Role of interchange instability in flux transfer event origin

It is shown that the interaction of the interplanetary magnetic field (IMF), when it has southward component, with the geomagnetic field leads to the formation of an enhanced pressure layer (EPL) near the magnetopause. Currents flowing on the boundary between the EPL and the magnetosheath prevent the IMF from penetrating the magnetosphere. However, the outward boundary of the EPL is unstable. The interchange instability permanently destroys the EPL. Separate filaments of the EPL move away from the Earth. New colder plasma of the magnetosheath with a frozen magnetic field replaces the hotter EPL plasma, and the process of EPL formation and destruction repeats itself.The instability increment is calculated for various magnitudes of the azimuthal wave number, k_y, and curvature radius of the magnetic field lines, R_c. The disturbances with R⁻¹_e\leqk_y\leq4R⁻¹_e (where R_e is the Earth’s radius) and R_c\simeqR_e are the most unstable.A possible result of the interchange instability of the EPL may be patchy reconnection, displayed as flux transfer events (FTEs) near the magnetopause.     

Compressional wave events in the dawn plasma sheet observed by Interball-1

Compressional waves with periods greater than 2 min (about 10–30 min) at low geomagnetic latitudes, namely compressional Pc5 waves, are studied. The data set obtained with magnetometer MIF-M and plasma analyzer instrument CORALL on board the Interball-1 are analyzed. Measurements performed in October 1995 and October 1996 in the dawn plasma sheet at −30 R_E ≤ X_GSM and |Z_GSM| ≤ 10 R_E are considered. Anti-phase variations of magnetic field and ion plasma pressures are analyzed by searching for morphological similarities in the two time series. It is found that longitudinal and transverse magnetic field variations with respect to the background magnetic field are of the same order of magnitude. Plasma velocities are processed for each time period of the local dissimilarity in the pressure time series. VeloCity disturbances occur mainly transversely to the local field line. The data reveal the rotation of the veloCity vector. Because of the field line curvature, there is no fixed position of the rotational plane in the space. These vortices are localized in the regions of anti-phase variations of the magnetic field and plasma pressures, and the vortical flows are associated with the compressional Pc5 wave process. A theoretical model is proposed to explain the main features of the nonlinear wave processes. Our main goal is to study coupling of drift Alfven wave and magnetosonic wave in a warm inhomogeneous plasma. A vortex is the partial solution of the set of the equations when the compression is neglected. A compression effect gives rise to a nonlinear soliton-like solution.     

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 B _Z 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) B _min = const, where B _min 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 effect of gravity on the stability of a line-tied coronal magnetohydrostatic equilibrium

Abstract

The magnetohydrodynamic stability of a class of magnetohydrostatic equilibria is investigated. The effect of gravity is included as well as the stabilising influence of the dense photospheric line-tying.

Although the two-dimensional equilibria exhibit a catastrophe point, when the ratio of plasma pressure to magnetic pressure exceeds a critical value, arcade structures, with both footpoints connected to the photosphere, become unstable to three-dimensional disturbances before the catastrophe point is reached.

Numerical results for field lines that are open into the solar corona suggest that they are completely stable. Although there is no definite proof of stability, this would allow the point of non-equilibrium to be reached.     

Characteristics of Pc4–5 pulsations obtained using the method of bistatic backscatter of HF radio waves,the EISCAT HF heating facility,and ground-based magnetometers

The results of studying the Pc4–5 pulsation parameters based on the method of bistatic backscatter of radio waves, using the EISCAT/Heating HF facility (Tromsø, Norway) and IMAGE ground-based magnetometers (Scandinavia), are presented. The observations were performed during the morning hours on October 3, 2006, when a substorm developed on the nightside. An analysis of the observational data obtained from 1000 to 1020 UT indicated that wave-like disturbances with periods corresponding to Pc4–5 pulsations (80–240 s) existed at that time. The variations in the full vector of the ionospheric irregularity motion and the electric field strength in an artificially disturbed high-latitude ionospheric F region has been reconstructed based on simultaneous Doppler observations on two paths. A general conformity is observed among the time variations in Pc4–5 pulsations in the magnetic and ionospheric data: between the velocity amplitude (|V|) and the X component of the Earth’s magnetic field and between the irregularity motion azimuth and the Y component. Large-scale waves, corresponding to the natural resonances of magnetic field lines (small values of the azimuthal number |m| ～ 2–4), and small-scale waves (large values |m| ～ 17–20) were simultaneously registered during the experiment based on magnetic data. It has been indicated that the periods of wave-like processes registered using the method of bistatic backscatter and ground-based magnetometers were in agreement with one another. The formation of wave-like processes is explained by the nonstationary impact of the solar wind and IMF on the Earth’s magnetosphere. The variations in the IMF, according to the ACE satellite measurements, were characterized by a sharp increase in the solar wind plasma dynamic pressure that occurred at about 09 UT on October 3, 2006, and was accompanied by rapid polarity reversals of the north-ward-southward (B _z) and transverse (B _y) IMF components.     

Geomagnetotail dynamics: Different types of equilibriums and transitions between them

Two time scales are distinguished in the geomagnetotail dynamics. The small scale (T ₁) corresponds to disturbances propagating in the tail lobes, which have a relatively strong magnetic field and low plasma density. The larger scale (T ₂) corresponds to plasma motions in the plasma sheet and has a relatively weak magnetic field and a relatively higher density. A disturbance, which is initiated by a localized burst of magnetic reconnection and appears in the geomagnetotail on the time scale T ₁, generates the upset of equilibrium in the plasma sheet zones with intermediate spatial dimensions (about R _E). The theoretical considerations and numerical simulation indicate that the relaxation process, which subsequently proceeds on the larger time scale (T ₂), results in the appearance of extremely thin embedded current sheets and in the generation of fast plasma flows. This process gives an effective mechanism by which the magnetic energy stored in the geomagnetotail is transformed into the plasma flow kinetic energy. Such fast flows can also generate eddy plasma motions on smaller spatial scales. On the one hand, fast MHD components of this process carry a disturbance in other plasma sheet zones, where new magnetic reconnection bursts can originate at a large distance from the zone of an initial nonlinear disturbance. As a result, new recurrent processes of relaxation originate on the T ₂ time scale. Alternation originating in such a way is apparently the characteristic feature of eddy disturbances actually observed in the plasma sheet.     

Hydromagnetic waves in rapidly rotating spherical shells generated by poloidal decay modes

Abstract

This paper presents the first attempt to examine the stability of a poloidal magnetic field in a rapidly rotating spherical shell of electrically conducting fluid. We find that a steady axisymmetric poloidal magnetic field loses its stability to a non-axisymmetric perturbation when the Elsasser number A based on the maximum strength of the field exceeds a value about 20. Comparing this with observed fields, we find that, for any reasonable estimates of the appropriate parameters in planetary interiors, our theory predicts that all planetary poloidal fields are stable, with the possible exception of Jupiter. The present study therefore provides strong support for the physical relevance of magnetic stability analysis to planetary dynamos. We find that the fluid motions driven by magnetic instabilities are characterized by a nearly two-dimensional columnar structure attempting to satisfy the Proudman-Taylor theorm. This suggests that the most rapidly growing perturbation arranges itself in such a way that the geostrophic condition is satisfied to leading order. A particularly interesting feature is that, for the most unstable mode, contours of the non-axisymmetric azimuthal flow are closely aligned with the basic axisymmetric poloidal magnetic field lines. As a result, the amplitude of the azimuthal component of the instability is smaller than or comparable with that of the poloidal component, in contrast with the instabilities generated by toroidal decay modes (Zhang and Fearn, 1994). It is shown, by examining the same system with and without fluid inertia, that fluid inertia plays a secondary role when the magnetic Taylor number T_m ? 10⁵. We find that the direction of propagation of hydromagnetic waves driven by the instability is influenced strongly by the size of the inner core.     

Convection in a rotating magnetic system and Taylor's constraint

Abstract

A system is considered in which electrically conducting fluid is contained between two rigid horizontal planes and bounded laterally by a circular cylinder. The fluid is permeated by a strong azimuthal magnetic field. The strength of the field increases linearly with distance from the vertical axis of the cylinder, about which the entire system rotates rapidly. An unstable temperature gradient is maintained by heating the fluid from below and cooling from above. When viscosity and inertia are neglected, an arbitrary geostrophic velocity, which is aligned with the applied azimuthal magnetic field and independent of the axial coordinate, can be superimposed on the basic axisymmetric state. In this inviscid limit, the geostrophic velocity which occurs at the onset of convection is such that the net torque on geostrophic cylinders vanishes (Taylor's condition). The mathematical problem which describes the ensuing marginal convection is nonlinear, and was discussed previously for the planar case by Soward (1986). Here new features are isolated which result from the cylindrical geometry. New asymptotic solutions are derived valid when Taylor's condition is relaxed to include viscous effects.     

An asymptotic model for resistive instability in the Earth's outer core

Abstract

Numerical work indicates that resistive instability may be the dominant mode of instability in the Earth's outer core for realistic core parameter regimes. In this paper, we assume that the Elsasser number is large in order to obtain an asymptotic analysis of resistive instability in an electrically conducting fluid confined to a rotating cylindrical shell of infinite extent in the axial direction. The dimensionless equations of motion are linearized about an ambient magnetic field which is purely azimuthal and depends only on the cylindrical radial variable. Applying the theory of ordinary differential equations with a large parameter, we obtain an asymptotic approximation to the solution. Relatively simple analytic expressions for the complex frequencies are obtained by applying the boundary conditions for insulating boundaries at the cylindrical sidewalls and then assuming that the ambient magnetic field vanishes at one or both of those sidewalls. The results appear to be consistent with previous numerical work.     

Variations in the polar precipitation equatorward boundary during the interaction between the Earth’s magnetosphere and solar wind streams from isolated solar sources

The position of the auroral luminosity equatorward boundary during the interaction between the Earth’s magnetosphere and isolated solar wind streams from different solar sources has been statistically studied based on the ground and satellite observations of auroras. These studies continue the series of the works performed in order to develop the technique for predicting auroras based on the characteristics of the interplanetary medium and auroral disturbances. The dependences of the minimal position of the auroral luminosity equatorward boundary (Φ′) on the values of the azimuthal component of the interplanetary electric field (E _y ) and AL indices of magnetic activity, averaged over 6 and 24 h, are presented. The distribution limits for each type of isolated solar wind streams on the Φ′-E _y and Φ′-AL planes have been determined.     

On the effects of a bumpy core-mantle interface

Motivated by the high degree of correlation between the variable parts of the magnetic and gravitational potentials of the Earth discovered by Hide and Malin (using a harmonic analysis approach and utilizing the geomagnetic data) when one field is suitably displaced relative to the other, Moffatt and Dillon (1976) studied a simple planar model in an attempt to find a quantitative explanation for the suggestion that this high degree of correlation may be due to the influences produced by bumps on the core-mantle interface. Moffatt and Dillon assumed that the core-mantle interface was z = η(x) where |?η/?χ| ? 1 and such that in the core [z < η(x)] a uniform flow (U₀, 0, 0) prevails in the presence of a uniform ‘toroidal’ field (B₀, 0, 0); (here z is the vertical coordinate and x is the eastward distance). The whole system rotates uniformly about the vertical with angular velocity Ω. The present work extends the model discussed by Moffatt and Dillon to include a horizontal component of angular velocity Ω_H and a uniform small poloidal field B_p. In addition, the uniform toroidal field is here replaced by one which vanishes everywhere in the mantle and increases linearly, from zero on the interface, with z. It is shown that the presence of Ω_H and B_p, together with the present choice of toroidal magnetic field, has a profound effect both on the correlation between the variable parts of the magnetic and gravitational fields of the Earth, and on how far the disturbances caused by the topography of the interface [which is necessarily three-dimensional i.e. z = η(x, y) here] can penetrate into the liquid core. In particular it is found that the highest value of the correlation function is +0.79 which corresponds to a situation in which the magnetic potential is displaced both latitudinally and longitudinally relative to the gravitational potential.     

Thermal and magnetic instabilities in a rapidly rotating fluid sphere

Abstract

A linear analysis is used to study the stability of a rapidly rotating, electrically-conducting, self-gravitating fluid sphere of radius r ₀, containing a uniform distribution of heat sources and under the influence of an azimuthal magnetic field whose strength is proportional to the distance from the rotation axis. The Lorentz force is of a magnitude comparable with that of the Coriolis force and so convective motions are fully three-dimensional, filling the entire sphere. We are primarily interested in the limit where the ratio q of the thermal diffusivity κ to the magnetic diffusivity η is much smaller than unity since this is possibly of the greatest geophysical relevance.

Thermal convection sets in when the temperature gradient exceeds some critical value as measured by the modified Rayleigh number R_c. The critical temperature gradient is smallest (R_c reaches a minimum) when the magnetic field strength parameter Λ ? 1. [R_c and Λ are defined in (2.3).] The instability takes the form of a very slow wave with frequency of order κ/r ² ₀ and its direction of propagation changes from eastward to westward as Λ increases through Λ _c ? 4.

When the fluid is sufficiently stably stratified and when Λ > Λ_m ? 22 a new mode of instability sets in. It is magnetically driven but requires some stratification before the energy stored in the magnetic field can be released. The instability takes the form of an eastward propagating wave with azimuthal wavenumber m = 1.     

Geophysical effects of the interplanetary magnetic cloud on October 18–19, 1995, as deduced from observations at Irkutsk

During an interaction of the Earth’s magnetosphere with the interplanetary magnetic cloud on October 18–19, 1995, a great magnetic storm took place. Extremely intense disturbances of the geomagnetic field and ionosphere were recorded at the midlatitude observatory at Irkutsk (Φ′≈45°, Λ′≈177°, L≈2) in the course of the storm. The most important storm features in the ionosphere and magnetic field are: a significant decrease in the geomagnetic field Z component during the storm main phase; unusually large amplitudes of geomagnetic pulsations in the Pi1 frequency band; extremely low values of critical frequencies of the ionospheric F2-layer; an appearance of intense E_s-layers similar to auroral sporadic layers at the end of the recovery phase. These magnetic storm manifestations are typical for auroral and subauroral latitudes but are extremely rare in middle latitudes. We analyze the storm-time midlatitude phenomena and attempt to explore the magnetospheric storm processes using the data of ground observations of geomagnetic pulsations. It is concluded that the dominant mechanism responsible for the development of the October 18–19, 1995 storm is the quasi-stationary transport of plasma sheet particles up to L≈2 shells rather than multiple substorm injections of plasma clouds into the inner magnetosphere.     

Trends in the F2 ionospheric layer due to long-term variations in the Earth's magnetic field

The Earth's magnetic field presents long-term variations with changes in strength and orientation. Particularly, changes in the dip angle (I) and, consequently, in the sin(I)cos(I) factor, affect the thermospheric neutral winds that move the conducting plasma of the ionosphere. In this way, a lowering or lifting of the F2-peak (hmF2) is induced together with changes in foF2, depending on season, time and location. A simple theoretical approximation, developed in a previous work, is extended to a worldwide latitude–longitude grid to assess hmF2 and foF2 trends due to Earth's magnetic field secular variations. Compared to the greenhouse gases effects over the ionosphere, the Earth's magnetic field may be able to produce stronger trends which vary with season, time and location. However, to elucidate the origin of F2-region trends, long-term variations in the three possible known mechanisms should be considered altogether—greenhouse gases, geomagnetic activity and Earth's magnetic field.     

日面方位磁场扰动和行星际磁场螺旋结构

文采用球坐标下2.5维理想MHD模型,对日球子午面内方位磁场扰动的传播进行数值模拟,重点分析它对行星际磁场螺旋角的影响. 本文认为,观测到的行星际磁场螺旋角大于Parker模型的预言值,是太阳表面不断向行星际发出同向方位磁场扰动的结果;太阳较差自转在太阳内部产生的方位磁场为这类扰动提供了源头. 模拟结果表明,采用持续时间等于周期的十分之一、扰动幅度为103nT量级的正向方位磁场扰动,就可使1 AU处行星际磁场的螺旋角增加2°左右,与有关观测结果相符. 模拟结果还表明,上述方位磁场扰动对日球子午面内的太阳风特性和磁场位形的影响基本上可以忽略.     

Comparison of the plasma pressure distributions over the equatorial plane and at low altitudes under magnetically quiet conditions

The distribution of plasma pressure over the equatorial plane is compared with the plasma pressure and the position of the electron precipitation boundaries at low altitudes under the conditions of low geomagnetic activity. The pressure at the equatorial plane is determined using data of the THEMIS international five-satellite mission; the pressure at low altitudes, using data of the DMSP satellites. Plasma pressure isotropy and the validity of the condition of the magnetostatic equilibrium at a low level of geomagnetic activity are taken into account. Plasma pressure in such a case is constant along the magnetic field line and can be considered a “natural tracer” of the field line. It is shown that the plasma ring surrounding the Earth at geocentric distances of ～6 to ～10–12R _E is the main source of the precipitations in the auroral oval.     

The effects of IMF and convection on thermal ion outflow in magnetosphere-ionosphere coupling

We study the influence of the interplanetary magnetic field (IMF) and convection electric field on the rate and destination of polar wind and other thermal (low-energy) ion outflows, and its resulting effects on magnetosphere–ionosphere coupling, using single-particle trajectory simulations in conjunction with ion velocity distribution measurements on Akebono and IMF and ionospheric convection data. We find that the ions preferentially feed the dusk sector of the plasma sheet when the IMF is duskward (B_y>0), and are more evenly distributed in the plasma sheet when the IMF is dawnward. The flow of oxygen ions originating from the noon or dusk sectors of the polar cap has a higher probability of reaching the magnetosphere and beyond compared with that from the dawn or midnight sectors, due to the increased centrifugal acceleration associated with the larger magnetic field curvature near noon and the increased convection electric field in the dusk sector. The flow is enhanced and confined to lower L-shells at times of strongly southward IMF, compared with that at times of northward IMF. The outflow rate to both the plasma sheet and the magnetotail correlates strongly with the ion temperature. As a result, the IMF and the convection electric fields affect both the overall magnitude and the detailed distribution of mass transfer from the ionosphere to the magnetosphere in magnetosphere–ionosphere coupling.     

Theory of azimuthally small-scale hydromagnetic waves in the axisymmetric magnetosphere with finite plasma pressure

The structure of monochromatic MHD-waves with large azimuthal wave number m 1 in a two-dimensional model of the magnetosphere has been investigated. A joint action of the field line curvature, finite plasma pressure, and transversal equilibrium current leads to the phenomenon that waves, standing along the field lines, are travelling across the magnetic shells. The wave propagation region, the transparency region, is bounded by the poloidal magnetic surface on one side and by the resonance surface on the other. In their meaning these surfaces correspond to the usual and singular turning points in the WKB-approximation, respectively. The wave is excited near the poloidal surface and propagates toward the resonance surface where it is totally absorbed due to the ionospheric dissipation. There are two transparency regions in a finite-beta magnetosphere, one of them corresponds to the Alfvén mode and the other to the slow magneto-sound mode.     

Magnetic instabilities in rapidly rotating spherical geometries II. more realistic fields and resistive instabilities

Abstract

Magnetic instabilities play an important role in the understanding of the dynamics of the Earth's fluid core. In this paper we continue our study of the linear stability of an electrically conducting fluid in a rapidly rotating, rigid, electrically insulating spherical geometry in the presence of a toroidal basic state, comprising magnetic field B_MB _O(r, θ)1ø and flow U_MU _O(r, θ)1ø The magnetostrophic approximation is employed to numerically analyse the two classes of instability which are likely to be relevant to the Earth. These are the field gradient (or ideal) instability, which requires strong field gradients and strong fields, and the resistive instability, dependent on finite resistivity and the presence of a zero in the basic state B _O(r,θ). Based on a local analysis and numerical results in a cylindrical geometry we have established the existence of the field gradient instability in a spherical geometry for very simple basic states in the first paper of this series. Here, we extend the calculations to more realistic basic states in order to obtain a comprehensive understanding of the field gradient mode. Having achieved this we turn our attention to the resistive instability. Its presence in a spherical model is confirmed by the numerical calculations for a variety of basic states. The purpose of these investigations is not just to find out which basic states can become unstable but also to provide a quantitative measure as to how strong the field must become before instability occurs. The strength of the magnetic field is measured by the Elsasser number; its critical value _c describing the state of marginal stability. For the basic states which we have studied we find _c 200–1000 for the field gradient mode, whereas for the resistive modes _c 50–160. For the field gradient instability, _c increases rapidly with the azimuthal wavenumber m whereas in the resistive case there is no such pronounced difference for modes corresponding to different values of m. The above values of _c indicate that both types of instability, ideal and resistive, are of relevance to the parameter regime found inside the Earth. For the resistive mode, as is increased from _c, we find a shortening lengthscale in the direction along the contour B_O = 0. Such an effect was not observable in simpler (for example, cylindrical) models.     

Magnetic instabilities in rapidly rotating spherical geometries. III. The effect of differential rotation

Abstract

We investigate the influence of differential rotation on magnetic instabilities for an electrically conducting fluid in the presence of a toroidal basic state of magnetic field B ₀ = B_MB₀(r, θ)1 _φ and flow U₀ = U_MU₀ (r, θ)1_φ, [(r, θ, φ) are spherical polar coordinates]. The fluid is confined in a rapidly rotating, electrically insulating, rigid spherical container. In the first instance the influence of differential rotation on established magnetic instabilities is studied. These can belong to either the ideal or the resistive class, both of which have been the subject of extensive research in parts I and II of this series. It was found there, that in the absence of differential rotation, ideal modes (driven by gradients of B ₀) become unstable for A_c ? 200 whereas resistive instabilities (generated by magnetic reconnection processes near critical levels, i.e. zeros of B₀) require A_c ? 50. Here, Λ is the Elsasser number, a measure of the magnetic field strength and Λ_c is its critical value at marginal stability. Both types of instability can be stabilised by adding differential rotation into the system. For the resistive modes the exact form of the differential rotation is not important whereas for the ideal modes only a rotation rate which increases outward from the rotation axis has a stabilising effect. We found that in all cases which we investigated Λ_c increased rapidly and the modes disappeared when R_m ≈ O(Λ_C), where the magnetic Reynolds number R_m is a measure of the strength of differential rotation. The main emphasis, however, is on instabilities which are driven by unstable gradients of the differential rotation itself, i.e. an otherwise stable fluid system is destabilised by a suitable differential rotation once the magnetic Reynolds number exceeds a certain critical value (R_m )_c. Earlier work in the cylindrical geometry has shown that the differential rotation can generate an instability if R_m ) ?O(Λ). Those results, obtained for a fixed value of Λ = 100 are extended in two ways: to a spherical geometry and to an analysis of the effect of the magnetic field strength Λ on these modes of instability. Calculations confirm that modes driven by unstable gradients of the differential rotation can exist in a sphere and they are in good agreement with the local analysis and the predictions inferred from the cylindrical geometry. For Λ = O(100), the critical value of the magnetic Reynolds number (R_m )_c Λ 100, depending on the choice of flow U₀ . Modes corresponding to azimuthal wavenumber m = 1 are the most unstable ones. Although the magnetic field B ₀ is itself a stable one, the field strength plays an important role for this instability. For all modes investigated, both for cylindrical and spherical geometries, (R_m )_c reaches a minimum value for 50 ≈ Λ ≈ 100. If Λ is increased, (R_m )_c ∝ Λ, whereas a decrease of Λ leads to a rapid increase of (R_m )_c, i.e. a stabilisation of the system. No instability was found for Λ ≈ 10 — 30. Optimum conditions for instability driven by unstable gradients of the differential rotation are therefore achieved for ≈ Λ 50 — 100, R_m ? 100. These values lead to the conclusion that the instabilities can play an important role in the dynamics of the Earth's core.