We consider the one-dimensional equilibrium problem of a shear-flow boundary layer within an ‘extended-fluid model’ of a plasma that includes the Hall and the electron pressure terms in Ohm’s law, as well as dynamic equations for anisotropic pressure for each species and first-order finite-Larmor-radius (FLR) corrections to the ion dynamics. We provide a generalized version of the analytic expressions for the equilibrium configuration given in Cerri et al., (Phys. Plasmas, vol. 20 (11), 2013, 112112), highlighting their intrinsic asymmetry due to the relative orientation of the magnetic field $\boldsymbol{B}$, $\boldsymbol{b}=\boldsymbol{B}/|\boldsymbol{B}|$, and the fluid vorticity $\unicode[STIX]{x1D74E}=\unicode[STIX]{x1D735}\times \boldsymbol{u}$ (‘$\unicode[STIX]{x1D74E}\boldsymbol{b}$ asymmetry’). Finally, we show that FLR effects can modify the Chapman–Ferraro current layer at the flank magnetopause in a way that is consistent with the observed structure reported by Haaland et al., (J. Geophys. Res. (Space Phys.), vol. 119, 2014, pp. 9019–9037). In particular, we are able to qualitatively reproduce the following key features: (i) the dusk–dawn asymmetry of the current layer, (ii) a double-peak feature in the current profiles and (iii) adjacent current sheets having thicknesses of several ion Larmor radii and with different current directions.

Fully compressible magnetohydrodynamic (MHD) turbulence is investigated in the framework of the multiple-scale direct-interaction approximation. With the aid of the propagators (correlation and Green’s functions), fluctuating fields are solved, and turbulent correlations are estimated in highly compressible turbulence. We focus on the expression of the turbulent electromotive force (EMF). Obliqueness between the mean magnetic field and the mean-density gradient, the mean internal density gradient and the non-equilibrium mean velocity contributes to the EMF in the presence of the density variance, which is ubiquitous in turbulence in strongly variable density flows such as the shock-front region. This density-variance effect is expected to locally enhance the turbulence intensity across the shock front, leading to a fast reconnection.

We develop a mean-field theory of compressibility effects in turbulent magnetohydrodynamics and passive scalar transport using the quasi-linear approximation and the spectral $\unicode[STIX]{x1D70F}$-approach. We find that compressibility decreases the $\unicode[STIX]{x1D6FC}$ effect and the turbulent magnetic diffusivity both at small and large magnetic Reynolds numbers, $Rm$. Similarly, compressibility decreases the turbulent diffusivity for passive scalars both at small and large Péclet numbers, $Pe$. On the other hand, compressibility does not affect the effective pumping velocity of the magnetic field for large $Rm$, but it decreases it for small $Rm$. Density stratification causes turbulent pumping of passive scalars, but it is found to become weaker with increasing compressibility. No such pumping effect exists for magnetic fields. However, compressibility results in a new passive scalar pumping effect from regions of low to high turbulent intensity both for small and large Péclet numbers. It can be interpreted as compressible turbophoresis of non-inertial particles and gaseous admixtures, while the classical turbophoresis effect exists only for inertial particles and causes them to be pumped to regions with lower turbulent intensity.

There has been a growing interest, over the past few years, on understanding the effect on radio frequency waves due to turbulence in the scrape-off layer of tokamak plasmas. While the far scrape-off layer density width is of the order of centimetres in contemporary tokamaks, in ITER (International Thermonuclear Experimental Reactor), and in future fusion reactors, the corresponding width will be of the order of tens of centimetres. As such, this could impact the spectral properties of the waves and, consequently, the transport of wave energy and momentum to the core plasma. The turbulence in the scrape-off layer spans a broad range of spatial scales and includes blobs and filaments that are elongated along the magnetic field lines. The propagation of radio frequency waves through this tenuous plasma is given by Maxwell’s equations. The characteristic properties of the plasma appear as a permittivity tensor in the expression for the current in Ampere’s equation. This paper develops a formalism for expressing the permittivity of a turbulent plasma using the homogenization technique. This technique has been extensively used to express the dielectric properties of composite materials that are spatially inhomogeneous, for example, due to the presence of micro-structures. In a similar vein, the turbulent plasma in the scrape-off layer is spatially inhomogeneous and can be considered as a composite material in which the micro-structures are filaments and blobs. The classical homogenization technique is not appropriate for the magnetized plasma in the scrape-off layer, as the radio frequency waves span a broad range of wavelengths and frequencies – from tens of megahertz to hundreds of gigahertz. The formalism in this paper makes use of the Fourier space components of the electric and magnetic fields of the radio frequency waves for the scattered fields and fields inside the filaments and blobs. These are the eigenvectors of the dispersion matrix which, using the Green’s function approach, lead to a homogenized dielectric tensor.

In a reactor plasma like demonstration power station (DEMO), when using the radio frequency (RF) for heating or current drive in the lower hybrid (LH) frequency range (Franke et al., Fusion Engng Des., vol. 96–97, 2015, p. 46; Cardinali et al., Plasma Phys. Control. Fusion, vol. 59, 2017, 074002), a large fraction of the ion population (the continuously born $\unicode[STIX]{x1D6FC}$-particle, and/or the neutral beam injection (NBI) injected ions) is characterized by a non-thermal distribution function. The interaction (propagation and absorption) of the LH wave must be reformulated by considering the quasi-linear approach for each species separately. The collisional slowing down of such an ion population in a background of an electron and ion plasma is balanced by a quasi-linear diffusion in velocity space due to the propagating electromagnetic wave. In this paper, both propagations are considered by including the ion distribution function, solution of the Fokker–Planck equation, which describes the collisional dynamics of the $\unicode[STIX]{x1D6FC}$-particles including the effects of frictional slowing down, energy diffusion and pitch-angle scattering. Analytical solutions of the Fokker–Planck equation for the distribution function of $\unicode[STIX]{x1D6FC}$-particles with a background of ions and electrons at steady state are included in the calculation of the dielectric tensor. In the LH frequency domain, ray tracing (including quasi-linear damping), can be analytically solved by iterating with the Fokker–Planck solution, and the interaction of the LH wave with $\unicode[STIX]{x1D6FC}$-particles, thermal ions and electrons can be accounted self-consistently and the current drive efficiency can be evaluated in this more general scenario.

This paper summarizes the results of an experimental program at Caltech wherein magnetohydrodynamically driven plasma jets are created and diagnosed. The theory modelling these jets, the main experimental results and their relevance to astrophysical jets are presented. The model explains how the jets are driven and why they self-collimate. Characteristic kink and Rayleigh–Taylor instabilities are shown to occur and the ramifications of these instabilities are discussed. Extending the experimental results to the astrophysical situation reveals a shortcoming in ideal magnetohydrodynamics (MHD) that must be remedied by replacing the ideal MHD Ohm’s law by the generalized Ohm’s law. It is shown that when the generalized Ohm’s law is used and the consequences of weak ionization are taken into account, an accretion disk behaves much like the electrodes, mass source and power supply used in the experiment.

We want to study the connections between the magnetic field generated inside the Sun and the solar wind impacting Earth, especially the influence of north–south asymmetry on the magnetic and velocity fields. We study a solar-like 11-year cycle in a quasi-static way: an asymmetric dynamo field is generated through a 2.5-dimensional (2.5-D) flux-transport model with the Babcock–Leighton mechanism, and then is used as bottom boundary condition for compressible 2.5-D simulations of the solar wind. We recover solar values for the mass loss rate, the spin-down time scale and the Alfvén radius, and are able to reproduce the observed delay in latitudinal variations of the wind and the general wind structure observed for the Sun. We show that the phase lag between the energy of the dipole component and the total surface magnetic energy has a strong influence on the amplitude of the variations of global quantities. We show in particular that the magnetic torque variations can be linked to topological variations during a magnetic cycle, while variations in the mass loss rate appear to be driven by variations of the magnetic energy.

We investigate the onset of the classical magnetohydrodynamic (MHD) tearing instability (TI) and focus on non-modal (transient) growth rather than the tearing mode. With the help of pseudospectral theory, the operators of the linear equations are shown to be highly non-normal, resulting in the possibility of significant transient growth at the onset of the TI. This possibility increases as the Lundquist number $S$ increases. In particular, we find evidence, numerically, that the maximum possible transient growth, measured in the $L_{2}$-norm, for the classical set-up of current sheets unstable to the TI, scales as $O(S^{1/4})$ on time scales of $O(S^{1/4})$ for $S\gg 1$. This behaviour is much faster than the time scale $O(S^{1/2})$ when the solution behaviour is dominated by the tearing mode. The size of transient growth obtained is dependent on the form of the initial perturbation. Optimal initial conditions for the maximum possible transient growth are determined, which take the form of wave packets and can be thought of as noise concentrated at the current sheet. We also examine how the structure of the eigenvalue spectrum relates to physical quantities.

An increase in symmetry is observed for a low density non-collisional plasma, in a simple magnetic mirror machine, due to the application of external oscillating magnetic fields of 1.5 MHz frequency. The increase in symmetry is attributed to an increase in stability of the flute mode and is dependent on the field’s polarization and trap magnetic field strength.

Gyrokinetic simulations of drift waves in low-magnetic-shear stellarators reveal that simulation domains comprised of multiple turns can be required to properly resolve critical mode structures important in saturation dynamics. Marginally stable eigenmodes important in saturation of ion temperature gradient modes and trapped electron modes in the Helically Symmetric Experiment (HSX) stellarator are observed to have two scales, with the envelope scale determined by the properties of the local magnetic shear and an inner scale determined by the interplay between the local shear and magnetic field-line curvature. Properly resolving these modes removes spurious growth rates that arise for extended modes in zero-magnetic-shear approximations, enabling use of a zero-magnetic-shear technique with smaller simulation domains and attendant cost savings. Analysis of subdominant modes in trapped electron mode (TEM)-driven turbulence reveals that the extended marginally stable modes play an important role in the nonlinear dynamics, and suggests that the properties induced by low magnetic shear may be exploited to provide another route for turbulence saturation.

To consider the contribution of the spin–orbit interaction in the extraordinary wave spectrum we derive a generalization of the separate spin evolution quantum hydrodynamics. Applying the corresponding nonlinear Pauli equation we include the Fermi spin current contribution in the spin evolution. We find that the spectrum of extraordinary waves consists of three branches: two of them are well-known extraordinary waves and the third one is the spin-electron acoustic wave. A change of the extraordinary wave spectrum due to the spin–orbit interaction is also obtained.

Tokamak start-up is strongly dependent on the state of the initial plasma formed during plasma breakdown. We have investigated through numerical simulations the effects that the pre-filling pressure and induced electric field have on pure ohmic heating during the breakdown process. Three breakdown modes during the discharge are found, as a function of different initial parameters: no breakdown mode, successful breakdown mode and runaway mode. No breakdown mode often occurs with low electric field or high pre-filling pressure, while runaway electrons are usually easy to generate at high electric field or low pre-filling pressure (${<}1.33\times 10^{-4}$  Pa). The plasma behaviours and the physical mechanisms under the three breakdown modes are discussed. We have identified the electric field and pressure values at which the different modes occur. In particular, when the electric field is $0.3~\text{V}~\text{m}^{-1}$ (the value at which ITER operates), the pressure range for possible breakdown becomes narrow, which is consistent with Lloyd’s theoretical prediction. In addition, for $0.3~\text{V}~\text{m}^{-1}$, the optimal pre-filling pressure range obtained from our simulations is $1.33\times 10^{-3}\sim 2.66\times 10^{-3}$  Pa, in good agreement with ITER’s design. Besides, we also find that the Townsend discharge model does not appropriately describe the plasma behaviour during tokamak breakdown due to the presence of a toroidal field. Furthermore, we suggest three possible operation mechanisms for general start-up scenarios which could better control the breakdown phase.

Sufficiently strong electric fields in plasmas can accelerate charged particles to relativistic energies. In this paper we describe the dynamics of positrons accelerated in such electric fields, and calculate the fraction of created positrons that become runaway accelerated, along with the amount of radiation that they emit. We derive an analytical formula that shows the relative importance of the different positron production processes, and show that, above a certain threshold electric field, the pair production by photons is lower than that by collisions. We furthermore present analytical and numerical solutions to the positron kinetic equation; these are applied to calculate the fraction of positrons that become accelerated or thermalized, which enters into rate equations that describe the evolution of the density of the slow and fast positron populations. Finally, to indicate operational parameters required for positron detection during runaway in tokamak discharges, we give expressions for the parameter dependencies of detected annihilation radiation compared to bremsstrahlung detected at an angle perpendicular to the direction of runaway acceleration. Using the full leading-order pair-production cross-section, we demonstrate that previous related work has overestimated the collisional pair production by at least a factor of four.

In this paper we have studied the effect of the density and temperature of negative ions on the nonlinear dust-acoustic wave propagation in a Lorentzian dusty plasma. We have considered both adiabatic and non-adiabatic dust charge variation. The presence of both low and high populations of negative ions are considered. Separate models have been developed because the two populations give rise to opposite polarity of grain charges. In both models electrons are assumed to follow a kappa velocity distribution while the positive and negative ions satisfy a Maxwellian velocity distribution. Adiabatic dust charge variation shows the propagation of a dust-acoustic soliton in cases of both a high and low population of negative ions whose amplitude depends on the negative ion temperature and negative ion density. On the other hand, non-adiabatic dust charge variation generates a stable oscillatory dust-acoustic shock when the negative ion population is low. An unstable potential has been predicted from this analysis when the negative ion population is high and the dust charge variation is non-adiabatic.

Magnetic field ripple is inherent in tokamaks since the toroidal magnetic field is generated by a finite number of toroidal field coils. The field ripple results in departures from axisymmetry that cause radial transport losses of particles and heat. These ripple losses are a serious concern for alphas near their birth speed $v_{0}$ since alpha heating of the background plasma is required to make fusion reactors into economical power plants. Ripple in tokamaks gives rise to at least two alpha transport regimes of concern. As the slowing down time $\unicode[STIX]{x1D70F}_{s}$ is much larger than the time for an alpha just born to make a toroidal transit, a regime referred to as the $1/\unicode[STIX]{x1D708}\propto \unicode[STIX]{x1D70F}_{s}$ regime can be encountered, with $\unicode[STIX]{x1D708}$ the appropriate alpha collision frequency. In this regime the radial transport losses increase as $v_{0}\unicode[STIX]{x1D70F}_{s}/R$, with $R$ the major radius of the tokamak. The deleterious effect of ripple transport is mitigated by electric and magnetic drifts within the flux surface. When drift tangent to the flux surface becomes significant another ripple regime, referred to as the $\sqrt{\unicode[STIX]{x1D708}}$ regime, is encountered where a collisional boundary layer due to the drift plays a key role. We evaluate the alpha transport in both regimes, taking account of the alphas having a slowing down rather than a Maxwellian distribution function and their being collisionally scattered by a collision operator appropriate for alphas. Alpha ripple transport is found to be in the $\sqrt{\unicode[STIX]{x1D708}}$ regime where it will be a serious issue for typical tokamak reactors as it will be well above the axisymmetric neoclassical level and can be large enough to deplete the alpha slowing down distribution function unless toroidal rotation is strong.