Collisionless Magnetized Plasma Research Articles

Beta dependence of electron heating in decaying whistler turbulence: Particle-in-cell simulations

Two-dimensional particle-in-cell simulations have been carried out to study electron beta dependence of decaying whistler turbulence and electron heating in a homogeneous, collisionless magnetized plasma. Initially, applied whistler fluctuations at relatively long wavelengths cascade their energy into shorter wavelengths. This cascade leads to whistler turbulence with anisotropic wavenumber spectra which are broader in directions perpendicular to the background magnetic field than in the parallel direction. Comparing the development of whistler turbulence at different electron beta values, it is found that both the wavenumber spectrum anisotropy and electron heating anisotropy decrease with increasing electron beta. This indicates that higher electron beta reduces the perpendicular energy cascade of whistler turbulence. Fluctuation energy dissipation by electron Landau damping responsible for the electron parallel heating becomes weaker at higher electron beta, which leads to more isotropic heating. It suggests that electron kinetic processes are important in determining the properties of whistler turbulence. This kinetic property is applied to discuss the generation of suprathermal strahl electron distributions in the solar wind.

Kinetic description of quasi-stationary axisymmetric collisionless accretion disk plasmas with arbitrary magnetic field configurations

A kinetic treatment is developed for collisionless magnetized plasmas occurring in high-temperature, low-density astrophysical accretion disks, such as are thought to be present in some radiatively inefficient accretion flows onto black holes. Quasi-stationary configurations are investigated, within the framework of a Vlasov-Maxwell description. The plasma is taken to be axisymmetric and subject to the action of slowly time-varying gravitational and electromagnetic fields. The magnetic field is assumed to be characterized by a family of locally nested but open magnetic surfaces. The slow collisionless dynamics of these plasmas is investigated, yielding a reduced gyrokinetic Vlasov equation for the kinetic distribution function. For doing this, an asymptotic quasi-stationary solution is first determined, represented by a generalized bi-Maxwellian distribution expressed in terms of the relevant adiabatic invariants. The existence of the solution is shown to depend on having suitable kinetic constraints and conditions leading to particle trapping phenomena. With this solution, one can treat temperature anisotropy, toroidal and poloidal flow velocities, and finite Larmor-radius effects. An asymptotic expansion for the distribution function permits analytic evaluation of all the relevant fluid fields. Basic theoretical features of the solution and their astrophysical implications are discussed. As an application, the possibility of describing the dynamics of slowly time-varying accretion flows and the self-generation of magnetic field by means of a “kinetic dynamo effect” are discussed. Both effects are shown to be related to intrinsically kinetic physical mechanisms.

Number-conserving linear-response study of low-velocity ion stopping in a collisional magnetized classical plasma

The results of a theoretical investigation of the low-velocity stopping power of ions in a magnetized collisional and classical plasma are reported. The stopping power for an ion is calculated through the linear-response (LR) theory. The collisions, which lead to a damping of the excitations in the plasma, are taken into account through a number-conserving relaxation time approximation in the LR function. In order to highlight the effects of collisions and magnetic field, we present a comparison of our analytical and numerical results obtained for nonzero damping or magnetic field with those for vanishing damping or magnetic field. It is shown that the collisions remove the anomalous friction obtained previously [Nersisyan et al., Phys. Rev. E 61, 7022 (2000)] for the collisionless magnetized plasmas at low ion velocities. One of the major objectives of this paper is to compare and to contrast our theoretical results with those obtained through a diffusion coefficient formulation based on the Dufty-Berkovsky relation evaluated for a magnetized one-component plasma modeled with target ions and electrons.

Lower-hybrid waves generated by anomalous Doppler resonance in auroral plasmas

AbstractThis paper describes some aspects of lower-hybrid wave activity in space plasmas. Lower-hybrid waves are particularly important since they can transfer energy efficiently between electrons and ions in a collisionless magnetized plasma. We consider the ‘fan’ or anomalous Doppler resonance instability driven by energetic electron tails and show that it is responsible for the generation of lower-hybrid waves. We also demonstrate that observations of their intensity are sufficient to drive the modulational instability.

Strong Dependency of Ion Acceleration on Ion Beam Divergency in Magnetized Collisionless Plasma Sheath

The ion acceleration inside the collisionless plasma sheath is investigated at the presence of external magnetic field. By using the fluid model, the number and momentum equations of the ions and the Boltzmann and Poisson equations are solved numerically in the case that the ion beam has a small divergency at the plasma sheath boundary. It is shown that the kinetic energy of the ions has a strong dependency to the magnitude of divergency when the magnetic field has a small component parallel to the sheath boundary.

The dynamics of ions entering the magnetized plasma sheath obliquely – collisional and collisionless situations

The characteristics of ions that enter the plasma sheath with an oblique incident angle have been investigated in the presence of an external magnetic field. The ion dynamics in a collisional and collisionless magnetized plasma sheath have been numerically calculated by using a fluid model. Several values for the ion velocity at the sheath edge, orientation and strength of the magnetic field and the ion-neutral collision frequency have been considered. The results show that in a collisionless magnetized plasma sheath, the behaviour of ions that obliquely enter the sheath with some specific velocities at the sheath edge and at some specific orientations and strengths of magnetic field, is more complicated than that of ions with normal entrance angles. For the oblique entrance of ions, the weak magnetic fields cause some fluctuations in ion velocity around its boundary value, i.e. the ion velocity does not accelerate. However, the numerical calculations show that the ion dynamics in a collisional magnetized plasma sheath are the same for both normal and inclined entrance of ions into the sheath.

Ion dynamics in plasma sheath under the effect of E× B and collisional forces

Using the fluid model, we investigated the velocity, kinetic energy and the density distribution of the ions in collisional and collisionless magnetized plasma sheath. Considering an external magnetic field, the ion movement under the effect of magnetic, electric and collisional forces has been analyzed numerically. The nonexistence of fluctuations in ions kinetic energy in collisionless strong magnetized plasma sheath and increasing the ions velocity in depth direction due to the collisions in some positions in the sheath are shown. The fluctuations of ion velocity in weak magnetized plasma sheath are shown too when ions enter the sheath with oblique incident angle.

Collisional effects in magnetized plasma sheath with two species of positive ions

The effects of ion–neutral collision on the characteristics of a magnetized plasma sheath which consists of two species of positive ions are investigated. It is assumed that the ions have different masses. In contrast to our previous work, the effects of ion–neutral collision frequency are added to the magnetized plasma sheath. Using a three-fluid hydrodynamic model and some dimensionless variables, the dimensionless equations are obtained and solved numerically. By taking into account the ion–neutral collision effects on a magnetized three-component plasma sheath, it is shown that apart from the presence of the second ion species, by increasing the collision frequency of two ions with neutrals, the amplitude of fluctuations of ion species density distributions increases and the position of these fluctuations is shifted towards the plasma sheath edge. Also, by increasing the ion–neutral collision frequency these fluctuations turn off faster than those in a collisionless case. It is shown that in the collisional magnetized plasma sheath, the effects of the presence of the heavier ion species on the lighter ion density turn off much faster in comparison with what happens in a collisionless magnetized plasma sheath. Furthermore, it is found that in a collisionless plasma sheath by increasing the density of the heavier ion species, the normalized electrostatic potential decreases while in a collisional plasma sheath the presence of the heavier ion species does not have any considerable effect on the normalized electrostatic potential. In addition, it is shown that when the distance of each ion species from the plasma sheath boundary becomes larger than five times the electron Debye length (x > 5λDe) the fluctuations of the ion species velocities disappear by increasing the ion–neutral collision frequency. Also, it is found that the electron density distribution decreases by increasing the ion–neutral collision frequency.

Application of a Grid‐Free Kinetic Model to the Collisionless Sheath

AbstractIn this work we present a grid‐free hierarchical treecode, developed for simulation of bounded plasmas. The code follows both electrons and ions dynamics, resolving 1 spatial and 3 velocity coordinates. The code was applied for the simulation of a magnetized collisionless plasma in front of a material wall. The results obtained are in very good agreement with those of Particle‐in‐Cell simulation. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A guiding centre direct implicit scheme for magnetized plasma simulations

A new implicit fully electromagnetic particle in cell method is presented in which the full ion dynamic and all the electron guiding centre drifts of a magnetized collisionless plasma are retained. This code retains the inertial effects on the electrons. It must be used for time steps larger or so than an electron cyclotron period, it is only valid for an electron plasma beta β e < 1 . Therefore, it is efficient only with strongly magnetized electrons. On the opposite, the constraint on the ions β i < m i / m e (where m i / m e is the ion to electron mass ratio) is very weak. This method allows for the simulation of an ion-beam instability (triggering electrostatic ion cyclotron waves and filamentation of the plasma), the propagation of MHD waves, and ion-temperature anisotropies (mirror and/or cyclotron waves), at a relatively low cost. This method could become a useful tool for the modelization of space plasmas, quite complementary with other methods such as Hall-MHD, hybrid codes, or other implicit particle codes.

Kinetic theory of hydromagnetic turbulence. I. Formal results for parallel propagation

Formal weak turbulence kinetic equations for magnetized collisionless plasmas are derived. The kinetic theory of plasma turbulence found in the literature is largely applicable for unmagnetized plasmas, and most of the available literature only deal with electrostatic Langmuir turbulence problem. However, real plasmas in nature and laboratory are usually immersed in magnetic fields. At present there is no practical kinetic theory for turbulence in magnetized plasmas. The present paper and a companion article [P. H. Yoon and T.-M. Fang, Phys. Plasmas 14, 102303 (2007)] constitute a first step in the formulation of general kinetic theory for magnetized plasmas. For the sake of simplicity, it is assumed that turbulent fluctuations predominantly propagate along the direction of ambient magnetic field vector, and that the characteristic frequency associated with the fluctuations is much lower than the electron gyrofrequency, i.e., hydromagnetic turbulence. The effects of spontaneous thermal fluctuation and spatial inhomogeneity are also ignored.

Kinetic modeling of a sheath layer in a magnetized collisionless plasma

A sheath layer in a magnetized collisionless plasma is analyzed by the one-dimensional kinetic equation. The plasma is bounded by an absorbing wall and a plasma source with a shifted Maxwellian velocity distribution function that is characterized by a temperature, a drifting velocity parallel to the magnetic field, and a cutoff velocity. The magnetic field is assumed to be strong enough so that the ion Larmor radius is comparable to the Debye length. In order to include the polarization effect of ions due to a strong electric field, equations describing the potential profile are derived from the gyrokinetic Vlasov equation in a frame moving with the E×B drift. A new algorithm for evaluating the loss of particles in gyration at the wall is introduced. The condition of the stable sheath formation for a magnetized plasma is discussed. The dependence of the electric field at the wall on the angle and the strength of the magnetic field is examined and compared with the results of full-kinetic particle-in-cell simulation. The effect of the polarization and the loss of gyration particles on the wall electric field are also discussed.

Collisionless magnetohydrodynamics with gyrokinetic effects

Anisotropic magnetohydrodynamics equations, which also capture the dynamics of quasi-transverse small scales obeying the gyrokinetic ordering, are derived using fourth-rank moment closures, based on a refined description of linear Landau damping and finite Larmor radius (FLR) corrections. This “FLR-Landau fluid model” reproduces the dispersion relation of low-frequency waves, up to scales that, in the case of quasi-transverse kinetic Alfvén waves, can be much smaller than the ion gyroradius. The mirror instability, which requires temperature anisotropy, is also captured, together with its quenching at small scales. This model that accurately reproduces the collisionless dissipation of low-frequency modes, should provide an efficient tool to simulate mesoscale turbulence in a magnetized collisionless plasma.

FLR–Landau fluids for collisionless plasmas

Fluid descriptions of collisionless magnetized plasma are reviewed, with a special focus on Landau fluid models. Simpler than gyrofluids derived from the gyrokinetic equation, these models were first introduced as extensions of anisotropic MHD retaining linear Landau damping, and have recently been generalized by including finite Larmor radius effects in order to describe transverse scales significantly smaller than the ion gyroradius. Such FLR–Landau fluids satisfactorily compare with the hot plasma theory of linear kinetic Alfvén waves, and also accurately reproduce the mirror instability of anisotropic plasmas, including its quenching at small scales. They should provide an efficient tool to simulate phenomena involving a broad range of scales, in regimes where nonlinear kinetic effects such as wave particle trapping can be neglected.

A hybrid-Vlasov model based on the current advance method for the simulation of collisionless magnetized plasma

We present a numerical scheme for the integration of the Vlasov–Maxwell system of equations for a non-relativistic plasma, in the hybrid approximation, where the Vlasov equation is solved for the ion distribution function and the electrons are treated as a fluid. In the Ohm equation for the electric field, effects of electron inertia have been retained, in order to include the small scale dynamics up to characteristic lengths of the order of the electron skin depth. The low frequency approximation is used by neglecting the time derivative of the electric field, i.e. the displacement current in the Ampere equation. The numerical algorithm consists in coupling the splitting method proposed by Cheng and Knorr in 1976 [C.Z. Cheng, G. Knorr, J. Comput. Phys. 22 (1976) 330–351.] and the current advance method (CAM) introduced by Matthews in 1994 [A.P. Matthews, J. Comput. Phys. 112 (1994) 102–116.] In its present version, the code solves the Vlasov–Maxwell equations in a five-dimensional phase space (2-D in the physical space and 3-D in the velocity space) and it is implemented in a parallel version to exploit the computational power of the modern massively parallel supercomputers. The structure of the algorithm and the coupling between the splitting method and the CAM method (extended to the hybrid case) is discussed in detail. Furthermore, in order to test the hybrid-Vlasov code, the numerical results on propagation and damping of linear ion-acoustic modes and time evolution of linear elliptically polarized Alfvén waves (including the so-called whistler regime) are compared to the analytical solutions. Finally, the numerical results of the hybrid-Vlasov code on the parametric instability of Alfvén waves are compared with those obtained using a two-fluid approach.

Towards fluid simulations of dispersive MHD waves in a warm collisionless plasma

A Landau fluid model suited for the description of the weakly nonlinear dynamics of long wavelength dispersive MHD waves in a magnetized collisionless plasma is presented, that should be useful to study the formation and stability of solitary structures such as magnetic holes or shocklets observed for example in the solar wind and the terrestrial magnetosheath. First simulations in a slab geometry are reported, that focus on the evolution of plane fast magnetosonic waves. Accurate comparisons are made with analytic predictions of the Landau damping rate for various plasma parameters and wave characteristics. In a regime where Landau damping dominates, Alfvén modes eventually become prevalent, which results in the arrest of dissipation at a time that is shorter for waves with larger initial amplitude. In contrast, magnetosonic solitary waves in the form of density and magnetic field depressions are found to emerge in a regime where Landau dissipation is initially negligible compared with nonlinear and dispersive effects. Excellent agreement is also found for the growth rate of the mirror instability at long wavelength but modeling the arrest of the instability at small scales within fluid simulations remains a challenging issue.

A Landau fluid model for warm collisionless plasmas

A Landau fluid model for a collisionless electron-proton magnetized plasma that accurately reproduces the dispersion relation and the Landau damping rate of all the magnetohydrodynamic waves is presented. It is obtained by an accurate closure of the hydrodynamic hierarchy at the level of the fourth-order moments, based on linear kinetic theory. It retains nongyrotropic corrections to the pressure and heat flux tensors up to the second order in the ratio between the considered frequencies and the ion cyclotron frequency.

Fluid formalism for collisionless magnetized plasmas

A comprehensive analysis of the finite-Larmor-radius (FLR) fluid moment equations for collisionless magnetized plasmas is presented. It is based on perturbative but otherwise general solutions for the second and third rank fluid moments (the stress and stress flux tensors), with closure conditions still to be specified on the fourth rank moment. The single expansion parameter is the ratio between the largest among the gyroradii and any other characteristic length, which is assumed to be small but finite in a magnetized medium. This formalism allows a complete account of the gyroviscous stress, the pressure anisotropy, and the anisotropic heat fluxes, and is valid for arbitrary magnetic geometry, arbitrary plasma pressure, and fully electromagnetic nonlinear dynamics. As the result, very general yet notably compact perturbative systems of FLR collisionless fluid equations, applicable to either fast (sonic or Alfvénic) or slow (diamagnetic) motions, are obtained.

Collisionless magnetohydrodynamic turbulence in two dimensions

In this paper we give a formulation of two-dimensional (2D) collisionless magnetohydrodynamic (MHD) turbulence that includes the effects of both electron inertia and electron pressure (or parallel electron compressibility) and is applicable to strongly magnetized collisionless plasmas. We place particular emphasis on the departures from the 2D classical MHD turbulence results produced by the collisionless MHD effects. We investigate the fractal/multi-fractal aspects of spatial intermittency. The fractal model for intermittent collisionless MHD turbulence appears to be able to describe the observed k −1 spectrum in the solar wind. Multi-fractal scaling behaviors in the inertial range are first deduced, and are then extrapolated down to the dissipative microscales. We then consider a parabolic-profile model for the singularity spectrum f ( α), as an explicit example of a multi-fractal scenario. These considerations provide considerable insights into the basic mechanisms underlying spatial intermittency in 2D fully developed collisionless MHD turbulence.

Flow Shear Effects on Plasma Microinstability in Open-Ended Magnetic Configurations

The external and independent control of parallel and perpendicular flow shears in collisionless magnetized plasmas is realized using segmented plasma sources. Then, ion flow velocity shears parallel to the magnetic-field lines are observed to destabilize not only the drift-wave but also the ion-cyclotron instabilities depending on the sign of the parallel shear in the absence of field-aligned electron drift flow in laboratory experiments. On the other hand, perpendicular ion flow velocity shears are demonstrated to suppress both the drift-wave and the ion-cyclotron instabilities, and furthermore, the suppressions are found to take place independently of the sign of the perpendicular shear.