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.     

Analytical description of charged particle motion in a reconnecting current sheet

We have obtained an analytical solution to the equation of motion in the guiding center approximation for nonrelativistic charged particles in a reconnecting current sheet with a three-component magnetic field. Given the electric field attributable to magnetic reconnection, the solution describes stable and unstable three-dimensional particle orbits. We have found the domain of input parameters at which the motion is stable. A physical interpretation of the processes affecting the stability of the motion is given. Charge separation is shown to take place in the sheet during the motion: oppositely charged particles are localized mostly in different regions of the current sheet. A formula is derived for the particle energy in stable and unstable orbits. The results obtained by numerical and analytical methods are compared.     

Consistency of fields and particle motion in the ‘Speiser’ model of the current sheet

The consistency between fields and particle motion in the region of the current sheet where the field lines link through the current sheet has been investigated.     

Electric and magnetic drift of non-adiabatic ions in the Earth's geomagnetic tail current sheet

It has been shown recently that non-adiabatic particles in the Earth's magnetotail drift across the tail roughly as predicted for adiabatic particles with 90° pitch angles. In this paper we show that this result implies the existence of an approximate invariant of the motion. Adding the effect of convection associated electric fields, we can then obtain the approximate bounce averaged motion of non-adiabatic particles in the magnetotail. Thus the particle motion and energization due to combined magnetic and electric drifts in the magnetotail are easily predicted.     

Large-scale transport of plasma in the Earth's plasma sheet: comparative analysis for adiabatic and non-adiabatic cases

A system of multi-fluid MHD-equations is used to compare adiabatic and non-adiabatic transport of the energetic particles in the magnetospheric plasma sheet. A “slow-flow” approximation is considered to study large-scale transport of the anisotropic plasma consisting of energetic electrons and protons. Non-adiabatic transport of the energetic plasma is caused by scattering of the particles in the presence of both wave turbulence and arbitrary time-varying electric fields penetrating from the solar wind into the magnetosphere. The plasma components are devided into particle populations defined by their given initial effective values of the magnetic moment per particle. The spatial scales are also given to estimate the non-uniformity of the geomagnetic field along the chosen mean path of a particle. The latters are used to integrate approximately the system of MHD-equations along each of these paths. The behaviour of the magnetic moment mentioned above and of the parameter which characterizes the pitch-angle distribution of the particles are studied self-consistently in dependence on the intensity of non-adiabatic scattering of the particles. It is shown that, in the inner magnetosphere, this scattering influences the particles in the same manner as pitch-angle diffusion does. It reduces the pitch-angle anisotropy in the plasa. The state of the plasma may be unstable in the current sheet of the magnetotail. If the initial state of the plasma does not correspond to the equilibrium one, then, in this case, scattering influences the particles so as to remove the plasma further from the equilibrium state. The coefficient of the particle diffusion across the geomagnetic field lines is evaluated. This is done by employing the Langevin approach to take the stochastic electric forces acting on the energetic particles in the turbulent plasma into account. The behaviour of the energy density of electrostatic fluctuations in the magnetosphere is estimated.     

Investigating thermal evolution of the self-gravitating one dimensional molecular cloud by smoothed particle hydrodynamics

The heating of the ion-neutral (or ambipolar) diffusion may affect the thermal phases of the molecular clouds. We present an investigation on the effect of this heating mechanism in the thermal instability of the molecular clouds. A weakly ionized one-dimensional slab geometry, which is allowed for self-gravity and ambipolar diffusion, is chosen to study its thermal phases. We use the thermodynamic evolution of the slab to obtain the regions where slab cloud becomes thermally unstable. We investigate this evolution using the model of ambipolar diffusion with two-fluid smoothed particle hydrodynamics, as outlined by Hosking and Whitworth. Firstly, some parts of the technique are improved to test the pioneer works on behavior of the ambipolar diffusion in an isothermal self-gravitating slab. Afterwards, the improved two-fluid technique is used for thermal evolution of the slab. The results show that the thermal instability may persist inhomogeneities with a large density contrast at the intermediate parts of the cloud. We suggest that this feature may be responsible for the planet formation in the intermediate regions of a collapsing molecular cloud and/or may also be relevant to the formation of star forming dense cores in the clumps.     

The motion and radiation of electrons in a neutral sheet

The motion and radiation of an electron in the neighbourhood of a neutral sheet are discussed. Formulae for the synchrotron and cyclotron radiation of an electron in an inhomogeneous field are obtained. The results are compared with radiation in a homogeneous field. It is predicted that the momentum of charged particles flying from a neutral sheet may take discrete eigenvalues.     

Stationary incompressible MHD perturbationsgenerated by a current source in a moving plasma

We consider the inductive interaction between a conducting body and a magnetizedincompressible plasma in relative uniform motion, which has application to the Io–Jupitersystem, for example. An incompressible plasma only supports one mode of propagation, namelythe Alfvén mode. In the case of free oscillations, this mode propagates the perturbations in themagnetic field and in the plasma velocity unattenuated along the direction of the backgroundfield, while the plasma pressure balances the magnetic pressure. The situation changes in thepresence of source currents and in a flowing plasma. In particular, the parallel plasma vorticityand parallel plasma current are propagated unattenuated along the familiar Alfvéncharacteristics, while the field and velocity perturbations suffer Laplacian decay in the near field.We study these perturbations in the frame of the body and compare them to the case of no sourceterms.     

The effect of an electric field induced by a time-dependent ring current on the particle drift motion

The effect of an electric field induced by a rapidly decaying ring current on the motion of charged particles in the magnetosphere has been investigated using Euler potentials. For a model consisting of the earth dipole and the symmetric ring current, the electric field satisfies the condition E . B = 0.

Under this circumstance, the E × B drift of the particle can be identified as the motion of the magnetic field lines and vice versa. The time dependent electric field induced can be evaluated in a Spherical polar coordinate system by the formula

where and β are Euler potentials.

A model calculation on the particle drift velocity v_D = E × B/B² shows that the radial component of the drift velocity is in good agreement with those deduced from whistler duct studies.     

Whistler wave instabilities in collisionless current sheet

Instability of whistler wave in collisionless current sheet is studied with numerical solution of the general dispersion relation obtained in Ref.[4] for the physical model A. As revealed by the results, the whistler wave can be directly absorbed by collisionless current sheets. On the neutral sheet (z/d_i = 0) oblique whistler waves over a rather wide range of wave numbers can propagate, while they are basically stable. In the ionic inertial region (z/d_i < 1), the obliquely propagating whistler wave is unstable. On the edge of the ionic inertial region (z/d_i = 1), the whistler wave is still unstable, with an increase in the growth rate, and in the frequency of the unstable wave. The growth rate is larger for the whistler wave propagating towards the neutral sheet (k_zd_i < 0) than away from the neutral sheet (k_zd_i > 0).     

Tearing modes in the magnetopause current sheet

A simple method is proposed to investigate the stability of a charge neutral magnetopause current sheet with respect to the tearing-mode instability. This method may serve as a useful tool in understanding the processes of local opening of the closed magnetosphere.     

Non-linear tearing structures in equilibrium current sheet

A family of exact analytic solutions of the time-independent Vlasov-Maxwell equations is presented. The solutions describe two-dimensional equilibrium current sheet with magnetic field structures resembling that produced by the tearing instability. In particular, the solutions presented here do not restrict the field in the magnetic island to small magnitude. It is shown that as the scale length of the magnetic island increases, the thickness of the current sheet increases while the average current and the average magnetic energy decrease. The tearing structures described by the solutions may exist in the magnetotail current sheet, the magnetopause current layer and the field-aligned auroral sheet current.     

The periodicity of a charged particle motion in a magnetic dipole field

The author's purpose is to present in this article the evidence of his intuition on the periodic behavior of a charged particle, moving in a magnetic dipole field, that is achieved by adopting the Alfvén's analysis of the motion into the composite of two motions and studying the contribution of these motions into the general behavior of the charged particle, separately.     

Pitch-angle scattering of energetic particles in the current sheet of the magnetospheric tail and stationary distribution functions

An investigation of pitch-angle scattering of energetic particles in magnetic field configurations with a current sheet similar to that observed in the geomagnetotail has been performed. The magnetic field model is specified by two parameters which are the current sheet thickness in units of particle gyroradius and the angle between the magnetic field lines and the sheet plane. Computations of a considerable number of trajectories (about 20,000 for each model case) has provided the possibility of obtaining the matrix of pitch-angle scattering and the corresponding kernel function of the integral equation for the stationary particle distribution function. Solution of this equation shows that isotropic distributions are formed only in the case of a sufficiently thick current sheet. Particle scattering in a thin field reversal region leads to the formation of an anisotropic stationary distribution. The results can be used for interpretation of the data on the spatial distribution of energetic particle fluxes in the near part of the magnetospheric tail and in the vicinity of the outer boundary of the radiation belt.     

Fast oscillations and particle acceleration in the neutral sheet

This paper suggests that fast periodic oscillations in the neutral sheet occur after it is perturbed strongly. An analytic solution of the oscillation process, of which the period T is about 1 ms, is obtained on the basis of the snow-plow model. This dynamical process causes the periodic appearance and disappearance of a diffusive region in the sheet. A time interval t, during which the diffusive region exists, is about 10^–2-10^–3 T. Under the assumption of a relatively weak electric field and the spectrum index = 1 of Langmuir turbulence, we obtain an analytic solution of the quasi-linear equation of the distribution function of particles with a periodic electric field. We show that the combined acceleration by the electric field and turbulence can produce the periodic streams of energetic electrons. Their energy can reach about 50 keV. These periodic streams of electrons could produce the microwave millisecond spike emission.     

The formation of solar prominences by thermal instability in a current sheet

The energy balance equation for the upper chromosphere or lower corona contains a radiative loss term which is destabilizing, because a slight decrease in temperature from the equilibrium value causes more radiation and hence a cooling of the plasma; also a slight increase in temperature has the effect of heating the plasma. In spite of this tendency towards thermal instability, most of the solar atmosphere is remarkably stable, since thermal conduction is very efficient at equalizing any temperature irregularity which may arise. However, the effectiveness of thermal conduction in transporting heat is decreased considerably in a current sheet or a magnetic flux tube, since heat can be conducted quickly only along the magnetic field lines. This paper presents a simple model for the thermal equilibrium and stability of a current sheet. It is found that, when its length exceeds a certain maximum value, no equilibrium is possible and the plasma in the sheet cools. The results may be relevant for the formation of a quiescent prominence.     

Resonant interaction of an electrostatic wave with electrons in a current sheet

A one-dimensional model of a current-sheet with a static electric potential is considered. Free electrons and protons move in opposite directions under the influence of the potential and we seek a solution for the potential in a bounded region in space (over the sheet width). The general solution is found to be plasma oscillations. Then introducing a short wavelength, monochromatic wave as a perturbation, it is shown by the method of stationary phase that electrons in resonance give a growth- (damping-) rate similar to the Landau formula. There is the possibility, however, that the wave can both grow and damp in different regions when traversing the sheet as it will sample electrons from various parts of the zero-order distribution function.     

Gravity in one dimension: Stability of a three particle system

The autonomous dynamical system consisting of parallel planes of constant mass density moving under their mutual gravitational attraction is of interest for testing diverse astrophysical models of gravitational relaxation. The simplest non-integrable system consists of three sheets. In this paper the dynamics and stability of this one-dimensional solar system is systematically investigated. A linear transformation of the coordinates reduces the problem to that of a falling body constrained by oblique boundaries. By constructing a Poincare surface of section, it is found that regions of stability and chaos coexist. This behavior is predicted by the KAM theorem for systems having smoother trajectories in phase space, but does not apply here because of the discontinuity in acceleration experienced by each sheet during an encounter. The results of numerical experiments indicate that chaotic regions may be associated with trajectories which contain nearly triple collisions of the three particles.     

Radio observations of the fine structure inside a post-CME current sheet

A solar radio burst was observed in a coronal mass ejection/flare event by the Solar Broadband Radio Spectrometer at the Huairou Solar Observing Station on2004 December 1. The data exhibited various patterns of plasma motions, suggestive of the interaction between sunward moving plasmoids and the flare loop system during the impulsive phase of the event. In addition to the radio data, the associated whitelight, Hα, extreme ultraviolet light, and soft and hard X-rays were also studied.     

Spatial galaxy distribution function for a three-component system

We derive the distribution function and the allied thermodynamic quantities for a system of galaxies with three mass species. A new clustering parameter b ₃ that inherently takes into account the masses and the number of galaxies of each kind, emerges directly from the calculations. Our general conclusion is that the inclusion of the third component does not significantly effect the overall features of the distribution function.