Modulational instability of fast magnetosonic waves emitted from a pinching current sheet

We investigate how fast magnetosonic waves can be produced from a pinching current sheet, by using 3-D MHD code. We show that after magnetic pinch of the current sheet due to pressure imbalance, the current sheet begins to expand by an excess of plasma pressure at the center of the current sheet. During the expansion phase, strong fast magnetosonic waves can be created at the steep region of the density gradient and propagate away from the current sheet. It is shown that the fast magnetosonic waves become unstable against modulational instability, as found by Sakai (1983). After the emission of the fast magnetosonic waves, the current sheet will relax to a new equilibrium state, where the current sheet can be heated by adiabatic compression. The emission processes of the fast magnetosonic waves from the current sheet, as well as the modulational instability of these waves that can lead to effective plasma heating through the Landau damping of the slow waves, are important for an understanding of coronal heating and coronal transient brightening.     

Generalized analytical models of Syrovatskii’s current sheet

Two-dimensional stationary magnetic reconnection models that include a thin Syrovatskii-type current sheet and four discontinuous magnetohydrodynamic flows of finite length attached to its endpoints are considered. The flow pattern is not specified but is determined from a self-consistent solution of the problem in the approximation of a strong magnetic field. Generalized analytical solutions that take into account the possibility of a current sheet discontinuity in the region of anomalous plasma resistivity have been found. The global structure of the magnetic field in the reconnection region and its local properties near the current sheet and attached discontinuities are studied. In the reconnection regime in which reverse currents are present in the current sheet, the attached discontinuities are trans-Alfvénic shock waves near the current sheet endpoints. Two types of transitions from nonevolutionary shocks to evolutionary ones along discontinuous flows are shown to be possible, depending on the geometrical model parameters. The relationship between the results obtained and numerical magnetic reconnection experiments is discussed.     

Mhd Study of Coronal Waves: A Numerical Approach

The solar corona, modelled by a low β, resistive plasma slab sustains MHD wave propagations due to footpoint motions in the photosphere. The density, magnetic profile and driver are considered to be neither very smooth nor very steep. The numerical simulation presents the evolution of MHD waves and the formation of current sheet. Steep gradients in slow wave at the slab edges which are signature of resonance layer where dissipation takes place are observed. Singularity is removed by the inclusion of finite resistivity. Dissipation takes place around the resonance layer where the perturbation develops large gradients. The width of the resonance layer is calculated. The thickness of the Alfvén resonance layer is more than that of the slow wave resonance layer. Attempt is made to distinguish between slow and Alfvén wave resonance layers. Fast waves develop into kink modes. As plasma evolves the current sheets which provide the heating at the edges gets distorted and fragment into two current sheets at each edge which in turn come closer when the twist is enhanced. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the non-adiabatic particle scattering in the earth''s magnetotail current sheet

The empirical model of disturbed magnetosphere of Tsyganenko and Usmanov (1982) and the semi-empirical model of the storm-time magnetospheric configuration of Tsyganenko (1981) are used to find the critical energy for non-adiabatic particle scattering in the midnight sector. Computed values of E_crit vs L are compared with the appropriate experimental data of Imhof et al. (1977). It is found that none of the considered models is able to reproduce the observed steep decrease of E_crit with L. The steepest slope is given by the Tsyganenko model which includes a current sheet with the finite thickness. The current sheet thickness is a crucial parameter in the non-adiabatic scattering problem. In discussion we point to natural limitations of an empirical model as far as the current sheet thickness is to be determined. Imhof et al.'s data as well as some magnetic field data sets seem to indicate that magnetosphere models incorporating a thin current sheet and allowing for the thickness dependence on the geocentric distance would probably be closer to reality than the considered models, at least during higher levels of magnetic activity.     

The warm current sheet model, and its implications on the temporal behaviour of the geomagnetic tail

A simple model current sheet is studied numerically. Consistent fields and particle trajectories, and their dependence on electron and proton temperature, convection velocity and normal field, B_z, linking through the current sheet, are presented and discussed. It is shown that the protons, which are the major current carriers, largely retain the decoupling of the motion in the x-y plane from the normal oscillations as in the ‘cold’ current sheet. The positive potential of the current sheet is shown to be sufficient to trap some energetic electrons, the motion of which enables the predominance of energetic electrons towards the dawn side of the tail to be understood. Semi-empirical relationships for the thickness and the potential of the current sheet are obtained.

The consequences of such a current sheet on the behaviour of the geomagnetic tail are investigated. Using Faraday's law and the consistent cross tail electric field it is shown that the effect of a southward turning of the interplanetary field is to lead to a decrease in B_z,an increase of the current sheet conductivity, and a growth of stored field energy, i.e. the current sheet blocks merging. The decrease of the resistance of the current sheet is limited by the finite width of the tail. Finally, it is pointed out that if the conditions which bring about the growth of field energy persist, then the collapse of the field lines characteristic of substorms may occur.     

Coupled guided modes in the magnetotails: spatial structure and ballooning instability

The problem of the spatial structure of coupled azimuthally small-scale Alfvén and slow magnetosonic (SMS) waves is solved in an axisymmetric magnetotail model with a current sheet. It is shown that the linear transformation of these waves occurs in the current sheet on magnetic field lines stretched into the magnetotail. From the ionosphere to the current sheet these modes are linearly independent. Due to the high ionospheric conductivity the structure of coupled modes along magnetic field lines represents standing waves with very different typical scales in different parts of the field line. In most of the field line their structure is determined by the large-scale Alfvén wave structure. Near the ionosphere and in the current sheet, small-scale SMS wave field starts to dominate. In these regions coupled modes becomes small-scale. Such modes are neutrally stable on the field lines that do not cross the current sheet, but switch to the ballooning instability regime on field lines crossing the current sheet. An external source is required to generate these modes and this paper considers external currents in the ionosphere as a possible driver. In the direction across magnetic shells the coupled modes are waves running away from the magnetic shell on which they were generated.     

Fundamental wave of type III solar radio bursts and whistler waves

It is demonstrated by a numerical simulation that both the whistler waves and plasma waves are excited by a common solar electron beam. The excitation of the whistler waves is ascribed to the loss-cone distribution which arises at a later phase of the passage of the beam at a given height due to a velocity dispersion in the electron beam with a finite length. It is highly probable that the fundamental of type III bursts are caused by the coalescence of the whistler waves and the plasma waves excited by a common electron beam, although the plasma waves must suffer induce scatterings by thermal ions to have small wave numbers before the coalescence to occur.     

Magnetohydrodynamic waves in a neutral sheet

The magnetohydrodynamic continua and normal modes for waves propagating in a finite magnetic neutral sheet are identified. The normal modes have characteristics similar to hydromagnetic waves observed near the Earth in association with geomagnetic substorms.     

Wave excitation in three-dimensional discs by external potential

We study the excitation of density and bending waves and the associated angular momentum transfer in gaseous discs with finite thickness by a rotating external potential. The disc is assumed to be isothermal in the vertical direction and has no self-gravity. The disc perturbations are decomposed into different modes, each characterized by the azimuthal index m and the vertical index n , which specifies the nodal number of the density perturbation along the disc normal direction. The   n = 0  modes correspond to the two-dimensional density waves previously studied by Goldreich & Tremaine and others. In a three-dimensional disc, waves can be excited at both Lindblad resonances (LRs; for modes with   n = 0, 1, 2, …  ) and vertical resonances (VRs; for the   n ≥ 1  modes only). The torque on the disc is positive for waves excited at outer Lindblad/vertical resonances and negative at inner Lindblad/vertical resonances. While the   n = 0  modes are evanescent around corotation, the   n ≥ 1  modes can propagate into the corotation region where they are damped and deposit their angular momenta. We have derived analytical expressions for the amplitudes of different wave modes excited at LRs and/or VRs and the resulting torques on the disc. It is found that for   n ≥ 1  , angular momentum transfer through VRs is much more efficient than LRs. This implies that in some situations (e.g. a circumstellar disc perturbed by a planet in an inclined orbit), VRs may be an important channel of angular momentum transfer between the disc and the external potential. We have also derived new formulae for the angular momentum deposition at corotation and studied wave excitations at disc boundaries.     

Formation of fast magnetosonic shock waves during a two-current-loop collision in solar flares

We present a numerical simulation of the fast magnetosonic shock wave formation during a two-current-loop collision by using a magnetohydrodynamical model. It is shown that the rarefaction waves are generated in the initial stage when the two current loops start to collide. After the rarefaction waves propagate away from the excited region, the fast magnetosonic waves with density enhancement can be produced for the simulation when the current strength of the loop is weak. As the current becomes strong enough, the magnetosonic shock waves can be generated in the direction perpendicular to that of the two-loop collision.     

Dynamics of cosmic current layers with localized lower-hybrid-drift turbulence

A two-dimensional magnetohydrodynamic model of the dynamics of tail-like current layers caused by anomalous electrical resistivity in a plasma with lower-hybrid-drift (LHD) turbulence is considered. Additionally to the LHD-resistivity, a resistivity pulse in the magnetic neutral sheet is given initiating a magnetic reconnection process. Then the temporal and spatial evolution of the magnetic and electric fields, the plasma convection and the anomalous resistivity are obtained numerically. Taking into account more exact expressions for the LHD-resistivity in the current layer as done in former works, the LHD-turbulence is found to be excited farther from the neutral sheet, and thus, with the time, secondary current sheets are obtained in the plasma-magnetic field system. It is shown that the inductive electric field moving from the magnetic neutral sheet to the current layer periphery during the reconnection process may be considered as indicator of the plasma disturbances.     

Some properties of the current sheet in the geomagnetic tail

The topic of this report is that of the influence of noise, and of the finite length and width of the tail on the behaviour of the current sheet.The presence of a weak magnetic field linking through the current sheet leads to plasma containment and counterstreaming, with the consequence that both the plasma temperature and density are increased in the vicinity of the current sheet. The effect of these changes on the relationship between steady bulk parameters is discussed.The finite length of the tail significantly modifies the equilibrium situation in the near Earth tail, for streams mirroring at the Earthwards end of field lines lead to a reduction of merging. The finite width of the tail restricts the region of reduced merging rate to a triangular shaped area extending from the dusk magnetopause into the tail. The finite tail width is also important in the more distant tail, where magnetosheath particles which penetrate the magnetopause ends of the current sheet may become major current carriers, especially if B_z, is small and northwards.Finally, it is shown that the above factors, together with a non-adiabatic current sheet, are important to our understanding of the temporal behaviour of the tail.     

磁通量片的Helmholtz不稳定性

本文分析了被等离子体约束由两个间断面组成的有限厚度磁通量片的Helmholtz不稳定性,导出了不稳定条件,若片的厚度趋于无穷则此条件与一个间断面时相同。还给出了两个间断面的色散关系。结果表明,两个间断面时的磁致稳作用比一个间断面时有所减弱,而约束等离子体的致稳作用相对增强,但两种情况具有相同量级的不稳定增长率。     

太阳爆发过程中的大尺度磁重联电流片:理论和观测

从理论和观测两个方面来介绍和讨论出现在太阳爆发过程中的磁重联电流片及其物理本质和动力学特征。首先介绍在理论研究和理论模型中,磁重联电流片是如何在爆发磁结构当中形成并发展的,对观测研究有什么指导意义。然后介绍观测工作是从哪几个方面对理论模型预测的电流片进行证认和研究的。第三,将介绍观测研究给出了哪些过去所没有能够预期的结果,这些结果对深入研究耀斑一CME电流片以及其中的磁重联过程的理论工作有什么重要的、挑战性的意义。第四,讨论最新的与此有关的理论研究和数值实验。最后,对未来的研究方向和重要课题进行综述和展望。     

Time-fractional KdV equation for electron-acoustic waves in plasma of cold electron and two different temperature isothermal ions

The time fractional KdV equation is derived for small but finite amplitude electron-acoustic solitary waves in plasma of cold electron fluid with two different temperature isothermal ions. The effects of the time fractional parameter on the electrostatic solitary structures are presented. It is shown that the effect of time fractional parameter can be used to modify the amplitude of the electrostatic waves (viz. the amplitude, width and electric field) of the electron-acoustic solitary waves. The model may provide a possible explanation for the low-frequency component of the broadband electrostatic noise in the plasma sheet boundary layer of the Earth’s magnetotail where the electron beams are not present.     

Formation of vortices in the presence of sheared electron flows in the earth's ionosphere

It is shown that sheared electron flows can generate long as well as short wavelength (in comparison with the ion gyroradius) electrostatic waves in a nonuniform magnetplasma. For this purpose, we derive dispersion relations by employing two-fluid and hybrid models; in the two-fluid model the dynamics of both the electrons and ions are governed by the hydrodynamic equations and the guiding center fluid drifts, whereas the hybrid model assumes kinetic ions and fluid electrons. Explicit expressions for the growth rates and thresholds are presented. Linearly excited waves attain finite amplitudes and start interacting among themselves. The interaction is governed by the nonlinear equations containing the Jacobian nonlinearities. Stationary solutions of the nonlinear mode coupling equations can be represented in the form of a dipolar vortex and a vortex street. Conditions under which the latter arise are given. Numerical results for the growth rates of linearly excited modes as well as for various types of vortices are displayed for the parameters that are relevant for the F-region of the Earth's ionosphere. It is suggested that the results of the present investigation are useful in understanding the properties of nonthermal electrostatic waves and associated nonlinear vortex structures in the Earth's ionosphere.     

A mechanism for the formation of plasmoids and kink waves in the heliospheric current sheet

Satellite observations of the heliospheric current sheet indicate that the plasma flow velocity is low at the center of the current sheet and high on the two sides of current sheet. In this paper, we investigate the growth rates and eigenmodes of the sausage, kind, and tearing instabilities in the heliospheric current sheet with the observed sheared flow. These instabilities may lead to the formation of the plasmoids and kink waves in the solar wind. The results show that both the sausage and kink modes can be excited in the heliospheric current sheet with a growth time 0.05–5 day. Therefore, these modes can grow during the transit of the solar wind from the Sun to the Earth. The sausage mode grows faster than the kink mode for < 1.5, while the streaming kink instability has a higher growth rate for > 1.5. Here is the ratio between the plasma and magnetic pressures away from the current layer. If a finite resistivity is considered, the streaming sausage mode evolves into the streaming tearing mode with the formation of magnetic islands. We suggest that some of the magnetic clouds and plasmoids observed in the solar wind may be associated with the streaming sausage instability. Furthermore, it is found that a large-scale kink wave may develop in the region with a radial distance greater than 0.5–1.5 AU.Also at Department of Earth and Space Science, University of Science and Technology of China, Hefei Anhui 230029, China.     

新磁重联理论

本文研究了磁流体力学与高频等离子体波（ 包括纵横模式） 之间的精巧的相互作用。研究表明,这些等离激元会在电流片内诱发一种阻抗不稳定,并最终导至磁重联,出现爆发性不稳定。在高涨的离声湍动情况下,高温电流片模型必须采用反常电导率,而非库仑电导率。理论估算的结果与观测相一致。因此这种计及等离激元有质动力作用的新磁重联理论,基本上能解释耀斑现象。     

The analytic properties of the flapping current sheets in the earth magnetotail

The current sheet in Earth’s magnetotail often flaps, and the flapping waves could be induced propagating towards the dawn and dusk flanks, which could make the current sheet dynamic. To explore the dynamic characteristics of current sheet associated with the flapping motion holistically and provide reasonable physical interpretations, detailed direct calculation and analysis have been applied to one approximate analytic model of magnetic field in the flapping current sheet. The main results from the model demonstrate: (1) the magnetic fluctuation amplitude is attenuated from the center of current sheet to the lobe regions; The larger wave amplitude would induce the larger magnetic amplitude; (2) the curvature of magnetic field lines (MFLs), with maximum at the center of current sheet, is only dependent on the displacement Z along the south-north direction from the center of current sheet, regardless of the tilt of current sheet; (3) the half-thickness of neutral sheet, h, the minimum curvature radius of MFLs, R_cmin, and the tilt angle of current sheet, δ, satisfies h=R_cmin cos δ; (4) the gradient of magnetic strength forms a double-peak profile, and the peak value would be more intense if the local current sheet is more tilted; (5) current density j and its j_y, j_z components reach the extremum at the center of CS. j and j_z would be more intense if the local current sheet is more tilted, but it is not the case for j_y; and (6) the field-aligned component of current density mainly appears in the neutral sheet, and the sign of it would change alternatively as the flapping waves passing by. To check the validity of the model, one simulation on the virtual measurements has been made, and the results are in well consistence with actual observations of Cluster.     

A Model for the Source of Quasi-Harmonic Bursts on the Crab Pulsar

A model for the source of microwave bursts from the Crab pulsar in the form of a current sheet with a transversemagnetic field has been investigated. The emission generation mechanism is based on the excitation of plasma waves at the double plasma resonance frequencies in a nonrelativistic nonequilibrium plasma followed by their scattering into electromagnetic waves that escape from the current sheet into the neutron star magnetosphere. The basic parameters of the source explaining the observed characteristics of quasi-harmonic bursts in the interpulses of radio emission from this pulsar have been established.