A one-dimensional (1-D) model for thinning of the Earth's plasma sheet (Chao et al., Planet. Space Sci., vol. 25, 1977, p. 703) according to the current disruption (CD) model of auroral breakup is extended to two dimensions. A rarefaction wave, which is a signature component of the CD model, is generated with an initial disturbance. In the 1-D gas model, the rarefaction wave propagates tailward at sound velocity and is assumed to cause thinning. Extending to a two-dimensional (2-D) gas model of a simplified plasma sheet configuration, the rarefaction wave is weakened, and the thinning ceases to propagate. Extending further to a 2-D plasma model by adding magnetic field into the lobes, the rarefaction wave is quickly lost in the plasma sheet recompression, but the plasma sheet thinning is still present. It propagates at a slower velocity than a 1-D model suggests, behind a wave train of pulses of increased pressure generated by the thinning process itself. This shows that the dynamics of plasma sheet thinning may be dominated by sheet–lobe interactions that are absent from the 1-D model and may not support the behaviour assumed by the CD model.

Thermal effects on the properties of four electromagnetic waves propagating in the pulsar magnetosphere are analysed. It is shown that thermal effects change only quantitatively the dispersion properties of superluminal ordinary O-mode freely escaping the pulsar magnetosphere; whereas properties of the extraordinary X-mode remain unchanged. The research shows that for two subluminal waves propagating along magnetic field lines thermal effects result in essential absorption. However, this attenuation occurs at considerable distances from the neutron star, and there is no doubt of their existence.

The nature of the turbulent energy transfer rate is studied using direct numerical simulations of weakly collisional space plasmas. This is done comparing results obtained from hybrid Vlasov–Maxwell simulations of collisionless plasmas, Hall magnetohydrodynamics and Landau fluid models reproducing low-frequency kinetic effects, such as the Landau damping. In this turbulent scenario, estimates of the local and global scaling properties of different energy channels are obtained using a proxy of the local energy transfer. This approach provides information on the structure of energy fluxes, under the assumption that the turbulent cascade transfers most of the energy that is then dissipated at small scales by various kinetic processes in these kinds of plasmas.

The onset of magnetic reconnection in space, astrophysical and laboratory plasmas is reviewed discussing results from theory, numerical simulations and observations. After a brief introduction on magnetic reconnection and approach to the question of onset, we first discuss recent theoretical models and numerical simulations, followed by observations of reconnection and its effects in space and astrophysical plasmas from satellites and ground-based detectors, as well as measurements of reconnection in laboratory plasma experiments. Mechanisms allowing reconnection spanning from collisional resistivity to kinetic effects as well as partial ionization are described, providing a description valid over a wide range of plasma parameters, and therefore applicable in principle to many different astrophysical and laboratory environments. Finally, we summarize the implications of reconnection onset physics for plasma dynamics throughout the Universe and illustrate how capturing the dynamics correctly is important to understanding particle acceleration. The goal of this review is to give a view on the present status of this topic and future interesting investigations, offering a unified approach.

Using analytical theory and hybrid-kinetic numerical simulations, we demonstrate that, in a collisionless plasma, long-wavelength ion-acoustic waves (IAWs) with amplitudes $\delta n/n_0 \gtrsim 2/\beta$ (where $\beta \gg {1}$ is the ratio of thermal to magnetic pressure) generate sufficient pressure anisotropy to destabilize the plasma to firehose and mirror instabilities. These kinetic instabilities grow rapidly to reduce the pressure anisotropy by pitch-angle scattering and trapping particles, respectively, thereby impeding the maintenance of Landau resonances that enable such waves’ otherwise potent collisionless damping. The result is wave dynamics that evince a weakly collisional plasma: the ion distribution function is near-Maxwellian, the field-parallel flow of heat resembles its Braginskii form (except in regions where large-amplitude magnetic mirrors strongly suppress particle transport), and the relations between various thermodynamic quantities are more ‘fluid-like’ than kinetic. A nonlinear fluctuation–dissipation relation for self-sustaining IAWs is obtained by solving a plasma-kinetic Langevin problem, which demonstrates suppressed damping, enhanced fluctuation levels and weakly collisional thermodynamics when IAWs with $\delta n/n_0 \gtrsim 2/\beta$ are stochastically driven. We investigate how our results depend upon the scale separation between the wavelength of the IAW and the Larmor radius of the ions, and discuss briefly their implications for our understanding of turbulence and transport in the solar wind and the intracluster medium of galaxy clusters.

When mass falls on the polar regions of a neutron star in a binary X-ray source system, it tends to spread out over the entire surface. A long-standing question in research on this problem is: will the mass be anchored on the magnetic field lines and drag the field with it or is there a special mechanism that allows the mass to slip through the magnetic field lines, leading to much less distortion? As the amount of mass falling on the neutron star can actually be comparable with the neutron star mass, the question of which alternative holds is very important. We suggest an efficient mechanism that will allow the mass to slip through the lines. The mechanism is based on a strong ideal Schwarzschild (Structure and Evolution of the Stars. Princeton University Press, 1958) instability. As the instability itself is ideal, it cannot directly force the mass to slip though the lines. However, it can create a cascade of eddies whose scale extends down to a resistive scale, at the same time mixing the field lines up without breaking them. On this scale the mass can cross the lines. This instability is efficient enough that it can produce a mass flow in the plasma without growing to a large amplitude but saturates at a small one. The instability determines the mass per flux distribution of the accumulated material on different lines so that the equilibrium is marginal to the instability on every line. This makes the equilibrium unique. Thus, as the extra mass on the neutron star grows, the state of the outer shell proceeds through a sequence of unique critically unstable equilibria. In an appendix, an attempt is made to track the critical equilibria over long times.

The fundamental difference between incompressible ideal magnetohydrodynamics and the dynamics of a non-conducting fluid is that magnetic fields exert a tension force that opposes their bending; magnetic fields behave like elastic strings threading the fluid. It is natural, therefore, to expect that a magnetic field tangled at small length scales should resist a large-scale shear in an elastic way, much as a ball of tangled elastic strings responds elastically to an impulse. Furthermore, a tangled field should support the propagation of ‘magnetoelastic waves’, the isotropic analogue of Alfvén waves on a straight magnetic field. Here, we study magnetoelasticity in the idealised context of an equilibrium tangled field configuration. In contrast to previous treatments, we explicitly account for intermittency of the Maxwell stress, and show that this intermittency necessarily decreases the frequency of magnetoelastic waves in a stable field configuration. We develop a mean-field formalism to describe magnetoelastic behaviour, retaining leading-order corrections due to the coupling of large- and small-scale motions, and solve the initial-value problem for viscous fluids subjected to a large-scale shear, showing that the development of small-scale motions results in anomalous viscous damping of large-scale waves. Finally, we test these analytic predictions using numerical simulations of standing waves on tangled, linear force-free magnetic-field equilibria.

The turbulent amplification of cosmic magnetic fields depends upon the material properties of the host plasma. In many hot, dilute astrophysical systems, such as the intracluster medium (ICM) of galaxy clusters, the rarity of particle–particle collisions allows departures from local thermodynamic equilibrium. These departures – pressure anisotropies – exert anisotropic viscous stresses on the plasma motions that inhibit their ability to stretch magnetic-field lines. We present an extensive numerical study of the fluctuation dynamo in a weakly collisional plasma using magnetohydrodynamic (MHD) equations endowed with a field-parallel viscous (Braginskii) stress. When the stress is limited to values consistent with a pressure anisotropy regulated by firehose and mirror instabilities, the Braginskii-MHD dynamo largely resembles its MHD counterpart, particularly when the magnetic field is dynamically weak. If instead the parallel viscous stress is left unabated – a situation relevant to recent kinetic simulations of the fluctuation dynamo and, we argue, to the early stages of the dynamo in a magnetized ICM – the dynamo changes its character, amplifying the magnetic field while exhibiting many characteristics reminiscent of the saturated state of the large-Prandtl-number (${Pm}\gtrsim {1}$) MHD dynamo. We construct an analytic model for the Braginskii-MHD dynamo in this regime, which successfully matches simulated dynamo growth rates and magnetic-energy spectra. A prediction of this model, confirmed by our numerical simulations, is that a Braginskii-MHD plasma without pressure-anisotropy limiters will not support a dynamo if the ratio of perpendicular and parallel viscosities is too small. This ratio reflects the relative allowed rates of field-line stretching and mixing, the latter of which promotes resistive dissipation of the magnetic field. In all cases that do exhibit a viable dynamo, the generated magnetic field is organized into folds that persist into the saturated state and bias the chaotic flow to acquire a scale-dependent spectral anisotropy.

The relationship between nonlinear large-scale dynamo action and the generation and transport of magnetic helicity is investigated at moderate values of the magnetic Reynolds number ($Rm$). The model consists of a helically forced, sheared flow in a Cartesian domain. The boundary conditions are periodic in the horizontal and impenetrable for the vertical. The magnetic field is required to be vertical at the upper and lower boundaries. There are two consequences of this choice; one is that the magnetic helicity is not gauge invariant, the second is that fluxes of magnetic helicity are allowed in and out of the domain. We select the winding gauge, define all the contributions to the evolution of the helicity in this gauge and measure these contributions for various solutions of the dynamo equations. We vary $Rm$ and the shear strength, and find a rich landscape of dynamo solutions including travelling waves, pulsating waves and non-wave-like solutions. We find that, at the $Rm$ considered, the main contribution to the growth of magnetic helicity comes from processes throughout the volume of the fluid and that boundary terms respond by limiting the growth. We find that, in this magnetic Reynolds number regime, helicity conservation is not a strong constraint on large-scale dynamo action. We speculate on what may happen at higher $Rm$.

Kinetic plasma simulations are nowadays commonly used to study a wealth of nonlinear behaviours and properties in laboratory and space plasmas. In particular, in high-energy physics and astrophysics, the plasma usually evolves in ultra-strong electromagnetic fields produced by intense laser beams for the former or by rotating compact objects such as neutron stars and black holes for the latter. In these ultra-strong electromagnetic fields, the gyro-period is several orders of magnitude smaller than the time scale on which we desire to investigate the plasma evolution. Some approximations are required such as, for instance, artificially decreasing the electromagnetic field strength, which is certainly not satisfactory. The main flaw of this downscaling is that it cannot reproduce particle acceleration to ultra-relativistic speeds with a Lorentz factor above $\gamma \approx 10^3$–$10^4$. In this paper, we design a new algorithm able to catch particle motion and acceleration to a Lorentz factor of up to $10^{15}$ or even higher by using Lorentz boosts to special frames where the electric and magnetic field are parallel. Assuming that these fields are locally uniform in space and constant in time, we solve analytically the equation of motion in a tiny region smaller than the length scale of the spatial and temporal gradient of the field. This analytical integration of the orbit severely reduces the constraint on the time step, allowing us to use large time steps, avoiding resolving the ultra-high gyro-frequency. We performed simulations in ultra-strong spatially and time-dependent electromagnetic fields, showing that our particle pusher is able to follow accurately the exact analytical solution for very long times. This property is crucial to properly capture for instance lepton electrodynamics in electromagnetic waves produced by fast rotating neutron stars. We conclude with a simple implementation of our new pusher into a one-dimensional relativistic electromagnetic particle-in-cell code, testing it against plasma oscillations, two-stream instabilities and strongly magnetized relativistic shocks.

In this paper, we discuss the results of a new particle pusher in realistic ultra-strong electromagnetic fields such as those encountered around rotating neutron stars. After presenting the results of this algorithm in simple fields and comparing them to expected exact analytical solutions, we present new simulations for a rotating magnetic dipole in vacuum for a millisecond pulsar by using the Deutsch solution. Particles are injected within the magnetosphere, neglecting radiation reaction, interaction among them and their feedback on the fields. Our simulations are therefore not yet fully self-consistent because the Maxwell equations are not solved according to the current produced by these particles. The code highlights the symmetrical behaviour of particles of opposite charge to mass ratio, $q/m$, with respect to the north and south hemispheres. The relativistic Lorentz factor $\gamma$ of the accelerated particles is proportional to this ratio $q/m$: protons reach up to $\gamma _p \simeq 10^{10.7}$, whereas electrons reach up to $\gamma _e \simeq 10^{14}$. Our simulations show that particles could either be captured by the neutron star, trapped around it or ejected far from it, well outside the light cylinder. Actually, for a given charge to mass ratio, particles follow similar trajectories. These particle orbits show some depleted directions, especially at high magnetic inclination with respect to the rotation axis for positive charges and at low inclination for negative charges because of symmetry. Other directions are preferred and loaded with a high density of particles, some directions concentrating the highest or lowest acceleration efficiencies.

We consider the tilting instability of a magnetically confined spheromak using three-dimensional magnetohydrodynamic and relativistic particle-in-cell calculations with an application to astrophysical plasmas, specifically those occurring in magnetar magnetospheres. The instability is driven by the counter-alignment of the spheromak's intrinsic magnetic dipole with the external magnetic field. Initially, the spheromak rotates – tilts – trying to lower its magnetic potential energy. As a result, a current sheet forms between the internal magnetic field of a spheromak and the confining field. Magnetic reconnection sets in; this leads to the annihilation of the newly counter-aligned magnetic flux of the spheromak. This occurs on a few Alfvén time scales. In the case of a higher-order (second-order) spheromak, the internal core is first pushed out of the envelope, resulting in formation of two nearly independent tilting spheromaks. Thus, the magnetically twisted outer shell cannot stabilize the inner core. During dissipation, helicity of the initial spheromak is carried away by torsional Alfvén waves, violating the assumptions of the Taylor relaxation theorem. In applications to magnetar giant flares, fast development of tilting instabilities and no stabilization of the higher-order spheromaks make it unlikely that trapped spheromaks are responsible for the tail emission lasting hundreds of seconds.

Monte Carlo methods are often employed to numerically integrate kinetic equations, such as the particle-in-cell method for the plasma kinetic equation, but these methods suffer from the introduction of counting noise to the solution. We report on a cautionary tale of counting noise modifying the nonlinear saturation of kinetic instabilities driven by unstable beams of plasma. We find a saturated magnetic field in under-resolved particle-in-cell simulations due to the sampling error in the current density. The noise-induced magnetic field is anomalous, as the magnetic field damps away in continuum kinetic and increased particle count particle-in-cell simulations. This modification of the saturated state has implications for a broad array of astrophysical phenomena beyond the simple plasma system considered here, and it stresses the care that must be taken when using particle methods for kinetic equations.

We apply field–particle correlations – a technique that tracks the time-averaged velocity-space structure of the energy density transfer rate between electromagnetic fields and plasma particles – to data drawn from a hybrid Vlasov–Maxwell simulation of Alfvén-ion cyclotron turbulence. Energy transfer in this system is expected to include both Landau and cyclotron wave–particle resonances, unlike previous systems to which the field–particle correlation technique has been applied. In this simulation, the energy transfer rate mediated by the parallel electric field $E_{\Vert }$ comprises approximately 60 % of the total rate, with the remainder mediated by the perpendicular electric field $E_{\bot }$. The parallel electric field resonantly couples to protons, with the canonical bipolar velocity-space signature of Landau damping identified at many points throughout the simulation. The energy transfer mediated by $E_{\bot }$ preferentially couples to particles with $v_{tp}\lesssim v_{\bot }\lesssim 3v_{tp}$, where $v_{tp}$ is the proton thermal speed, in agreement with the expected formation of a cyclotron diffusion plateau. Our results demonstrate clearly that the field–particle correlation technique can distinguish distinct channels of energy transfer using single-point measurements, even at points in which multiple channels act simultaneously, and can be used to determine quantitatively the rates of particle energization in each channel.

We report on an analytical and numerical study of the dynamics of a three-dimensional array of identical magnetic flux tubes in the reduced-magnetohydrodynamic description of the plasma. We propose that the long-time evolution of this system is dictated by flux-tube mergers, and that such mergers are dynamically constrained by the conservation of the pertinent (ideal) invariants, viz. the magnetic potential and axial fluxes of each tube. We also propose that in the direction perpendicular to the merging plane, flux tubes evolve in a critically balanced fashion. These notions allow us to construct an analytical model for how quantities such as the magnetic energy and the energy-containing scale evolve as functions of time. Of particular importance is the conclusion that, like its two-dimensional counterpart, this system exhibits an inverse transfer of magnetic energy that terminates only at the system scale. We perform direct numerical simulations that confirm these predictions and reveal other interesting aspects of the evolution of the system. We find, for example, that the early time evolution is characterized by a sharp decay of the initial magnetic energy, which we attribute to the ubiquitous formation of current sheets. We also show that a quantitatively similar inverse transfer of magnetic energy is observed when the initial condition is a random, small-scale magnetic seed field.

When two collisionless plasma shells collide, they interpenetrate and the overlapping region may turn Weibel unstable for some values of the collision parameters. This instability grows magnetic filaments which, at saturation, have to block the incoming flow if a Weibel shock is to form. In a recent paper (Bret, J. Plasma Phys., vol. 82, 2016b, 905820403), it was found by implementing a toy model for the incoming particle trajectories in the filaments, that a strong enough external magnetic field $\unicode[STIX]{x1D63D}_{0}$ can prevent the filaments blocking the flow if it is aligned with them. Denoting by $B_{f}$ the peak value of the field in the magnetic filaments, all test particles stream through them if $\unicode[STIX]{x1D6FC}=B_{0}/B_{f}>1/2$. Here, this result is extended to the case of an oblique external field $B_{0}$ making an angle $\unicode[STIX]{x1D703}$ with the flow. The result, numerically found, is simply $\unicode[STIX]{x1D6FC}>\unicode[STIX]{x1D705}(\unicode[STIX]{x1D703})/\cos \unicode[STIX]{x1D703}$, where $\unicode[STIX]{x1D705}(\unicode[STIX]{x1D703})$ is of order unity. Noteworthily, test particles exhibit chaotic trajectories.

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.

The evolution of a linearly polarized, long-wavelength Alfvén wave propagating in a collisionless magnetized plasma with a sheared parallel-directed velocity flow is here studied by means of two-dimensional hybrid Vlasov–Maxwell (HVM) simulations. The unperturbed sheared flow has been represented by an exact solution of the HVM set of equations of (Malara et al., Phys. Rev. E, vol. 97, 2018, 053212), thus avoiding spurious oscillations that would arise from the non-stationary initial state and inevitably affect the dynamics of the system. We have considered the evolution of both a small and a moderate amplitude Alfvén wave, in order to separate linear wave–shear flow couplings from kinetic effects, the latter being more relevant for larger wave amplitudes. The phase mixing generated by the shear flow modifies the initial perturbation, leading to the formation of small-scale transverse fluctuations at scales comparable with the proton inertial length/Larmor radius. By analysing both the polarization and group velocity of perturbations in the shear regions, we identify them as kinetic Alfvén waves (KAWs). In the moderate amplitude run, kinetic effects distort the proton distribution function in the shear region. This leads to the formation of a proton beam, at the Alfvén speed and parallel to the magnetic field. Such a feature, due to the parallel electric field associated with KAWs, positively compares with solar wind observations of suprathermal ion populations, suggesting that it may be related to the presence of ion-scale KAW-like fluctuations.

Magnetic field quantization is an important issue for degenerate environments such as neutron stars, radio pulsars and magnetars etc., due to the fact that these stars have a magnetic field higher than the quantum critical field strength of the order of $4.4\times 10^{13}~\text{G}$, accordingly, the cyclotron energy may be equal to or even much more than the Fermi energy of degenerate particles. We shall formulate here the exotic physics of strongly magnetized neutron stars, known as pulsars, specifically focusing on the outcomes of the quantized magnetic pressure. In this scenario, while following the modified quantum hydrodynamic model, we shall investigate both linear and nonlinear fast magnetosonic waves in a strongly magnetized, weakly ionized degenerate plasma consisting of neutrons and an electron–ion plasma in the atmosphere of a pulsar. Here, linear analysis depicts that sufficiently long, fast magnetosonic waves may exist in a weakly dispersive pulsar having finite phase speed at cutoff. To investigate one-dimensional nonlinear fast magnetosonic waves, a neutron density expression as a function of both the electron magnetic and neutron degenerate pressures, is derived with the aid of Riemann’s wave solution. Consequently, a modified Korteweg–de Vries equation is derived, having a rarefractive solitary wave solution. It is found that the basic properties such as amplitude, width and phase speed of the fast magnetoacoustic waves are significantly altered by the electron magnetic and the neutron degenerate pressures. The results of this theoretical investigation may be useful for understanding the formation and features of the solitary structures in astrophysical compact objects such as pulsars, magnetars and white dwarfs etc.

We study the longitudinal stability of beam–plasma systems in the presence of a density inhomogeneity in the background plasma. Previous works have focused on the non-relativistic regime where hydrodynamical models are used to evolve pre-existing Langmuir waves within inhomogeneous background plasmas. Here, for the first time we study the problem with kinetic equations in a fully relativistic way. We do not assume the existence of Langmuir waves, and we focus on the rate and the mechanism by which waves are excited in such systems from an initial perturbation. We derive the structure of the unstable modes and compute an analytical approximation for their growth rates. Our computation is limited to dilute and cold beams, and shows an excellent agreement with particle-in-cell simulations performed using the SHARP code. We show that, due to such an inhomogeneity, the virulent beam–plasma instabilities in the intergalactic medium are not suppressed but their counterparts in the solar wind can be suppressed as evidenced by propagating type-III solar radio bursts.