A collisionless shock structure results from the nonlinear interaction between charged particles and electromagnetic fields. Yet, a collisionless shock is globally governed by the mass, momentum and energy conservation requirements. A stable shock structure must ensure that the fluxes of the conserved quantities are constant on average, and, therefore, is determined by this necessity. Here, we study an observed high upstream temperature high Mach number shock and show that the conservation laws cannot be fulfilled unless the shock is spatially inhomogeneous along the shock front and time-dependent.

The magnetohydrodynamic (MHD) equations, as a collisional fluid model that remains in local thermodynamic equilibrium (LTE), have long been used to describe turbulence in myriad space and astrophysical plasmas. Yet, the vast majority of these plasmas, from the solar wind to the intracluster medium (ICM) of galaxy clusters, are only weakly collisional at best, meaning that significant deviations from LTE are not only possible but common. Recent studies have demonstrated that the kinetic physics inherent to this weakly collisional regime can fundamentally transform the evolution of such plasmas across a wide range of scales. Here, we explore the consequences of pressure anisotropy and Larmor-scale instabilities for collisionless, $\beta \gg 1$, turbulence, focusing on the role of a self-organizational effect known as ‘magneto-immutability’. We describe this self-organization analytically through a high-$\beta$, reduced ordering of the Chew–Goldberger–Low-MHD (CGL-MHD) equations, finding that it is a robust inertial-range effect that dynamically suppresses magnetic-field-strength fluctuations, anisotropic-pressure stresses and dissipation due to heat fluxes. As a result, the turbulent cascade of Alfvénic fluctuations continues below the putative viscous scale to form a robust, nearly conservative, MHD-like inertial range. These findings are confirmed numerically via Landau-fluid CGL-MHD turbulence simulations that employ a collisional closure to mimic the effects of microinstabilities. We find that microinstabilities occupy a small (${\sim }5\,\%$) volume-filling fraction of the plasma, even when the pressure anisotropy is driven strongly towards its instability thresholds. We discuss these results in the context of recent predictions for ion-vs-electron heating in low-luminosity accretion flows and observations implying suppressed viscosity in ICM turbulence.

The response tensor is derived for a relativistically streaming, strongly magnetized, one-dimensional Jüttner distribution of electrons and positrons, referred to as a pulsar plasma. This is used to produce a general treatment of wave dispersion in a pulsar plasma. Specifically, relativistic streaming, the spread in Lorentz factors in a pulsar rest frame and cyclotron resonances are taken into account. Approximations to the response tensor are derived by making approximations to relativistic plasma dispersion functions appearing in the general form of the response tensor. The cold-plasma limit, the highly relativistic limit and limits related to cyclotron resonances are considered. The theory developed in this paper has applications to generalized Faraday rotation in pulsars and magnetars.

Electron heating and acceleration in collisionless shocks is a long-standing problem. Rapid isotropization of heated electrons cannot be explained solely by the cross-shock potential. In addition, the macroscopic cross-shock potential prevents efficient reflection and injection into the diffusive acceleration regime. Recent observations have shown that small-scale electric fields are present in the shock front, together with the large-scale cross-shock potential. These small-scale fields have been found also in the upstream and downstream regions. Electron heating in shocks is produced by the combined action of the large- and small-scale fields. The large-scale potential determines the energy transferred to the electrons. The small-scale electrostatic fields scatter electrons. Here we study the scattering of electrons on the typical waveforms, namely solitary bipolar spikes and wavepackets. The main effect is the generation of backstreaming electrons with large pitch angles. It is found that wavepackets are more efficient in electron reflection in the interaction of electrons both with a single spike and with multiple spikes.

A specific set of dimensionless plasma and turbulence parameters is introduced to characterize the nature of turbulence and its dissipation in weakly collisional space and astrophysical plasmas. Key considerations are discussed for the development of predictive models of the turbulent plasma heating that characterize the partitioning of dissipated turbulent energy between the ion and electron species and between the perpendicular and parallel degrees of freedom for each species. Identifying the kinetic physical mechanisms that govern the damping of the turbulent fluctuations is a critical first step in constructing such turbulent heating models. A set of ten general plasma and turbulence parameters are defined, and reasonable approximations along with the exploitation of existing scaling theories for magnetohydrodynamic turbulence are used to reduce this general set of ten parameters to just three parameters in the isotropic temperature case: the ion plasma beta, the ion-to-electron temperature ratio and the isotropic driving wavenumber. A critical step forward in this study is to identify the dependence of all of the proposed kinetic mechanisms for turbulent damping in terms of the same set of fundamental plasma and turbulence parameters. Analytical estimations of the scaling of each damping mechanism on these fundamental parameters are presented. The power of this approach is illustrated in the development of the first phase diagram for the turbulent damping mechanisms as a function of the ion plasma beta and isotropic driving wavenumber for unity ion-to-electron temperature ratio, showing the regions of this two-dimensional parameter space in which ion Landau and transit-time damping, electron Landau and transit-time damping, ion cyclotron damping, ion stochastic heating, collisionless magnetic reconnection and kinetic ‘viscous’ heating play a role in the damping of the turbulent fluctuations.

To expand on recent work, we introduce collisional terms in the analysis of the warm ion–electron, two-fluid equations for a homogeneous plasma at rest. Consequently, the plasma is now described by six variables: the magnetisation, the ratio of masses over charges, the electron and ion sound speeds, the angle between the wave vector and the magnetic field and a new parameter describing the electron–ion collision frequency. This additional parameter does not introduce new wave modes compared with the collisionless case, but does result in complex mode frequencies. Both for the backward and forward propagating modes the imaginary components are negative and thus quantify collisional damping. We provide convenient (polynomial) expressions to quantify frequencies and damping rates in all short- and long-wavelength limits, including the cutoff and resonance limits, whilst the one-fluid magnetohydrodynamic limit is retained with the familiar undamped slow, Alfvén and fast waves. As collisions only introduce a damping, the previously introduced labelling of the wave modes S, A, F, M, O and X can be kept and assigned based on their long- and short-wavelength behaviour. The obtained damping at cutoff and resonance limits is parametrised with the collision frequency, and can be tailored to match known kinetic damping expressions. It is demonstrated that varying the angle can introduce crossings between the wave modes, as was already present in the ideal ion–electron case, but also a collision frequency exceeding a critical collision frequency can lead to crossings at angles where previously only avoided crossings were found.

Transit-time damping (TTD) is a process in which the magnetic mirror force – induced by the parallel gradient of magnetic field strength – interacts with resonant plasma particles in a time-varying magnetic field, leading to the collisionless damping of electromagnetic waves and the resulting energization of those particles through the perpendicular component of the electric field, $E_\perp$. In this study, we utilize the recently developed field–particle correlation technique to analyse gyrokinetic simulation data. This method enables the identification of the velocity-space structure of the TTD energy transfer rate between waves and particles during the damping of plasma turbulence. Our analysis reveals a unique bipolar pattern of energy transfer in the velocity-space characteristic of TTD. By identifying this pattern, we provide clear evidence of TTD's significant role in the damping of strong plasma turbulence. Additionally, we compare the TTD signature with that of Landau damping (LD). Although they both produce a bipolar pattern of phase-space energy density loss and gain about the parallel resonant velocity of the Alfvénic waves, they are mediated by different forces and exhibit different behaviours as the perpendicular velocity $v_\perp \to 0$. We also explore how the dominant damping mechanism varies with ion plasma beta $\beta _i$, showing that TTD dominates over LD for $\beta _i > 1$. This work deepens our understanding of the role of TTD in the damping of weakly collisional plasma turbulence and paves the way to seek the signature of TTD using in situ spacecraft observations of turbulence in space plasmas.

Understanding the partitioning of turbulent energy between ions and electrons in weakly collisional plasmas is crucial for the accurate interpretation of observations and modelling of various astrophysical phenomena. Many such plasmas are ‘imbalanced’, wherein the large-scale energy input is dominated by Alfvénic fluctuations propagating in a single direction. In this paper, we demonstrate that when strongly-magnetised plasma turbulence is imbalanced, nonlinear conservation laws imply the existence of a critical value of the electron plasma beta (the ratio of the thermal to magnetic pressures) that separates two dramatically different types of turbulence in parameter space. For betas below the critical value, the free energy injected on the largest scales is able to undergo a familiar Kolmogorov-type cascade to small scales where it is dissipated, heating electrons. For betas above the critical value, the system forms a ‘helicity barrier’ that prevents the cascade from proceeding past the ion Larmor radius, causing the majority of the injected free energy to be deposited into ion heating. Physically, the helicity barrier results from the inability of the system to adjust to the disparity between the perpendicular-wavenumber scalings of the free energy and generalised helicity below the ion Larmor radius; restoring finite electron inertia can annul, or even reverse, this disparity, giving rise to the aforementioned critical beta. We relate this physics to the ‘dynamic phase alignment’ mechanism (that operates under yet lower beta conditions and in pair plasmas), and characterise various other important features of the helicity barrier, including the nature of the nonlinear wavenumber-space fluxes, dissipation rates, and energy spectra. The existence of such a critical beta has important implications for heating, as it suggests that the dominant recipient of the turbulent energy, ions or electrons, can depend sensitively on the characteristics of the plasma at large scales.

In this paper, we investigate the kinetic stability of classical, collisional plasma – that is, plasma in which the mean-free-path $\lambda$ of constituent particles is short compared with the length scale $L$ over which fields and bulk motions in the plasma vary macroscopically, and the collision time is short compared with the evolution time. Fluid equations are typically used to describe such plasmas, since their distribution functions are close to being Maxwellian. The small deviations from the Maxwellian distribution are calculated via the Chapman–Enskog (CE) expansion in $\lambda /L \ll 1$, and determine macroscopic momentum and heat fluxes in the plasma. Such a calculation is only valid if the underlying CE distribution function is stable at collisionless length scales and/or time scales. We find that at sufficiently high plasma $\beta$, the CE distribution function can be subject to numerous microinstabilities across a wide range of scales. For a particular form of the CE distribution function arising in strongly magnetised plasma (viz. plasma in which the Larmor periods of particles are much smaller than collision times), we provide a detailed analytic characterisation of all significant microinstabilities, including peak growth rates and their associated wavenumbers. Of specific note is the discovery of several new microinstabilities, including one at sub-electron-Larmor scales (the ‘whisper instability’) whose growth rate in certain parameter regimes is large compared with other instabilities. Our approach enables us to construct the kinetic stability maps of classical, two-species collisional plasma in terms of $\lambda$, the electron inertial scale $d_e$ and the plasma $\beta$. This work is of general consequence in emphasising the fact that high-$\beta$ collisional plasmas can be kinetically unstable; for strongly magnetised CE plasmas, the condition for instability is $\beta \gtrsim L/\lambda$. In this situation, the determination of transport coefficients via the standard CE approach is not valid.

Linearized gravity around a rotating black hole or compact object introduces the concept of a gravitomagnetic field, which originates from the matter–current in the rotating object. Plasma in proximity to this object is subsequently subjected to motion guided by this gravitomagnetic term (where mass serves as the effective charge) in addition to the conventional magnetic field. Such an interplay of fields complicates the accessible plasma waves of the system and thus merits exploration to delineate this interplay, to identify any observable signatures of the gravitomagnetic field in weakly magnetized systems, and to motivate future numerical work in a fully relativistic setting where the effects may be stronger. In this work we analyse the dispersion of the upper and lower hybrid electrostatic waves in a plasma immersed in both magnetic and gravitomagnetic fields. In particular, we discuss the effective augmentation or cancellation of the two fields under the right conditions for the upper hybrid wave. In contrast, the lower hybrid wave experiences a frequency up-shift from the gravitomagnetic field regardless of whether it is parallel or antiparallel to the magnetic field for the studied field strengths.

Magnetic reconnection is an important process in astrophysical environments, as it reconfigures magnetic field topology and converts magnetic energy into thermal and kinetic energy. In extreme astrophysical systems, such as black hole coronae and pulsar magnetospheres, radiative cooling modifies the energy partition by radiating away internal energy, which can lead to the radiative collapse of the reconnection layer. In this paper, we perform two- and three-dimensional simulations to model the MARZ (Magnetic Reconnection on Z) experiments, which are designed to access cooling rates in the laboratory necessary to investigate reconnection in a previously unexplored radiatively cooled regime. These simulations are performed in GORGON, an Eulerian two-temperature resistive magnetohydrodynamic code, which models the experimental geometry comprising two exploding wire arrays driven by 20 MA of current on the Z machine (Sandia National Laboratories). Radiative losses are implemented using non-local thermodynamic equilibrium tables computed using the atomic code Spk, and we probe the effects of radiation transport by implementing both a local radiation loss model and $P_{1/3}$ multi-group radiation transport. The load produces highly collisional, super-Alfvénic (Alfvén Mach number $M_A \approx 1.5$), supersonic (Sonic Mach number $M_S \approx 4-5$) strongly driven plasma flows which generate an elongated reconnection layer (Aspect Ratio $L/\delta \approx 100$, Lundquist number $S_L \approx 400$). The reconnection layer undergoes radiative collapse when the radiative losses exceed the rates of ohmic and compressional heating (cooling rate/hydrodynamic transit rate = $\tau _{\text {cool}}^{-1}/\tau _{H}^{-1}\approx 100$); this generates a cold strongly compressed current sheet, leading to an accelerated reconnection rate, consistent with theoretical predictions. Finally, the current sheet is also unstable to the plasmoid instability, but the magnetic islands are extinguished by strong radiative cooling before ejection from the layer.

Collisionless shocks are frequently analysed using the magnetohydrodynamics (MHD) formalism, even though MHD assumes a small mean free path. Yet, isotropy of pressure, the fruit of binary collisions and assumed in MHD, may not apply in collisionless shocks. This is especially true within a magnetized plasma, where the field can stabilize an anisotropy. In a previous article (Bret & Narayan, J. Plasma Phys., vol. 88, no. 6, 2022b, p. 905880615), a model was presented capable of dealing with the anisotropies that may arise at the front crossing. It was solved for any orientation of the field with respect to the shock front. Yet, for some values of the upstream parameters, several downstream solutions were found. Here, we complete the work started in Bret & Narayan (J. Plasma Phys., vol. 88, no. 6, 2022b, p. 905880615) by showing how to pick the physical solution out of the ones offered by the algebra. This is achieved by 2 means: (i) selecting the solution that has the downstream field obliquity closest to the upstream one. This criterion is exemplified on the parallel case and backed up by particle-in-cell simulations. (ii) Filtering out solutions which do not satisfy a criteria already invoked to trim multiple solutions in MHD: the evolutionarity criterion, that we assume valid in the collisionless case. The end result is a model in which a given upstream configuration results in a unique, or no downstream configuration (as in MHD). The largest departure from MHD is found for the case of a parallel shock.

A conducting cylinder with a uniform magnetic field along its axis and radial temperature gradient is considered at the stationary state. At large temperature gradients the azimuthal Hall electrical current creates an axial magnetic field whose strength may be comparable with the original one. It is shown that the magnetic field, generated by the azimuthal Hall current, leads to the decrease of a magnetic field originated by external sources, and this suppression increases with an increase of the electromotive force, connected with thermodiffusion. Obtained results can help to investigate the influence of the Hall current on the coupled magnetothermal evolution of magnetic and electric fields in neutron stars, white dwarfs and, possibly, in laboratory facilities.

The excitation conditions of the magnetorotational instability (MRI) are studied for axially unbounded Taylor–Couette (TC) flows of various gap widths between the cylinders. The cylinders are considered as made from both perfect-conducting or insulating material and the conducting fluid with a finite but small magnetic Prandtl number rotates with a quasi-Keplerian velocity profile. The solutions are optimized with respect to the wavenumber and the Reynolds number of the rotation of the inner cylinder. For the axisymmetric modes, we find the critical Lundquist number of the applied axial magnetic field: the lower, the wider the gap between the cylinders. A similar result is obtained for the induced cell structure: the wider the gap, the more spherical the cells are. The marginal rotation rate of the inner cylinder – for a fixed size of the outer cylinder – always possesses a minimum for not too wide and not too narrow gap widths. For perfect-conducting walls the minimum lies at $r_{{\rm in}}\simeq 0.4$, where $r_{{\rm in}}$ is the ratio of the radii of the two rotating cylinders. The lowest magnetic field amplitudes to excite the instability are required for TC flows between perfect-conducting cylinders with gaps corresponding to $r_{{\rm in}}\simeq ~0.2$. For even wider and also for very thin gaps the needed magnetic fields and rotation frequencies are shown to become rather huge. Also the non-axisymmetric modes with $|m|=1$ have been considered. Their excitation generally requires stronger magnetic fields and higher magnetic Reynolds numbers in comparison with those for the axisymmetric modes. If TC experiments with too slow rotation for the applied magnetic fields yield unstable modes of any azimuthal symmetry, such as the currently reported Princeton experiment (Wang et al., Phys. Rev. Lett., vol. 129, 115001), then also other players, including axial boundary effects, than the MRI-typical linear combination of current-free fields and differential rotation should be in the game.

We describe the interaction of parallel-propagating Alfvén waves with ion-acoustic waves and other Alfvén waves, in magnetized, high-$\beta$ collisionless plasmas. This is accomplished through a combination of analytical theory and numerical fluid simulations of the Chew–Goldberger–Low (CGL) magnetohydrodynamic (MHD) equations closed by Landau-fluid heat fluxes. An asymptotic ordering is employed to simplify the CGL-MHD equations and derive solutions for the deformation of an Alfvén wave that results from its interaction with the pressure anisotropy generated either by an ion-acoustic wave or another, larger-amplitude Alfvén wave. The difference in time scales of acoustic and Alfvénic fluctuations at high-$\beta$ means that interactions that are local in wavenumber space yield little modification to either mode within the time it takes the acoustic wave to Landau damp away. Instead, order-unity changes in the amplitude of Alfvénic fluctuations can result after interacting with frequency-matched acoustic waves. Additionally, we show that the propagation speed of an Alfvén-wave packet in an otherwise homogeneous background is a function of its self-generated pressure anisotropy. This allows for the eventual interaction of separate co-propagating Alfvén-wave packets of differing amplitudes. The results of the CGL-MHD simulations agree well with these predictions, suggesting that theoretical models relying on the interaction of these modes should be reconsidered in certain astrophysical environments. Applications of these results to weak Alfvénic turbulence and to the interaction between the compressive and Alfvénic cascades in strong, collisionless turbulence are also discussed.

The particle-in-cell (PIC) method is successfully used to study magnetized plasmas. However, this requires large computational costs and limits simulations to short physical run times and often to set-ups of less than three spatial dimensions. Traditionally, this is circumvented either via hybrid-PIC methods (adopting massless electrons) or via magneto-hydrodynamic-PIC methods (modelling the background plasma as a single charge-neutral magneto-hydrodynamical fluid). Because both methods preclude modelling important plasma-kinetic effects, we introduce a new fluid-PIC code that couples a fully explicit and charge-conserving multi-fluid solver to the PIC code SHARP through a current-coupling scheme and solve the full set of Maxwell's equations. This avoids simplifications typically adopted for Ohm's law and enables us to fully resolve the electron temporal and spatial scales while retaining the versatility of initializing any number of ion, electron or neutral species with arbitrary velocity distributions. The fluid solver includes closures emulating Landau damping so that we can account for this important kinetic process in our fluid species. Our fluid-PIC code is second-order accurate in space and time. The code is successfully validated against several test problems, including the stability and accuracy of shocks and the dispersion relation and damping rates of waves in unmagnetized and magnetized plasmas. It also matches growth rates and saturation levels of the gyro-scale and intermediate-scale instabilities driven by drifting charged particles in magnetized thermal background plasmas in comparison with linear theory and PIC simulations. This new fluid-SHARP code is specially designed for studying high-energy cosmic rays interacting with thermal plasmas over macroscopic time scales.

Observations, mainly of outbursts in dwarf novae, imply that the anomalous viscosity in highly ionized accretion discs is magnetic in origin and requires that the plasma ${\beta \sim 1}$. Until now, most simulations of the magnetic dynamo in accretion discs have used a local approximation (known as the shearing box). While these simulations demonstrate the possibility of a self-sustaining dynamo, the magnetic activity generated in these models saturates at $\beta \gg 1$. This long-standing discrepancy has previously been attributed to the local approximation itself. There have been recent attempts at simulating magnetic activity in global accretion discs with parameters relevant to the dwarf novae. These too find values of $\beta \gg 1$. We speculate that the tension between these models and the observations may be caused by numerical magnetic diffusivity. As a pedagogical example, we present exact time-dependent solutions for the evolution of weak magnetic fields in an incompressible fluid subject to linear shear and magnetic diffusivity. We find that the maximum factor by which the initial magnetic energy can be increased depends on the magnetic Reynolds number as ${\mathcal {R}}_{m}^{2/3}$. We estimate that current global numerical simulations of dwarf nova discs have numerical magnetic Reynolds numbers around six orders of magnitude less than the physical value found in dwarf nova discs of ${\mathcal {R}}_{m} \sim 10^{10}$. We suggest that, given the current limitations on computing power, expecting to be able to compute realistic dynamo action in observable accretion discs using numerical MHD is, for the time being, a step too far.

Astrophysical flows may be studied by reproducing similar conditions using a coaxial plasma accelerator operating in the deflagration regime (or plasma deflagration accelerator). This allows for the recreation and investigation of dynamics present in complex highly coupled plasma systems at the laboratory scale. We report on measurements of the plasma density, temperature, plasma potential and velocity found using a quadruple Langmuir probe (QLP) on such a deflagration accelerator in the form of the Stanford Coaxial High ENerGy (CHENG) device operating with multiple gases – specifically argon, nitrogen and hydrogen. Experiments show a general decrease in bulk plasma velocity with gas atomic mass from upwards of $120\ {\rm km}\ {\rm s}^{-1}$ with hydrogen to less than $30\ {\rm km}\ {\rm s}^{-1}$ with argon. There was an accompanying increase in peak plasma density with increasing atomic mass from ${\sim }3\times 10^{20}\ {\rm m}^{-3}$ with hydrogen to ${\sim }1.5 \times 10^{21}\ {\rm m}^{-3}$ with argon. It was found that the momentum flux and internal energy density also generally increase with atomic mass while the particle flux is constant between shots. Further investigation is needed to understand these correlations and the underlying physics. Lastly, comparisons with scaling laws show that while the CHENG device may be operated in such a way as to simulate the effects of bulk solar wind movement, it may not properly capture the thermal effects.

We study the underlying physics of cosmic ray (CR)-driven instabilities that play a crucial role for CR transport across a wide range of scales, from interstellar to galaxy cluster environments. By examining the linear dispersion relation of CR-driven instabilities in a magnetised electron–ion background plasma, we establish that both the intermediate and gyroscale instabilities have a resonant origin, and show that these resonances can be understood via a simple graphical interpretation. These instabilities destabilise wave modes parallel to the large-scale background magnetic field at significantly distinct scales and with very different phase speeds. Furthermore, we show that approximating the electron–ion background plasma with either magnetohydrodynamics (MHD) or Hall-MHD fails to capture the fastest-growing instability in the linear regime, namely the intermediate-scale instability. This finding highlights the importance of accurately characterising the background plasma for resolving the most unstable wave modes. Finally, we discuss the implications of the different phase speeds of unstable modes on particle–wave scattering. Further work is needed to investigate the relative importance of these two instabilities in the nonlinear, saturated regime and to develop a physical understanding of the effective CR transport coefficients in large-scale CR hydrodynamics theories.