Recent efforts to include kinetic effects in fluid simulations of plasmas have been very promising. Concerning collisionless magnetic reconnection, it has been found before that damping of the pressure tensor to isotropy leads to good agreement with kinetic runs in certain scenarios. An accurate representation of kinetic effects in reconnection was achieved in a study by Wang et al. (Phys. Plasmas, vol. 22, 2015, 012108) with a closure derived from earlier work by Hammett and Perkins (Phys. Rev. Lett., vol. 64, 1990, 3019). Here, their approach is analysed on the basis of heat flux data from a Vlasov simulation. As a result, we propose a new local closure in which heat flux is driven by temperature gradients. This way, a more realistic approximation of Landau damping in the collisionless regime is achieved. Previous issues are addressed and the agreement with kinetic simulations in different reconnection set-ups is improved significantly. To the authors’ knowledge, the new fluid model is the first to perform well in simulations of the coalescence of large magnetic islands.

Spectral densities of plasma fluctuations are calculated for the thermal case using classical molecular dynamics (MD) assuming Coulomb interactions and a short-range cutoff radius. The aim of the calculation is to verify limits and performances of such calculations in the light of possible generalizations, e.g. collisional or non-ideal plasmas. Results are presented for ideal, collisionless, fully ionized thermal plasmas. Comparison with the analytical theory reveals a generally satisfactory agreement with possibility for improvement when more strict numerical parameters are used albeit with a strong increase in computational cost. The largest deviations have been observed in the vicinity of the weakly damped eigenmodes. The agreement is strong in other parts of the spectrum, where Landau damping is prominent, and overcomes the effects stemming from the excess collisionality and coupling as well as from the exclusion of short-range collisions.

So far, only one distribution function giving rise to a collisionless nonlinear force-free current sheet equilibrium allowing for a plasma beta less than one is known (Allanson et al., Phys. Plasmas, vol. 22 (10), 2015, 102116; Allanson et al., J. Plasma Phys., vol. 82 (3), 2016a, 905820306). This distribution function can only be expressed as an infinite series of Hermite functions with very slow convergence and this makes its practical use cumbersome. It is the purpose of this paper to present a general method that allows us to find distribution functions consisting of a finite number of terms (therefore easier to use in practice), but which still allow for current sheet equilibria that can, in principle, have an arbitrarily low plasma beta. The method involves using known solutions and transforming them into new solutions using transformations based on taking integer powers ($N$) of one component of the pressure tensor. The plasma beta of the current sheet corresponding to the transformed distribution functions can then, in principle, have values as low as $1/N$. We present the general form of the distribution functions for arbitrary $N$ and then, as a specific example, discuss the case for $N=2$ in detail.

Turbulence in an accretion disk launches Alfvén waves (AWs) that propagate away from the disk along magnetic-field lines. Because the Alfvén speed varies with distance from the disk, the AWs undergo partial non-WKB reflection, and counter-propagating AWs subsequently interact, causing AW energy to cascade to small scales and dissipate. To investigate this process, we introduce an Elsasser-like formulation of general relativistic magnetohydrodynamics (GRMHD) and develop the theory of general relativistic reduced MHD in an inhomogeneous medium. We then derive a set of equations for the mean-square AW amplitude $M_{+}$ and turbulent heating rate $Q$ under the assumption that, in the plasma rest frame, AWs propagating away from the disk are much more energetic than AWs propagating toward the disk. For the case in which the background flow is axisymmetric and time independent, we solve these equations analytically to determine $M_{+}$ and $Q$ as functions of position. We find that, for an idealized thin disk threaded by a large-scale poloidal magnetic field, the AW energy flux is ${\sim}(\unicode[STIX]{x1D70C}_{\text{b}}/\unicode[STIX]{x1D70C}_{\text{d}})^{1/2}\unicode[STIX]{x1D6FD}_{\text{net,d}}^{-1/2}$ times the disk’s radiative flux, where $\unicode[STIX]{x1D70C}_{\text{b}}$ and $\unicode[STIX]{x1D70C}_{\text{d}}$ are the mass densities at the coronal base and disk midplane, respectively, and $\unicode[STIX]{x1D6FD}_{\text{net,d}}$ is the ratio (evaluated at the disk midplane) of plasma-plus-radiation pressure to the pressure of the average vertical magnetic field. This energy flux could have a significant impact on disk coronae and outflows. To lay the groundwork for future global simulations of turbulent disk coronae and jets, we derive a set of averaged GRMHD equations that account for reflection-driven AW turbulence using a sub-grid model.

When two plasmas collide, their interaction can be mediated by collisionless plasma instabilities or binary collisions between particles of each shell. By comparing the maximum growth rate of the collisionless instabilities with the collision frequency between particles of the shells, we determine the critical density separating the collisionless formation from the collisional formation of the resulting shock waves. This critical density is also the density beyond which the shock downstream is field free, as plasma instabilities do not have time to develop electromagnetic patterns. We further determine the conditions on the shells initial density and velocity for the downstream to be collisional. If these quantities fulfil the determined conditions, the collisionality of the downstream also prevents the shock from accelerating particles or generating strong magnetic fields. We compare the speed of sound with the relative speed of collision between the two shells, thus determining the portion of the parameter space where strong shock formation is possible for both classical and degenerate plasmas. Finally, we discuss the observational consequences in several astrophysical settings.

The depletion of neutral helium atoms has been studied in an unmagnetised spherical plasma created by DC discharge in a multidipole confinement field. Knowing the neutral density profile is critical to predicting the equilibrium flow of such plasmas. A model of the emissivity due to electron-impact excitation of neutral atoms in the plasma has been derived and used to fit radiance measurements of several neutral transitions to extract the radial profile of neutral density for plasmas of varying temperature and density. We report a depletion of the core neutral density varying between negligible levels to 80 % of the edge neutral density depending on the input power and fuelling. The corresponding ionisation fraction varies between 30–80 % in the plasma core. A simple neutral diffusion model is sufficient to describe the shape of neutral density profile implied by the radiance measurements. We have used the measurements to include a drag force due to neutral charge-exchange collisions in simulations of driven plasma flow. The simulation predicts a better fit to Mach probe flow measurements when this neutral drag is accounted for. This work shows that accounting for a realistic neutral profile is important to predict the plasma flow geometry and its magnetohydrodynamics (MHD) stability.

We have derived the universal eikonal-Glauber Thomas–Fermi model for atomic collision cross-sections with many-electron atoms, such as iron and tungsten atoms, including the influence of atomic screening in fusion devices and plasma technologies. The eikonal-Glauber method is employed to obtain the analytic expressions for the effective atomic charge, the scattering phase shift and the atomic cross-section in terms of the atomic form factor and the Mott–Massey screening parameter. The result shows that the effective atomic charge would be the same as the case of the net nuclear charge for the large momentum transfer domain and becomes zero without momentum transfer due to the influence of bound atomic electrons. It is shown that the eikonal scattering phase shift and the total eikonal-Glauber scattering cross-section increase with increasing charge number $Z$ of the nucleus of the target atom. It is also found that the charge dependence of the total eikonal-Glauber scattering cross-section decreases with an increase of the scaled collision energy since the atomic form factor is small for large collision energies.

In this paper the full set of stochastic differential equations (SDEs) are presented describing the guiding centre motion of test charged particles in a plasma with an arbitrary inhomogeneous magnetic field, when the drift approximation is applicable. The derivation is based on the Ito formula which is used to determine stochastic differentials of functions of the non-gyro-averaged velocity diffusion in strict correspondence with the general kinetic equations involving Coulomb collision operators. The drift SDEs are obtained by calculating the Ito stochastic integrals within time intervals admitting the gyro-averaging procedure. The proposed SDEs reproduce the well-known Monte Carlo operators for orbital invariants, however additionally accounting for the spatial drift caused by the cross-field diffusion process with a classical diffusion coefficient. All SDE coefficients are explicitly expressed in terms of the Rosenbluth potentials in a gyro-tropic or isotropic background plasma. The SDEs are presented in particular for the case of an axisymmetric toroidal magnetic configuration to describe the spatial two-dimensional poloidal diffusion process providing a detailed description of neoclassical orbital effects.

A gyrokinetic reduction is based on a specific ordering of the different small parameters characterizing the background magnetic field and the fluctuating electromagnetic fields. In this tutorial, we consider the following ordering of the small parameters: $\unicode[STIX]{x1D716}_{B}=\unicode[STIX]{x1D716}_{\unicode[STIX]{x1D6FF}}^{2}$ where $\unicode[STIX]{x1D716}_{B}$ is the small parameter associated with spatial inhomogeneities of the background magnetic field and $\unicode[STIX]{x1D716}_{\unicode[STIX]{x1D6FF}}$ characterizes the small amplitude of the fluctuating fields. In particular, we do not make any assumption on the amplitude of the background magnetic field. Given this choice of ordering, we describe a self-contained and systematic derivation which is particularly well suited for the gyrokinetic reduction, following a two-step procedure. We follow the approach developed in Sugama (Phys. Plasmas, vol. 7, 2000, p. 466): In a first step, using a translation in velocity, we embed the transformation performed on the symplectic part of the gyrocentre reduction in the guiding-centre one. In a second step, using a canonical Lie transform, we eliminate the gyroangle dependence from the Hamiltonian. As a consequence, we explicitly derive the fully electromagnetic gyrokinetic equations at the second order in $\unicode[STIX]{x1D716}_{\unicode[STIX]{x1D6FF}}$.