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.

We report the observation of a nonlinear wave packet propagating through a relaxed Taylor state in the Swarthmore Spheromak eXperiment (SSX) device. The wave packet is launched by a fast, pulsed, high current (${\approx}21~\text{kA}$) single-turn theta-pinch coil mounted outside the plasma vessel. The theta-pinch coil is energized by discharging a 40 kV, 2 kJ capacitor circuit. The wave packet velocity is super-thermal and super-Alfvénic; its group velocity is more consistent with a whistler pulse than other characteristic velocities. We also observe a fast density pulse which indicates that it is not Alfvénic in nature.

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.

Stochastic heating refers to an increase in the average magnetic moment of charged particles interacting with electromagnetic fluctuations whose frequencies are smaller than the particles’ cyclotron frequencies. This type of heating arises when the amplitude of the gyroscale fluctuations exceeds a certain threshold, causing particle orbits in the plane perpendicular to the magnetic field to become stochastic rather than nearly periodic. We consider the stochastic heating of protons by Alfvén-wave (AW) and kinetic-Alfvén-wave (KAW) turbulence, which may make an important contribution to the heating of the solar wind. Using phenomenological arguments, we derive the stochastic-proton-heating rate in plasmas in which $\unicode[STIX]{x1D6FD}_{\text{p}}\sim 1$–30, where $\unicode[STIX]{x1D6FD}_{\text{p}}$ is the ratio of the proton pressure to the magnetic pressure. (We do not consider the $\unicode[STIX]{x1D6FD}_{\text{p}}\gtrsim 30$ regime, in which KAWs at the proton gyroscale become non-propagating.) We test our formula for the stochastic-heating rate by numerically tracking test-particle protons interacting with a spectrum of randomly phased AWs and KAWs. Previous studies have demonstrated that at $\unicode[STIX]{x1D6FD}_{\text{p}}\lesssim 1$, particles are energized primarily by time variations in the electrostatic potential and thermal-proton gyro-orbits are stochasticized primarily by gyroscale fluctuations in the electrostatic potential. In contrast, at $\unicode[STIX]{x1D6FD}_{\text{p}}\gtrsim 1$, particles are energized primarily by the solenoidal component of the electric field and thermal-proton gyro-orbits are stochasticized primarily by gyroscale fluctuations in the magnetic field.

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.

The confinement of the guiding-centre trajectories in a stellarator is determined by the variation of the magnetic field strength $B$ in Boozer coordinates $(r,\unicode[STIX]{x1D703},\unicode[STIX]{x1D711})$, but $B(r,\unicode[STIX]{x1D703},\unicode[STIX]{x1D711})$ depends on the flux surface shape in a complicated way. Here we derive equations relating $B(r,\unicode[STIX]{x1D703},\unicode[STIX]{x1D711})$ in Boozer coordinates and the rotational transform to the shape of flux surfaces in cylindrical coordinates, using an expansion in distance from the magnetic axis. A related expansion was done by Garren and Boozer (Phys. Fluids B, vol. 3, 1991a, 2805) based on the Frenet–Serret frame, which can be discontinuous anywhere the magnetic axis is straight, a situation that occurs in the interesting case of omnigenity with poloidally closed $B$ contours. Our calculation in contrast does not use the Frenet–Serret frame. The transformation between the Garren–Boozer approach and cylindrical coordinates is derived, and the two approaches are shown to be equivalent if the axis curvature does not vanish. The expressions derived here help enable optimized plasma shapes to be constructed that can be provided as input to VMEC and other stellarator codes, or to generate initial configurations for conventional stellarator optimization.

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 $\unicode[STIX]{x1D716}_{\unicode[STIX]{x1D6FF}}$.