Showing papers on "Dipole model of the Earth's magnetic field published in 1999"

The Transport of Cosmic Rays across a Turbulent Magnetic Field

Abstract: We present a new analysis of the transport of cosmic rays in a turbulent magnetic field that varies in all three spatial dimensions. The analysis utilizes a numerical simulation that integrates the trajectories of an ensemble of test particles from which we obtain diffusion coefficients based on the particle motions. We find that the diffusion coefficient parallel to the mean magnetic field is consistent with values deduced from quasi-linear theory, in agreement with earlier work. The more interesting and less understood transport perpendicular to the average magnetic field is found to be enhanced (above the classical scattering result) by the random walk, or braiding, of the magnetic field. The value of κ⊥ obtained is generally larger than the classical scattering value but smaller than the quasi-linear value. The computed values of κ⊥/κ∥, for a representation of the interplanetary magnetic field, are 0.02-0.04; these values are of the same general magnitude as those assumed in recent numerical simulations of cosmic-ray modulation and transport in the heliosphere, and give reasonable agreement with spacecraft observations of cosmic rays. Some consequences of these results for the interpretation of heliospheric observations are discussed.

A doubling of the Sun's coronal magnetic field during the past 100 years

Abstract: The solar wind is an extended ionized gas of very high electrical conductivity, and therefore drags some magnetic flux out of the Sun to fill the heliosphere with a weak interplanetary magnetic field1,2. Magnetic reconnection—the merging of oppositely directed magnetic fields—between the interplanetary field and the Earth's magnetic field allows energy from the solar wind to enter the near-Earth environment. The Sun's properties, such as its luminosity, are related to its magnetic field, although the connections are still not well understood3,4. Moreover, changes in the heliospheric magnetic field have been linked with changes in total cloud cover over the Earth, which may influence global climate5. Here we show that measurements of the near-Earth interplanetary magnetic field reveal that the total magnetic flux leaving the Sun has risen by a factor of 1.4 since 1964: surrogate measurements of the interplanetary magnetic field indicate that the increase since 1901 has been by a factor of 2.3. This increase may be related to chaotic changes in the dynamo that generates the solar magnetic field. We do not yet know quantitatively how such changes will influence the global environment.

Cosmic ray modulation and the solar magnetic field

Abstract: We show that the variations of the interplanetary magnetic field strength (B) over a 22-year period are tracked by the inverted profile of the cosmic ray density measured by neutron monitors. We suggest that global changes in the Sun's magnetic field are more important for long-term modulation than magnetic field enhancements resulting from the merging of high-speed flows and coronal mass ejections in the outer heliosphere. The unexpectedly close relationship that we find between the “tilt angle” of the heliospheric current sheet and the cosmic ray density away from solar minimum for both polarity states of the solar magnetic field may be accounted for by the anticorrelation between the cosmic ray density and field strength variations.

The polar cusp location and its dependence on dipole tilt

Abstract: Polar cusp crossings at high altitudes are seen in the POLAR data as decreases in the magnetic field and increases in magnetosheath-like plasma. Close to 500 polar cusp crossings identified from the magnetic field, low-energy electron and ion data observed by POLAR, are used to determine the statistical location of the polar cusp. When compared with Tsyganenko's 1989 vacuum model with an ellipsoidal magnetopause [Tsyganenko, 1989], the medians of the cusp crossings are located between the magnetic field lines with invariant latitudes of 80° and 82°. Statistically the shape of the polar cusp in this region is consistent with this model although there is much scatter around the median value. The position of the cusp is significantly dependent on the dipole tilt angle. When dipole tilts more toward the Sun, the cusp moves more poleward to higher invariant latitude from 77.2° at −30° tilt, to 80.0° at 0° tilt, to 81.8° at 30° or roughly 1° for every 14° of tilt.

Magnetopause from pressure balance

Abstract: The shape of the magnetopause and the field due to magnetopause currents are calculated from the requirement that the pressure in the magnetosheath be balanced by magnetic pressure inside the magnetosphere. The field due to magnetopause currents is calculated to be consistent with the iteratively adjusted magnetopause shape. The field due to current systems inside the magnetosphere is taken from the T96 model [Tsyganenko, 1996], which carries information from ∼47,000 magnetic field observations. Many different magnetospheric configurations were found for a variety of conditions. Changes in the shape of the magnetopause with varying dipole tilt angle stood out. The magnetotail and the nose (the point closest to the Sun) were found to shift vertically, in opposite directions, for nonzero dipole tilt. The vertical offset of the nose from the Earth-Sun line varied linearly with dipole tilt angle, reaching ∼3 RE for maximal tilt and having a weak dependence on solar wind dynamic pressure. The formation of a secondary stagnation point just above the sunward cusp was indicated for absolute dipole tilts in excess of 15°. The magnitude of the field strength at its local maximum just behind the cusp was determined as a function of dipole tilt angle and the subsolar field strength. Calculated magnetopause shapes and observed magnetopause crossings were found to be consistent when the tilt angle was taken into account. Variations in the latitude of the magnetic cusps with dynamic pressure, interplanetary magnetic field Bz, and dipole tilt were reasonably consistent with observed variations in the latitude of the particle cusp.

A Test for Coronal Magnetic Field Extrapolations

Abstract: As models for the physical properties of the corona above solar active regions grow more sophisticated, we will require better means for testing them. In this paper we discuss and apply such a test to a magnetic field model for an active region. This test is based on the expectation that the temperatures at different points on a given magnetic field line should be well correlated because of the rapid transport of heat along field lines in the corona. We use radio observations of an active region to measure the temperatures on field lines as they cross two isogauss surfaces (at 430 and 750 G) in the corona. The field lines and isogauss surfaces are derived from a coronal magnetic field model obtained via a nonlinear force-free field extrapolation of a photospheric vector magnetogram; for comparison, we also investigate a potential-field extrapolation of the same magnetogram. In a region in which strongly sheared fields are present, the nonlinear force-free field model does indeed show a good correlation between the temperatures in the two surfaces at points on the same field line, while the potential-field model does not. This diagnostic acts both as a test of the magnetic field model as well as of the interpretation of the radio data, and we show how this test can also aid in understanding the radio data.

Alfvén wave phase mixing driven by velocity shear in two‐dimensional open magnetic configurations

Abstract: Phase mixing of torsional Alfven waves in axisymmetric equilibrium magnetic configurations with purely poloidal magnetic field and stationary flow along the field lines in resistive viscous plasmas is studied. The characteristic wavelength along the magnetic field lines is assumed to be much smaller than the characteristic scale of inhomogeneity in the magnetic field direction, and the WKB method is used to obtain an analytic solution describing phase mixing. The general solution is applied to a particular configuration with the radial magnetic field and flow under the assumptions that the magnetic field and density are independent of the polar angle in the spherical coordinates and the flow velocity is independent of the radial coordinate. The only source of phase mixing in this configuration is velocity shear. The analytical solution is compared with a numerical simulation of the fully nonlinear resistive MHD equations. The numerical and analytical results are in good agreement. Consequences for wave energy deposition into the solar corona and solar wind and for the evolution of the Alfven wave energy spectrum are discussed.

Electromagnetic showers in a strong magnetic field

Abstract: We present the results concerning the main shower characteristics in a strong magnetic field obtained through shower simulation. The processes of magnetic bremsstrahlung and pair production were taken into account for values of the parameter >>1. We compare our simulation results with a recently developed cascade theory in a strong magnetic field.

Magnetic braking of the present Sun

Abstract: Magnetic braking is essential for angular momentum transport in late-type stars which have convective envelopes. The mechanism may be entirely responsible for the slow rotation of the present Sun, on which a braking model is normally calibrated. Recent or current satellite missions such as Helios and Ulysses have jointly revealed a more complete picture of the solar corona, and more specifically of the solar wind. The wealth of these data at or near the solar minimum is valuable for constraining the dipolar solar braking model. In this paper, we use recently available observations (at or near the solar minimum) to constrain a solar magnetic braking model based on a dipolar field structure. It is found that the Ulysses data indicate a spherical Alfven surface at high latitudes. We infer from a thermal wind model that it is located at 16 Ro˙, which is larger than the 12 Rodot; deduced from the Helios data for the equatorial region near the solar minimum. It is also found that the braking model with a transition from a dipole to a split monopole field is generally consistent with Ulysses observations, provided that a linear relation between dead zone extent and dipole field strength is satisfied. Thus either the dipole field retains a sizeable dead zone but is much stronger than the standard value, ∼ 1 G, or the field has standard strength but an exceedingly small dead zone (<2 R x o˙). The magnetic braking rate as constrained by Ulysses data is found to be 2.1× 1030 dyn cm, which is about a quarter of the value deduced earlier from the Weber & Davis model and does not differ significantly from that deduced by Pizzo et al.

Magnetic Null Points due to Multiple Sources of Solar Photospheric Flux

Abstract: How common are magnetic null points in the highly complex magnetic field of the solar atmosphere? In this work we seek to model the magnetic structure of quiet regions by placing magnetic sources and sinks on a hexagonal network of supergranule cells to represent the intense magnetic fields that occur at the boundaries of these cells. The resulting potential coronal magnetic field is then computed analytically and searched numerically for magnetic null points, which are classified according to their types and spine directions. Two relations from the theory of vector fields relate the numbers of null points to the numbers of sources and sinks and these are used to check the numerical results. Previous results relating these quantities for monopolar and dipolar magnetic fields are described and a new one for a particular class of quadrupolar fields arising in this study is derived. We model a three-cell configuration and study the effects of increasing the strength of a central sink and of moving the central sink. A twelve-cell configuration is studied in lesser detail.

Model pulsar magnetospheres: the perpendicular rotator

Abstract: The simplest model illustrating the effect of the magnetospheric charge-current field on the structure of a pulsar magnetic field has the region within the light-cylinder filled with the Goldreich–Julian charge density which corotates with the neutron star, but has no electric currents along the magnetic field lines. This model has previously been studied for the axisymmetric case, with the rotation and magnetic dipolar axes aligned. The analogous problem is now solved with the two axes mutually perpendicular, so that not only the material current arising from the rotating charges but also the displacement current contributes. Again, the constructed magnetic field B0 crosses the light-cylinder normally, and there is no energy flux to infinity. However, in a more realistic model there is a flow of current along B0, generating a field B1 which has a non-vanishing toroidal component at the light-cylinder, so yielding a finite integrated Poynting flux.

Observations of polar cap arcs on FAST

Abstract: FAST satellite observations of spatially localized regions of electron and ion precipitation with concomitant paired upward and downward field-aligned currents and duskward electric field enhancements at high (> 80° invariant latitude) magnetic latitudes are presented. Each pass of several across the polar cap was made during a period of persistent northward interplanetary magnetic field, and was characterized by the presence of several of these precipitation regions. In each case, the precipitation regions were associated with jets of enhanced antisunward convection, with electron precipitation restricted to the upward current region, and no energetic electron outflow in the downward current region, and ion precipitation spread over broader regions, possibly by time-of-flight effects. We compare these low-altitude features to those expected for source regions lying in a reconnection site at the lobe magnetopause, a bursty bulk flow in the plasma sheet, and a surface wave on the low-latitude boundary layer (LLBL). We find that the lobe reconnection model successfully describes the observed electrodynamics of the arcs, as well as the electron and ion source temperatures, but can not readily explain the presence of precipitating O+ and He+ in addition to H+ and He++. The plasma sheet source model can explain the composition of the ion precipitation but predicts higher electron and ion source temperatures than are observed, may require the coincidence of bursty bulk flows with extensions of the plasma sheet into the lobe, and may not be consistant with other observations of auroral phenomenology. The LLBL surface wave model does not readily explain the observed electrodynamics of the arcs and is not consistent with the observed offsets between electron and ion precipitation.

A two-dimensional simulation of the Kelvin-Helmholtz instability with magnetic shear

Abstract: The Kelvin-Helmholtz instability is a mechanism for transport of mass and momentum from the solar wind to the magnetosphere Using a two-dimensional compressional MHD simulation, we explore the mass and momentum transport at the boundary for different magnetic field configurations corresponding to the flank low-latitude boundary layer We used data taken from Phan and Paschmann [1996] and Paschmann et al [1993] to better approximate the density and magnetic field structure of the boundary layer for low- and high-shear magnetic fields We found that mass transport was the largest for the low-shear magnetic field configuration where the magnetic field in the magnetosheath was almost parallel to the magnetospheric magnetic field The largest momentum transport occurred for cases where the magnetic field in the magnetosheath was parallel or antiparallel to the magnetospheric magnetic field

Observations of heliospheric planar and offset‐planar magnetic structures

Abstract: Planar magnetic structures are regions of solar wind plasma where the magnetic field orientation is constrained within a fixed plane for durations of several hours. Within these structures, magnetic field discontinuities are seen, with the discontinuity surfaces being almost co-planar. The results of a survey of planar magnetic strutures detected by the Ulysses spacecraft are presented. When searching for these events using minimum variance analysis, a large population was detected of magnetic field structures whose directions described small circles in the spacecraft's field of view (as opposed to great circles described by “classic” planar magnetic structures). It is likely that these “small-circle” events represents Alfvenic structures. Variations in the nature of the structures at various heliographic latitudes and differing solar wind conditions are described. Implications of the results of the survey are discussed.

A study of the inner magnetosphere based on data of Polar

Abstract: A statistical study of the near-Earth equatorial magnetic field depression has been done on the basis of a set of data from 20 months of Polar magnetic field experiment in 1996-1997, supported by simultaneous information on the solar wind state by Wind and IMP 8 spacecraft. This work addresses the spatial distribution of the magnetic field, produced by magnetospheric currents near the dipole equator at radial distances between 2.0 and 4.5 R E , and its dependence on the ground Dst field, solar wind pressure, and interplanetary magnetic field (IMF). The observed radial and local time variation of the regression coefficients in the expansion for the disturbance field is interpreted in terms of the relative contribution of the principal magnetospheric currents. The inner field has a significant noon-midnight and dawn-dusk asymmetry, sensitive to Dst and to the solar wind pressure. The results confirm the high quality of the Polar magnetic field experiment (MFE) data in a wide range of altitudes and will be a useful guide for the modeling of the inner magnetosphere.

Instability of a pseudo-relativistic model of matter with self-generated magnetic field

Abstract: For a pseudo-relativistic model of matter, based on the no-pair Hamiltonian, we prove that the inclusion of the interaction with the self-generated magnetic field leads to instability for all positive values of the fine structure constant This is true no matter whether this interaction is accounted for by the Breit potential, by an external magnetic field which is chosen to minimize the energy, or by the quantized radiation field

Dissipation and wave-ion interaction in the solar wind: Links between fluid and kinetic theory

Abstract: In this paper we establish links between turbulence dissipation and wave-particle interactions in the solar corona and wind. Based on quasilinear theory, a set of anisotropic, multi-component fluid equations is derived, which describe the wave-particle interactions of ions with Alfven waves and ion-cyclotron waves or magnetosonic waves propagating along the mean magnetic field. The associated equations for the wave spectrum and the heating and acceleration of the ions are derived. In fast solar wind streams heavy ions have about equal thermal speeds as the protons and flow faster than them. In order to explain the observed relations, T j / T p ≈ m j /m p and U j U p ≈ V A , a numerical fluid-type model is developed, which takes into account the relevant wave-particle interactions. It is shown that left- and right-handed polarized waves propagating away from the Sun parallel to the interplanetary magnetic field can resonantly heat and accelerate minor ions preferentially with respect to the protons in close agreement with the measured characteristics of ion velocity distributions. Finally, some results from a simple analytical model are discussed.

Simultaneous satellite and ground-based observations of a discretely driven field line resonance

Abstract: An analysis is presented of a set of toroidal field line resonances observed on the ground by CANOPUS magnetometers and scanning auroral photometers on December 13, 1990, following a substorm onset at 0750 UT and intensification at 0850 UT. Magnetic and electric field data from the CRRES satellite provide evidence that the resonance was also observed in the magnetosphere. To our knowledge, this is the first report of discretely driven resonances observed by ground-based magnetometers and photometers and confirmed using satellite data. A spectral peak at 2.1 mHz is present in all data sets at approximately the same invariant latitude and universal time, indicating that CANOPUS and CRRES are observing the same resonance. Peaks are also present at 1.4 and 1.7 mHz in the ground-based magnetometer and CRRES data at a slightly higher latitude with corresponding spectral peaks apparent in the photometer data. The ground signature for each resonance indicates an antisunward phase velocity, suggesting that the excitation source is in the vicinity of the dayside magnetosphere, consistent with a waveguide model of the magnetosphere but not with a cavity model. This fact, combined with a possibly enhanced solar wind dynamic pressure, suggests that the substorm was not directly responsible for exciting the resonances. The interaction of the resonances with the substorm remains unclear except for the luminosity fluctuations associated with the resonances.

Relevance of cme to the structure of large-scale solar magnetic fields

Abstract: The relevance of the occurrence rate and location of CME events to two main systems (giant and supergiant) of the large-scale solar magnetic field structure has been investigated. The clustering of CME events and solar flares toward the neutral line of the global field system (neutral line of the source surface field) corroborates the finding by Hundhausen that CME locations track the heliomagnetic equator. A good correlation has been revealed between the CME occurrence rate and variations of the index of the effective solar multipole, that characterizes the typical scale of the global solar magnetic field. The CME rate exhibits sharp jumps/decreases when the index of the effective solar multipole passes through n=4. The observations of X-ray 'blow-out' effects have been analyzed as probable manifestations of CMEs on the disk and have been compared with the large-scale magnetic field structure. As shown by the analysis, the X-ray arcades straddle the neutral line and occur, or at least tend to occur, where the neutral line exhibits a sharp bend. A conclusion is made that CME events are caused by interaction of two large-scale field systems, one of them (the global field system) determining the location of CMEs and another (the system of closed magnetic fields) their occurrence rate.

Topological Differences Between Force-Free Field Models

Abstract: The potential and linear force-free field models for the magnetic field in the solar corona are often used in the analysis of flares. The field is calculated using boundary values measured in the low solar atmosphere. The topology of the field calculated using these models is then compared to the position of flare emissions. We demonstrate that the topology of the field according to each of these models, with the same boundary conditions in place, is not in general even qualitatively equivalent. An argument is given for a similar discrepancy between a linear force-free field solution and a nonlinear force-free field solution.

Oscillations in a magnetic solar model. I. Parallel propagation in a chromospheric and coronal magnetic field with constant Alfvén speed

Abstract: Oscillation eigenmodes are studied for a planar solar model with a non-uniform horizontal magnetic field in the atmosphere. The three layer atmospheric model is the same as in Tirry et al. (1998). The analysis in that paper is extended to a wide range of parameters. Different types of oscillation modes are determined for a wide range of the magnetic field strength and for different degrees of the spherical harmonic. The emphasis is on the possible coupling of global solar oscillation modes to localized continuum eigenmodes of the magnetic atmosphere. For propagation parallel to the magnetic field, the global oscillation modes can couple only to slow continuum modes and this is found to occur for a rather large range of parameters. In addition to the damping of global oscillation modes due to resonant absorption it was found that the interaction of global eigenmodes with slow continuum modes leads to unanticipated behaviour of global eigenmodes. The rather strange behaviour in the slow continuum involves the disappearance and appearance of global modes and splitting and merging of global modes. Additionally, frequency shifts of global modes due to the magnetic field have been examined. The shifts are compared to observations.

A numerical method to compute Euler potentials for non dipolar magnetic fields

Abstract: . The magnetospheric magnetic field may be conveniently described by two scalar functions (α, β), known as the Euler potentials. They are not uniquely defined, and they may be difficult to derive for configuration more complex than a simple dipole. We propose here a simple numerical method to compute one possible pair (α, β). In magnetospheric regions of closed field lines, α can be chosen as a function of the tube volume of unit magnetic flux. The method can be applied to a wide class of magnetic fields which describe the magnetospheric domain of closed field lines and the conjugated ionosphere. Here, it is used with the T87 Tsyganenko model. The results coincide with the dipolar potentials at close distances from the Earth. At larger distances, they display an increasing distortion with the radial distance (or the invariant latitude in the ionosphere) and the magnetic activity. In the magnetosphere, the contours of α and β are stretched towards the nightside. In the ionosphere, they also extend towards the nightside and present major distortions in a narrow ring at the polar cap boundary, which maps distant boundary layers in the magnetosphere. Key words. Ionosphere (ionosphere-magnetosphere interactions; modeling and forecasting). Magnetospheric physics (plasma convection).

Transport effects in the evolution of the global solar magnetic field

Abstract: The axisymmetric component of the large-scale solar magnetic fields has a pronounced poleward branch at higher latitudes. In order to clarify the origin of this branch we construct an axisymmetric model of the passive transport of the mean poloidal magnetic field in the convective zone, including meridional circulation, anisotropic diffusivity, turbulent pumping and density pumping. For realistic values of the transport coefficients we find that diffusivity is prevalent, and the latitudinal distribution of the field at the surface simply reflects the conditions at the bottom of the convective zone. Pumping effects concentrate the field to the bottom of the convective zone; a significant part of this pumping occurs in a shallow subsurface layer, normally not resolved in dynamo models. The phase delay of the surface poloidal field relative to the bottom poloidal field is found to be small. These results support the double dynamo wave models, may be compatible with some form of a mixed transport scenario, and exclude the passive transport theory for the origin of the polar branch.

Geomagnetic effects of the Earth’s ellipticity

Abstract: We analyse the external field generated by a uniform distribution of magnetic susceptibility contained in an oblate spheroidal shell when it is magnetized by an internal magnetic field of arbitrary complexity. The situation is more relevant to the Earth than that of a spherical shell considered by Runcorn (1975a) (in the context of lunar magnetism), because of the larger flattening of the Earth than that of the Moon. We find that, to first order in the susceptibility, each internal harmonic in a spheroidal harmonic expansion of the magnetic potential generates just one non-vanishing external field coefficient, unlike in the spherical case when all harmonics vanish identically. The field generated is proportional to the susceptibility, thickness of the shell and square of the Earth’s eccentricity, and hence it appears that this field amplification mechanism will be very ineffective for the Earth.

Pair production in a time-dependent magnetic field

Abstract: The production of electron–positron pairs in a time-dependent magnetic field is estimated in the hypotheses that the magnetic field is uniform over large distances with respect to the pair localization and it is so strong that the spacing of the Landau levels is larger than the rest mass of the particles. This calculation is presented since it has been suggested that extremely intense and varying magnetic fields may be found around some astrophysical objects.

Spectral analysis of the magnetic field inside particle propagation channels detected by ULYSSES

Abstract: Prior studies have identified particle propagation channels in the interplanetary medium where nearly scatter– free propagation occurs. These channels have been identified to exist as far away from the Sun as ∼4 AU. We report here a study that has examined, using spacecraft–based instrumentation, the nature of the fluctuations of the interplanetary magnetic fields inside two such propagation channels as well as in the regions outside the channels. We show that the power spectral fluctuations of the total magnitude of the magnetic field in the entire channel duration encountered are the order of a factor of 10 lower inside the channels than outside. Somewhat surprisingly, in the 1–40 mHz frequency range, we find little change in the slope of the power law spectra from outside to inside the channels. These results provide evidence that the dominant control on the particle pitch angle diffusion coefficients in the channels is the level of power available for particle scattering, and not changes in the shape of the spectra themselves. We have examined the power spectra of each component of the magnetic field and determined that the loss of spectral power is due to a reduction of compressible fluctuations, the solenoidal components of the spectra remaining similar inside and outside the channels.