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.

Resonant filament-assisted mode conversion (FAMC) scattering of high harmonic fast waves (HHFW) by cylindrical field-aligned density inhomogeneities can efficiently redirect a fraction of the launched HHFW power flux into the parallel direction. Within a simplified analytic approach, this contribution compares the parallel propagation, reflection and dissipation of nearly resonant FAMC modes for three magnetic field line geometries in the scrape-off layer, in the presence of radio-frequency (RF) sheaths at field line extremities and phenomenological wave damping in the plasma volume. When a FAMC mode, excited at the HHFW antenna parallel location and guided along the open magnetic field lines, impinges onto a boundary at normal incidence, we show that it can excite sheath RF oscillations, even toroidally far away from the HHFW launcher. The RF sheaths then dissipate part of the power flux carried by the incident mode, while another part reflects into the FAMC mode with the opposite wave vector parallel to the magnetic field. The reflected FAMC mode in turn propagates and can possibly interact with the sheath at the opposite field line boundary. The two counter-propagating modes then form in the bounded magnetic flux tube a lossy cavity excited by the HHFW scattering. We investigate how the presence of field line boundaries affects the total HHFW power redirected into the filament, and its splitting between sheath and volume losses, as a function of relevant parameters in the model.

A wave turbulence theory is developed for inertial electron magnetohydrodynamics (IEMHD) in the presence of a relatively strong and uniform external magnetic field $\boldsymbol {B_0} = B_0 \hat {\boldsymbol {e}}_\|$. This regime is relevant for scales smaller than the electron inertial length $d_e$. We derive the kinetic equations that describe the three-wave interactions between inertial whistler or kinetic Alfvén waves. We show that for both invariants, energy and momentum, the transfer is anisotropic (axisymmetric) with a direct cascade mainly in the direction perpendicular ($\perp$) to $\boldsymbol {B_0}$. The exact stationary solutions (Kolmogorov–Zakharov spectra) are obtained for which we prove the locality. We also found the Kolmogorov constant $C_K \simeq 8.474$. In the simplest case, the study reveals an energy spectrum in $k_\perp ^{-5/2} k_\|^{-1/2}$ (with k the wavenumber) and a momentum spectrum enslaved to the energy dynamics in $k_\perp ^{-3/2} k_\|^{-1/2}$. These solutions correspond to a magnetic energy spectrum ${\sim }k_\perp ^{-9/2}$, which is steeper than the EMHD prediction made for scales larger than $d_e$. We conclude with a discussion on the application of the theory to space plasmas.

We present a new method for formulating closures that learn from kinetic simulation data. We apply this method to phase mixing in a simple gyrokinetic turbulent system – temperature-gradient-driven turbulence in an unsheared slab. The closure, called the learned multi-mode (LMM) closure, is constructed by, first, extracting an optimal basis from a nonlinear kinetic simulation using singular value decomposition. Subsequent nonlinear fluid simulations are projected onto this basis and the results are used to formulate the closure. We compare the closure with other closures schemes over a broad range of the relevant two-dimensional parameter space (collisionality and gradient drive). We find that the turbulent kinetic system produces phase-mixing rates much lower than the linear expectations, which the LMM closure is capable of capturing. We also compare radial heat fluxes. A Hammett–Perkins closure, generalized to include collisional effects, is quite successful throughout the parameter space, producing ${\sim }14\,\%$ root-mean-square (r.m.s.) error. The LMM closure is also very effective: when trained at three (two) points (in a 35 point parameter grid), the LMM closure produces $8\,\%$ ($12\,\%$) r.m.s. errors. The LMM procedure can be readily generalized to other closure problems.

This paper discusses the toroidal localisation of magnetic reconnection during sawtooth crashes. Numerical analysis with realistic heat diffusion coefficients shows that heat distributes itself helically along the torus faster than the temporal resolution of any existing ECE diagnostics. It makes local and global (helically axisymmetric) magnetic reconnection indistinguishable for an observer, while a local crash where the heat stays confined within a finite helical region could be distinguished. Statistical analysis of sawtooth crashes with the ECEI diagnostic is conducted in ASDEX Upgrade. The displacement of the heat within a finite helical region has not been observed. The statistical data supports global magnetic reconnection.

Shock waves in plasma are usually dealt with using magnetohydrodynamics (MHD). Yet, MHD entails the assumption of a short mean free path, which is not fulfilled in a collisionless plasma. Recently, for pair plasmas, we devised a model allowing one to account for kinetic effects within a MHD-like formalism. Its relies on an estimate of the anisotropy generated when crossing the front, with a subsequent assessment of the stability of this anisotropy in the downstream. We solved our model for parallel, perpendicular and switch-on shocks. Here we bridge between all these cases by treating the problem of an arbitrarily, but coplanar, oriented magnetic field. Even though the formalism presented is valid for anisotropic upstream temperatures, only the case of a cold upstream is solved. We find extra solutions which are not part of the MHD catalogue, and a density jump that is notably less in the quasi-parallel, highly magnetized, regime. Given the complexity of the calculations, this work is mainly devoted to the presentation of the mathematical aspect of our model. A forthcoming article will be devoted to the physics of the shocks here defined.

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$^{-3}$.

The Vlasov–Fokker–Planck (VFP) equation, a variant of the Boltzmann equation, is frequently used to model the dynamics of laboratory and astrophysical plasmas. A common approach in solving the VFP equation in numerical and analytic studies is to expand the momentum part of the distribution function $f$ (i.e. the particle density in phase-space) in terms of known functions. The Cartesian tensor and spherical harmonic expansion have been widely used, leading to the question of how to convert between the different coefficients of the two expansions. This problem is also familiar in multipole expansions of an electrostatic (or gravitational) potential. The coefficients of the Cartesian tensor expansion of the potential are called (Cartesian) multipole moments and the ones of the spherical harmonic expansion are called spherical multipole moments. In this paper, we investigate the relation between the two kinds of multipole moments and provide a general formalism to convert between them. We subsequently apply this formalism to the coefficients of the expansions of the distribution function $f$. A free, open-source command-line tool which implements this formalism is provided.

Vertical displacement normal modes in shaped tokamak plasmas are studied analytically, based on the reduced ideal-magnetohydrodynamic model. With the help of quadratic forms, and using the appropriate eigenfunction for vertical displacements with toroidal mode number $n=0$ and dominant elliptical-angle mode number $m=1$, a dispersion relation is derived, including the effects of ideal or resistive walls through a single parameter, $D_w(\gamma )$, which is, in general, a function of the complex eigenfrequency $\gamma = -{\rm i}\omega$. For the resistive-wall case, the dispersion relation is cubic in $\gamma$. One root corresponds to the well-known, non-rotating resistive-wall vertical mode, growing on the resistive-wall time scale. The other two roots are weakly damped by wall resistivity, but oscillate with a frequency below the poloidal Alfvén frequency, which makes them immune to continuum damping, but subject to possible instability due to resonant interaction with fast ions.

For a magnetised plasma in a straight magnetic guide field, we derive a set of four-dimensional kinetic equations, which can capture electromagnetic turbulence in the drift kinetic limit. To do so, we start from the gyrokinetic equations, employ a Laguerre decomposition in the perpendicular velocity direction, retaining only the dominant gyroaverage contributions and only the first two Laguerre moments that source the electromagnetic fluctuations. The model conserves free energy, and can describe electromagnetic turbulence for a plasma at the transition between fluid and gyrokinetic regimes ($k_\perp \rho _i\approx 1$ range of scales), as dominant finite-Larmor-radius (FLR) effects are considered. In addition to the three dimensions in positions space, we retain the parallel velocity dependence, which we describe via a Hermite representation. Employing this system, but without any other physics-based assumptions for the plasma species that can bias results, will allow us to investigate how fluid effects transition into the kinetic range, and analyse the interplay between spatial and velocity space mixing for electromagnetic plasma turbulence.

A method is demonstrated to rapidly calculate the shapes and properties of quasi-axisymmetric and quasi-helically symmetric stellarators. In this approach, optimization is applied to the equations of magnetohydrodynamic equilibrium and quasisymmetry, expanded in the small distance from the magnetic axis, as formulated by Garren & Boozer [Phys. Fluids B, vol. 3, 1991, p. 2805]. Due to the reduction of the equations by the expansion, the computational cost is significantly reduced, to times of the order of 1 cpu second, enabling wide and high-resolution scans over parameter space. In contrast to traditional stellarator optimization, here, the cost function serves to maximize the volume in which the expansion is accurate. A key term in the cost function is $\| \boldsymbol {\nabla }\boldsymbol B \|$, the norm of the magnetic field gradient, to maximize scale lengths in the field. Using this method, a database of $5\times 10^5$ optimized configurations is calculated and presented. Quasisymmetric configurations are observed to exist in continuous bands, varying in the ratio of the magnetic axis length to average major radius. Several qualitatively new types of configuration are found, including quasi-helically symmetric fields in which the number of field periods is two or more than six.

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.

Plasmas whose Coulomb-collision rates are very small may relax on shorter timescales to non-Maxwellian quasi-equilibria, which, nevertheless, have a universal form, with dependence on initial conditions retained only via an infinite set of Casimir invariants enforcing phase-volume conservation. These are distributions derived by Lynden-Bell (Mon. Not. R. Astron. Soc., vol. 136, 1967, p. 101) via a statistical-mechanical entropy-maximisation procedure, assuming perfect mixing of phase-space elements. To show that these equilibria are reached dynamically, one must derive an effective ‘collisionless collision integral’ for which they are fixed points – unique and inevitable provided the integral has an appropriate H-theorem. We describe how such collision integrals are derived and what assumptions are required for them to have a closed form, how to prove the H-theorems for them, and why, for a system carrying sufficiently large electric-fluctuation energy, collisionless relaxation should be fast. It is suggested that collisionless dynamics may favour maximising entropy locally in phase space before converging to global maximum-entropy states. Relaxation due to interspecies interaction is examined, leading, inter alia, to spontaneous transient generation of electron currents. The formalism also allows efficient recovery of ‘true’ collision integrals for both classical and quantum plasmas.

The energy functional of ideal magnetohydrodynamics (MHD) is extended to the regime of finite resistivity and transformed into an intuitive form, which separates pressure-gradient, current-density drive and stabilising phenomena, analogously to the ideal version of the functional derived by Greene and Johnson (Plasma Phys., vol. 10, issue 8, 1968, pp. 729–745). The resulting resistive energy functional is not in the form of a solvable eigenvalue problem but is intended to analyse the energetic composition of eigenfunctions which were calculated in advance by solving the MHD equations. The new resistive energy functional provides information on the different energetic drives and stabilising phenomena of an eigenfunction. The new energy functional has been implemented in the CASTOR3D code in general 3D curvilinear coordinates and successfully validated across three different coordinate systems for a numerical test case.

Different kinds of waves and instabilities in the F-region of the ionosphere excited by the relative streaming of the dust beam to the background plasma are studied in the present paper. The dispersion relations of different waves are obtained on different time scales. It is found from our numerical results that there are both a stable upper hybrid wave on the electron vibration time scale and a stable dust ion cyclotron wave on the ion vibration time scale. However, the chaotic behaviour appears on the dust particles vibration time scale due to the relative streaming of the dust particles to the background plasma. Such instabilities may drive plasma irregularities that could affect radar backscatter from the clouds.

Independent assessment of the feasibility of controlled nuclear fusion in the proposed SPARC tokamak (Creely et al., J. Plasma Phys., vol. 86, 2020, 865860502; Rodriguez-Fernandez et al., J. Plasma Phys., vol. 86, 2020, 865860503) is difficult because of the uncertainties concerning energy transport in the plasma. We discuss a SPARC scenario – where a burning plasma is obtained – with the help of a well-known general constraint on transport in weakly collisional, axisymmetric, toroidal, low-$\beta$ turbulent plasma (Rogister et al., Phys. Fluids B, vol. 4, 1992, p. 804). This constraint is useful in reducing uncertainties on auxiliary heating as the fusion gain begins to be large. No particular ad hoc model for transport coefficients is invoked. The crucial roles of both suitable tuning of ion cyclotron radiofrequency power and high-temperature pedestal are highlighted.

We revise in detail and in a pedagogical way the analysis of the boundary layer theory of warm tearing modes in slab, reduced magnetohydrodynamics (MHD), when magnetic reconnection is driven by electron inertia and/or resistivity, and ion-sound Larmor radius effects are included. By comparison with the numerical solution of the corresponding eigenvalue problem, we interpret these results by means of a heuristic approach, which in the warm-electron regime, we show to be in general not feasible without knowledge of the scaling of the gradient of the magnetic flux function, differently from what happens in the cold-electron regimes. We put in evidence for a non-trivial relation between the first derivative of the magnetic flux function and of the velocity parallel to the neutral line, evaluated in its proximity, by thus providing insight to the multiple boundary layer analysis that Pegoraro & Schep (Plasma Phys. Control. Fusion, vol. 28, 1986, p. 647) first showed to be required in warm-tearing regimes. In this way, we also suggest and justify a general operational definition of the reconnecting layer width and we discuss the linear appearance of microscopic scales related to the gradients of the eigenfunctions of the tearing modes.

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.

The influence of magnetohydrodynamic eigenmodes destabilized by energetic ions on the momentum of these ions and concomitant sheared plasma rotation are studied. Two mechanisms affecting rotation are revealed: (i) spatial channelling (SC) – radially separated emission and absorption of the momentum; (ii) mode induced redistribution (MIR) across the magnetic field of the momentum of energetic ions. Forces arising during SC and MIR produce both toroidal and poloidal rotations. In addition, the momentum emission during SC leads to a radial flux of fast ions and generation of a radial electric field. Using the developed theory, estimates were made for the ITER (International Thermonuclear Experimental Reactor) 15 MA baseline scenario. They show that a global toroidicity-induced Alfvén eigenmode destabilized by alpha particles and neutral beam injection can result in significant radial electric field and forces applied to plasma. However, available data are not sufficient for a reliable prediction of the effects of SC and MIR in ITER. In general, one can expect that sheared rotation arising after destabilization of Alfvén modes and fast magnetoacoustic modes by energetic ions will tend to suppress the turbulence and improve plasma performance. The importance of plasma rotation is supported, in particular, by the fact that during the JET DTE1 experimental campaign the best parameters were achieved in a deuterium–tritium discharge where the rotation frequency was largest.

We present the effective optical potential of the interaction of an electron with an atom in dense semiclassical plasma of noble gases. This potential takes into account the collective screening effect and the quantum mechanical effect of diffraction. The influence of diffraction and screening effects on the characteristics of electron–atom collisions was investigated. Scattering phase shifts decrease with increase of the de Broglie wave. The electron–atom momentum-transfer cross-section at $\lambda _{B}\to 0$ tends to the data obtained earlier with a neglecting of the diffraction effect.