We compare, in an extensive and systematic way, linear theory results obtained with the hybrid (ion kinetic and electron fluid), the gyrokinetic and the fully kinetic plasma models. We present a test case with parameters that are relevant for solar wind turbulence at small scales, which is a topic now recognized to need a kinetic treatment, to a certain extent. We comment on the comparison of low-frequency single modes (Alfvén/ion-cyclotron, ion-acoustic and fast modes) for a wide range of propagation angles, and on the overall spectral properties of the linear operators, for quasi-perpendicular propagation. The methodology and the results presented in this paper will be valuable when choosing which model should be used in regimes where the assumptions of each model are not trivially satisfied.

The results obtained by the plasma physics community for the validation and the prediction of turbulence and transport in magnetized plasmas come mainly from the use of very central processing unit (CPU)-consuming particle-in-cell or (gyro)kinetic codes which naturally include non-Maxwellian kinetic effects. To date, fluid codes are not considered to be relevant for the description of these kinetic effects. Here, after revisiting the limitations of the current fluid theory developed in the 19th century, we generalize the fluid theory including kinetic effects such as non-Maxwellian super-thermal tails with as few fluid equations as possible. The collisionless and collisional fluid closures from the nonlinear Landau Fokker–Planck collision operator are shown for an arbitrary collisionality. Indeed, the first fluid models associated with two examples of collisionless fluid closures are obtained by assuming an analytic non-Maxwellian distribution function (e.g. the INMDF (Izacard, O. 2016b Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas. Phys. Plasmas 23, 082504) that stands for interpreted non-Maxwellian distribution function). One of the main differences with the literature is our analytic representation of the distribution function in the velocity phase space with as few hidden variables as possible thanks to the use of non-orthogonal basis sets. These new non-Maxwellian fluid equations could initiate the next generation of fluid codes including kinetic effects and can be expanded to other scientific disciplines such as astrophysics, condensed matter or hydrodynamics. As a validation test, we perform a numerical simulation based on a minimal reduced INMDF fluid model. The result of this test is the discovery of the origin of particle and heat diffusion. The diffusion is due to the competition between a growing INMDF on short time scales due to spatial gradients and the thermalization on longer time scales. The results shown here could provide the insights to break some of the unsolved puzzles of turbulence.

Measurements of local plasma parameters in dusty plasma are crucial for understanding the physics issues related to such systems. The Langmuir probe, a small electrode immersed in the plasma, provides such measurements. However, designing of a Langmuir probe system in a dusty plasma environment demands special consideration. First, the probe has to be miniaturized enough so that its perturbation on the ambient dust structure is minimal. At the same time, the probe dimensions must be such that a well-defined theory exists for interpretation of its characteristics. The associated instrumentation must also support the measurement of current collected by the probe with high signal to noise ratio. The most important consideration, of course, comes from the fact that the probes are prone to dust contamination, as the dust particles tend to stick to the probe surface and alter the current collecting area in unpredictable ways. This article describes the design and operation of a Langmuir probe system that resolves these challenging issues in dusty plasma. In doing so, first, different theories that are used to interpret the probe characteristics in collisionless as well as in collisional regimes are discussed, with special emphasis on application. The critical issues associated with the current–voltage characteristics of Langmuir probe obtained in different operating regimes are discussed. Then, an algorithm for processing these characteristics efficiently in presence of ion-neutral collisions in the probe sheath is presented.

The paper studies the influence of the background plasma density fluctuations on the dynamics of the Langmuir turbulence generated by electron beams, for parameters typical for solar type III beams and plasmas near 1 AU. A self-consistent Hamiltonian model based on the Zakharov and the Newton equations is used, which presents several advantages compared to the Vlasov approach. Beams generating Langmuir turbulence can be accelerated as a result of wave transformation effects or/and decay cascade processes; in both cases, the beam-driven Langmuir waves transfer part of their energy to waves of smaller wavenumbers, which can be reabsorbed later on by beam particles of higher velocities. As a consequence, beams can conserve a large part of their initial kinetic energy while propagating and radiating wave turbulence over long distances in inhomogeneous plasmas. Beam particles can also be accelerated in quasi-homogeneous plasmas due to the second cascade of wave decay, the wave transformation processes being very weak in this case. The net gains and losses of energy of a beam and the wave turbulence it radiates are calculated as a function of the average level of plasma density fluctuations and the beam parameters. The results obtained provide relevant information on the mechanism of energy reabsorption by beams radiating Langmuir turbulence in solar wind plasmas.

Kinetic-range turbulence in magnetized plasmas and, in particular, in the context of solar wind turbulence has been extensively investigated over the past decades via numerical simulations. Among others, one of the widely adopted reduced plasma models is the so-called hybrid-kinetic model, where the ions are fully kinetic and the electrons are treated as a neutralizing (inertial or massless) fluid. Within the same model, different numerical methods and/or approaches to turbulence development have been employed. In the present work, we present a comparison between two-dimensional hybrid-kinetic simulations of plasma turbulence obtained with two complementary approaches spanning approximately two decades in wavenumber – from the magnetohydrodynamics inertial range to scales well below the ion gyroradius – with a state-of-the-art accuracy. One approach employs hybrid particle-in-cell simulations of freely decaying Alfvénic turbulence, whereas the other consists of Eulerian hybrid Vlasov–Maxwell simulations of turbulence continuously driven with partially compressible large-scale fluctuations. Despite the completely different initialization and injection/drive at large scales, the same properties of turbulent fluctuations at k_{\bot }\unicode[STIX]{x1D70C}_{i}\gtrsim 1$k_{\bot }\unicode[STIX]{x1D70C}_{i}\gtrsim 1$ are observed, where k_{\bot }$k_{\bot }$ is the fluctuations’ wavenumber perpendicular to the background magnetic field and \unicode[STIX]{x1D70C}_{i}$\unicode[STIX]{x1D70C}_{i}$ is the ion Larmor radius. The system indeed self-consistently ‘reprocesses’ the turbulent fluctuations while they are cascading towards smaller and smaller scales, in a way which actually depends on the plasma beta parameter (\unicode[STIX]{x1D6FD}$\unicode[STIX]{x1D6FD}$ is the ratio between the thermal and the magnetic pressures). Small-scale turbulence has been found to be mainly populated by kinetic Alfvén wave (KAW) fluctuations for \unicode[STIX]{x1D6FD}\geqslant 1$\unicode[STIX]{x1D6FD}\geqslant 1$, whereas KAW fluctuations are only sub-dominant for low-\unicode[STIX]{x1D6FD}$\unicode[STIX]{x1D6FD}$.

The semi-Lagrangian discontinuous Galerkin method, coupled with a splitting approach in time, has recently been introduced for the Vlasov–Poisson equation. Since these methods are conservative, local in space and able to limit numerical diffusion, they are considered a promising alternative to more traditional semi-Lagrangian schemes. In this paper we study the conservation of important physical invariants and the long-time behaviour of the semi-Lagrangian discontinuous Galerkin method. To that end we conduct a theoretical analysis and perform a number of numerical simulations. In particular, we find that the entropy is non-decreasing for the discontinuous Galerkin scheme, while unphysical oscillations in the entropy are observed for the traditional method based on cubic spline interpolation.

We present a case study of the flank magnetosheath crossing by the Spektr-R satellite. High time resolution measurements of the ion flux value and its direction provided by the BMSW (Fast Solar Wind Monitor) instrument are examined at different distances from the magnetosheath boundaries – the bow shock and the magnetopause. The magnetosheath behind the quasi-perpendicular bow shock is analysed. The time resolution of these data – 31 ms – is sufficient for observing the frequency spectra of plasma fluctuations both at the magnetohydrodynamics (MHD) and ion kinetic scales. Generally, MHD scales are characterised by Kolmogorov-like spectra {\sim}f^{-5/3}${\sim}f^{-5/3}$ while spectra at kinetic scales are steeper with a break existing between the two scales. We examine evolution of spectral parameters such as power density and slopes, and the break frequency together with the evolution of properties of the probability distribution function. We find out that (i) power spectral densities of the two quantities change differently toward the magnetosheath (MSH) boundaries, (ii) the spectra slopes do not change significantly across the magnetosheath, (iii) the break frequency of the spectrum changes toward the magnetopause. In the middle MSH the spectra are affected by instabilities supposed to be ion cyclotron instabilities. We demonstrate that the plasma is low intermittent in the middle MSH and highly intermittent near its boundaries in the absence of large-scale variations.

The recently developed energy conserving semi-implicit method (ECsim) for particle-in-cell (PIC) simulation is applied to multiple-scale problems where the electron-scale physics needs to be only partially retained and the interest is on the macroscopic or ion-scale processes. Unlike hybrid methods, the ECsim is capable of providing kinetic electron information, such as wave–electron interaction (Landau damping or cyclotron resonance) and non-Maxwellian electron velocity distributions. However, like hybrid methods, the ECsim does not need to resolve all electron scales, allowing time steps and grid spacings orders of magnitude larger than in explicit PIC schemes. The additional advantage of the ECsim is that the stability at large scale is obtained while conserving energy exactly. Three examples are presented: ion acoustic waves, electron acoustic instability and reconnection processes.

Relativistic strongly magnetized plasmas are produced in laboratories thanks to state-of-the-art laser technology but can naturally be found around compact objects such as neutron stars and black holes. Detailed studies of the behaviour of relativistic plasmas require accurate computations able to catch the full spatial and temporal dynamics of the system. Numerical simulations of ultra-relativistic plasmas face severe restrictions due to limitations in the maximum possible Lorentz factors that current algorithms can reproduce to good accuracy. In order to circumvent this flaw and repel the limit to \unicode[STIX]{x1D6FE}\approx 10^{9}$\unicode[STIX]{x1D6FE}\approx 10^{9}$, we design a new fully implicit scheme to solve the relativistic particle equation of motion in an external electromagnetic field using a three-dimensional Cartesian geometry. We show some examples of numerical integrations in constant electromagnetic fields to prove the efficiency of our algorithm. The code is also able to follow the electric drift motion for high Lorentz factors. In the most general case of spatially and temporally varying electromagnetic fields, the code performs extremely well, as shown by comparison with exact analytical solutions for the relativistic electrostatic Kepler problem as well as for linearly and circularly polarized plane waves.

According to magnetohydrodynamics (MHD), the encounter of two collisional magnetized plasmas at high velocity gives rise to shock waves. Investigations conducted so far have found that the same conclusion still holds in the case of collisionless plasmas. For the case of a flow-aligned field, MHD stipulates that the field and the fluid are disconnected, so that the shock produced is independent of the field. We present a violation of this MHD prediction when considering the encounter of two cold pair plasmas along a flow-aligned magnetic field. As the guiding magnetic field grows, isotropization is progressively suppressed, resulting in a strong influence of the field on the resulting structure. A micro-physics analysis allows us to understand the mechanisms at work. Particle-in-cell simulations also support our conclusions and show that the results are not restricted to a strictly parallel field.

High-frequency photons travelling in plasma exhibit a linear polarizability that can influence the dispersion of linear plasma waves. We present a detailed calculation of this effect for Langmuir waves as a characteristic example. Two alternative formulations are given. In the first formulation, we calculate the modified dispersion of Langmuir waves by solving the governing equations for the electron fluid, where the photon contribution enters as a ponderomotive force. In the second formulation, we provide a derivation based on the photon polarizability. Then, the calculation of ponderomotive forces is not needed, and the result is more general.

The multiple colliding laser pulse concept formulated by Bulanov et al. (Phys. Rev. Lett., vol. 104, 2010b, 220404) is beneficial for achieving an extremely high amplitude of coherent electromagnetic field. Since the topology of electric and magnetic fields of multiple colliding laser pulses oscillating in time is far from trivial and the radiation friction effects are significant in the high field limit, the dynamics of charged particles interacting with the multiple colliding laser pulses demonstrates remarkable features corresponding to random walk trajectories, limit circles, attractors, regular patterns and Lévy flights. Under extremely high intensity conditions the nonlinear dissipation mechanism stabilizes the particle motion resulting in the charged particle trajectory being located within narrow regions and in the occurrence of a new class of regular patterns made by the particle ensembles.

The present problem deals with the study of gravitational (Jeans) instability of magnetized, rotating, anisotropic plasmas considering quantum effects. The basic equations of the considered system are constructed using combined Chew–Goldberger–Low (CGL) fluid model and quantum magnetohydrodynamic (QMHD) fluid model. A dispersion relation is obtained using the normal mode technique which is discussed for transverse and longitudinal modes of propagation. It is found that a rotating quantum plasma influences the gravitational mode in transverse propagation but not in longitudinal propagation. The presence of rotation decreases the critical wavenumber and it has a stabilizing effect on the Jeans instability criterion of magnetized quantum plasma in transverse propagation. The firehose instability is unaffected due to the presence of uniform rotation and quantum corrections. We observe from the numerical analysis that region of instability and critical Jeans wavenumber are both decreased due to the presence of uniform rotation. The stabilizing influence of uniform rotation is observed for magnetized, rotating, anisotropic plasmas in the presence of quantum correction. In the case of a longitudinal mode of propagation we found the Jeans instability criterion is not affected by rotation. The quantum diffraction term has a stabilizing effect on the growth rate of the Jeans instability when the wave propagates along the direction of the magnetic field.

Relativistic electron beam transport through a high-density, magnetized plasma is studied numerically and theoretically. An electron beam injected into a cold plasma excites Weibel and two-stream instabilities that heat the beam and saturate. In the absence of an applied magnetic field, the heated beam continues to propagate. However, when a magnetic field of particular strength is applied along the direction of beam propagation, a secondary instability of off-angle whistler modes is excited. These modes then couple nonlinearly creating a large amplitude parallel-propagating whistler that stops the beam. Here, we will show these phenomena in detail and explain the mechanism of whistler mediated beam stagnation.

The effect of the magnetic field gradient in the discharge channel of a Hall thruster on the ionization of the neutral gas and power deposition on the wall is studied through adopting the 2D-3V particle-in-cell (PIC) and Monte Carlo collisions (MCC) model. The research shows that by gradually increasing the magnetic field gradient while keeping the maximum magnetic intensity at the channel exit and the anode position unchanged, the ionization region moves towards the channel exit and then a second ionization region appears near the anode region. Meanwhile, power deposition on the walls decreases initially and then increases. To avoid power deposition on the walls produced by electrons and ions which are ionized in the second ionization region, the anode position is moved towards the channel exit as the magnetic field gradient is increased; when the anode position remains at the zero magnetic field position, power deposition on the walls decreases, which can effectively reduce the temperature and thermal load of the discharge channel.

The bootstrap current and flow velocity of a low-collisionality stellarator plasma are calculated. As far as possible, the analysis is carried out in a uniform way across all low-collisionality regimes in general stellarator geometry, assuming only that the confinement is good enough that the plasma is approximately in local thermodynamic equilibrium. It is found that conventional expressions for the ion flow speed and bootstrap current in the low-collisionality limit are accurate only in the 1/\unicode[STIX]{x1D708}$1/\unicode[STIX]{x1D708}$-collisionality regime and need to be modified in the \sqrt{\unicode[STIX]{x1D708}}$\sqrt{\unicode[STIX]{x1D708}}$-regime. The correction due to finite collisionality is also discussed and is found to scale as \unicode[STIX]{x1D708}^{2/5}$\unicode[STIX]{x1D708}^{2/5}$.

In this paper, we present two codes for the linear stability analysis of the ion temperature gradient instability in toroidal geometry using a gyrokinetic multi-waterbag model for ion dynamics. The first one solves the linearized ion dynamics as an initial value problem, while the second relies on an asymptotic expansion in the so-called ballooning representation allowing us to build a tractable eigenvalue problem. Results from the two codes are presented and compared for equilibria based on modified Cyclone parameters. A good agreement between both codes is found for a class of equilibria with a narrow extent in perpendicular velocity and for which trapped particle orbits are ignored. The local spectrum computed by the eigenvalue is shown to agree remarkably well with previous Cyclone results when trapped particle orbits are included. Lastly we discuss how the equilibrium building procedure for this type of waterbag model requires particular care when dealing with closed equilibrium contours related to the presence of trapped particle orbits.

Although, for current laser pulse energies, the weakly nonlinear regime of laser wakefield acceleration is known to be the optimal for reaching the highest possible electron energies, the capabilities of upcoming large laser systems will provide the possibility of running highly nonlinear regimes of laser pulse propagation in underdense or near-critical plasmas. Using an extended particle-in-cell (PIC) model that takes into account all the relevant physics, we show that such regimes can be implemented with external guiding for a relatively long distance of propagation and allow for the stable transformation of laser energy into other types of energy, including the kinetic energy of a large number of high energy electrons and their incoherent emission of photons. This is despite the fact that the high intensity of the laser pulse triggers a number of new mechanisms of energy depletion, which we investigate systematically.