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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.
Space plasma physics, pushed by the impressive recent technological developments, is undergoing a period of intense progress. This progress is achieved first at the level of observations, including both remote and in situ measurements, but also on the theoretical side, mainly by means of large scale numerical simulations made possible by the dramatic increase of computational resources. In particular, three-dimensional mainly hybrid but also fully kinetic simulations are today feasible, and large intervals in spatial and time scales can at last be accessed by fluid simulations. Addressing fundamental problems such as, e.g. magnetic reconnection, nonlinear dynamics or turbulence development in the kinetic range, are no longer just a heart's desire today.
The long-term evolution of large-amplitude Alfvén waves propagating in the solar wind is investigated by performing two-dimensional MHD simulations within the expanding box model. The linear and nonlinear phases of the parametric decay instability are studied for both circularly polarized waves in parallel propagation and for arc-polarized waves in oblique propagation. The non-monochromatic case is also considered. In the oblique case, the direct excitation of daughter modes transverse to the local background field is found for the first time in an expanding environment, and this transverse cascade seems to be favored for monochromatic mother waves. The expansion effect reduces the instability growth rate, and it can even suppress its onset for the lowest frequency modes considered here, possibly explaining the persistence of these outgoing waves in the solar wind.
With the aim to develop a tool for simulating turbulence in collisionless magnetized plasmas, fluid models retaining low-frequency kinetic effects such as Landau damping and finite Larmor radius (FLR) corrections are discussed. It turns out that, in the absence of ion-cyclotron resonance, the dispersion and damping of kinetic Alfvén waves at scales as small as a fraction of the ion Larmor radius are accurately reproduced when using fluid estimates of the non-gyrotropic moments, at leading-order within a large-scale asymptotics. Differently, evaluations based on the low-frequency linear kinetic theory are necessary in regimes of large temperature anisotropies, and in particular in the presence of the mirror instability. Combining both descriptions leads to a new Landau fluid model retaining large-scale FLR nonlinearities, while reproducing the linear dynamics of low-frequency modes at the sub-ionic scales.
It is shown that two circularly polarized Alfvén waves that propagate along the ambient magnetic field in an uniform plasma trigger non oscillating electromagnetic field components when they cross each other. The non-oscilliating field components can accelerate ions and electrons with great efficiency. This work is based on particle-in-cell (PIC) numerical simulations and on analytical non-linear computations. The analytical computations are done for two counter-propagating monochromatic waves. The simulations are done with monochromatic waves and with wave packets. The simulations show parallel electromagnetic fields consistent with the theory, and they show that the particle acceleration results in plasma cavities and, if the waves amplitudes are high enough, in ion beams. These acceleration processes could be relevant in space plasmas. For instance, they could be at work in the auroral zone and in the radiation belts of the Earth magnetosphere. In particular, they may explain the origin of the deep plasma cavities observed in the Earth auroral zone.
A widely accepted scenario of magnetic reconnection in collisionless space plasmas is the breakage of magnetic field lines in X-points. In laboratory, reconnection is commonly studied in pinches, current channels embedded into twisted magnetic fields. No model of magnetic reconnection in space plasmas considers both null-points and pinches as peers. We have performed a particle-in-cell simulation of magnetic reconnection in a three-dimensional configuration where null-points are present initially, and Z-pinches are formed during the simulation along the lines of spiral null-points. The non-spiral null-points are more stable than spiral ones, and no substantial energy dissipation is associated with them. On the contrary, turbulent magnetic reconnection in the pinches causes the magnetic energy to decay at a rate of ~1.5% per ion gyro period. Dissipation in similar structures is a likely scenario in space plasmas with large fraction of spiral null-points.
The role of magnetic helicity is investigated in kinetic Alfvén wave and oblique whistler turbulence in presence of a relatively intense external magnetic field b0e∥. In this situation, turbulence is strongly anisotropic and the fluid equations describing both regimes are the reduced electron magnetohydrodynamics (REMHD) whose derivation, originally made from the gyrokinetic theory, is also obtained here from compressible Hall magnetohydrodynamics (MHD). We use the asymptotic equations derived by Galtier and Bhattacharjee (2003 Phys. Plasmas10, 3065–3076) to study the REMHD dynamics in the weak turbulence regime. The analysis is focused on the magnetic helicity equation for which we obtain the exact solutions: they correspond to the entanglement relation, n + ñ = −6, where n and ñ are the power law indices of the perpendicular (to b0) wave number magnetic energy and helicity spectra, respectively. Therefore, the spectra derived in the past from the energy equation only, namely n = −2.5 and ñ = −3.5, are not the unique solutions to this problem but rather characterize the direct energy cascade. The solution ñ = −3 is a limit imposed by the locality condition; it is also the constant helicity flux solution obtained heuristically. The results obtained offer a new paradigm to understand solar wind turbulence at sub-ion scales where it is often observed that −3 < n < −2.5.
A Hybrid Vlasov–Maxwell (HVM) model is presented and recent results about the link between kinetic effects and turbulence are reviewed. Using five-dimensional (2D in space and 3D in the velocity space) simulations of plasma turbulence, it is found that kinetic effects (or non-fluid effects) manifest through the deformation of the proton velocity distribution function (DF), with patterns of non-Maxwellian features being concentrated near regions of strong magnetic gradients. The direction of the proper temperature anisotropy, calculated in the main reference frame of the distribution itself, has a finite probability of being along or across the ambient magnetic field, in general agreement with the classical definition of anisotropy T⊥/T∥ (where subscripts refer to the magnetic field direction). Adopting the latter conventional definition, by varying the global plasma beta (β) and fluctuation level, simulations explore distinct regions of the space given by T⊥/T∥ and β∥, recovering solar wind observations. Moreover, as in the solar wind, HVM simulations suggest that proton anisotropy is not only associated with magnetic intermittent events, but also with gradient-type structures in the flow and in the density. The role of alpha particles is reviewed using multi-ion kinetic simulations, revealing a similarity between proton and helium non-Maxwellian effects. The techniques presented here are applied to 1D spacecraft-like analysis, establishing a link between non-fluid phenomena and solar wind magnetic discontinuities. Finally, the dimensionality of turbulence is investigated, for the first time, via 6D HVM simulations (3D in both spaces). These preliminary results provide support for several previously reported studies based on 2.5D simulations, confirming several basic conclusions. This connection between kinetic features and turbulence open a new path on the study of processes such as heating, particle acceleration, and temperature-anisotropy, commonly observed in space plasmas.
Non-diffusive transport, for which the particle mean free path grows nonlinearly in time, is envisaged for many space and laboratory plasmas. In particular, superdiffusion, i.e. 〈Δx2〉 ∝ tα with α > 1, can be described in terms of a Lévy random walk, in which case the probability of free-path lengths has power-law tails. Here, we develop a direct numerical simulation to reproduce the Lévy random walk, as distinct from the Lévy flights. This implies that in the free-path probability distribution Ψ(x, t) there is a space-time coupling, that is, the free-path length is proportional to the free-path duration. A power-law probability distribution for the free-path duration is assumed, so that the numerical model depends on the power-law slope μ and on the scale distance x0. The numerical model is able to reproduce the expected mean square deviation, which grows in a superdiffusive way, and the expected propagator P(x, t), which exhibits power-law tails, too. The difference in the power-law slope between the Lévy flights propagator and the Lévy walks propagator is also estimated.
Magnetic reconnection is one of the key processes in astrophysical and laboratory plasmas: it is the opposite of a dynamo. Looking at energy, a dynamo transforms kinetic energy in magnetic energy while reconnection takes magnetic energy and returns it to its kinetic form. Most plasma processes at their core involve first storing magnetic energy accumulated over time and then releasing it suddenly. We focus here on this release. A key concept in analysing reconnection is that of the separatrix, a surface (line in 2D) that separates the fresh unperturbed plasma embedded in magnetic field lines not yet reconnected with the hotter exhaust embedded in reconnected field lines. In kinetic physics, the separatrices become a layer where many key processes develop. We present here new results relative to the processes at the separatrices that regulate the plasma flow, the energization of the species, the electromagnetic fields and the instabilities developing at the separatrices.
The HYPER-II device has been constructed in Kyushu University to investigate the flow structure formation in an ion-unmagnetized plasma, which is an intermediate state of plasma and consists of unmagnetized ions and magnetized electrons. High density plasmas are produced by electron cyclotron resonance heating, and the flow field structure in an inhomogeneous magnetic field is investigated with a directional Langmuir probe method and a laser-induced fluorescence method. The experimental setup has been completed and the diagnostic systems have been installed to start the experiments. A set of coaxial electrodes will be introduced to control the azimuthal plasma rotation, and the effect of plasma rotation to generation of rectilinear flow structure will be studied. The HYPER-II experiments will clarify the overall flow structure in the inhomogeneous magnetic field and contribute to understanding characteristic feature of the intermediate state of plasma.
The von-Kármán plasma experiment is a novel versatile experimental device designed to explore the dynamics of basic magnetic induction processes and the dynamics of flows driven in weakly magnetized plasmas. A high-density plasma column (1016–1019 particles. m−3) is created by two radio-frequency plasma sources located at each end of a 1 m long linear device. Flows are driven through J × B azimuthal torques created from independently controlled emissive cathodes. The device has been designed such that magnetic induction processes and turbulent plasma dynamics can be studied from a variety of time-averaged axisymmetric flows in a cylinder. MHD simulations implementing volume-penalization support the experimental development to design the most efficient flow-driving schemes and understand the flow dynamics. Preliminary experimental results show that a rotating motion of up to nearly 1 km/s is controlled by the J × B azimuthal torque.
The West Virginia University Hot hELIcon eXperiment (HELIX) provides variable density and ion temperature plasmas, with controllable levels of thermal anisotropy, for space relevant laboratory experiments in the Large Experiment on Instabilities and Anisotropy (LEIA) as well as fundamental studies of helicon source physics in HELIX. Through auxiliary ion heating, the ion temperature anisotropy (T⊥/T∥) is variable from 1 to 20 for parallel plasma beta (β = 8πnkTi∥/B2) values that span the range of 0.0001 to 0.01 in LEIA. The ion velocity distribution function is measured throughout the discharge volume in steady-state and pulsed plasmas with laser induced fluorescence (LIF). The wavelengths of very short wavelength electrostatic fluctuations are measured with a coherent microwave scattering system. Operating at low neutral pressures triggers spontaneous formation of a current-free electric double layer. Ion acceleration through the double layer is detected through LIF. LIF-based velocity space tomography of the accelerated beam provides a two-dimensional mapping of the bulk and beam ion distribution functions. The driving frequency for the m = 1 helical antenna is continuously variable from 8.5 to 16 MHz and frequency dependent variations of the RF coupling to the plasma allow the spontaneously appearing double layers to be turned on and off without modifying the plasma collisionality or magnetic field geometry. Single and multi-species plasmas are created with argon, helium, nitrogen, krypton, and xenon. The noble gas plasmas have steep neutral density gradients, with ionization levels reaching 100% in the core of the plasma source. The large plasma density in the source enables the study of Aflvén waves in the HELIX device.