Plasma sheet coefficient of diffusion: Predictions and observations

The theory of a plasma sheet with medium scale developed turbulence predicts a value for the plasma sheet diffusion coefficient in the Z direction. Its value becomes very near to the diffusion coefficient calculated from the assumption of isotropic turbulence on the basis of ISEE-2 velocity fluctuations in the X and Y directions. INTERBALL/Tail CORALL bulk velocity measurements make it possible to determine velocity fluctuations in the Z direction and calculate the diffusion coefficient in this Z direction. It is shown that INTERBALL/Tail observations are in very good agreement with theory predictions.     

Outstanding issues in understanding the dynamics of the inner plasma sheet and ring current during storms and substorms

The paper deals with five selected issues of the dynamical coupling of the near-Earth plasma sheet and magnetosphere, (1) substorm initiation, (2) dipolarization, (3) pressure release of the outer magnetosphere via the auroral energy conversion process, (4) magnetization of the very high beta plasma assembling at the inner edge of the tail, and (5) penetration of energetic particles into the ring current below L 4. One outstanding and strongly debated subject is not discussed here, the origin of the substorm current wedge. The main conclusions (or personal preferences) are: (1) the substorm is initiated by formation of a near-Earth neutral line; (2) dipolarization occurs through magnetic flux transport by the earthward reconnection flow and not by current diffusion; (3) the auroral energy conversion process, the “auroral pressure valve”, contributes substantially to the pressure release during the substorms; (4) high beta ( 10) plasma breaks up into smaller scale blobs under slow magnetization; and (5) deep and prolonged penetration of hot plasma sheet plasma into the middle magnetosphere produces currents and electric fields which lead to the growth of the storm-time ring current.     

Substorms in the inner plasma sheet

Thin Current Sheets (TCS) are regularly formed prior to substorm breakup, even in the near-Earth plasma sheet, as close as the geostationary orbit. A self-consistent kinetic theory describing the response of the plasma sheet to an electromagnetic perturbation is given. This perturbation corresponds to an external forcing, for instance caused by the solar wind (not an internal instability). The equilibrium of the configuration of this TCS in the presence of a time varying perturbation is shown to produce a strong parallel thermal anisotropy (T T) of energetic electrons and ions (E>50keV) as well as an enhanced diamagnetic current carried by low energy ions (E<50keV). Both currents tend to enhance the confinement of this current sheet near the magnetic equator. These results are compared with data gathered by GEOS-2 at the geostationary orbit, where the magnetic signatures of TCS, and parallel anisotropics are regularly observed prior to breakup. By ensuring quasi-neutrality everywhere we find, when low frequency electromagnetic perturbations are applied, that although the magnetic field line remains an equipotential to the lowest order in T_e/T_i, a field-aligned potential drop exists to the next order in (T_e/T_i). Thus the development of a TCS implies the formation of a field-aligned potential drop ( few hundred volts) to ensure the quasi-neutrality everywhere. For an earthward directed pressure gradient, a field-aligned electric field, directed towards the ionosphere, is obtained, on the western edge of the perturbation (i.e. western edge of the current sheet). Thus field aligned beams of electrons are expected to flow towards the equatorial region on the western edge of the current sheet. We study the stability of these electron beams and show that they are unstable to “High Frequency” (HF) waves. These “HF” waves are regularly observed at frequencies of the order of the proton gyrofrequency (f_H+) just before, or at breakup. The amplitude of these HF waves is so large that they can produce a strong pitch-angle diffusion of energetic ions and a spatial diffusion that leads to a reduction of the diamagnetic current. The signature of a fast ion diffusion is indeed regularly observed during the early breakup; it coincides with the sudden development of large amplitude transient fluctuations, ballooning modes, observed at much lower frequencies (fH+). These results suggest that the HF waves, generated by field-aligned electron beams, provide the dissipation which is necessary to destabilize low frequency (ballooning) modes.     

Fractal Structure of the Heliospheric Plasma Sheet at the Earth''''s Orbit

An analysis of the data from the Wind and IMP-8 spacecraft revealed that a slow solar wind, flowing in the heliospheric plasma sheet, represents a set of magnetic tubes with plasma of increased density (N > 10cm-3 at the Earth's orbit). They have a fine structure at several spatial scales (fractality), from 2°-3°(at the Earth's orbit, it is equivalent to 3.6-5.4h, or (5.4-8.0)×106km) to the minimum about 0.025°, i.e. the angular size of the nested tubes is changed nearly by two orders of magnitude. The magnetic tubes at each observed spatial scale are diamagnetic, i.e. their surface sustains a flow of diamagnetic (or drift) current that decreases the magnetic field within the tube itself and increases it outside the tube. Furthermore, the value of β= 8π[N(Te + Tp)]/B2 within the tube exceeds the value of βoutside the tube. In many cases total pressure P = N(Te + Tp) + B2/8πis almost constant within and outside the tubes at any one of the aforementioned scales.     

Comparative study of plasma wave activity in the plasma sheet boundary and near Earth plasma sheet

The general structure of low frequency wave activity in the Earth's plasma sheet and its boundary layer is studied on the basis of the measurements made by ‘Prognoz-8’ satellite in the northern night and morning parts of the magnetotail. Pronounced wave activity is permanently observed in the high latitude parts of the plasma sheet boundary layer. The level of perturbations diminishes when a spacecraft moves towards tail lobes and drops rather sharply when it moves to the central plasma sheet. The peaks near the low hybrid resonance frequency (correlating with the local strength of the magnetic field) are evident in the electric field fluctuations spectra. A plasma instability of low hybrid type driven by transverse current is though to be the possible candidate for the excitation of these waves. Wave activity in tail lobes is related mainly to the isolated hot and cold plasma streams.     

Kink-like mode of a double gradient instability in a compressible plasma current sheet

A linear MHD instability of the electric current sheet, characterized by a small normal magnetic field component, varying along the sheet, is investigated. The tangential magnetic field component is modeled by a hyperbolic function, describing Harris-like variations of the field across the sheet. For this problem, which is formulated in a 3D domain, the conventional compressible ideal MHD equations are applied. By assuming Fourier harmonics along the electric current, the linearized 3D equations are reduced to 2D ones. A finite difference numerical scheme is applied to examine the time evolution of small initial perturbations of the plasma parameters. This work is an extended numerical study of the so called “double gradient instability”, – a possible candidate for the explanation of flapping oscillations in the magnetotail current sheet, which has been analyzed previously in the framework of a simplified analytical approach for an incompressible plasma. The dispersion curve is obtained for the kink-like mode of the instability. It is shown that this curve demonstrates a quantitative agreement with the previous analytical result. The development of the instability is investigated also for various enhanced values of the normal magnetic field component. It is found that the characteristic values of the growth rate of the instability shows a linear dependence on the square root of the parameter, which scales uniformly the normal component of the magnetic field in the current sheet.     

The model of turbulent plasma sheet during IMF Bz > 0

Theory of the plasma sheet with medium-scale developed turbulence gives the possibility to explain the main processes of plasma sheet bifurcation and theta-aurora formation during IMF B_z > 0. The model suggests that during IMF B_z > 0 small bulge structure in the plasma sheet center is formed. The polarization of the bulge due to dawnward electron motion and duskward ion motion decreases the large-scale electric field in the bulge region. The decrease of the large-scale field in the conditions of constant coefficient of diffusion leads to the bulge growth. The results of plasma sheet bifurcation and theta-aurora formation modelling are presented.     

Inconsistency of magnetic field and plasma velocity variations in the distant plasma sheet: Violation of the “frozen-in” criterion?

Measurements of the magnetic field and low energy plasma by the GEOTAIL spacecraft have been used to study the relationship between variations of the plasma velocity and of the magnetic field in the distant (100–200 R_E) and middle (40–80 R_E) tail. The analysis was carried out separately for the tail lobes and the plasma sheet. It is shown that the absolute values of the magnetic field and plasma velocity, as well as their corresponding components (V_X and B_X, V_Y and B_Y, V_Z and B_Z), are linearly connected in the tail lobes. In the plasma sheet, however, the plasma velocity and the magnetic field do not seem to be related to one another. The distant plasma sheet seems to be in a regime of turbulence. The diffusion coefficients estimated from our data set of the velocity parameters in the plasma sheet are in good agreement with the theoretical predictions of Antonova and Ovchinnikov (1996, 1999).     

Current fluctuations in the Earth''s magnetosphere caused by lower-hybrid-drift turbulence

Nonlinear calculations of the anomalous electrical conductivity in the plasma of the earth's plasma mantle, the tail plasma sheet boundary layer and the ionospheric F-region density-trough are presented provided that lower-hybrid-drift turbulence exists. It is shown that in these regions the stabilization of the wave growth is mainly caused by current relaxation. Further, the fluctuations of the electrical currents are estimated via Ampère's and Ohm's laws. It is found that the lower-hybrid-drift turbulence causes maximum anomalous collision frequencies of the order of 10⁻² Hz in the magnetosphere. The maximum current fluctuations are about 3 10⁻⁹ A/m². The theoretical results are in agreement with ISEE and Prognoz-8 measurements.     

使用GAO-YONG湍流方程组对扩压器流动的计算

采用基于同位网格的SIMPLE方法求解GAO-YONG不可压湍流方程组,对二维扩压器流动进行了数值模拟.通过界面速度动量插值法解决了压力锯齿波问题,并且采用了正交贴体网格和二阶QUICK格式离散对流项以提高计算精度.与实验结果以及BL(Baldw-Lomax)模型计算结果的比较表明,不需要任何经验系数及壁面函数的GAO-YONG不可压湍流模型方程组能够对有压力梯度的湍流流动做出很好的预测.计算发现,在机械能方程中引入平均流压力梯度的作用,对GAO-YONG湍流方程组正确模拟逆压力梯度流动起到了关键作用.      

ISEE-1 and 2 observations of field-aligned currents in the distant midnight magnetosphere

Magnetic field measurements obtained in the nightside magnetosphere by the co-orbiting ISEE-1 and 2 spacecraft have been examined for signatures of field-aligned currents (FAC). Such currents are found on the boundary of the plasma sheet both when the plasma sheet is expanding and when it is thinning. Plasma sheet boundary layer current structure and substorm associated dynamics can be determined using the two spacecraft, although for slow traversals of the FAC sheet the spatial/temporal ambiguity is still an issue. We often find evidence for the existence of waves on the plasma sheet boundary, leading to multiple crossings of the FAC sheet. At times the boundary layer FAC sheet orientation is nearly parallel to the X-Z GSM plane, suggesting ‘protrusions’ of plasma sheet into the lobes. The boundary layer current polarity is, as expected, into the ionosphere in the midnight to dawn local time sector, and outward near dusk. Current sheet thicknesses and velocities are essentially independent of plasma sheet expansion or thinning, having typical values of 1500 km and 20–40 km/s respectively. Characteristic boundary layer current densities are about 10 nanoamps per square meter.     

Driven reconnection in the near-Earth plasma sheet

In some recent MHD simulations of the near-Earth plasma sheet we studied onset and evolution of reconnection due to non-linear resistive instabilities. In our present contribution we show that these non-linear instabilities can be amplified significantly by inflow through the plasma sheet boundary and we discuss the consequences of that driving mechanism on the global dynamics of the instabilities. For high magnetic Reynolds numbers we find thin current sheets developing.     

Interaction of shocks with a current sheet and reconnection in the solar corona

Interaction of shocks with a current sheet is investigated within a 2D MHD model based on an improved FCT numerical scheme. Basic parameters of the problem are chosen to correspond to situations in the solar corona with low plasma β and moderate shock strength. Slow and fast MHD shocks are introduced with shock normal parallel to magnetic field lines. The interaction with the current sheet causes distortion of the shock front and this distorts the magnetic field lines and generates electric current. Large current densities are generated especially when the fast MHD shock becomes the intermediate MHD shock at the current sheet. Then peak values of the current density are about 3–4 times larger than the initial undisturbed values in the current sheet.     

Plasma sheet oscillations and their relation to substorm development: Cluster and double star TC1 case study

We examined two consecutive plasma sheet oscillation and dipolarization events observed by Cluster in the magnetotail, which are associated with a pseudo-breakup and a small substorm monitored by the IMAGE spacecraft. Energy input from the solar wind and an associated enhancement of the cross-tail current lead to current sheet thinning and plasma sheet oscillations of 3–5 min periods, while the pseudo-breakups occur during the loading phase within a spatially limited area, accompanied by a localized dipolarization observed by DSP TC1 or GOES 12. That is, the so-called “growth phase” is a preferable condition for both pseudo-breakup and plasma sheet oscillations in the near-Earth magnetotail. One of the plasma sheet oscillation events occurs before the pseudo-breakup, whereas the other takes place after pseudo-breakup. Thus there is no causal relationship between the plasma sheet oscillation events and pseudo-breakup. As for the contribution to the subsequent small substorm, the onset of the small substorm took place where the preceding plasma sheet oscillations can reach the region.     

Numerical study of magnetic reconnection possibly occurring near heliospheric current sheet

The third-order accurate upwind compact difference scheme has been applied for the numerical study of the magnetic reconnection driven by a plasma blob impacting the heliospheric current sheet, under the framework of the two-dimensional compressible magnetohydrodynamics. The results show that the driven reconnection near the current sheet could occur in about 10–30 min for the interplanetary high magnetic Reynolds number, R_M = 2000–10,000, a stable magnetic reconnection structure can be formed in hour order of magnitude, and there appear some basic properties such as the multiple X-line reconnections, vortex structures, filament current systems, splitting and collapse of the high-density plasma blob. These results are helpful in understanding and identifying the magnetic reconnection phenomena possibly occurring near the heliospheric current sheets.     

Study of three dimensional structure of the fast convection flow in the plasma sheet by MHD simulations on the basis of spontaneous fast reconnection model

Three dimensional structure of the fast convection flow in the plasma sheet is examined using magnetohydrodynamic (MHD) simulations on the basis of spontaneous fast reconnection model. The fast flow observed in the near-Earth magnetotail is one of the key phenomena in order to understand the causal relationship between magnetic substorm and magnetic reconnection. In this paper, we focus on this earthward fast flow in the near-Earth magnetotail. Our previous studies have shown that the fast reconnection produces the Alfvénic fast reconnection outflow and drastic magnetic field dipolarization in the finite extent. In this paper, the results of our simulations are compared with those of the in-situ observations in the geomagnetotail. They have consistent temporal profiles of the plasma quantities. It is suggested that the fast convection flows are caused by spontaneous fast reconnection.     

Observations of magnetohydrodynamic turbulence in the 3D heliosphere

The solar wind is a high Reynolds’ number plasma flow of solar origin that permeates the whole heliosphere. It is also the only accessible medium in which to study collisionless magnetohydrodynamic turbulence performing direct measurements. This represents a topic of fundamental importance to both plasma physics and astrophysics. During the past decades, in situ observations on the ecliptic and at high heliographic latitudes have been very valuable to shed some light on the intricate nature of space plasma turbulence. In this brief review, we will mainly describe the evolution experienced by the turbulence as the solar wind expands into the interplanetary space. We will also address implications due to different processes of local generation of turbulence which might be at work on the ecliptic and at high latitude. Moreover, the fact that solar wind fluctuations are not isotropic and poorly single scale-invariant, two of the fundamental hypotheses at the basis of Kolmogorov’s theory (K41), will give us the possibility to discuss also the relevance of intermittency in the study of space plasma turbulence.     

Multi-point observations of earthward fast flow in the plasma sheet by virtual satellites located in the MHD simulation domain

Time profiles of some physical values in earthward fast flows in the plasma sheet are observed at three dimensionally different positions by employing virtual satellites located in the three-dimensional magnetohydrodynamic simulation domain, and these simulations are done on the basis of the spontaneous fast reconnection model. In the spontaneous fast reconnection evolution, the width of the flow channel is narrow in the dawn-dusk direction, and it does not spread until the plasma collides with the magnetic loop. The enhancements in B_z and V_x are larger at the center of the fast flow channel than those at its dawn and dusk edges, reflecting the differences in the reconnection rate in the diffusion region. The enhancement in V_x is shorter near the plasma sheet boundary layer than that near the neutral sheet, reflecting the changes in the thickness of the flow channel.