In this paper, we report a new type of instability of electron holes (EHs) interacting with passing ions. The nonlinear interaction of EHs and ions is investigated using a new theory of hole kinematics. It is shown that the oscillation in the velocity of the EH parallel to the magnetic field direction becomes unstable when the hole velocity in the ion frame is slower than a few times the cold ion sound speed. This instability leads to the emission of ion-acoustic waves from the solitary hole and decay in its magnitude. The instability mechanism can drive significant perturbations in the ion density. The instability threshold, oscillation frequency and instability growth rate derived from the theory yield quantitative agreement with the observations from a novel high-fidelity hole-tracking particle-in-cell code.

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 ${\sim}f^{-5/3}$ 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.

We examine the excitation of breather structures in a degenerate relativistic plasma consisting of non-extensive electrons and cold ions. For this purpose, the multiple time scale perturbation technique is used to obtain a nonlinear Schrödinger equation (NLSE). We then consider different localized solutions regarding analytical breather solutions of the NLSE, and examine their properties in the frame of the present plasma system, i.e. a degenerate relativistic non-extensive plasma. The results of the present investigation may be useful for the understanding of the basic features of the nonlinear excitations that may occur in dense astrophysical plasmas.

Ion angular current and energy distributions are important parameters for ion thrusters, which are typically measured at a few tens of centimetres to a few metres distance from the thruster exit. However, fully kinetic particle-in-cell (PIC) simulations are not able to simulate such domain sizes due to high computational costs. Therefore, a parallelisation strategy of the code is presented to reduce computational time. The calculated ion beam angular distributions in the plume region are quite sensitive to boundary conditions of the potential, possible additional source contributions (e.g. from secondary electron emission at vessel walls) and charge exchange collisions. Within this work a model for secondary electrons emitted from the vessel wall is included. In order to account for limits of the model due to its limited domain size, a correction of the simulated angular ion energy distribution by the potential boundary is presented to represent the conditions at the location of the experimental measurement in $1~\text{m}$ distance. In addition, a post-processing procedure is suggested to include charge exchange collisions in the plume region not covered by the original PIC simulation domain for the simulation of ion angular distributions measured at $1~\text{m}$ distance.

The nonlinear dynamics of energetic-particle (EP) driven geodesic acoustic modes (EGAM) is investigated here. A numerical analysis with the global gyrokinetic particle-in-cell code ORB5 is performed, and the results are interpreted with the analytical theory, in close comparison with the theory of the beam-plasma instability. Only axisymmetric modes are considered, with a nonlinear dynamics determined by wave–particle interaction. Quadratic scalings of the saturated electric field with respect to the linear growth rate are found for the case of interest. As a main result, the formula for the saturation level is provided. Near the saturation, we observe a transition from adiabatic to non-adiabatic dynamics, i.e. the frequency chirping rate becomes comparable to the resonant EP bounce frequency. The numerical analysis is performed here with electrostatic simulations with circular flux surfaces, and kinetic effects of the electrons are neglected.

Optimised stellarators and other magnetic-confinement devices having the property that the average magnetic curvature is favourable for all particle orbits are called maximum-$J$ devices. They have recently been shown to be immune to trapped-particle instabilities driven by the density gradient. Gyrokinetic simulations reveal, however, that another instability can arise, which is also associated with particle trapping but causes less transport than typical trapped-electron modes. The nature of this instability is clarified here. It is shown to be similar to the ‘ubiquitous mode’ in tokamaks and is driven by ion free energy, but requires trapped electrons to exist.

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.

In this plasma model, consisting of ions and electrons with pressure variations in both the components in the presence of stationary dust, both compressive and rarefactive Korteweg–de Vries (KdV) solitons of interesting character are established. Based on high dust charge, characteristics of soliton growth are found to be amplified for various pairs of ion and electron streaming speeds. It is noteworthy to mention that for some pairs of ion and electron initial streaming speeds, only compressive KdV solitons with either decreasing or increasing growth are shown to reflect. Contrary to this, for some other pairs of ion and electron streaming speeds, the amplitudes of both rarefactive and compressive solitons are seen to be produced, changing from rarefactive to compressive growth. At the stationary background of the massive dust particles, the lighter particles suffer appreciable initial drifts (backwards streaming) which characteristically change the growth of solitons. For inclusion of higher-order nonlinearity, only compressive modified Korteweg–de Vries (MKdV) solitons of much higher amplitude are found to exist whereas for the same set of parameter values both compressive and rarefactive KdV solitons are found to exist. Smaller values of electron streaming speed are seen to produce high amplitude MKdV solitons. We also observe that due to higher-order nonlinearity, the nonlinear monotonic growth of amplitudes of MKdV solitons is supported by the almost equal streaming speed pairs of ions and electrons for relatively small values of $Z_{d}$, where $Z_{d}$ is the number of charges in a dust particle

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 $\unicode[STIX]{x1D6FE}\approx 10^{9}$, 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.

Nanopulse atmospheric carbon monoxide discharges and corresponding afterglows have been investigated in a wide range of applied reduced electric field (130 < E/N < 200 Td) and different pulse durations (2–50 ns). The results have been obtained by solving an appropriate Boltzmann equation for the electron energy distribution function (EEDF) coupled to the kinetics of vibrational and electronic excited states as well as to a simplified plasma chemistry for the different species formed during the activation of CO. The molar fraction of electronically excited states generated in the discharge is sufficient to create structures in the EEDF in the afterglow regime. On the other hand, only for long duration pulses (i.e. 50 ns), non-equilibrium vibrational distributions can be observed especially in the afterglow. The trend of the results for the case study E/N = 200 Td, $\unicode[STIX]{x1D70F}_{\text{pulse}}=2$  ns is qualitatively and quantitatively similar to the corresponding case for CO2 implying that the activation of CO2 by cold plasmas should take into account the kinetics of formed CO with the same accuracy as the CO2 itself.

Based on the beating of two Laguerre–Gaussian laser beams in a rippled plasma medium, the effective factors such as plasma density, Gouy phase and orbital angular momentums of input lasers on the output twisted terahertz radiation are investigated. As a result, the amplitude of the generated vortex terahertz radiation is an increasing function of plasma density. The vortex terahertz intensity is strongly dependent on the orbital angular momentum of the input lasers. The terahertz output amplitude increases by decreasing the orbital angular momentum of the Laguerre–Gaussian input lasers. Here, by employing a suitably ripple wavenumber, the destroyer effect of the relative Gouy phase of the input lasers is removed, and perfect phase matching is satisfied.

Five-dimensional gyrokinetic continuum simulations of electrostatic plasma turbulence in a straight, open-field-line geometry have been performed using a full-$f$ discontinuous-Galerkin approach implemented in the Gkeyll code. While various simplifications have been used for now, such as long-wavelength approximations in the gyrokinetic Poisson equation and the Hamiltonian, these simulations include the basic elements of a fusion-device scrape-off layer: localised sources to model plasma outflow from the core, cross-field turbulent transport, parallel flow along magnetic field lines, and parallel losses at the limiter or divertor with sheath-model boundary conditions. The set of sheath-model boundary conditions used in the model allows currents to flow through the walls. In addition to details of the numerical approach, results from numerical simulations of turbulence in the Large Plasma Device, a linear device featuring straight magnetic field lines, are presented.

We present a novel framework for finite element particle-in-cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov–Maxwell system. We derive a semi-discrete Poisson bracket, which retains the defining properties of a bracket, anti-symmetry and the Jacobi identity, as well as conservation of its Casimir invariants, implying that the semi-discrete system is still a Hamiltonian system. In order to obtain a fully discrete Poisson integrator, the semi-discrete bracket is used in conjunction with Hamiltonian splitting methods for integration in time. Techniques from finite element exterior calculus ensure conservation of the divergence of the magnetic field and Gauss’ law as well as stability of the field solver. The resulting methods are gauge invariant, feature exact charge conservation and show excellent long-time energy and momentum behaviour. Due to the generality of our framework, these conservation properties are guaranteed independently of a particular choice of the finite element basis, as long as the corresponding finite element spaces satisfy certain compatibility conditions.

Velocity distribution functions which feature extended tails with power-law dependence have been consistently observed in the solar wind environment and are frequently modelled by the so-called Kappa distributions. Different forms of Kappa distributions are commonly employed in analytical studies, and despite their similarities, they can produce different effects on the dispersion properties that occur in a plasma. We consider two different and widely used forms of Kappa distributions, in both isotropic and anisotropic cases, and systematically discuss their effects on the dispersion relations of Langmuir and ion-sound waves. It is shown that in the case of Langmuir waves, one of the forms leads to the expression for the Bohm–Gross dispersion relation, valid for plasmas with Maxwellian velocity distributions, while the other form of Kappa functions leads to a dispersion relation with significant difference regarding the Maxwellian case, particularly in the case of small values of the kappa index. For ion-sound waves, the dispersion relations obtained with the different forms of Kappa distributions are different among themselves, and also different from the Maxwellian case, with difference which increases for small values of the kappa index. Some results obtained from numerical solution of the dispersion relations are presented, which illustrate the magnitude of the perceived differences. Some results obtained with relativistic particle-in-cell simulations are also presented, which allow the comparison between the dispersion relations obtained from analytical calculations and the frequency–wavelength distribution of wave fluctuations which are observed in numerical experiments.

The Weibel instability, driven by a temperature anisotropy, is investigated within different kinetic descriptions based on the semi-Lagrangian full kinetic and relativistic Vlasov–Maxwell model, on the multi-stream approach, which is based on a Hamiltonian reduction technique, and finally, with the full pressure tensor fluid-type description. Dispersion relations of the Weibel instability are derived using the three different models. A qualitatively different regime is observed in Vlasov numerical experiments depending on the excitation of a longitudinal plasma electric field driven initially by the combined action of the stream symmetry breaking and weak relativistic effects, in contrast with the existing theories of the Weibel instability based on their purely transverse characters. The multi-stream model offers an alternate way to simulate easily the coupling with the longitudinal electric field and particularly the nonlinear regime of saturation, making numerical experiments more tractable, when only a few moments of the distribution are considered. Thus a numerical comparison between the reduced Hamiltonian model (the multi-stream model) and full kinetic (relativistic) Vlasov simulations has been investigated in that regime. Although nonlinear simulations of the fluid model, including the dynamics of the pressure tensor, have not been carried out here, the model is strongly relevant even in the three-dimensional case.

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.

The influence of finite Larmor radius correction, tensor viscosity and uniform rotation on self-gravitational and firehose instabilities is discussed in the framework of the quantum magnetohydrodynamic and Chew–Goldberger–Low (CGL) fluid models. The general dispersion relation is obtained for transverse and longitudinal modes of propagation. In both the modes of propagation the dispersion relation is further analysed with respect to the direction of the rotational axis. In the analytical discussion the axis of rotation is considered in parallel and in the perpendicular direction to the magnetic field. (i) In the transverse mode of propagation, when rotation is parallel to the direction of the magnetic field, the Jeans instability criterion is affected by the rotation, finite Larmor radius (FLR) and quantum parameter but remains unaffected due to the presence of tensor viscosity. The calculated critical Jeans masses for rotating and non-rotating dense degenerate plasma systems are $3.5M_{\odot }$ and $2.1M_{\odot }$ respectively. It is clear that the presence of rotation enhances the threshold mass of the considered system. (ii) In the case of longitudinal mode of propagation when rotation is parallel to the direction of the magnetic field, Alfvén and viscous self-gravitating modes are obtained. The Alfvén mode is modified by FLR corrections and rotation. The analytical as well as graphical results show that the presence of FLR and rotation play significant roles in stabilizing the growth rate of the firehose instability by suppressing the parallel anisotropic pressure. The viscous self-gravitating mode is significantly affected by tensor viscosity, anisotropic pressure and the quantum parameter while it remains free from rotation and FLR corrections. When the direction of rotation is perpendicular to the magnetic field, the rotation of the considered system coupled the Alfvén and viscous self-gravitating modes to each other. The finding of the present work is applicable to strongly magnetized dense degenerate plasma.

We experimentally study the excitation and propagation of acoustic solitary waves in a one-dimensional dusty plasma (i.e. a Yukawa chain) with $n=65$ particles interacting through a screened Coulomb potential. The lattice constant $a=1.02\pm 0.02$ mm. Waves are launched by applying a 100 mW laser pulse to one end of the chain for laser pulse durations from 0.10 to 2.0 s. We observe damped solitary waves which propagate for distances ${\gtrsim}30a$ with an acoustic speed $c_{s}=11.5\pm 0.2~\text{mm}~\text{s}^{-1}$. The maximum velocity perturbation increases with laser pulse duration for durations ${\leqslant}0.5$ s and then saturates at ${\approx}15\,\%$. The wave speed is found to be independent of the maximum amplitude, indicating that the formation of nonlinear solitons is prevented by neutral-gas damping.

The collisionless axisymmetric zonal flow residual calculation for a tokamak plasma is generalized to include electromagnetic perturbations. We formulate and solve the complete initial value zonal flow problem by retaining the fully self-consistent axisymmetric spatial perturbations in the electric and magnetic fields. Simple expressions for the electrostatic, shear and compressional magnetic residual responses are derived that provide a fully electromagnetic test of the zonal flow residual in gyrokinetic codes. Unlike the electrostatic potential, the parallel vector potential and the parallel magnetic field perturbations need not relax to flux functions for all possible initial conditions.

The two-dimensional Terry–Horton equation is shown to exhibit the Dimits shift when suitably modified to capture both the nonlinear enhancement of zonal/drift-wave interactions and the existence of residual Rosenbluth–Hinton states. This phenomenon persists through numerous simplifications of the equation, including a quasilinear approximation as well as a four-mode truncation. It is shown that the use of an appropriate adiabatic electron response, for which the electrons are not affected by the flux-averaged potential, results in an $\boldsymbol{E}\times \boldsymbol{B}$ nonlinearity that can efficiently transfer energy non-locally to length scales of the order of the sound radius. The size of the shift for the nonlinear system is heuristically calculated and found to be in excellent agreement with numerical solutions. The existence of the Dimits shift for this system is then understood as an ability of the unstable primary modes to efficiently couple to stable modes at smaller scales, and the shift ends when these stable modes eventually destabilize as the density gradient is increased. This non-local mechanism of energy transfer is argued to be generically important even for more physically complete systems.