The special issue ‘Collisions in collisionless plasmas’ is intended to provide a collection of relevant contributions from different scientific fields in plasma physics, including experiments, theory, and numerical modeling, focused on the role of collisions on the dynamical evolution of weakly collisional plasma systems.

A reduced four-dimensional (integrated over perpendicular velocity) gyrokinetic model of slab ion temperature gradient-driven turbulence is used to study the phase-space scales of free energy dissipation in a turbulent kinetic system over a broad range of background gradients and collision frequencies. Parallel velocity is expressed in terms of Hermite polynomials, allowing for a detailed study of the scales of free energy dynamics over the four-dimensional phase space. A fully spectral code – the DNA code – that solves this system is described. Hermite free energy spectra are significantly steeper than would be expected linearly, causing collisional dissipation to peak at large scales in velocity space even for arbitrarily small collisionality. A key cause of the steep Hermite spectra is a critical balance – an equilibration of the parallel streaming time and the nonlinear correlation time – that extends to high Hermite number n. Although dissipation always peaks at large scales in all phase space dimensions, small-scale dissipation becomes important in an integrated sense when collisionality is low enough and/or nonlinear energy transfer is strong enough. Toroidal full-gyrokinetic simulations using the Gene code are used to verify results from the reduced model. Collision frequencies typically found in present-day experiments correspond to turbulence regimes slightly favoring large-scale dissipation, while turbulence in low-collisionality systems like ITER and space and astrophysical plasmas is expected to rely increasingly on small-scale dissipation mechanisms. This work is expected to inform gyrokinetic reduced modeling efforts like Large Eddy Simulation and gyrofluid techniques.

The effective potential acting on particles in plasmas being essentially the Debye-shielded Coulomb potential, the particles collisional transport in thermal equilibrium is calculated for all impact parameters b, with a convergent expression reducing to Rutherford scattering for small b. No cutoff at the Debye length scale is needed, and the Coulomb logarithm is only slightly modified.

This work shows the basic foundation of the particle-based representation of low temperature plasma description. In particular, the Monte Carlo Collision (MCC) recipe has been described for the case of electron-atom and ion-atom collisions. The model has been applied to the problem of plasma plume expansion from an electric Hall-effect type thruster. The presence of low energy secondary electrons from electron-atom ionization on the electron energy distribution function (EEDF) have been identified in the first 3 mm from the exit plane where, due to the azimuthal heating the ionization continues to play an important role. In addition, low energy charge-exchange ions from ion-atom electron transfer collisions are evident in the ion energy distribution functions (IEDF) 1 m from the exit plane.

Kinetic instabilities in weakly collisional, high beta plasmas are investigated using two-dimensional hybrid expanding box simulations with Coulomb collisions modeled through the Langevin equation (corresponding to the Fokker-Planck one). The expansion drives a parallel or perpendicular temperature anisotropy (depending on the orientation of the ambient magnetic field). For the chosen parameters the Coulomb collisions are important with respect to the driver but are not strong enough to keep the system stable with respect to instabilities driven by the proton temperature anisotropy. In the case of the parallel temperature anisotropy the dominant oblique fire hose instability efficiently reduces the anisotropy in a quasilinear manner. In the case of the perpendicular temperature anisotropy the dominant mirror instability generates coherent compressive structures which scatter protons and reduce the temperature anisotropy. For both the cases the instabilities generate temporarily enough wave energy so that the corresponding (anomalous) transport coefficients dominate over the collisional ones and their properties are similar to those in collisionless plasmas.

A linearised kinetic equation describing electrostatic perturbations of a Maxwellian equilibrium in a weakly collisional plasma forced by a random source is considered. The problem is treated as a kinetic analogue of the Langevin equation and the corresponding fluctuation-dissipation relations are derived. The kinetic fluctuation-dissipation relation reduces to the standard “fluid” one in the regime where the Landau damping rate is small and the system has no real frequency; in this case the simplest possible Landau-fluid closure of the kinetic equation coincides with the standard Langevin equation. Phase mixing of density fluctuations and emergence of fine scales in velocity space is diagnosed as a constant flux of free energy in Hermite space; the fluctuation-dissipation relations for the perturbations of the distribution function are derived, in the form of a universal expression for the Hermite spectrum of the free energy. Finite-collisionality effects are included. This work is aimed at establishing the simplest fluctuation-dissipation relations for a kinetic plasma, clarifying the connection between Landau and Hermite-space formalisms, and setting a benchmark case for a study of phase mixing in turbulent plasmas.

Ripples in magnetic or electrostatic confinement fields give rise to trapping separatrices, and conventional neoclassical transport theory describes the collisional trapping/detrapping of particles with fractured distribution function. Our experiments and novel theory have now characterized a new kind of neoclassical transport processes arising from chaotic (nominally collisionless) separatrix crossings, which occur due to E × B plasma rotation along θ−ruffled or wave-perturbed separatrices. This chaotic neoclassical transport becomes dominant at low collisionality when the collisional spreading of particle energy during the dynamical period is less than the separatrix energy ruffle.

We consider the development of accurate and efficient numerical methods for the solution of the Vlasov–Landau equation describing a collisional plasma. The methods combine a Lagrangian approach for the Vlasov solver with a fast spectral method for the solution of the Landau operator. To this goal, new modified spectral methods for the Landau integral which are capable to capture correctly the Maxwellian steady state are introduced. A particular care is devoted to the construction of Implicit–Explicit and Exponential Runge–Kutta methods that permit to achieve high-order and efficient time integration of the collisional step. Several numerical tests are reported which show the high accuracy of the numerical schemes here presented.

A detailed comparison between the Landau and the Dougherty collision operators has been performed by means of Eulerian simulations, in the case of relaxation toward equilibrium of a spatially homogeneous field-free plasma in three-dimensional velocity space. Even though the form of the two collisional operators is evidently different, we found that the collisional evolution of the relevant moments of the particle distribution function (temperature and entropy) are similar in the two cases, once an ‘ad hoc’ time rescaling procedure has been performed. The Dougherty operator is a nonlinear differential operator of the Fokker-Planck type and requires a significantly lighter computational effort with respect to the complete Landau integral; this makes self-consistent simulations of plasmas in presence of collisions affordable, even in the multi-dimensional phase space geometry.

Using particle-in-cell (PIC) simulations with a Monte Carlo treatment of the Coulomb collision operator, we study the transition in electron dynamics of magnetic reconnection for various levels of collisionality. The weakly collisional cases considered all fall into the so-called Hall or kinetic regime. Nevertheless, collisions may still alter the electron kinetic physics characteristic of collisionless reconnection, where adiabatic trapping energizes the electrons and leads to strong anisotropy of the electron velocity distribution and pressure. This anisotropy can support extended current sheets, associated with secondary island formation and turbulent flux rope interactions in three dimensional systems. The collisional simulations demonstrate how weak collisions may modify or eliminate these electron structures in the kinetic regimes. While the reconnection rate is not sensitive to the collisionality in the range studied, we find that increasing collisionality reduces the level of electron energization near the reconnection site. Finally, the results provide guidance for new laboratory reconnection experiments that will access the weakly collisional regimes.

Magnetic reconnection and associated heating of ions and electrons in strongly magnetized, weakly collisional plasmas are studied by means of gyrokinetic simulations. It is shown that an appreciable amount of the released magnetic energy is dissipated to yield (irreversible) electron and ion heating via phase mixing. Electron heating is mostly localized to the magnetic island, not the current sheet, and occurs after the dynamical reconnection stage. Ion heating is comparable to electron heating only in high-β plasmas, and results from both parallel and perpendicular phase mixing due to finite Larmor radius (FLR) effects; in space, ion heating is mostly localized to the interior of a secondary island (plasmoid) that arises from the instability of the current sheet.

A simple 1D model is presented for the heating caused by cylindrically-symmetric plasma waves in a non-neutral plasma column due to the addition of a symmetric squeeze potential applied to the center of the column. We study this model by using analytical techniques and by using a numerical grids method solution, and we compare the results of this model to previous work (Ashourvan and Dubin (2014)). squeeze divides the plasma into passing and trapped particles; the latter cannot pass over the squeeze potential. In collisionless theory, enhanced heating is caused by additional bounce harmonics induced by the squeeze in the particle distribution, leading to Landau resonances at energies En for which the bounce frequency ωb(E) and wave frequency ωm satisfy ωm = nωb(En). As a result, heating is substantially higher than the case with no squeeze, even when ωm is much greater than the thermal bounce frequency ωb(T). Adding collisions to the theory creates a boundary layer at the separatrix between trapped and passing particles that further enhances the heating at small ωm/kmvs, where km is the axial wavenumber and vs is the velocity at the separatrix. However, at large ωm/vs, the heating from the separatrix boundary layer is only a small correction to the heating from collisionless resonances in the trapped particle distribution function.

We study Landau damping in the 1+1D Vlasov–Poisson system using a Fourier–Hermite spectral representation. We describe the propagation of free energy in Fourier–Hermite phase space using forwards and backwards propagating Hermite modes recently developed for gyrokinetic theory. We derive a free energy equation that relates the change in the electric field to the net Hermite flux out of the zeroth Hermite mode. In linear Landau damping, decay in the electric field corresponds to forward propagating Hermite modes; in nonlinear damping, the initial decay is followed by a growth phase characterized by the generation of backwards propagating Hermite modes by the nonlinear term. The free energy content of the backwards propagating modes increases exponentially until balancing that of the forward propagating modes. Thereafter there is no systematic net Hermite flux, so the electric field cannot decay and the nonlinearity effectively suppresses Landau damping. These simulations are performed using the fully-spectral 5D gyrokinetics code SpectroGK, modified to solve the 1+1D Vlasov–Poisson system. This captures Landau damping via Hou–Li filtering in velocity space. Therefore the code is applicable even in regimes where phase mixing and filamentation are dominant.

In this paper we revisit the paradigm of space science turbulent dissipation traditionally considered as myth (Coroniti, Space Sci. Rev., vol. 42, 1985, pp. 399–410). We demonstrate that due to approach introduced by Pitaevskii (Sov. J. Expl Theor. Phys., vol. 44, 1963, pp. 969–979; (in Russian)) (the effect of a finite Larmor radius on a classical collision integral) dissipation induced by effective interaction with microturbulence produces a significant effect on plasma dynamics, especially in the vicinity of the reconnection region. We estimate the multiplication factor of collision frequency in the collision integral for short wavelength perturbations. For waves propagating transverse to the background magnetic field, this factor is approximately $({\it\rho}_{e}k_{x})^{2}$ with ${\it\rho}_{e}$ an electron gyroradius and where $k_{x}$ is a transverse wavenumber. We consider recent spacecraft observations in the Earth’s magnetotail reconnection region to the estimate possible impact of this multiplication factor. For small-scale reconnection regions this factor can significantly increase the effective collision frequency produced both by lower-hybrid drift turbulence and by kinetic Alfvén waves. We discuss the possibility that the Pitaevskii’s effect may be responsible for the excitation of a resistive electron tearing mode in thin current sheets formed in the outflow region of the primary X-line.

Chaotic electromagnetic fields are common in many relativistic plasma environments, where they can be excited by instabilities on kinetic spatial scales. When strong electric fluctuations exist on sub-electron scales, they may lead to small angle, stochastic deflections of the electrons’ pitch angles. Under certain conditions, this closely resembles the effect of Coulomb collisions in collisional plasmas. The electric pitch-angle diffusion coefficient acts as an effective collision – or ‘quasi-collision’ – frequency. We show that quasi-collisions may radically alter the expected radiative transport properties of candidate plasmas. In particular, we consider the quasi-collisional generalization of the classical Faraday effect.

In this paper, the stability of Newtonian and non-Newtonian viscoelastic collisional shear-velocity dusty plasmas is studied, using the framework of a generalized hydrodynamic (GH) model. Motivated by Banerjee et al.’s work (Banerjee et al., New J. Phys., vol. 12 (12), 2010, p. 123031), employing linear perturbation theory as well as the local approximation method in the inhomogeneous direction, the dispersion relations of the Fourier modes are obtained for Newtonian and non-Newtonian dusty plasma systems in the presence of a dust–neutral friction term. The analysis of the obtained dispersion relation in the non-Newtonian case shows that the inhomogeneous viscosity force depending on the velocity shear profile can be the genesis of a free energy source which leads the shear system to be unstable. Study of the dust–neutral friction effect on the instability of the considered systems using numerical analysis of the dispersion relation in the Newtonian case demonstrates that the maximum growth rate decreases considerably by increasing the collision frequency in the hydrodynamic regime, while this reduction can be neglected in the kinetic regime. Results show a more significant stabilization role of the dust–neutral friction term in the non-Newtonian cases, through decreasing the maximum growth rate at any fixed wavenumber and construction of the instable wavenumber region. The results of the present investigation will greatly contribute to study of the time evolution of viscoelastic laboratory environments with externally applied shear; where in these experiments the dust–neutral friction process can play a considerable role.