Confirmation of quiet pulsar model by the boundary element method

A method for solving the force-free surface problem for the pulsar magnetosphere is outlined. The given formulation is extended to an oblique rotator problem. Since we solve equation subject to the boundary values—i.e., the boundary element method (BEM) developed in Paper I is used—we can directly determine the force-free surface. Another merit of this method rests in the fact that we only use a two-dimensional grid, in spite of the problem being three-dimensional. A numerical calculation has been performed to confirm the solution by the particle method (Krause-Polstorff and Michel, 1985).     

A self-consistent model of the magnetosphere with centrifugal wind,I

Under the purely centrifugal approximation (gravity and pressure force are neglected), stellar magnetospheres are classified into three main types of different physical properties in the two-dimensional parameter space. They are characterized essentially by the strength of the magnetic field and the plasma density, at the base of the magnetosphere. Among the three types, the type II magnetosphere has moderate surface densities for a given field strength, and is expected to possess a centrifugal wind blowing across the magnetic field lines without affecting them appreciably. Such a situation may be realized through a modification of the electric field from that under the ideal-MHD condition, owing to the inertia of a plasma. In order to illustrate this mechanism, the type II magnetosphere is taken up for a numerical simulation. The effect of artificial viscosity is avoided by integrating the characteristic equations for both components of the plasma, instead of solving the fluid equations directly. Our model reproduces a disk-like outflow of the centrifugal wind across the magnetic field lines which are closed through the equatorial plane.     

A new scenario for impulsive bursts of hard electromagnetic radiation in space plasma

We discuss the peculiarities of fast magnetic reconnection in the essentially nonequilibrium magnetosphere of a compact relativistic object: a neutron star, a magnetar, a white dwarf. Such a magnetosphere is produced by the interaction of a large-amplitude shock wave with a strong stellar magnetic field. We present an analytical solution of the generalized two-dimensional problem on the magnetosphere’s structure, the shape of its boundary, and the direct and reverse currents in a reconnecting current sheet. The uncompensated magnetic force acting on the reverse current is determined. Characteristic parameters of the nonequilibrium magnetosphere of compact stellar objects are estimated. We show that the excess magnetic energy of the magnetosphere is comparable to the mechanical energy brought into it by the shock at the instant of impact. The possibility of particle acceleration to enormous energies is discussed.     

The Varying Multipolar Structure of the Sun's Magnetic Field and the Evolution of the Solar Magnetosphere Through the Solar Cycle

The Sun's magnetic field extends far from the photosphere, into the corona, defining a magnetically dominated region before being drawn out radially by the solar wind flow. This region, where the internal sources of the solar field dominate the plasma structures and the energetic particle movement, can be properly considered the solar magnetosphere. The magnetic field in this region can be approximately described by models that extrapolate photospheric magnetic field observations under some simplifying assumptions. In this paper we use a potential field model which describes the solar field up to a source surface at 3.25 R_s, where the field is constrained to become radial. We present the variation of the magnitude and inclination of the various multipolar components throughout the solar magnetic cycle that characterise the changes in the structure of the solar magnetosphere over a period of 22 years. We also present some 3-D images of the coronal magnetic structure to show the global evolution of the solar magnetosphere throughout the solar cycle and discuss the importance of taking this structure into account in order to relate interplanetary and solar features.     

Plasma magnetosphere of rotating magnetized neutron star in the braneworld

Plasma magnetosphere surrounding rotating magnetized neutron star in the braneworld has been studied. For the simplicity of calculations Goldreich-Julian charge density is analyzed for the aligned neutron star with zero inclination between magnetic field and rotation axis. From the system of Maxwell equations in spacetime of slowly rotating star in braneworld, second-order differential equation for electrostatic potential is derived. Analytical solution of this equation indicates the general relativistic modification of an accelerating electric field and charge density along the open field lines by brane tension. The implication of this effect to the magnetospheric energy loss problem is underlined. It was found that for initially zero potential and field on the surface of a neutron star, the amplitude of the plasma mode created by Goldreich-Julian charge density will increase in the presence of the negative brane charge. Finally we derive the equations of motion of test particles in magnetosphere of slowly rotating star in the braneworld. Then we analyze particle motion in the polar cap and show that brane tension can significantly change conditions for particle acceleration in the polar cap region of the neutron star.     

On some problems concerning the calculation of the form of the magnetopause and the electric field on the magnetopause in the framework of the continuum medium model

In order to understand the reason of the existence of the electric field in the magnetosphere, and for the theoretical evaluation of its value, it is necessary to find the solution of the problem of determination of the magnetosphere boundary form in the frameworks of the continuum medium model which takes into account part of the magnetospheric plasma movement in supporting the magnetospheric boundary equilibrium. A number of problems for finding the distribution of the pressure, the density, the magnetic field and the electric field on the particular tangential discontinuity is considered in the case when the form of discontinuity is set (the direct problem) and a number of problems for finding the form of the discontinuity and the distribution of the above-mentioned physical quantities on the discontinuity is considered when the law of the change of the external pressure along the boundary is set (for example, with the help of the approximate Newton equation). The problem which is considered here, which deals with the calculation of the boundary form and with the calculation of the distribution of the corresponding physical quantities on the discontinuity of the 1st kind for the compressible fluid with the magnetic field with field lines which are perpendicular to the plane of the flow in question, concerns the last sort of problems. The comparison of the results of the calculation with the data in the equatorial cross-section of the magnetosphere demonstrates that the calculated form of the boundary, the value of the velocity of the return flow and the value of the electric field on the magnetopause, agree satisfactorily with the observational data.     

Magnetospheric surface flow with strong discontinuities

The theory of strong discontinuities in plasma with anisotropic pressure is applied for interpretation of the recent plasma and magnetic experiments on the boundary and in the tail of the magnetosphere. The properties of the discontinuities are described. It is supposed that on the boundary and in the tail of the magnetosphere anisotropic discontinuities occur with a nonzero normal component of the magnetic field. The general consequence of this assumption is the existence of the magnetospheric surface flow expanding from the subsolar point. The consequence does not contradict the data obtained on IMP 5. For the investigation of the low latitude part of the flow, the use of electrostatic analysers is desirable with the entrance oriented along the magnetospheric surface. The well-known qualitative scheme of the hydrodynamical flow with strong discontinuities in the tail is generalized by means of the three anisotropic discontinuities: the contact one coinciding with the magnetic neutral sheet, and the two discontinuities with the nonzero normal flow of the mass simulating the boundary of the plasma sheet. The result of the scheme of the components of the bulk velocity in the plasma sheet agrees with the recent observations on the Vela 4B. The scheme connects the well-known phenomena of the blocking and the thinning of the plasma sheet in the initial phase of the substorm. According to the general principles of the reconnection the dynamical dissipation is decreased by the blocking of the flow in the plasma sheet. The decrease leads to a drift of the plasma sheet boundary in the neutral sheet direction. The reverse picture is probably a result of a relaxation of the blocking.     

Mapping of the cusp plasma precipitation on the surface of Mercury

The presence of a magnetosphere around Mercury plays a fundamental role on the way the solar wind plasma interacts with the planet. Since the observations suggest that Mercury should occupy a large fraction of its magnetosphere and because of lack of an atmosphere, significant differences in solar wind-magnetosphere coupling are expected to exist with respect to the Earth case. On the basis of a modified Tsyganenko T96 model we describe the geometry of the magnetic field that could characterize Mercury, and its response to the variations of the impinging solar wind and of the interplanetary magnetic field. The investigation is focused on the shape and dimension of the open magnetic field regions (cusps) that allow the direct penetration of magnetosheath plasma through the exosphere of Mercury, down to its surface. The precipitating particle flux and energy are evaluated as a function of the open field line position, according to different solar wind conditions. A target of this study is the evaluation of the sputtered particles from the crust of the planet, and their contribution to the exospheric neutral particle populations. Such estimates are valuable in the frame of a neutral particle analyser to be proposed on board of the ESA/BepiColombo mission.     

The dawn polar cap boundary at high altitude

Comparison of hot plasma data from ATS-6 and GEOS-1 when the satellites were near dawn L.T. conjunction reveals the presence of strong gradients separating plasmas differing by more than two orders of magnitude in keV particle fluxes. These gradients are observed at off-equatorial geomagnetic latitudes of 25–30° on field lines outside the synchronous orbit. They are associated with magnetic storms and are distinct from magnetopause crossings. Interpretation of these events in terms of a boundary between magnetospheric and polar-cap plasma leads to the following conclusions: (1) the polar cap/lobe region is essentially devoid of keV plasma at these times; (2) the field lines defining this boundary are significantly distorted from a dipolar to a more stretched form consistent with the presence of a storm-ring current, (3) smaller substorm-scale motions are superposed on the gross motion of the boundary with some evidence present for structure in the plasma spatial profile, and (4) magnetosheath-like plasma finds access to the inner magnetosphere at dawn L.T., much as it does near noon, along polar-cap boundary-layer field lines which close through the low latitude magnetospheric boundary layer.     

The effect of the atmosphere and ionosphere on long period magnetospheric micropulsations

A study is made of the screening effect of the atmosphere and ionosphere which lets only part of a magnetospheric micropulsation signal reach the ground. We obtain analytical expressions relating the magnetic field in the magnetosphere to that on the ground, which are confirmed by computing a full solution. Only the part of the signal with no vertical current will be seen on the ground; this agrees with previous work. Using this result, we find that the reflection condition of a transverse hydromagnetic wave incident on the top of the ionosphere indicates a ‘fixed-end’ boundary condition for the field line. To a first approximation, micropulsation polarisations observed on the ground must be rotated through a right angle to obtain those in the magnetosphere. The strength of the electric field predicted in the ionosphere agrees with radio aurorae observations.     

Nonlinear Force-Free Reconstruction of the Global Solar Magnetic Field: Methodology

We present a novel numerical method that allows the calculation of nonlinear force-free magnetostatic solutions above a boundary surface on which only the distribution of the normal magnetic field component is given. The method relies on the theory of force-free electrodynamics and applies directly to the reconstruction of the solar coronal magnetic field for a given distribution of the photospheric radial field component. The method works as follows: we start with any initial magnetostatic global field configuration (e.g. zero, dipole), and along the boundary surface we create an evolving distribution of tangential (horizontal) electric fields that, via Faraday’s equation, give rise to a respective normal-field distribution approaching asymptotically the target distribution. At the same time, these electric fields are used as boundary condition to numerically evolve the resulting electromagnetic field above the boundary surface, modeled as a thin ideal plasma with non-reflecting, perfectly absorbing outer boundaries. The simulation relaxes to a nonlinear force-free configuration that satisfies the given normal-field distribution on the boundary. This is different from existing methods relying on a fixed boundary condition – the boundary evolves toward the a priori given one, at the same time evolving the three-dimensional field solution above it. Moreover, this is the first time that a nonlinear force-free solution is reached by using only the normal field component on the boundary. This solution is not unique, but it depends on the initial magnetic field configuration and on the evolutionary course along the boundary surface. To our knowledge, this is the first time that the formalism of force-free electrodynamics, used very successfully in other astrophysical contexts, is applied to the global solar magnetic field.     

The Kelvin-Helmholtz instability on the magnetopause

Conditions for the development of Kelvin-Helmholtz (K-H) waves on the magnetopause have been known for more than 15 years; more recently, spacecraft observations have stimulated further examination of the properties of K-H waves. For amagnetopause with no boundary layer, two different modes of surface waves have been identified and their properties have been investigated for various assumed orientations of magnetic field and flow velocity vectors. The power radiated into the magnetosphere from the velocity shear at the boundary has been estimated. Other calculations have focused on the consequences of finite thickness boundary layers, both uniform and non-uniform. The boundary layer is found to modify the wave modes present at the magnetopause and to yield a criterion for the wavelength of the fastest growing surface waves. The paper concludes by questioning the extent to which the inferences from boundary layer models are model dependent and identifies areas where further work is needed or anticipated.     

A mathematical magnetospheric field model with independent physical parameters

A quantitative magnetospheric magnetic field model has been calculated in three dimensions. The model is based on an analytical solution of the Chapman-Ferraro problem. For this solution, the magnetopause was assumed to be an infinitesimally thin discontinuity with given geometry. The shape of the dayside magnetopause is in agreement with measurements derived from spacecraft boundary crossings.The magnetic field of the magnetopause currents can be derived from scalar potentials. The scalar potentials result from solutions of Laplace's equation with Neumann's boundary conditions. The boundary values and the magnetic flux through the magnetopause are determined by all magnetic sources which are located inside and outside the magnetospheric cavity. They include the Earth's dipole field, the fields of the equatorial ring current and tail current systems, and the homogeneous interplanetary magnetic field. In addition, the flux through the magnetopause depends on two constants of interconnection which provide the possibility of calculating static interconnection between magnetospheric and interplanetary field lines. Realistic numerical values for both constants have been derived empirically from observed displacements of the polar cusps which are due to changes in the orientation of the interplanetary field. The transition from a closed to an open magnetosphere and vice versa can be computed in terms of a change of the magnetic boundary conditions on the magnetopause. The magnetic field configuration of the closed magnetosphere is independent of the amount and orientation of the interplanetary field. In contrast, the configuration of the open magnetosphere confirms the observational finding that field line interconnection occurs primarily in the polar cusp and high latitude tail regions.The tail current system reflects explicitly the effect of dayside magnetospheric compression which is caused by the solar wind. In addition, the position of the plasma sheet relative to the ecliptic plane depends explicitly on the tilt angle of the Earth's dipole. Near the tail axis, the tail field is approximately in a self-consistent equilibrium with the tail currents and the isotropic thermal plasma.The models for the equatorial ring current depend on the D_st-parameter. They are self-consistent with respect to measured energy distributions of ring current protons and the axially symmetric part of the magnetospheric field.     

The structure of the magnetopause

The solar wind is a magnetized flowing plasma that intersects the Earth's magnetosphere at a velocity much greater than that of the compressional fast mode wave that is required to deflect that flow. A bow shock forms that alters the properties of the plasma and slows the flow, enabling continued evolution of the properties of the flow on route to its intersection with the magnetopause. Thus the plasma conditions at the magnetopause can be quite unlike those in the solar wind. The boundary between this “magnetosheath” plasma and the magnetospheric plasma is many gyroradii thick and is surrounded by several boundary layers. A very important process occurring at the magnetopause is reconnection whereby there is a topological change in magnetic flux lines so that field lines can connect the solar wind plasma to the terrestrial plasma, enabling the two to mix. This connection has important consequences for momentum transfer from the solar wind to the magnetosphere. The initiation of reconnection appears to be at locations where the magnetic fields on either side of the magnetopause are antiparallel. This condition is equivalent to there being no guide field in the reconnection region, so at the reconnection point there is truly a magnetic neutral or null point. Lastly reconnection can be spatially and temporally varying, causing the region of the magnetopause to be quite dynamic.     

Observation of a flux transfer event on the earthward side of the magnetopause

The medium energy particle spectrometer (electrons of energy > 20 keV, protons > 25 keV) on board ISEE-2 has measured very similar pitch angle distributions and intensities during “flux transfer” events in the magnetosheath and events previously designated as “inclusion” events in the magnetosphere on a single pass through the magnetopause. This is interpreted as strong evidence that magnetic field lines in the magnetosphere can connect to field lines in the magnetosheath, at least locally and for brief times, allowing the same population ofparticles to be observed on both sides of the boundary. In addition, a simple mathematical model is provided incorporating a time constant for the process re-supplying particles to the open flux tube. The observed data are satisfactorily reproduced using a time constant of 46 s, which is comparable to the half-bounce time of protons at this position.     

Self-consistent electromagnetic field in a nearly co-rotating magnetosphere

An example of the self-consistent solution which belongs to the non-trivial solution, obtained in a previous paper (Kaburaki, 1985), is found in a nearly co-rotating inner magnetosphere. Though the stellar wind is neglected there compared with the co-rotatinal velocity, drift motion around the magnetic axis, which is a manifestation of inertial effects, is determined self-consistently with the electromagnetic field. In this process, explicit expressions for the energy integral in the rotating frame and for the density distribution are also obtained. These expressions contain a fundamental length, which is to be evaluated according to physical conditions of a magnetosphere and determines the asymptotic-kinetic energy of a plasma particle at infinity. The electric current associated with the drift motion is too small to alter the original magnetic field, but the electric field is modified by the inertial effects even in the inner magnetosphere. The integrated Ohm's law is used to describe a force balance in the rotating frame, in the limits of weak and strong magnetic field.     

The global structure of the pulsar magnetospheres

The model of the pulsar magnetosphere filled with massless charged particles (rest massm=0) is considered. The gas of charged massless particles can be found in two different phases: (1) dynamical phase (DP), when the particles move with nonvanishing energy along some base line, determined by the electromagnetic field only, (2) statical phase (SP), when the particles have vanishing energy =0. The pulsar magnetosphere occurs to be divided into regions of different types: (a) the accelerating regions (DP-regions) containing only DP, (b) the capture regions, containing only SP, (3) leaky capture regions, where DP moves through SP. The leaky capture regions are the active regions, which are responsible for the pulsar radioemission. In the case of oblique magnetic moment the equation for the capture surface has been obtained. The capture region is formed around this surface. Expressions for jumps of the electromagnetic field, the current density and the charge density on the capture region boundary have been obtained. The problem of the pulsar magnetosphere is stated mathematically in the case of oblique magnetic moment and ejection of only electrons.     

New Boundary Integral Equation Representation for Finite Energy Force-Free Magnetic Fields in Open Space above the Sun

A boundary integral equation to describe a force-free magnetic field with finite energy content in the open space above the solar surface is found. This is a new representation for a 3-D nonlinear force-free field in terms of the boundary field and its normal gradient at the boundary. Therefore the magnetic field observed on the solar surface can be incorporated into the formulation directly and a standard numerical technique, the boundary element method, can be applied to solve the field. A numerical test case demonstrates the power of the method by recovering the analytical solution to the desired accuracy and its application to practical solar magnetic field problems is straightforward and promising.     

Interplanetary magnetic field structure and solar wind parameters as inferred from solar magnetic field observations and by using a numerical 2-D MHD model

An attempt is made to infer parameters of the solar corona and the solar wind by means of a numerical, self-consistent MHD simulation. Boundary conditions for the magnetic field are given from the observations of the large-scale magnetic field at the Sun. A two-region, planar (the ecliptic plane is assumed) model for the solar wind flow is considered. Region I of transonic flow is assumed to cover the distances from the solar surface up to 10R _S (R _S is the radius of the Sun). Region II of supersonic, super-Alfvénic flow extends between 10R _S and the Earth's orbit. Treatment for region I is that for a mixed initial-boundary value problem. The solution procedure is similar to that discussed by Endler (1971) and Steinolfson, Suess, and Wu (1982): a steady-state solution is sought as a relaxation to the dynamic equilibrium of an initial state. To obtain a solution to the initial value problem in region II with the initial distribution of dependent variables at 10R _S (deduced from the solution for region I), a numerical scheme similar to that used by Pizzo (1978, 1982) is applied. Solar rotation is taken into account for region II; hence, the interaction between fast and slow solar wind streams is self-consistently treated. As a test example for the proposed formulation and numerical technique, a solution for the problem similar to that discussed by Steinolfson, Suess, and Wu (1982) is obtained. To demonstrate the applicability of our scheme to experimental data, solar magnetic field observations at Stanford University for Carrington rotation 1682 are used to prescribe boundary conditions for the magnetic field at the solar surface. The steady-state solution appropriate for the given boundary conditions was obtained for region I and then traced to the Earth's orbit through region II. We compare the calculated and spacecraft-observed solar wind velocity, radial magnetic field, and number density and find that general trends during the solar rotation are reproduced fairly well although the magnitudes of the density in comparison are vastly different.     

Differences between solar wind plasmoids and ideal magnetohydrodynamic filaments

Plasma irregularities present in the solar wind are plasmoids, i.e. plasma-magnetic field entities. These actual plasmoids differ from ideal magnetohydrodynamic (MHD) filaments. Indeed, (1) their “skin” is not infinitely thin but has a physical thickness which is determined by the gyromotion of the thermal ions and electrons, (2) they are of finite extent and their magnetic flux is interconnected with the interplanetary magnetic flux, (3) when they penetrate into the magnetosphere their magnetic field lines become rooted in the ionosphere (i.e. in a medium with finite transverse conductivity), (4) the external Lorentz force acting on their boundary surface depends on the orientation of their magnetic moment with respect to the external magnetic field, (5) when their mechanical equilibrium is disturbed, hydromagnetic oscillations can be generated. It is also suggested that the front side of all solar wind plasmoids which have penetrated into the magnetosphere is the inner edge of the magnetospheric boundary layer while the magnetopause is considered to be the surface where the magnetospheric plasma ceases to have a trapped pitch angle distribution.