Magnetic Flux Tube Volume Research Articles

To the Interchange Instability Criterion in the Magnetosphere in the Presence of Velocity Shear

AbstractIn this paper, we address the issue of interchange instability excitation criterion in the magnetospheric plasma in the presence of the velocity shear using a magnetohydrodynamic approach. We conducted our analysis for the arbitrary β plasma configuration using a WKB approximation for wavelengths, λ, much smaller than the characteristic plasma inhomogeneity scale, L, and found two branches of waves. These two wave branches can exist due to the plasma velocity shear and one branch can be unstable for arbitrary angles between the plasma entropy parameter and magnetic flux tube volume gradients. The implications of these results for magnetospheric physics as well as comparison of our results with corresponding analysis of other authors are discussed.

On application of asymmetric Kan-like exact equilibria to the Earth magnetotail modeling

Abstract. A specific class of solutions of the Vlasov–Maxwell equations, developed by means of generalization of the well-known Harris–Fadeev–Kan–Manankova family of exact two-dimensional equilibria, is studied. The examined model reproduces the current sheet bending and shifting in the vertical plane, arising from the Earth dipole tilting and the solar wind nonradial propagation. The generalized model allows magnetic configurations with equatorial magnetic fields decreasing in a tailward direction as slow as 1∕x, contrary to the original Kan model (1∕x3); magnetic configurations with a single X point are also available. The analytical solution is compared with the empirical T96 model in terms of the magnetic flux tube volume. It is found that parameters of the analytical model may be adjusted to fit a wide range of averaged magnetotail configurations. The best agreement between analytical and empirical models is obtained for the midtail at distances beyond 10–15 RE at high levels of magnetospheric activity. The essential model parameters (current sheet scale, current density) are compared to Cluster data of magnetotail crossings. The best match of parameters is found for single-peaked current sheets with medium values of number density, proton temperature and drift velocity.

Experimental Study of the Plasmasphere Boundary Layer Using MAGION 5 Data

AbstractThe in situ cold plasma measurements onboard MAGION 5 were carried out with very good time resolution, and this permitted to analyze thin plasmasphere boundary layer (PBL) near the plasmapause. In this layer the plasma density N is decreasing exponentially with L: N~exp((LPP − L)/WB), where WB corresponds to the characteristic width of the PBL, the distance in L within which the density varies by a factor of e, and LPP is the position of the plasmapause. The density in the boundary layer is inversely proportional to the volume of the unit magnetic flux tube, whereas its width is proportional to the volume of magnetic flux tube. The characteristic width of the PBL linearly depends on the time elapsed since the most recent maximum value of KP. Empirical relation for the dependence of the PBL width on most recent maximum value of KP and on the lapse time between this maximum and the plasmapause observations is proposed.

Perturbation of the magnetic field in the Earth’s magnetosphere due to plateau creation in the radial distribution of plasma pressure

The nonlinear perturbation of a dipole field by a system of transverse currents, which arises due to the radial pressure distribution when the pressure is almost independent of the radial distance, is analyzed. This distribution of pressure was observed in the experiment. The radial dependences of the magnetic field depression, transverse current density, and volumes of magnetic flux tubes have been obtained at different values of the plasma parameter via nonlinear simulation. It is shown that a dependence of the volume of magnetic flux tube on the radial distance can change and a region of the negative gradient of volume can appear at some plasma-parameter values.

Anharmonic oscillatory flow braking in the Earth's magnetotail

AbstractPlasma sheet bursty bulk flows often oscillate around their equilibrium position at about 10 RE downtail. The radial magnetic field, pressure, and flux tube volume profiles usually behave differently earthward and tailward of this position. Using data from five Time History of Events and Macroscale Interactions during Substorms (THEMIS) probes, we reconstruct these profiles with the help of an empirical model and apply thin filament theory to show that the oscillatory flow braking can occur in an asymmetric potential. Thus, the thin filament oscillations appear to be anharmonic, with a power spectrum exhibiting peaks at both the fundamental frequency and the first harmonic. Such anharmonic oscillatory braking can explain the presence of the first harmonic in Pi2 pulsations (frequency doubling), which are simultaneously observed by magnetometers on the ground near the conjugate THEMIS footprints.

Dipole magnetic-field disturbance and generation of current systems by asymmetric plasma pressure

Nonlinear disturbance of the dipole field by nonaxisymmetric plasma pressure distribution was analyzed under the assumption of magnetostatic equilibrium for finite values of the plasma parameter at the pressure maximum area. The distributions of isolines of the constant value of magnetic-field component BZ and the volume of magnetic flux tube in the equatorial plane were obtained. At a finite plasma pressure, local minima and maxima of the magnetic field are formed. The formation of these local maxima and minima leads to the formation of contours (not surrounding the Earth) Bmin = const, where Bmin is the minimum magnetic field on the magnetic field line. This changes the direction of the gradient of the volume of the magnetic flux tube. The configuration of appearing field-aligned currents was determined. The results obtained are discussed in terms of their use in explaining a number of effects observed in the Earth’s magnetosphere.

The quiet evening auroral arc and the structure of the growth phase near‐Earth plasma sheet

AbstractThe plasma pressure and current configuration of the near‐Earth plasma sheet that creates and sustains the quiet evening auroral arc during the growth phase of magnetospheric substorms is investigated. We propose that the quiet evening arc (QEA) connects to the thin near‐Earth current sheet, which forms during the development of the growth phase enhancement of convection. The current sheet's large polarization electric fields are shielded from the ionosphere by an Inverted‐V parallel potential drop, thereby producing the electron precipitation responsible for the arc's luminosity. The QEA is located in the plasma sheet region of maximal radial pressure gradient and, in the east‐west direction, follows the vanishing of the approximately dawn‐dusk‐directed gradient or fold in the plasma pressure. In the evening sector, the boundary between the Region1 and Region 2 current systems occurs where the pressure maximizes (approximately radial gradient of the pressure vanishes) and where the approximately radial gradient of the magnetic flux tube volume also vanishes in an inflection region. The proposed intricate balance of plasma sheet pressure and currents may well be very sensitive to disruption by the arrival of equatorward traveling auroral streamers and their associated earthward traveling dipolarization fronts.

On near‐tail bubble penetration into geosynchronous altitude

Dipolarization of the magnetic field at the near‐Earth tail is usually associated with the local reduction of pV5/3 compared to that of the background, where p is the plasma pressure and V is the volume of the unit magnetic flux tube. This can be interpreted as a bubble, which can propagate earthward by the interchange process. How deep such a bubble can penetrate earthward, and what is the critical factor are critical questions that need to be answered. In this paper, we examine these issues by comparing near‐tail observations by inner probes of THEMIS with geosynchronous magnetic observations by GOES. We identified a number of bubble events associated with near‐tail dipolarization, which we call “tail bubble,” and checked geosynchronous disturbances. We find a statistical trend that geosynchronous disturbance is more likely to occur when associated with (or when hit by) an earthward moving tail bubble with a more‐depleted pV5/3. We estimated the background pV5/3 profile statistically and used it to determine expected equilibrium (or stop) positions for earthward moving bubbles where the bubble's pV5/3 is equal to that of the background. Statistically, we find that the equilibrium position is more inward for tail bubbles with a lower pV5/3, for which the probability of causing geosynchronous disturbance is higher. For example, the probability of a tail bubble being associated with geosynchronous disturbance is 75% if the bubble's equilibrium position is <8 RE. However, for all the events studied here, the bubble equilibrium positions are still outside the geosynchronous altitude. Although this result may be subject to change due to the uncertainty in estimating pV5/3 and the limited number of the events identified near geosynchronous altitude, we suggest that an overshooting of the penetrating bubbles beyond equilibrium positions is a possible explanation.

Simulation of the interchange instability in a magnetospheric substorm site

Abstract. We perform modeling of the interchange instability driven by longitudinal pressure asymmetry in the region of the pressure buildup that forms in the inner magnetosphere at the substorm growth phase. The simulation refers to the dawnward side of the Harang discontinuity and times after Bz IMF turning northward. The solution for the equilibrium state indicates tailward flows associated with vortices, which is in agreement with a previous finding of Ashour-Abdalla et al. (1999, 2002). We show that in the regions of equilibrium field-aligned currents (FACs), small initial perturbations in pVγ (p is the isotropic plasma pressure, V is the unit magnetic flux tube volume, γ=5/3 the adiabatic exponent), set up as ripples inclined to azimuth, grow in time. For the background FAC of ~10-6 A/m2, the linear growth rate of the instability is ~6 min. Starting from the 12th min of evolution, the perturbations exhibit nonlinear deformations, develop undulations and front steepening. An interesting peculiarity in the distribution of the associated small-scale FACs is that they become asymmetric with time. Specifically, the downward currents are more localised, reaching densities up to 15×10-6 A/m2 at the nonlinear stage. The upward FACs are more dispersed. When large enough, these currents are likely to produce the aurora. We also run our simulation for the initial perturbations of large transverse scales in order to demonstrate that the interchange instability can be responsible for pressure and cross-tail current spatial variations of great extent.

Field-aligned current mapping and the problem of the generation of magnetospheric convection

The solution of the problem of the generation of large-scale two-cell magnetospheric convection requires the understanding of the nature of Region 1 currents of Iijima and Potemra [The amplitude distribution of field-aligned currents at northern high latitudes observed by Triad. J. Geophys. Res. 81 (13), 2165–2174, 1976]. The azimuthal distribution of Region 1 currents is analyzed. The picture of field-aligned currents is mapped to the equatorial plane using Tsyganenko-96 and Tsyganenko-2001 magnetic field models. It is shown that the majority of Region 1 currents is mapped to the plasma sheet. The possible contribution of boundary layer processes to the generation of Region 1 currents is evaluated. Additional support of the action of the mechanism of “magnetospheric topology” generation of magnetospheric convection is obtained. Field-aligned currents in accordance with this mechanism are generated due to the existence of the plasma pressure gradients along the isosurfaces of magnetic flux tube volume. Such gradients appear due to the day–night magnetospheric asymmetry.

Radial plasma pressure gradients in the high latitude magnetosphere as sources of instabilities leading to the substorm onset

Various types of instabilities have been proposed as sources of inner magnetosphere substorm expansion phase onset. Distribution of plasma pressure in the plasma sheet, β parameter, volume of magnetic flux tube are the key parameters for understanding the processes leading the instability development. Here, the radial distribution of plasma pressure was recovered using the low-altitude polar-orbiting Aureol-3 precipitating particle data. Corresponding variations in the magnetic pressure and in the volume of magnetic flux tube were estimated using Tsyganenko 96 magnetic field model. It is shown that development of an instability responsible for the substorm expansion phase onset takes place in the regions of low β or at the boundary of the regions of high and low β. A possible role of the flute-like (interchange-like) instabilities is investigated. It is shown that the obtained profiles of radial plasma pressure gradients apparently are not sharp enough to develop the instability related to radial plasma pressure gradients. The role of the instability related to the existence of the azimuthal plasma pressure gradients is discussed. Such an instability can develop when the density of the field-aligned current reaches a definite threshold value. The instability develops faster in the region of upward field-aligned current, where the existing field-aligned potential drop leads to the magnetosphere–ionosphere decoupling.

Pressure balance inconsistency exhibited in a statistical model of magnetospheric plasma

While quantitative theories of plasma flow from the magnetotail to the inner magnetosphere typically assume adiabatic convection, it has long been understood that these convection models tend to overestimate the plasma pressure in the inner magnetosphere. This phenomenon is called the pressure crisis or the pressure balance inconsistency. In order to analyze it in a new and more detailed manner we utilize an empirical model of the proton and electron distribution functions in the near‐Earth plasma sheet (−50 RE < X < −10 RE), which uses the Tsyganenko [1989] magnetic field model and a plasma sheet representation based upon several previously published statistical studies. We compare our results to a statistically derived particle distribution function at geosynchronous orbit. In this analysis the particle distribution function is characterized by the isotropic energy invariant λ = EV2/3, where E is the particle's kinetic energy and V is the magnetic flux tube volume. The energy invariant is conserved in guiding center drift under the assumption of strong, elastic pitch angle scattering. If, in addition, loss is negligible, the phase space density f(λ) is also conserved along the same path. The statistical model indicates that f(λ, ) is approximately independent of X for X ≤ −35 RE but decreases with increasing X for X ≥ −35 RE. The tailward gradient of f(λ, ) might be attributed to gradient/curvature drift for large isotropic energy invariants but not for small invariants. The tailward gradient of the distribution function indicates a violation of the adiabatic drift condition in the plasma sheet. It also confirms the existence of a “number crisis” in addition to the pressure crisis. In addition, plasma sheet pressure gradients, when crossed with the gradient of flux tube volume computed from the Tsyganenko [1989] magnetic field model, indicate Region 1 currents on the dawn and dusk sides of the outer plasma sheet.

Interchange instability in the presence of the field‐aligned current: Application to the auroral arc formation

We have revisited the ideal MHD interchange instability for the case of the nonaligned gradients of the plasma pressure p and unit magnetic flux tube volume V, i.e., the background field‐aligned current (FAC) included. Several possibilities of a directional difference between ∇p and ∇V in the Earth's plasma sheet are considered. The growth of an interchange perturbation leading to the pressure‐gradient‐driven FAC striation is illustrated through numerical simulation in a simple model of the nightside region 1 FAC by Karty et al. [1984] and Yang et al. [1994]. It is shown that the FAC is being striated by the interchange process on a timescale from minutes to tens of minutes. The application to the quiet time discrete arc formation is discussed.

Substorm and convection bay compared: Auroral and magnetotail dynamics during convection bay

Using observations from eight spacecraft and a ground network, we study two subsequent bay‐like disturbances on December 10, 1996, initiated by southward interplanetary magnetic field intervals, one being a classic substorm and another one a convection bay. Both events showed enhanced convection and Dst decreases as well as Pi2 pulsations in the auroral zone. Contrasting to the well‐defined substorm signatures of the first event (poleward auroral expansion, substorm current wedge, strong particle injection to 6.6 RE) resulting from energy loading/unloading and near‐Earth reconnection in the tail, these signatures were virtually absent during the convection bay (CB). Distinctive features of the CB event were the same as those during the Steady Magnetospheric Convection intervals: (1) wide double oval at the nightside; (2) thick plasma sheet, relaxed lobe field, and enhanced magnetic flux closure (large Bz) and multiple bursty earthward flows (BBFs) in the midtail; (3) sporadic narrow soft injections to 6.6 RE; (4) auroral streamers associated with both BBFs and narrow injections. We emphasize the development of multiple and sporadic auroral streamers which start at the poleward oval boundary, propagate equatorward (in 3–8 min) and end with a long‐duration bright spot in the equatorward oval. We conclude that the plasma sheet and auroral dynamics during the convection bay was formed by sporadic narrow (a few RE wide) plasma streams (plasma bubbles) which transported the plasma sheet material from the distant magnetotail reconnection regions to the inner magnetosphere and may significantly contribute to the magnetospheric circulation on the nightside. We modeled the nightside tail configuration using magnetotail magnetic observations and low‐altitude particle boundaries to show that at the beginning of the convection bay the increase of magnetic flux tube volume with distance was small in the midtail. Therefore the “pressure crisis” in the tail was significantly reduced during the convection bay, and the efficient earthward transport by sporadic narrow plasma streams was probably able to balance the magnetospheric circulation to avoid the large‐scale instability of the magnetotail.

Thin current sheets and magnetotail dynamics

We investigate the formation of thin current sheets in Earth's magnetotail and the stability of the resulting plasma sheet structure. In the study of current sheet formation we concentrate on the mechanism based on a large gradient of the magnetic flux tube volume and derive a general expression for maximum current density using quasi‐static magnetotail theory. That expression relates the amount of magnetic flux transferred to the magnetotail to the maximum current density in the near‐Earth tail region. The analysis also includes the effects of varying solar wind plasma pressure and Mach number. The stability analysis addresses the resistive tearing mode, and how the presence of a thin current sheet changes the dispersion relation is investigated. For an infinitely extended double‐structured sheet the tearing dispersion curve has a single peak, similar to the dispersion relation of a sheet with a single scale. A qualitative argument suggests that a thin current sheet of finite length might lead to a double‐peaked dispersion curve. Several possible consequences of these results are discussed.

Auroral bulge formation as the result of isoline mapping of magnetic flux tube volume

The process of auroral bulge formation is modeled taking into account disruption of the near Earth tail current sheet and dipolarization of the magnetic field. The disruption of the near Earth tail current results in a considerable increase of magnetic flux tube volumes in that region. As a result, magnetic flux tube volume isolines in the equatorial plane move earthward. Their mapping to ionospheric altitudes leads to a configuration having a characteristic bulge near midnight. Thus, auroral bulge formation may be considered as the result of dipolarization of near midnight magnetic field. The increase in magnetic tube volume causes the decrease of particle pressure and formation of a pressure hole in the dipolarization region. On the east and west borders of such a region large plasma pressure gradients along magnetic flux tube volume isolines arise. Such gradients lead to the generation of powerful field-aligned currents of the Birkeland current wedge. The strength of such currents are estimated and compared with observations. Mechanisms of current disruption and field line dipolarization are discussed.

Entropy antidiffusion instability and formation of a thin current sheet during geomagnetic substorms

In our recent study of the equilibrium configuration of the near‐Earth magnetotail, it is found that a steeper profile of entropy function S leads to the formation of a thinner current sheet. Here S = pVγ, where p is the plasma pressure and V is the volume of a unit magnetic flux tube. In the presence of density gradient at the edges of the current sheet, the lower‐hybrid‐drift instability may lead to pressure diffusion. Since the pressure generally decreases and the entropy function S increases tailward, the diffusion of plasma pressure results in a steepening, or antidiffusion, of the entropy profile. This, in turn, leads to a thinner current sheet, which enhances the pressure diffusion. This positive feedback process is called the entropy antidiffusion instability. On the basis of MHD simulations with a pressure diffusion, we find that the entropy antidiffusion instability leads to a further thinning of the near‐Earth current sheet and the onset of dipolarization of near‐Earth geomagnetic field lines. The growth rate of the instability is linearly proportional to the diffusion coefficient. The growth time at the final stage for the formation of a very thin current sheet is ∼1 min. This instability may explain the observed explosive growth phase of substorms and the onset of dipolarization of geomagnetic field lines.

Azimuthal hot plasma pressure gradients and dawn-dusk electric field formation

Abstract The effects of hot plasma pressure gradients in the high latitude magnetosphere are analysed. It is shown that such a mechanism may in fact be responsible for Region 1 field-aligned currents and for the dawn-dusk electric field. The estimated azimuthal gradients in the plasma pressure may account for the observed field-aligned currents and also give the opportunity to determine the day-night plasma pressure changes along isosurfaces of magnetic flux tube volume. These pressure changes are then compared with experimentally measured pressure distribution and it is shown that the day-night plasma change, in the high latitude magnetosphere, may be high enough to sustain Region 1 currents. The closure of these currents in the high latitude magnetosphere may in turn be responsible for the dawn-dusk electric field and the dawn-dusk potential drop in the inner plasma sheet regions. The influence of the IMF on the magnetostatically equilibrium inner magnetospheric currents may qualitatively explain the IMF control of the dawn-dusk electric field and magnetospheric activity.

The inner magnetosphere source of dawn-dusk electric field and magnetospheric dynamics

The qualitative theory of the formation of inner magnetosphere dawn-dusk electric field based only on the assumption of the magnetostatic equilibrium in the asymmetric plasma trap was developed. The theory associates the generation of Region 1 field-aligned currents with the topology of magnetic field in the transition region where the magnetic field lines change from dipolar in the deep inner magnetosphere to stretched in the magnetotail. The mechanism of the plasma pressure gradients can be used to explain qualitatively the inner magnetosphere source of dawn-dusk electric field and the dynamics of substorm electric fields and currents. The antisunward stretching of the magnetic flux tube volume isolines in the equatorial plane during substorm growth phase brings to the increase of Region 1 field-aligned currents formed by the azimuthal plasma pressure gradients. The disruption of the cross-tail current and the dipolarization of the magnetic field lines causes the increase of magnetic flux tube volumes in the limited plasma sheet region. That makes possible to explain the formation of the nighttime pressure hole and the substorm current wedge.

Details of current disruption and diversion in simulations of magnetotail dynamics

Properties of current disruption and diversion are investigated on the basis of resistive MHD simulations which include the inner tail region with the transition toward a dipole field and the dynamic formation of a thin current sheet in the inner tail. As in earlier simulations, magnetotail instability leads to reconnection and plasmoid formation and ejection, accompanied by features of the substorm current wedge. In contrast to earlier simulations of the breakup of a thick current sheet, the presence of the thin current sheet leads to a much faster evolution on the timescale of few minutes and to larger electric fields (up to 20 mV/m), concentrated mostly in the dipolarizing region earthward of the reconnection site. The fast growth is relatively insensitive to the resistivity model used. The current “disruption” is largely a consequence of an expansion of the near‐Earth current sheet, associated with the dipolarization. It starts well earthward of the reconnection site in association with a pileup of magnetic flux and propagates tailward. Field‐aligned currents of region 1 type (toward the Earth on the dawnside and away on the duskside) at the near‐Earth boundary are found to increase both during the driven phase of the thin current sheet formation and during the energy release and current disruption phase. They result from a diversion of perpendicular into parallel currents, which is associated with a gradient of the magnetic flux tube volume directed away from midnight at the flank edges of the dipolarization region. Locally, the current diversion takes place earthward of the reconnection site, predominantly in shear layers above and below the neutral sheet rather than close to the neutral sheet. The peaks of the field‐aligned current densities associated with the substorm wedge do not follow field lines very closely, because of the presence of strong perpendicular currents, so that care must be taken in using these features for a mapping between the Earth and the equatorial plane.