in hot accretion flows.

A two-field Hamiltonian gyrofluid model for kinetic Alfvén waves retaining ion finite Larmor radius corrections and parallel magnetic field fluctuations is used to study direct turbulent cascades from the magnetohydrodynamic to the sub-ion scales. For moderate energy imbalance and weak enough magnetic fluctuations, the spectrum of the transverse magnetic field and that of the most energetic wave display a steep transition zone near the ion scale, while the parallel transfer (and thus the parallel dissipation) remains weak. In this regime, the perpendicular flux of generalized cross-helicity displays a significant decay past the ion scale, while the perpendicular energy flux remains almost constant. A phenomenological model suggests that the interactions between co-propagative waves present at the sub-ion scales can play a central role in the development of a transition zone in the presence of a helicity barrier.

We present a study of the linear properties of the ion-temperature gradient (ITG) modes with collisions modelled for the first time by the linearized gyrokinetic (GK) Coulomb collision operator (Frei et al., J. Plasma Phys., vol. 87, issue 5, 2021, 905870501) in the local limit. The study is based on a Hermite–Laguerre polynomial expansion of the perturbed ion distribution function applied to the linearized GK Boltzmann equation, yielding a hierarchy of coupled equations for the expansion coefficients, referred to as gyromoments. We explore the collisionless and high-collisional limits of the gyromoment hierarchy analytically. Parameter scans revealing the dependence of the ITG growth rate on the collisionality modelled using the GK Coulomb operator are reported, showing strong damping at small scales as the collisionality increases and, therefore, the need for a steeper gradient for the ITG onset at high collisionality to overcome the finite Larmor radius (FLR) collisional stabilization. The predictions on the ITG growth rate by the GK Coulomb operator are compared with other collision operator models, such as the Sugama, the Dougherty, as well as the momentum-conserving pitch-angle scattering and the Hirshman–Sigmar–Clarke collision operators derived for the first time in terms of gyromoments. The importance of FLR terms in the collision operators is pointed out by the appearance of a short wavelength ITG branch when collisional FLR terms are neglected, this branch being completely suppressed by FLR collisional effects. Energy diffusion is shown to be important at high collisionality and at small scale lengths. Among the GK collision operators considered in this work, the GK Sugama collision operator yields, in general, the smallest deviation compared with the GK Coulomb collision operator, while the largest deviations are found with the GK Dougherty operator. Convergence studies of the gyromoment method are reported and show that the drifts associated with the gradient and curvature of the magnetic field increase the required number of gyromoments at low collisionality. Nevertheless, the low number of gyromoments necessary for convergence at high collisionality constitutes an attractive numerical and analytical feature of the gyromoment approach to study the plasma dynamics in the boundary of fusion devices.

Collisionless shocks undergo structural changes with the increase of Mach number. Observations and numerical simulations indicate development of time-dependent rippling. It is not known at present what causes the rippling. However, effects of such rippling on the field pattern and ion motion and distributions can be studied without precise knowledge of the causes and detailed shape. It is shown that deviations of the normal component of the magnetic field from the constant value indicate certain spatial dependence of the rippling. Deviations of the motional electric field from the constant value indicate time dependence. It is argued that whistler waves should propagate towards upstream and downstream regions from the rippled ramp. It is shown that the downstream pattern of the fields and ion distributions should follow the rippling pattern, while collisionless relaxation should be faster than in the stationary planar case.

A particle-in-cell algorithm is derived with a canonical Poisson structure in the formalism of finite element exterior calculus. The resulting method belongs to the class of gauge-compatible splitting algorithms, which exactly preserve gauge symmetries and their associated conservation laws via the momentum map. We numerically demonstrate this time invariance of the momentum map and its usefulness in establishing precise initial conditions with a desired initial electric field and fixed background charge. The restriction of this canonical, finite element Poisson structure to the 1X2P $1\frac {1}{2}$-dimensional phase space is also considered and simulated numerically.