We develop a simple model for the kinematics of charged particles in regions of magnetic turbulence. We approximate the local magnetic field as smoothly varying in strength and direction, where adiabatic invariance prevails, or as presenting rapid changes in direction or ‘kinks’. Particles execute guiding centre gyromotion around a field line. However, in analogy to kinetic theory for collisional environments, when the particle undergoes a rapid change in direction by some angle $\unicode[STIX]{x1D703}$, it would instantaneously transition to Larmor motion around the new field line. This mimics Brownian motion wherein we replace collisions with other particles by rapid transitions or ‘collisions’ with other field lines. Using standard methods drawn from Brownian motion, we follow the evolution of the parallel and perpendicular components of the velocity, namely $v_{\Vert }$ and $v_{\bot }$, and rigorously show that kinetic energy isotropization necessarily emerges.

Consequences of fluctuating microscopic conductivity in mean-field electrodynamics of turbulent fluids are formulated and discussed. If the conductivity fluctuations are assumed to be uncorrelated with the velocity fluctuations then only the turbulence-originated magnetic diffusivity of the fluid is reduced and the decay time of a large-scale magnetic field or the cycle times of oscillating turbulent dynamo models are increased. If, however, the fluctuations of conductivity and flow in a certain well-defined direction are correlated, an additional diamagnetic pumping effect results, transporting the magnetic field in the opposite direction to the diffusivity flux vector $\langle \unicode[STIX]{x1D702}^{\prime }\boldsymbol{u}^{\prime }\rangle$. In the presence of global rotation, even for homogeneous turbulence fields, an alpha effect appears. If the characteristic values of the outer core of the Earth or the solar convection zone are applied, the dynamo number of the new alpha effect does not reach supercritical values to operate as an $\unicode[STIX]{x1D6FC}^{2}$-dynamo but oscillating $\unicode[STIX]{x1D6FC}\unicode[STIX]{x1D6FA}$-dynamos with differential rotation are not excluded.

In this paper we study the effects of the net magnetic helicity density on the hemispheric symmetry of the dynamo generated large-scale magnetic field. Our study employs the axisymmetric dynamo model which takes into account the nonlinear effect of magnetic helicity conservation. We find that, on the surface, the net magnetic helicity follows the evolution of the parity of the large-scale magnetic field. Random fluctuations of the $\unicode[STIX]{x1D6FC}$-effect and the helicity fluxes can invert the causal relationship, i.e. the net magnetic helicity or the imbalance of magnetic helicity fluxes can drive the magnetic parity breaking. We also found that evolution of the net magnetic helicity of the small-scale fields follows the evolution of the net magnetic helicity of the large-scale fields with some time lag. We interpret this as an effect of the difference of the magnetic helicity fluxes out of the Sun from the large and small scales.

The core toroidal plasma intrinsic rotation has been studied by experiments and simulations in the Joint Texas Experimental Tokamak (J-TEXT). The direction of core intrinsic rotation in the J-TEXT plasma is counter-current. As the plasma density ramps up, the rotation velocity increases in the counter-current direction. By comparing four different electron densities, linear local gyrokinetic simulations have been performed by the Gyrokinetic Electromagnetic Numerical Experiment code for the first time on J-TEXT. It is found that the most dominant turbulence is the ion temperature gradient at $0.2a$, where $a$ is the minor radius of the plasma and this is unchanged during the plasma density ramp up. By scanning the radial wave vectors, it is found that the residual stress term reverses from negative to positive when the plasma density exceeds a certain threshold. The pinch term is larger than the residual stress term at all four electron densities, which means that the pinch term is always dominant in the core of a J-TEXT plasma.

A careful examination of the effects of collisions on resonant wave–particle interactions leads to an alternate interpretation and deeper understanding of the quasilinear operator originally formulated by Kennel & Engelmann (Phys. Fluids, vol. 9, 1966, pp. 2377–2388) for collisionless, magnetized plasmas, and widely used to model radio frequency heating and current drive. The resonant and nearly resonant particles are particularly sensitive to collisions that scatter them out of and into resonance, as for Landau damping as shown by Johnston (Phys. Fluids, vol. 14, 1971, pp. 2719–2726) and Auerbach (Phys. Fluids, vol. 20, 1977, pp. 1836–1844). As a result, the resonant particle–wave interactions occur in the centre of a narrow collisional boundary when the collision frequency $\unicode[STIX]{x1D708}$ is very small compared to the wave frequency $\unicode[STIX]{x1D714}$. The diffusive nature of the pitch angle scattering combined with the wave–particle resonance condition enhances the collision frequency by $(\unicode[STIX]{x1D714}/\unicode[STIX]{x1D708})^{2/3}\gg 1$, resulting in an effective resonant particle collisional interaction time of $\unicode[STIX]{x1D70F}_{\text{int}}\sim (\unicode[STIX]{x1D708}/\unicode[STIX]{x1D714})^{2/3}/\unicode[STIX]{x1D708}\ll 1/\unicode[STIX]{x1D708}$. A collisional boundary layer analysis generalizes the standard quasilinear operator to a form that is fully consistent with Kennel–Englemann, but allows replacing the delta function appearing in the diffusivity with a simple integral (having the appropriate delta function limit) retaining the new physics associated with the narrow boundary layer, while preserving the entropy production principle. The limitations of the collisional boundary layer treatment are also estimated, and indicate that substantial departures from Maxwellian are not permitted.

The modelling of edge carbon transport and emission on EAST tokamak under resonant magnetic perturbation (RMP) fields has been conducted with the three-dimensional edge transport code EMC3-EIRENE. The measured vertical distribution of CVI emission by the extreme ultraviolet spectrometer system for the perturbed case shows a reduction in the CVI emission by 20 % compared to the equilibrium case. The chord-integrated CVI emission can be reconstructed by EMC3-EIRENE modelling, which presents an increase in the CVI emission with RMP fields. The discrepancy between experiments and simulations has been investigated by parameter study to examine the sensitivity of the simulation results on the edge plasma conditions and the impurity perpendicular transport. It is found that the variation of edge plasma conditions for the equilibrium case cannot resolve the discrepancy in the CVI emission between simulations and measurements. The simulations with enhanced impurity perpendicular transport coefficient allows a reasonable agreement with the measured reduction of CVI emission.

Using transport models, the impacts of trapped electrons on zonal flows and turbulence in helical field configurations are studied. The effect of the trapped electrons on the characteristic quantities of the linear response for zonal flows is investigated for two different field configurations in the Large Helical Device. The turbulent potential fluctuation, zonal flow potential fluctuation and ion energy transport are quickly predicted by the reduced models for which the linear and nonlinear simulation results are used to determine dimensionless parameters related to turbulent saturation levels and typical zonal flow wavenumbers. The effects of zonal flows on the turbulent transport for the case of the kinetic electron response are much smaller than or comparable to those in an adiabatic electron condition for the two different field configurations. It is clarified that the effect of zonal flows on the turbulent transport due to the trapped electrons changes, depending on the field configurations.

The linear MHD (magnetohydrodynamic) stability for high beta plasmas in the inward shifted Large Helical Device (LHD) configurations has been investigated for a wide range of magnetic Reynolds numbers $S$ using numerical simulations based on the kinetic MHD model with kinetic thermal ions where the beta is the ratio of the plasma pressure to the magnetic pressure. It is found that the dependence of the linear growth rate of the resistive ballooning modes on the $S$ number changes from $\unicode[STIX]{x1D6FE}\propto S^{-1/3}$ to $\unicode[STIX]{x1D6FE}\propto S^{-1}$ by the kinetic thermal ion effects so that the resistive ballooning modes are significantly suppressed as the $S$ number increases. For a high $S$ number comparable to experimental values, the most unstable modes are interchange modes. The kinetic thermal ion effects change the most unstable interchange mode from the ideal mode to the resistive mode. This transition of the interchange modes by kinetic thermal ion effects is consistent with the shift of the marginal stability boundary for the ideal interchange modes observed in the LHD experiments.

The neutral beam (NB) fast ion confinement in the Large Helical Device (LHD) is studied for several full field ($B_{t}\sim 2.75~\text{T}$) magnetic configurations by a combination of neutron measurement and simulations. To investigate the NB fast ion confinement, we have performed a series of short-pulse NB injection experiments. The experiment results are analysed by the integrated code TASK3D-a. From this investigation, the effective particle diffusion coefficients of the tangential and perpendicular NBs are approximately $D^{\text{eff}}\sim 0.1~\text{m}^{2}~\text{s}^{-1}$ and $D^{\text{eff}}\sim 1~\text{m}^{2}~\text{s}^{-1}$ in the standard configuration. It is clarified that the NB fast ion confinement improves when the plasmas are shifted inward. Moreover, it is also found that the simulation, which considers the deuteron dilution effect due to the presence of impurity ions, can describe a neutron emission rate consistent with the measurement.

The formation and control of strongly nonlinear standing plasma waves (SPWs) from a trivial equilibrium by a chirped frequency drive are discussed. If the drive amplitude exceeds a threshold, after passage through the linear resonance in this system, the excited wave preserves the phase locking with the drive, yielding a controlled growth of the wave amplitude. We illustrate these autoresonant waves via Vlasov–Poisson simulations, showing the formation of sharply peaked excitations with local electron density maxima significantly exceeding the unperturbed plasma density. The Whitham averaged variational approach applied to a simplified water bag model yields the weakly nonlinear evolution of the autoresonant SPWs and the autoresonance threshold. If the chirped driving frequency approaches some constant level, the driven SPW saturates at a target amplitude, avoiding the kinetic wave breaking.

Numerical simulations of Alfvén modes driven by energetic particles are performed with the gyrokinetic (GK) global particle-in-cell code ORB5. A reversed shear equilibrium magnetic field is adopted. A simplified configuration with circular flux surfaces and large aspect ratio is considered. The nonlinear saturation of beta-induced Alfvén eigenmodes (BAE) is investigated. The roles of the wave–particle nonlinearity of the different species, i.e. thermal ions, electrons and energetic ions are described, in particular for their role in the saturation of the BAE and the generation of zonal flows. The nonlinear redistribution of the electron population is found to be important in increasing the BAE saturation level and the zonal flow amplitude.

We discuss a family of Vlasov–Maxwell equilibrium distribution functions for current sheet equilibria that are intermediate cases between the Harris sheet and the force-free (or modified) Harris sheet. These equilibrium distribution functions have potential applications to space and astrophysical plasmas. The existence of these distribution functions had been briefly discussed by Harrison & Neukirch (Phys. Rev. Lett., vol. 102, (2009a), 135003), but here it is shown that their approach runs into problems in the limit where the guide field goes to zero. The nature of this problem will be discussed and an alternative approach will be suggested that avoids the problem. This is achieved by considering a slight variation of the magnetic field profile, which allows a smooth transition between the Harris and force-free Harris sheet cases.

The incompressibility constraint for fluid flow was imposed by Lagrange in the so-called Lagrangian variable description using his method of multipliers in the Lagrangian (variational) formulation. An alternative is the imposition of incompressibility in the Eulerian variable description by a generalization of Dirac’s constraint method using noncanonical Poisson brackets. Here it is shown how to impose the incompressibility constraint using Dirac’s method in terms of both the canonical Poisson brackets in the Lagrangian variable description and the noncanonical Poisson brackets in the Eulerian description, allowing for the advection of density. Both cases give the dynamics of infinite-dimensional geodesic flow on the group of volume preserving diffeomorphisms and explicit expressions for this dynamics in terms of the constraints and original variables is given. Because Lagrangian and Eulerian conservation laws are not identical, comparison of the various methods is made.

General equations for conservative yet dissipative (entropy producing) extended magnetohydrodynamics are derived from two-fluid theory. Keeping all terms generates unusual cross-effects, such as thermophoresis and a current viscosity that mixes with the usual velocity viscosity. While the Poisson bracket of the ideal version of this model has already been discovered, we determine its metriplectic counterpart that describes the dissipation. This is done using a new and general thermodynamic point of view to derive dissipative brackets, a means of derivation that is natural for understanding and creating dissipative dynamics without appealing to underlying kinetic theory orderings. Finally, the formalism is used to study dissipation in the Lagrangian variable picture where, in the context of extended magnetohydrodynamics, non-local dissipative brackets naturally emerge.

In recent years, several gauge-symmetric particle-in-cell (PIC) methods have been developed whose simulations of particles and electromagnetic fields exactly conserve charge. While it is rightly observed that these methods’ gauge symmetry gives rise to their charge conservation, this causal relationship has generally been asserted via ad hoc derivations of the associated conservation laws. In this work, we develop a comprehensive theoretical grounding for charge conservation in gauge-symmetric Lagrangian and Hamiltonian PIC algorithms. For Lagrangian variational PIC methods, we apply Noether’s second theorem to demonstrate that gauge symmetry gives rise to a local charge conservation law as an off-shell identity. For Hamiltonian splitting methods, we show that the momentum map establishes their charge conservation laws. We define a new class of algorithms – gauge-compatible splitting methods – that exactly preserve the momentum map associated with a Hamiltonian system’s gauge symmetry – even after time discretization. This class of algorithms affords splitting schemes a decided advantage over alternative Hamiltonian integrators. We apply this general technique to design a novel, explicit, symplectic, gauge-compatible splitting PIC method, whose momentum map yields an exact local charge conservation law. Our study clarifies the appropriate initial conditions for such schemes and examines their symplectic reduction.

Scattering phenomena between charged particles and highly excited Rydberg atoms are of critical importance in many processes in plasma physics and astrophysics. While a Maxwell–Boltzmann (MB) energy distribution for the charged particles is often assumed for calculations of collisional rate coefficients, in this contribution we relax this assumption and use two different energy distributions, a bimodal MB distribution and a $\unicode[STIX]{x1D705}$-distribution. Both variants share a high-energy tails occurring with higher probability than the corresponding MB distribution. The high-energy tail may significantly affect rate coefficients for various processes. We focus the analysis to specific situations by showing the dependence of the rate coefficients on the principal quantum number of hydrogen atoms in $n$-changing collisions with electrons in the excitation and ionization channels and in a temperature range relevant to the divertor region of a tokamak device. We finally discuss the implications for diagnostics of laboratory plasmas.

Motivated by recent observations of ‘electron-only’ magnetic reconnection, without an ion-scale sheet or ion outflows, in both the Earth’s magnetosheath and in numerical simulations, we study the formation and reconnection of electron-scale current sheets at low plasma $\unicode[STIX]{x1D6FD}$. We first show that ideal sheets collapse to thicknesses much smaller than the ion scales, by deriving an appropriate analogue of the Chapman–Kendall collapse solution. Second, we show that, in practice, reconnection onset happens in these collapsing sheets once they reach a critical aspect ratio, because the tearing instability then becomes faster than their collapse time scale. We show that this can happen for sheet thicknesses larger than the ion scale or at only a few times the electron scale, depending on plasma parameters and the aspect ratio of the collapsing structure, thereby unifying the usual picture of ion-coupled reconnection and the new regime of electron-only reconnection. We derive relationships between plasma $\unicode[STIX]{x1D6FD}$, ion-to-electron temperature ratio, the aspect ratio, electron outflow velocity and the final thickness of the sheets, and thus determine under what circumstances electron-scale sheets form and reconnect.

A distribution of the electric potentials around a charged absorbing particle in a drifting weakly ionised collisional plasma with negative ions is calculated in the linear hydrodynamic approach. Coulomb-like asymptote of the electric potential around the absorbing particle deforms under the action of the negative ions’ flow and exhibits a valley profile along the flow behind the particle. The presence of the flowing negative ions can be conducive to string formation in the dust structures at relatively large pressures.

This paper examines the velocity distribution function and cyclotron resonance conditions for a beam of electrons moving in a magnetic field which gradually changes with time. A spatial gradient of magnetic field is known to result in an unstable horseshoe distribution of electrons. The field gradient in time adds additional effects due to an induced electric field. The resultant anisotropic velocity distribution function, which we call a Luvdisk distribution, has some distinctive properties when compared to the horseshoe. Fitting the cyclotron resonance condition circle shows that the frequency of the resultant emission is under the local cyclotron frequency. While the spatial gradient results in the emission coming almost perpendicularly to the field, the direction of the radiation under a time-changing field has more variability. The Luvdisk distribution also arises when the magnetic field has a gradient both in space and time. The beam can be unstable if those gradients are added or subtracted from each other (if the gradients are of equal or different sign), which occurs even when the total change of magnetic field is negative. While the frequency of the emission is related to the final magnetic field value, its direction is indicative of the field’s history which produced the instability.