Marius M. Echim

A Review on Solar Wind Modeling: Kinetic and Fluid Aspects

The paper reviews the main advantages and limitations of the kinetic exospheric and fluid models of the solar wind (SW). The general theoretical background is outlined: the Boltzmann and Fokker–Planck equations, the Liouville and Vlasov equations, the plasma transport equations derived from an “equation of change”. The paper provides a brief history of the solar wind modeling. It discusses the hydrostatic model imagined by Chapman, the first supersonic hydrodynamic models published by Parker and the first generation subsonic kinetic model proposed by Chamberlain. It is shown that a correct estimation of the electric field, as in the second generation kinetic exospheric models developed by Lemaire and Scherer, provides a supersonic expansion of the corona, reconciling the hydrodynamic and the kinetic approach. The modern developments are also reviewed emphasizing the characteristics of several generations of kinetic exospheric and multi-fluid models. The third generation kinetic exospheric models consider kappa velocity distribution function (VDF) instead of a Maxwellian at the exobase and in addition they treat a non-monotonic variation of the electric potential with the radial distance; the fourth generation exospheric models include Coulomb collisions based on the Fokker–Planck collision term. Multi-fluid models of the solar wind provide a coarse grained description of the system and reproduce with success the spatio-temporal variation of SW macroscopic properties (density, bulk velocity). The main categories of multi-fluid SW models are reviewed: the 5-moment, or Euler, models, originally proposed by Parker to describe the supersonic SW expansion; the 8-moment and 16-moment fluid models, the gyrotropic approach with improved collision terms as well as the gyrotropic models based on observed VDFs. The outstanding problem of collisions, including the long range Coulomb encounters, is also discussed, both in the kinetic and multi-fluid context. Although for decades the two approaches have been seen as opposed, in this paper we emphasize their complementarity. The review of the kinetic and fluid models of the solar wind contributes also to a better evaluation of the open questions still existent in SW modeling and suggests possible future developments.

A magnetospheric generator driving ion and electron acceleration and electric currents in a discrete auroral arc observed by Cluster and DMSP

[1]xa0Simultaneous observations on April 28, 2001 by Cluster and DMSP-F14 reveal a stable discrete auroral arc and fluxes of field-aligned accelerated electrons and ions coincident with a magnetospheric plasma interface at an altitude of 4.5 RE in the dusk sector. We compare satellite data with a quasi-stationary magnetosphere-ionosphere coupling model based on a Vlasov solution for the magnetospheric generator. The model provides a self-consistent magnetospheric electric potential matching the Cluster observations. The ionospheric potential is derived from the current continuity equation and gives a field-aligned potential drop and a flux of precipitating energy in agreement with the DMSP data. Model results and data analysis suggest a quasi-stationary field-aligned acceleration of auroral electrons and ions with a magnetospheric generator. We associate the generator with the convergent perpendicular electric field at the interface of the plasma sheet boundary layer with the lobe or at the inner edge of the low latitude boundary layer.

Solar wind driving of dayside field‐aligned currents

[1]xa0Variations in the dayside field-aligned current (FAC) density (J//), field-aligned parallel potential drop (Δϕ//), peak precipitating electron energy (peak Ee), and precipitating electron energy flux (ɛ) as functions of solar wind (SW) and interplanetary magnetic field (IMF) are investigated with Defense Meteorological Satellite Program observations and a quasi-stationary low-latitude boundary layer (LLBL)–FAC coupling model. Region 1 (R1) J// responses to variations in SW velocity (Vsw) and density (nsw) at 8–16 magnetic local time (MLT) suggest that R1 at these local times is frequently open while R1 at 6–08 and 17–18 MLT is frequently closed. R2 is located mostly on closed field lines. In the afternoon open R1 at 12–16 MLT, an increase in nsw increases J//, decreases maximum peak Ee (proxy for Δϕ//), but has little effect on maximum ɛ. In the same R1 region, an increase in Vsw increases J//, maximum peak Ee, and maximum ɛ. The dependencies of J//, maximum peak Ee, and maximum ɛ are consistent with the Knight relation and the voltage generator at the magnetopause boundary in the afternoon open R1. In the midmorning and midafternoon, the response of J// to Vsw is higher for southward than for northward IMF. This can be attributed to the higher-velocity shear at the magnetopause boundary due to higher sunward convection in the LLBL inside the magnetopause. R1 in the closed-field lines near dawn and dusk appears to be more sensitive to merging rate (dΦ/dt = Vsw4/3BT2/3 sin8/3(θc/2)) than to SW dynamic pressure.

Turbulence-Generated Proton-Scale Structures In The Terrestrial Magnetosheath

Recent results of numerical magnetohydrodynamic simulations suggest that in collisionless space plasmas turbulence can spontaneously generate thin current sheets. These coherent structures can partially explain intermittency and the non-homogenous distribution of localized plasma heating in turbulence. In this Letter Cluster multi-point observations are used to investigate the distribution of magnetic field discontinuities and the associated small-scale current sheets in the terrestrial magnetosheath downstream of a quasi-parallel bow shock. It is shown experimentally, for the first time, that the strongest turbulence generated current sheets occupy the long tails of probability distribution functions (PDFs) associated with extremal values of magnetic field partial derivatives. During the analyzed one hour long time interval, about a hundred strong discontinuities, possibly proton-scale current sheets were observed.

Self-consistent solution for a collisionless plasma slab in motion across a magnetic field

The problem of the dynamics of a plasma slab moving across a magnetic field is treated in the framework of the kinetic theory. A velocity distribution function (VDF) is found for each plasma species, electrons and protons, in terms of the constants of motion defined by the geometry of the problem. The zero- and first-order moments of the VDF are introduced into the right-hand side term of Maxwells equations to compute the electric and magnetic vector potentials and corresponding fields. The solutions are found numerically. We obtain a region of plasma convection-the slab proper-where the plasma moves with a uniform velocity, V-x=V-0=(ExB/B-2)(x). At the core margins two plasma wings are formed, each being the result of a pair of interpenetrated boundary layers with different transition lengths. Inside these wings, the plasma velocity is not uniform, V(x)not equal(ExB/B-2)(x). It decreases from the maximum value obtained in the core to a minimum value in the central region of the wings where a flow reversal is found with the plasma convecting in the opposite direction to the core motion. There is also an asymmetry of the velocity gradient at the borders of the core, which results in a corresponding asymmetry in the thickness of the wings. Furthermore, it is found that the reversed plasma flow in the thinner wing is larger than that in the broader wing. For a fixed direction of the magnetic field the two plasma wings interchange position with respect to the center of the slab when the plasma bulk velocity reverses sign

Transport and entry of plasma clouds/jets across transverse magnetic discontinuities: Three‐dimensional electromagnetic particle‐in‐cell simulations

In this paper we use three-dimensional electromagnetic particle-in-cell simulations to investigate the interaction of a small-Larmor radius plasma cloud/jet with a transverse non-uniform magnetic field typical to a tangential discontinuity in a parallel geometry. The simulation setup corresponds to an idealized, yet relevant, magnetospheric configuration likely to be observed at the magnetopause during northward orientation of the interplanetary magnetic field. The numerical simulations are adapted to study the kinetic effects and their role on the transport and entry of localized plasma jets similar to those identified inside the Earths magnetosheath propagating towards the magnetopause. The simulations reveal the formation of a polarization electric field inside the main bulk of the plasma cloud that enables its forward transport and entry across the transverse magnetic field. The jet is able to penetrate the transition region when the height of the magnetic barrier does not exceed a certain critical threshold. Otherwise, the forward transport along the injection direction is stopped before full penetration of the magnetopause. Moreover, the jet is pushed back and simultaneously deflected in the perpendicular plane to the magnetic field. Our simulations evidence physical processes advocated previously by the theoretical model of impulsive penetration and revealed in laboratory experiments.

Complexity Phenomena and ROMA of the Earth's Magnetospheric Cusp, Hydrodynamic Turbulence, and the Cosmic Web

Abstract“Dynamic complexity” is a phenomenon observed for a nonlinearly interacting system within which multitudes of different sizes of large scale coherent structures emerge, resulting in a nglobally nonlinear stochastic behavior vastly different from that which could be surmised from the underlying equations of interaction. A characteristic of such nonlinear, complex phenomena is the appearance of intermittent fluctuating events with the mixing and distribution of correlated structures on all scales. We briefly review here a relatively recent method, ROMA (rank-ordered multifractal analysis), explicitly developed for analysis of the intricate details of the distribution and scaling of such types of intermittent structure. This method is then used for analysis of selected examples related to the dynamic plasmas of the cusp region of the Earth’s magnetosphere, velocity fluctuations of classical hydrodynamic turbulence, and the distribution of the structures of the cosmic gas obtained by use of large-scale, moving mesh simulations. Differences and similarities of the analyzed results among these complex systems will be contrasted and highlighted. The first two examples have direct relevance to the nEarth’s environment (i.e., geoscience) and are summaries of previously reported findings. The third example, although involving phenomena with much larger spatiotemporal scales, with its highly compressible turbulent behavior and the unique simulation technique employed in generating the data, provides direct motivation for applying such analysis to studies of similar multifractal processes in extreme environments of near-Earth surroundings. These new results are both exciting and intriguing.

The impulsive penetration mechanism: Advances in the numerical and experimental verification

The impulsive penetration mechanism describes the dynamics of a plasma irregularity (or plasmoid) at the interface between the magnetosheath and the Earths magnetosphere. The plasmoids motion perpendicular to B is self-sustained by a polarization electric field; its analytical expression can be derived by assuming that the magnetic moment of ions and electrons is adiabatically conserved. Numerical integration of trajectories injected into this E-field distribution crossed with the B-field of a tangential discontinuity demonstrates that the particle penetrates the discontinuity surface. Weak-double-layers (wdl) at the edges of the plasmoid confines the electrons and ions within the volume of the plasmoid. Inside the magnetosphere wdl move along geomagnetic field lines, the plasmoid expands and its density decreases. A positive density gradient develops inside the plasma element. In-situ experimental data seem to confirm this prediction of the model.

Ring-shaped velocity distribution functions in energy-dispersed structures formed at the boundaries of a proton stream injected into a transverse magnetic field: Test-kinetic results

In this paper, we discuss the formation of ring-shaped and gyro-phase restricted velocity distribution functions (VDFs) at the edges of a cloud of protons injected into non-uniform distributions of the electromagnetic field. The velocity distribution function is reconstructed using the forward test-kinetic method. We consider two profiles of the electric field: (1) a non-uniform E-field obtained by solving the Laplace equation consistent with the conservation of the electric drift and (2) a constant and uniform E-field. In both cases, the magnetic field is similar to the solutions obtained for tangential discontinuities. The initial velocity distribution function is Liouville mapped along numerically integrated trajectories. The numerical results show the formation of an energy-dispersed structure due to the energy-dependent displacement of protons towards the edges of the cloud by the gradient-B drift. Another direct effect of the gradient-B drift is the formation of ring-shaped velocity distribution functions within the velocity-dispersed structure. Higher energy particles populate the edges of the proton beam, while smaller energies are located in the core. Non-gyrotropic velocity distribution functions form on the front-side and trailing edge of the cloud; this effect is due to remote sensing of energetic particles with guiding centers inside the beam. The kinetic features revealed by the test-kinetic solutions have features similar to in-situ velocity distribution functions observed by Cluster satellites in the magnetotail, close to the neutral sheet.

Comparative study of forward and backward test-kinetic simulation approaches

In this paper we perform a comparative study of the forward and backward Liouville mapping applied to the modeling of ring-shaped and non-gyrotropic velocity distribution functions of particles injected in a sheared electromagnetic field. The test-kinetic method is used to compute the velocity distribution function in various areas of a proton cloud moving in the vicinity of a region with a sharp transition of the magnetic field and a non-uniform electric field. In the forward approach the velocity distribution function is computed for a two-dimensional spatial bin, while in the backward approach the distribution function is averaged over a spatial bin with the same size as for the forward method and using a two-dimensional trapezoidal integration scheme. It is shown that the two approaches lead to similar results for spatial bins where the velocity distribution function varies smoothly. On the other hand, with bins covering regions of configuration space characterized by sharp spatial gradients of the velocity distribution function, the forward and backward approaches will generally provide different results.