Global magnetohydrodynamic (MHD) instabilities are investigated in a computationally tractable two-dimensional model of the solar tachocline. The model’s differential rotation yields stability in the absence of a magnetic field, but if a magnetic field is present, a joint instability is observed. We analyse the nonlinear development of the instability via fully nonlinear direct numerical simulation, the generalized quasi-linear approximation (GQL) and direct statistical simulation (DSS) based upon low-order expansion in equal-time cumulants. As the magnetic diffusivity is decreased, the nonlinear development of the instability becomes more complicated until eventually a set of parameters is identified that produces a previously unidentified long-term cycle in which energy is transformed from kinetic energy to magnetic energy and back. We find that the periodic transitions, which mimic some aspects of solar variability – for example, the quasiperiodic seasonal exchange of energy between toroidal field and waves or eddies – are unable to be reproduced when eddy-scattering processes are excluded from the model.

The plasma in the scrape-off layer (SOL) has an important effect on the coupling of the waves in the ion cyclotron range of frequencies (ICRF). The high-frequency B-dot (HFB) probes have been installed to investigate the behaviour of ICRF waves on EAST. The fast and slow ICRF wave field amplitudes are measured and a domain parallel wavenumber is deduced. Results of measurements on a test experimental platform and EAST experiments are presented, which include vacuum and plasma situations. In vacuum it is found that field amplitudes increase linearly with ICRF power. Besides, during plasma operation, field amplitudes measured were decreased by an order of magnitude and no linear relation with power was observed. Fast and slow wave power densities fluctuate strongly with plasma density. The experimental results in the laboratory coincide with the simulation results and allow for validating of the measurement method.

The multipolar representation of the magnetic field has, for the lowest-order term, a magnetic dipole that dominates the far field. Thus the far-field representation of the magnetic field of the Earth, Sun and other celestial bodies is a dipole. Since these bodies consist of or are surrounded by plasma, which can support Alfvén waves, their propagation along dipole magnetic field lines is considered using a new coordinate system: dipolar coordinates. The present paper introduces multipolar coordinates, which are an example of conformal coordinates; conformal coordinates are orthogonal with equal scale factors, and can be extended from the plane to space, for instance as cylindrical or spherical dipolar coordinates. The application considered is to Alfvén waves propagating along a circle, that is a magnetic field line of a dipole, with transverse velocity and magnetic field perturbations; the various forms of the wave equation are linear second-order differential equations, with variable coefficients, specified by a background magnetic field, which is force free. The absence of a background magnetic force leads to a mean state of hydrostatic equilibrium, specified by the balance of gravity against the pressure gradient, for a perfect gas or incompressible liquid. The wave equation is simplified to a Gaussian hypergeometric type in the case of zero frequency, otherwise, for non-zero frequency, an extended Gaussian hypergeometric equation is obtained. The solution of the latter specifies the magnetic field perturbation spectrum, and also, via a polarisation relation, the velocity perturbation spectrum; both are plotted, over half a circle, for three values of the dimensionless frequency.

We propose that pressure anisotropy causes weakly collisional turbulent plasmas to self-organize so as to resist changes in magnetic-field strength. We term this effect ‘magneto-immutability’ by analogy with incompressibility (resistance to changes in pressure). The effect is important when the pressure anisotropy becomes comparable to the magnetic pressure, suggesting that in collisionless, weakly magnetized (high-$\unicode[STIX]{x1D6FD}$) plasmas its dynamical relevance is similar to that of incompressibility. Simulations of magnetized turbulence using the weakly collisional Braginskii model show that magneto-immutable turbulence is surprisingly similar, in most statistical measures, to critically balanced magnetohydrodynamic turbulence. However, in order to minimize magnetic-field variation, the flow direction becomes more constrained than in magnetohydrodynamics, and the turbulence is more strongly dominated by magnetic energy (a non-zero ‘residual energy’). These effects represent key differences between pressure-anisotropic and fluid turbulence, and should be observable in the $\unicode[STIX]{x1D6FD}\gtrsim 1$ turbulent solar wind.

The linear theory stability of different collisionless plasma sheath structures, including the classic sheath, inverse sheath and space-charge limited (SCL) sheath, is investigated as a typical eigenvalue problem. The three background plasma sheaths formed between a Maxwellian plasma source and a dielectric wall with a fully self-consistent secondary electron emission condition are solved by recent developed 1D3V (one-dimensional space and three-dimensional velocities), steady-state, collisionless kinetic sheath model, within a wide range of Maxwellian plasma electron temperature $T_{e}$. Then, the eigenvalue equations of sheath plasma fluctuations through the three sheaths are numerically solved, and the corresponding damping and growth rates $\unicode[STIX]{x1D6FE}$ are found: (i) under the classic sheath structure (i.e. $T_{e}<T_{ec}$ (the first threshold)), there are three damping solutions (i.e. $\unicode[STIX]{x1D6FE}_{1}$, $\unicode[STIX]{x1D6FE}_{2}$ and $\unicode[STIX]{x1D6FE}_{3}$, $0>\unicode[STIX]{x1D6FE}_{1}>\unicode[STIX]{x1D6FE}_{2}>\unicode[STIX]{x1D6FE}_{3}$) for most cases, but there is only one growth-rate solution $\unicode[STIX]{x1D6FE}$ when $T_{e}\rightarrow T_{ec}$ due to the inhomogeneity of sheath being very weak; (ii) under the inverse sheath structure, which arises when $T_{e}>T_{ec}$, there are no background ions in the sheath so that the fluctuations are stable; (iii) under the SCL sheath conditions (i.e. $T_{e}\geqslant T_{e\text{SCL}}$, the second threshold), the obvious ion streaming through the sheath region again emerges and the three damping solutions are again found.

We carry out expansions of non-symmetric toroidal ideal magnetohydrodynamic (MHD) equilibria with nested flux surfaces about a periodic cylinder, in which physical quantities are periodic of period $2\unicode[STIX]{x03C0}$ in the cylindrical angle $\unicode[STIX]{x1D703}$ and $z$. The cross-section of a flux surface at a constant toroidal angle is assumed to be approximately circular, and data are given on the cylindrical flux surface $r=1$. Furthermore, we assume that the magnetic field lines are closed on the lowest-order flux surface, and the magnetic shear is relatively small. We extend earlier work in a flat torus by Weitzner (Phys. Plasmas, vol. 23, 2016, 062512) and demonstrate that a power series expansion can be carried out to all orders using magnetic flux as an expansion parameter. The cylindrical metric introduces certain new features to the expansions compared to the flat torus. However, the basic methodology of dealing with resonance singularities remains the same. The results, even though lacking convergence proofs, once again support the possibility of smooth, low-shear non-symmetric toroidal MHD equilibria.

Simulations of one-dimensional Vlasov–Maxwell solutions with non-periodic boundary conditions are discussed. Results obtained using a recently developed filtered flux-balance simulation system are compared to those obtained using a filtered, Fourier–Fourier transformed system. Excellent agreement is confirmed except for the appearance of the Gibbs phenomenon on the discontinuous simulated solutions of the transformed system. Recovery of the flux-balance results from the Fourier transformed results using the inverse polynomial reconstruction method is demonstrated.

An iterative formulation of an arbitrarily short-wavelength solver for global gyrokinetic simulations is suggested. The solver is verified against solutions of the dispersion relation. It can be used to treat the nonlinear polarisation density which is important at the plasma edge. In the linear case, the solver is shown to be computationally efficient.

The propagation of dust-acoustic (DA) shock waves (SWs) is studied in a four-component dusty plasma system containing viscous dust fluids of opposite polarity, Schamel distributed ions and Boltzmann distributed electrons. The reductive perturbation method is employed to derive a modified Burgers equation which gives rise to the DA shock waves with stronger nonlinearity. The viscous force acting in the dust fluids is identified as a source of dissipation, and is responsible for the formation of the DA shock waves. The basic characteristics (viz., speed, amplitude, width) of the DA shock waves are found to be significantly modified by the combined effects of opposite polarity dust fluids and trapped ions. The applications of this investigation in different space plasma environments and laboratory devices are pinpointed.

An introduction to the physical interpretation of the Coulomb logarithm is given with particular emphasis on the quantum-mechanical corrections that are required at high temperatures. Excerpts from the literature are used to emphasize the historical understanding of the topic, which emerged more than a half-century ago. Several misinterpretations are noted. Quantum-mechanical effects are related to diffraction by scales of the order of the Debye screening length; they are not due to quantum uncertainty related to the much smaller distance of closest approach.

The results of a basic electron heat transport experiment using multiple localized heat sources in close proximity and embedded in a large magnetized plasma are presented. The set-up consists of three biased probe-mounted crystal cathodes, arranged in a triangular spatial pattern, that inject low energy electrons along a strong magnetic field into a pre-existing, cold afterglow plasma, forming electron temperature filaments. When the three sources are activated and placed within a few collisionless electron skin depths of each other, a non-azimuthally symmetric wave pattern emerges due to interference of the drift-Alfvén modes that form on each filament’s temperature gradient. Enhanced cross-field transport from chaotic ($\boldsymbol{E}\times \boldsymbol{B}$, where $\boldsymbol{E}$ is the electric field and $\boldsymbol{B}$ the magnetic field) mixing rapidly relaxes the gradients in the inner triangular region of the filaments and leads to growth of a global nonlinear drift-Alfvén mode that is driven by the thermal gradient in the outer region of the triangle. Azimuthal flow shear arising from the emissive cathode sources modifies the linear eigenmode stability and convective pattern. A steady-current model with emissive sheath boundary predicts the plasma potential and shear flow contribution from the sources.

This tutorial covers validation of gyrokinetic turbulent-transport models via comparison of measured turbulence with realistic simulations of fusion plasmas. It presents a brief history of validation of gyrokinetic simulations, the principal challenges encountered, a limited survey of common turbulence diagnostics used on tokamaks and stellarators, an overview of the fundamentals of synthetic diagnostic models and a discussion of frontiers in turbulent-transport model validation.