The Earth magnetopause, when sufficiently plane and stationary at a local scale, can be considered as a ‘quasi-tangential’ discontinuity, since the normal component of the magnetic field $B_n$ is typically very small but not zero. Contrary to observations, the ‘classic theory of discontinuities’ predicts that rotational and compressional jumps should be mutually exclusive in the general case $B_n \ne 0$, but allows only one exception: the tangential discontinuity provided that $B_n$ is strictly zero. Here we show that finite Larmor radius (FLR) effects play an important role in the quasi-tangential case, whenever the ion Larmor radius is not fully negligible with respect to the magnetopause thickness. By including FLR effects, the results suggest that a rotational discontinuity undergoes a change comparable to the change of a shear Alfvén into a kinetic Alfvén wave when considering linear modes. For this new kind of discontinuity, the co-existence of rotational and compressional variations at the magnetopause does no more imply that this boundary is a strict tangential discontinuity, even in one-dimensional (1-D)-like regions far from X lines if any. This result may lead to important consequences concerning the oldest and most basic questions of magnetospheric physics: how can the magnetopause be open, where and when? While the role of FLR is established theoretically, in this paper we show that it can be proved experimentally. For this, we make use of magnetospheric multiscale mission (MMS) data and process them with the most recent available four spacecraft tools. First, we present the different processing techniques that we use to estimate spatial derivatives, such as $grad(B)$ and $div(P)$, and the magnetopause normal direction. We point out why this normal direction must be determined with extremely high accuracy to make the conclusions unambiguous. Then, the results obtained by these techniques are presented in a detailed case study and on a statistical basis.

Magnetic reconnection is a basic particle acceleration mechanism in laboratory and astrophysical plasmas. Two-dimensional models have been critical to understanding the onset of reconnection in laboratory experiments, but are fundamentally limited in diagnosing ion acceleration along open magnetic field lines. These shortcomings have opened the way to three-dimensional (3-D) models of torsional reconnection, where localized rotational perturbations to a fan-spine magnetic null point topology have demonstrated bulk particle acceleration along open magnetic field lines. Previous computational studies of the torsional fan reconnection mode using both solar and laboratory parameters demonstrated collimated jet formation and acceleration along the spine axis, wherein the bulk particle final kinetic energy spectra were shown to fall within a relatively narrow range (${\sim }2$ keV). This paper introduces typical laboratory plasma parameters in the torsional spine mode of 3-D reconnection models to diagnose its efficacy in inducing rapid ion acceleration. Using laboratory-scale length helium plasma parameters typical of capacitive discharges (singly ionized helium), we solve for relativistic particle trajectories using solutions to the steady-state, resistive, kinematic magnetohydrodynamic equations in the fan-spine topology. We find that particle acceleration at the reconnection site is highly dependent on the injection radius, and the peak accelerated particles ($\approx$3 keV) are trapped about the magnetic null point. While a jet is formed by ions injected close to the peak fan plane perturbation radius, their final ion kinetic energies are an order of magnitude lower ($\approx$0.3 keV) than the mirrored particles. Analysing the time dependence of their limited representative energy spectra shows the torsional spine mode particles follow an evolution much different than the narrow spectra of the torsional fan mode. These results have implications for diagnostic expectations of future laboratory plasma experiments designed to induce the torsional spine reconnection mode.

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.

Where and under what conditions the transfer of energy between electromagnetic fields and particles takes place in the solar wind remains an open question. We investigate the conditions that promote the growth of kinetic instabilities predicted by linear theory to infer how turbulence and temperature-anisotropy-driven instabilities are interrelated. Using a large dataset from Solar Orbiter, we introduce the radial rate of strain, a novel measure computed from single-spacecraft data, which we interpret as a proxy for the double-adiabatic strain rate. The solar wind exhibits high absolute values of the radial rate of strain at locations with large temperature anisotropy. We measure the kurtosis and skewness of the radial rate of strain from the statistical moments to show that it is non-Gaussian for unstable intervals and increasingly intermittent at smaller scales with a power-law scaling. We conclude that the velocity field fluctuations in the solar wind contribute to the presence of temperature anisotropy sufficient to create potentially unstable conditions.

Prompted by the relevant problem of temperature inversion (i.e. gradient of density anti-correlated to the gradient of temperature) in astrophysics, we introduce a novel method to model a gravitationally confined multi-component collisionless plasma in contact with a fluctuating thermal boundary. We focus on systems with anti-correlated (inverted) density and temperature profiles, with applications to solar physics. The dynamics of the plasma is analytically described via the coupling of an appropriated coarse-grained distribution function and a temporally coarse-grained Vlasov dynamics. We derive a stationary solution of the system and predict the inverted density and temperature profiles of the two species for scenarios relevant for the corona. We validate our method by comparing the analytical results with kinetic numerical simulations of the plasma dynamics in the context of the two-species Hamiltonian mean-field model. Finally, we apply our theoretical framework to the problem of the temperature inversion in the solar corona, obtaining density and temperature profiles in remarkably good agreement with the observations.

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.

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.

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.

We investigate the effects of different guard geometries on the currents to needle-type Langmuir probes. The results are based on particle-in-cell numerical simulations. We show that if the guard length is less than 6–8 Debye lengths there can be a significant effect on the currents to the probe. A guard radius should not be larger than the Debye length, otherwise it can also significantly affect the currents. However, since guard radii are often close to the probe radius, the second condition is usually satisfied.

The two-time energy spectrum of weak magnetohydrodynamic turbulence is found by applying a wave-turbulence closure to the cumulant hierarchy constructed from the dynamical equations. Solutions are facilitated via asymptotic expansions in terms of the small parameter $\varepsilon$, describing the ratio of time scales corresponding to Alfvénic propagation and nonlinear interactions between counter-propagating Alfvén waves. The strength of nonlinearity at a given spatial scale is further quantified by an integration over all possible delta-correlated modes compliant in a given set of three-wave interactions that are associated with energy flux through the said scale. The wave-turbulence closure for the two-time spectrum uncovers a secularity occurring on a time scale of order $\varepsilon ^{-2}$, and the asymptotic expansion for the spectrum is reordered in a manner comparable to the one-time case. It is shown that for the regime of stationary turbulence, the two-time energy spectrum exponentially decays on a lagged time scale $(\varepsilon ^2 \gamma _k^s)^{-1}$ in proportion to the strength of the associated three-wave interactions, characterized by nonlinear decorrelation frequency $\gamma _k^s$. The scaling of the form $k_{\perp } v_0 \chi _0$ exhibited by this frequency is reminiscent of random sweeping by the outer scale with characteristic fluctuation velocity $v_0$ that is modified due to competition with Alfvénic propagation (characterized by $\chi _0$) at the said scale. A brief calculation of frequency broadening of the power spectrum due to nonlinear interactions is also presented.

Satellite data analysis of a compressed gyro-scale current sheet prior to magnetic reconnection in the magnetotail shows that electrostatic lower hybrid waves localized to the region of a transverse ambipolar electric field at the centre of the current sheet are driven by $\boldsymbol{E} \times \boldsymbol{B}$ velocity shear and result from compression. The presence and location of shear-driven waves around the centre of the current sheet, where the magnetic field reverses and the density gradient is minimal, is consistent with our model. This is notable because the free energy source is the curvature of the electron $\boldsymbol{E} \times \boldsymbol{B}$ flow and not the density gradient. Laboratory experiments and particle-in-cell (PIC) simulations have shown that shear-driven lower hybrid fluctuations are capable of producing anomalous cross-field transport (viscosity) and resistivity, which can trigger magnetic reconnection. We estimate the terms in the generalized Ohm's Law directly from MMS data as the spacecraft cross a gyro-scale current sheet. Our analysis shows that the wave effects (resistivity, diffusion and viscosity) and pressure anisotropy effects are comparable. We also find that the quasi-static electric field gradient is correlated with a non-gyrotropic electron distribution function, which is consistent with our model. Furthermore, theoretical arguments suggest agyrotropy is an indicator of the possibility for magnetic reconnection to occur.

Our earth is immersed in the near-earth space plasma environment, which plays a vital role in protecting our planet against the solar-wind impact and influencing space activities. It is significant to investigate the physical processes dominating the environment, for deepening our scientific understanding of it and improving the ability to forecast the space weather. As a crucial part of the National Major Scientific and Technological Infrastructure–Space Environment Simulation Research Infrastructure (SESRI) in Harbin, the Space Plasma Environment Research Facility (SPERF) builds a system to replicate the near-earth space plasma environment in the laboratory. The system aims to simulate the three-dimensional (3-D) structure and processes of the terrestrial magnetosphere for the first time in the world, providing a unique platform to reveal the physics of the 3-D asymmetric magnetic reconnection relevant to the earth's magnetopause, wave–particle interaction in the earth's radiation belt, particles’ dynamics during the geomagnetic storm, etc. The paper will present the engineering design and construction of the near-earth space plasma simulation system of the SPERF, with a focus on the critical technologies that have been resolved to achieve the scientific goals. Meanwhile, the possible physical issues that can be studied based on the apparatus are sketched briefly. The earth-based system is of great value in understanding the space plasma environment and supporting space exploration.

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.

We review the modulation stability of parallel-propagating/field-aligned whistler-mode chorus (WMC) waves propagating in a warm plasma from a formal perspective with a focus on wave–particle interactions via ponderomotive forces. The modulation instability criteria are characterised by the group velocity dispersion, $d c_g/dk$, for whistler-mode waves and a condition on the ratio between the group velocity $c_g$ and the electron sound speed $c_{s,e}$. We also demonstrate that in order to investigate the spatiotemporal evolution of the envelope and the formation of packets (according to this mechanism), one necessarily needs to account for the motion of ions within the system, leading to an ionic influence on the modulation instability threshold determined by the ion fraction of the plasma. Finally, we demonstrate that chirping may be captured when higher-order effects are included within the spatiotemporal evolution of the amplitude. This yields not only an explicit expression for the sweep rate but also identifies a possible origin for the power band gap that occurs at half the electron gyrofrequency. Numerical validation demonstrates that the interaction between wave packets is a source for the emergence of tones observed within mission data, and such interactions may be a major source of the electron energisation which WMC are responsible for.

On the basis of the energy invariants for the Weibel instability in a collisionless non-relativistic plasma, an analytical relation is obtained between the instantaneous values of the space-averaged energy density of the magnetic field, its dominant wavenumber and the average plasma anisotropy parameter. The relation is valid for arbitrary particle velocity distribution functions, including ones that vary with time at the nonlinear stage of instability. It is obtained under the assumption that the plasma is homogeneous along a certain axis, determined, for example, by an external magnetic field, and taking into account only the modes with wavevectors orthogonal to this axis. We give an estimate of the maximum magnetic field energy achievable during the Weibel instability and show that its ratio to the initial longitudinal energy of particles, even for a large initial plasma anisotropy parameter, cannot exceed the value approximately equal to 0.2. The obtained analytical relation is verified using two-dimensional particle-in-cell simulations.

Collisionless and weakly collisional plasmas often exhibit non-thermal quasi-equilibria. Among these quasi-equilibria, distributions with power-law tails are ubiquitous. It is shown that the statistical-mechanical approach originally suggested by Lynden-Bell (Mon. Not. R. Astron. Soc., vol. 136, 1967, p. 101) can easily recover such power-law tails. Moreover, we show that, despite the apparent diversity of Lynden-Bell equilibria, a generic form of the equilibrium distribution at high energies is a ‘hard’ power-law tail $\propto \varepsilon ^{-2}$, where $\varepsilon$ is the particle energy. The shape of the ‘core’ of the distribution, located at low energies, retains some dependence on the initial condition but it is the tail (or ‘halo’) that contains most of the energy. Thus, a degree of universality exists in collisionless plasmas.

Plasma turbulence plays a critical role in the transport of energy from large-scale magnetic fields and plasma flows to small scales, where the dissipated turbulent energy ultimately leads to heating of the plasma species. A major goal of the broader heliophysics community is to identify the physical mechanisms responsible for the dissipation of the turbulence and to quantify the consequent rate of plasma heating. One of the mechanisms proposed to damp turbulent fluctuations in weakly collisional space and astrophysical plasmas is electron Landau damping. The velocity-space signature of electron energization by Landau damping can be identified using the recently developed field–particle correlation technique. Here, we perform a suite of gyrokinetic turbulence simulations with ion plasma beta values $\beta _i = 0.01, 0.1, 1$ and $10$ and use the field–particle correlation technique to characterize the features of the velocity-space signatures of electron Landau damping in turbulent plasma conditions consistent with those observed in the solar wind and planetary magnetospheres. We identify the key features of the velocity-space signatures of electron Landau damping as a function of varying plasma $\beta _i$ to provide a critical framework for interpreting the results of field–particle correlation analysis of in situ spacecraft observations of plasma turbulence.

The structure of a collisionless shock affects ion motion in the shock front and is affected by the formed ion distribution. In high-Mach-number shocks, a significant fraction of incident ions are reflected by the macroscopic electric and magnetic fields in the shock front. Ions are non-specularly reflected by the combined electric deceleration and magnetic deflection. Here, a first analytical description of the non-specular reflection is presented. The contribution of the increasing magnetic field is evaluated and shown to enhance reflection. The distribution of non-specularly reflected ions ahead of the ramp is calculated and their velocities at the re-entry to the shock are found numerically. Dependence on the angle between the shock normal and the upstream magnetic field vector is illustrated.

In typical heliospheric collisionless shocks most of the mass, momentum and energy are carried by ions. Therefore, the shock structure should be most affected by ions. With the increase of the Mach number, ion reflection becomes more and more important, and reflected ions participate in shaping the shock profile. Ion reflection at the collisionless shock is a non-local process: the reflected–transmitted ions re-enter the shock front far from the reflection point. The direction and the magnitude of this shift depend on the shock angle. The distance between the reflection point and the re-entry point is of the order of the upstream ion convective gyroradius and exceeds the shock width. The non-locality of ion reflection may have implications for shock rippling since reflected ions may carry perturbations along the shock front.