In the single fluid, non-relativistic, ideal magnetohydrodynamic (MHD) plasma description, magnetic field lines play a fundamental role by defining dynamically preserved ‘magnetic connections’ between plasma elements. Here we show how the concept of magnetic connection needs to be generalized in the case of a relativistic MHD description where we require covariance under arbitrary Lorentz transformations. This is performed by defining 2-D magnetic connection hypersurfaces in the 4-D Minkowski space. This generalization accounts for the loss of simultaneity between spatially separated events in different frames and is expected to provide a powerful insight into the 4-D geometry of electromagnetic fields when $\boldsymbol{E}\boldsymbol{\cdot }\boldsymbol{B}=0$.

To properly describe heating in weakly collisional turbulent plasmas such as the solar wind, interparticle collisions should be taken into account. Collisions can convert ordered energy into heat by means of irreversible relaxation towards the thermal equilibrium. Recently, Pezzi et al. (Phys. Rev. Lett., vol. 116, 2016a, 145001) showed that the plasma collisionality is enhanced by the presence of fine structures in velocity space. Here, the analysis is extended by directly comparing the effects of the fully nonlinear Landau operator and a linearized Landau operator. By focusing on the relaxation towards the equilibrium of an out of equilibrium distribution function in a homogeneous force-free plasma, here it is pointed out that it is significant to retain nonlinearities in the collisional operator to quantify the importance of collisional effects. Although the presence of several characteristic times associated with the dissipation of different phase space structures is recovered in both the cases of the nonlinear and the linearized operators, the influence of these times is different in the two cases. In the linearized operator case, the recovered characteristic times are systematically larger than in the fully nonlinear operator case, this suggesting that fine velocity structures are dissipated more slowly if nonlinearities are neglected in the collisional operator.

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.

In strong electromagnetic regimes, gyrokinetic simulations have linked a substantial ion-scale turbulence stabilization to the presence of supra-thermal particles, capturing qualitatively well the experimental observations in different devices worldwide. An explanation for the underlying physical mechanism responsible for the fast-ion-induced turbulent transport reduction observed in the numerical simulations has been proposed only recently by Di Siena et al. (Nucl. Fusion, vol. 59, 2019, p. 124001; Nucl. Fusion, vol. 60, 2020, p. 089501). It involves a nonlinear cross-scale coupling (nonlinear interaction involving different modes at different wavenumbers) between ion-temperature-gradient and marginally stable Alfvén eigenmodes, which in turn increases zonal flow activity. In view of an optimization of this turbulence-stabilizing effect, the key parameters controlling the nonlinear cross-scale coupling are here identified. At the same time, these findings provide useful insights for reduced-turbulence models and integrative approaches, which might be trained on the results presented in this paper to grasp the underlying physics and the parameter scaling of the beneficial effects of fast particles on plasma turbulence.

We study the stability problem of a magnetohydrodynamic current sheet with the presence of a plasma jet. The flow direction is perpendicular to the normal of the current sheet and we analyse two cases: (1) the flow is along the antiparallel component of the magnetic field; (2) the flow is perpendicular to the antiparallel component of the magnetic field. A generalized equation set with the condition of incompressibility is derived and solved as a boundary value problem. For the first case we show that the streaming kink mode is stabilized by the magnetic field at $V_0/B_0 \lesssim 2$, where $V_0$ and $B_0$ are the jet speed and upstream Alfvén speed, and it is not affected by resistivity significantly. The streaming sausage mode is stabilized at $V_0/B_0 \lesssim 1$, and it can transit to the streaming tearing mode with a finite resistivity. The streaming tearing mode has larger growth rate than the pure tearing mode, though the scaling relation between the maximum growth rate and the Lundquist number remains unchanged. When the jet is perpendicular to the antiparallel component of the magnetic field, the most unstable sausage mode is usually perpendicular (wavevector along the jet) without a guide field. But with a finite guide field, the most unstable sausage mode can be oblique, depending on the jet speed and guide field strength.