Showing papers on "Dipole model of the Earth's magnetic field published in 2015"

First results of the MAVEN magnetic field investigation

Abstract: Two Mars Atmosphere and Volatile EvolutioN magnetic field sensors sample the ambient magnetic field at the outer edge of each solar array. We characterized relatively minor spacecraft-generated magnetic fields using in-flight subsystem tests and spacecraft maneuvers. Dynamic spacecraft fields associated with the power subsystem (≤1 nT) are compensated for using spacecraft engineering telemetry to identify active solar array circuits and monitor their electrical current production. Static spacecraft magnetic fields are monitored using spacecraft roll maneuvers. Accuracy of measurement of the environmental magnetic field is demonstrated by comparison with field directions deduced from the symmetry properties of the electron distribution function measured by the Solar Wind Electron Analyzer. We map the bow shock, magnetic pileup boundary, the V × B convection electric field and ubiquitous proton cyclotron, and 1 Hz waves in the ion foreshock region.

Modular model for Mercury's magnetospheric magnetic field confined within the average observed magnetopause

Abstract: Accurate knowledge of Mercury's magnetospheric magnetic field is required to understand the sources of the planet's internal field. We present the first model of Mercury's magnetospheric magnetic field confined within a magnetopause shape derived from Magnetometer observations by the MErcury Surface, Space ENvironment, GEochemistry, and Ranging spacecraft. The field of internal origin is approximated by a dipole of magnitude 190 nT RM3, where RM is Mercury's radius, offset northward by 479 km along the spin axis. External field sources include currents flowing on the magnetopause boundary and in the cross-tail current sheet. The cross-tail current is described by a disk-shaped current near the planet and a sheet current at larger (≳ 5 RM) antisunward distances. The tail currents are constrained by minimizing the root-mean-square (RMS) residual between the model and the magnetic field observed within the magnetosphere. The magnetopause current contributions are derived by shielding the field of each module external to the magnetopause by minimizing the RMS normal component of the magnetic field at the magnetopause. The new model yields improvements over the previously developed paraboloid model in regions that are close to the magnetopause and the nightside magnetic equatorial plane. Magnetic field residuals remain that are distributed systematically over large areas and vary monotonically with magnetic activity. Further advances in empirical descriptions of Mercury's magnetospheric external field will need to account for the dependence of the tail and magnetopause currents on magnetic activity and additional sources within the magnetosphere associated with Birkeland currents and plasma distributions near the dayside magnetopause.

The Present and Future Geomagnetic Field

Abstract: The Earth's magnetic field is the result of the superposition of a main field produced by the geodynamo within the core and of many other fields produced by a variety of secondary sources. Unfortunately, magnetometers can only measure the resulting field, and a single measurement cannot distinguish the contributions from each source. However, provided enough ground and satellite measurements are being acquired and processed in appropriate ways, a separation of the contributions from each type of field can be achieved and global models of the Earth's magnetic field constructed. The main purpose of this chapter is to provide an up-to-date review of such global models. We introduce the relevant types of magnetic data, review the models, and focus on the current behavior of the main field. We also report on the emerging field of geomagnetic data assimilation, which aims at both improving our understanding of the geodynamo and forecasting the main field evolution.

Minimizing magnetic fields for precision experiments

Abstract: An increasing number of measurements in fundamental and applied physics rely on magnetically shielded environments with sub nano-Tesla residual magnetic fields. State of the art magnetically shielded rooms (MSRs) consist of up to seven layers of high permeability materials in combination with highly conductive shields. Proper magnetic equilibration is crucial to obtain such low magnetic fields with small gradients in any MSR. Here, we report on a scheme to magnetically equilibrate MSRs with a 10 times reduced duration of the magnetic equilibration sequence and a significantly lower magnetic field with improved homogeneity. For the search of the neutron's electric dipole moment, our finding corresponds to a 40% improvement of the statistical reach of the measurement. However, this versatile procedure can improve the performance of any MSR for any application.

From solar to stellar corona: the role of wind, rotation and magnetism

Abstract: Observations of surface magnetic fields are now within reach for many stellar types thanks to the development of Zeeman-Doppler Imaging. These observations are extremely useful for constraining rotational evolution models of stars, as well as for characterizing the generation of magnetic field. We recently demonstrated that the impact of coronal magnetic field topology on the rotational braking of a star can be parametrized with a scalar parameter: the open magnetic flux. However, without running costly numerical simulations of the stellar wind, reconstructing the coronal structure of the large scale magnetic field is not trivial. An alternative -broadly used in solar physics- is to extrapolate the surface magnetic field assuming a potential field in the corona, to describe the opening of the field lines by the magnetized wind. This technique relies on the definition of a so-called source surface radius, which is often fixed to the canonical value of 2.5Rsun. However this value likely varies from star to star. To resolve this issue, we use our extended set of 2.5D wind simulations published in 2015, to provide a criteria for the opening of field lines as well as a simple tool to assess the source surface radius and the open magnetic flux. This allows us to derive the magnetic torque applied to the star by the wind from any spectropolarimetric observation. We conclude by discussing some estimations of spin-down time scales made using our technique, and compare them to observational requirements.

Quantifying the Difference Between the Flux-Tube Expansion Factor at the Source Surface and at the Alfv\'en Surface Using A Global MHD Model for the Solar Wind

Abstract: The potential field approximation has been providing a fast, and computationally inexpensive estimation for the solar corona's global magnetic field geometry for several decades. In contrast, more physics-based global magnetohydrodynamic (MHD) models have been used for a similar purpose, while being much more computationally expensive. Here, we investigate the difference in the field geometry between a global MHD model and the potential field source surface model (PFSSM) by tracing individual magnetic field lines in the MHD model from the Alfven surface (AS), through the source surface (SS), all the way to the field line footpoint, and then back to the source surface in the PFSSM. We also compare the flux-tube expansion at two points at the SS and the AS along the same radial line. We study the effect of solar cycle variations, the order of the potential field harmonic expansion, and different magnetogram sources. We find that the flux-tube expansion factor is consistently smaller at the AS than at the SS for solar minimum and the fast solar wind, but it is consistently larger for solar maximum and the slow solar wind. We use the Wang--Sheeley--Arge (WSA) model to calculate the associated wind speed for each field line, and propagate these solar-wind speeds to 1AU. We find a more than five hours deviation in the arrival time between the two models for 20% of the field lines in the solar minimum case, and for 40% of the field lines in the solar maximum case.

Parent magnetic field models for the IGRF-12

Abstract: We propose candidate models for IGRF-12. These models were derived from parent models built from 10 months of Swarm satellite data and 1.5 years of magnetic observatory data. Using the same parameterisation, a magnetic field model was built from a slightly extended satellite data set. As a result of discrepancies between magnetic field intensity measured by the absolute scalar instrument and that calculated from the vector instrument, we re-calibrated the satellite data. For the calibration, we assumed that the discrepancies resulted from a small perturbing magnetic field carried by the satellite, with a strength and orientation dependent on the Sun’s position relative to the satellite. Scalar and vector data were reconciled using only a limited number of calibration parameters. The data selection process, followed by the joint modelling of the magnetic field and Euler angles, leads to accurate models of the main field and its secular variation around 2014.0. The obtained secular variation model is compared with models based on CHAMP satellite data. The comparison suggests that pulses of magnetic field acceleration that were observed on short time scales average-out over a decade.

Null Point Distribution in Global Coronal Potential Field Extrapolations

Abstract: Magnetic null points are points in space where the magnetic field is zero. Thus, they can be important sites for magnetic reconnection by virtue of the fact that they are weak points in the magnetic field and also because they are associated with topological structures, such as separators, which lie on the boundary between four topologically distinct flux domains and therefore are also locations where reconnection occurs. The number and distribution of nulls in a magnetic field acts as a measure of the complexity of the field. In this article, the numbers and distributions of null points in global potential field extrapolations from high-resolution synoptic magnetograms are examined. Extrapolations from magnetograms obtained with the Michelson Doppler Imager (MDI) are studied in depth and compared with those from high-resolution SOlar Long-time Investigations of the Sun (SOLIS) and Heliospheric Magnetic Imager (HMI). The fall-off in the density of null points with height is found to follow a power law with a slope that differs depending on whether the data are from solar maximum or solar minimum. The distribution of null points with latitude also varies with the cycle as null points form predominantly over quiet-Sun regions and avoid active-region fields. The exception to this rule are the null points that form high in the solar atmosphere, and these null points tend to form over large areas of strong flux in active regions. From case studies of data acquired with the MDI, SOLIS, and HMI, it is found that the distribution of null points is very similar between data sets, except, of course, that there are far fewer nulls observed in the SOLIS data than in the cases from MDI and HMI due to its lower resolution.

Internally and externally induced deformations of the magnetospheric equatorial current as inferred from spacecraft data

Abstract: . Based on a data pool of 79 yearly files of space magnetometer data by Polar, Cluster, Geotail, and THEMIS satellites between 1995 and 2013, we developed a new quantitative model of the global shape of the magnetospheric equatorial current sheet as a function of the Earth's dipole tilt angle, solar wind ram pressure, and interplanetary magnetic field (IMF). This work upgrades and generalizes an earlier model of Tsyganenko and Fairfield (2004) by extending the modeling region to all local times, including the dayside sector. In particular, an essential feature of the new model is the bowl-shaped tilt-related deformation of the equatorial surface of minimum magnetic field, similar to that observed at Saturn, whose existence in the Earth's magnetosphere has been demonstrated in our recent work (Tsyganenko and Andreeva, 2014).

Parent magnetic field models for the IGRF-12GFZ-candidates

Abstract: We propose candidate models for IGRF-12. These models were derived from parent models built from 10 months of Swarm satellite data and 1.5 years of magnetic observatory data. Using the same parameterisation, a magnetic field model was built from a slightly extended satellite data set. As a result of discrepancies between magnetic field intensity measured by the absolute scalar instrument and that calculated from the vector instrument, we re-calibrated the satellite data. For the calibration, we assumed that the discrepancies resulted from a small perturbing magnetic field carried by the satellite, with a strength and orientation dependent on the Sun’s position relative to the satellite. Scalar and vector data were reconciled using only a limited number of calibration parameters. The data selection process, followed by the joint modelling of the magnetic field and Euler angles, leads to accurate models of the main field and its secular variation around 2014.0. The obtained secular variation model is compared with models based on CHAMP satellite data. The comparison suggests that pulses of magnetic field acceleration that were observed on short time scales average-out over a decade.

Long-term variation in the Sun's activity caused by magnetic Rossby waves in the tachocline

Abstract: Long-term records of sunspot number and concentrations of cosmogenic radionuclides (10Be and 14C) on the Earth reveal the variation of the Sun's magnetic activity over hundreds and thousands of years. We identify several clear periods in sunspot, 10Be, and 14C data as 1000, 500, 350, 200 and 100 years. We found that the periods of the first five spherical harmonics of the slow magnetic Rossby mode in the presence of a steady toroidal magnetic field of 1200-1300 G in the lower tachocline are in perfect agreement with the time scales of observed variations. The steady toroidal magnetic field can be generated in the lower tachocline either due to the steady dynamo magnetic field for low magnetic diffusivity or due to the action of the latitudinal differential rotation on the weak poloidal primordial magnetic field, which penetrates from the radiative interior. The slow magnetic Rossby waves lead to variations of the steady toroidal magnetic field in the lower tachocline, which modulate the dynamo magnetic field and consequently the solar cycle strength. This result constitutes a key point for long-term prediction of the cycle strength. According to our model, the next deep minimum in solar activity is expected during the first half of this century.

Magnetar activity via the density–shear instability in Hall-MHD

Abstract: We investigate the density-shear instability in Hall-MHD via numerical simulation of the full non-linear problem, in the context of magnetar activity. We confirm the development of the instability of a plane-parallel magnetic field with an appropriate intensity and electron density profile, in accordance with analytic theory. We find that the instability also appears for a monotonically decreasing electron number density and magnetic field, a plane-parallel analogue of an azimuthal or meridional magnetic field in the crust of a magnetar. The growth rate of the instability depends on the Hall properties of the field (magnetic field intensity, electron number density and the corresponding scale-heights), while being insensitive to weak resistivity. Since the Hall effect is the driving process for the evolution of the crustal magnetic field of magnetars, we argue that this instability is critical for systems containing strong meridional or azimuthal fields. We find that this process mediates the formation of localised structures with much stronger magnetic field than the average, which can lead to magnetar activity and accelerate the dissipation of the field and consequently the production of Ohmic heating. Assuming a 5 × 1014G magnetic field at the base of crust, we anticipate that magnetic field as strong as 1015G will easily develop in regions of typical size of a few 102 meters, containing magnetic energy of 1043erg, sufficient to power magnetar bursts. These active regions are more likely to appear in the magnetic equator where the tangential magnetic field is stronger.

The Evolution of Québec Earth Models Used to Model Geomagnetically Induced Currents

Abstract: Geomagnetically induced currents (GIC) in power systems can interfere with the system operation and, in extreme cases, can damage transformers and cause power blackouts. A notable example is the magnetic disturbance of March 13, 1989 that caused a blackout of the Hydro-Quebec system. The size of the GIC depends on the inducing magnetic-field variations, earth conductivity structure, and system characteristics. This paper examines the earth models developed for Quebec and shows how the changes in earth models have changed the electric-field values calculated for the March 13, 1989 storm. These calculations are made using data from two magnetic observatories: one at the southern end of Quebec and one at the northern end. It is shown how the choice of magnetic-field data and uncertainty in the earth model influence the calculated electric-field values.

A Determination of the North–South Heliospheric Magnetic Field Component from Inner Corona Closed-loop Propagation

Abstract: A component of the magnetic field measured in situ near the Earth in the solar wind is present from north–south fields from the low solar corona. Using the Current-sheet Source Surface model, these fields can be extrapolated upward from near the solar surface to 1 AU. Global velocities inferred from a combination of interplanetary scintillation observations matched to in situ velocities and densities provide the extrapolation to 1 AU assuming mass and mass flux conservation. The north–south field component is compared with the same ACE in situ magnetic field component—the Normal (Radial Tangential Normal) Bn coordinate—for three years throughout the solar minimum of the current solar cycle. We find a significant positive correlation throughout this period between this method of determining the Bn field compared with in situ measurements. Given this result from a study during the latest solar minimum, this indicates that a small fraction of the low-coronal Bn component flux regularly escapes from closed field regions. The prospects for Space Weather, where the knowledge of a Bz field at Earth is important for its geomagnetic field effects, is also now enhanced. This is because the Bn field provides the major portion of the Geocentric Solar Magnetospheric Bz field coordinate that couples most closely to the Earth's geomagnetic field.

Limitations of force-free magnetic field extrapolations: revisiting basic assumptions

Abstract: Force-free extrapolations are widely used to study the magnetic field in the solar corona based on surface measurements. The extrapolations assume that the ratio of internal energy of the plasma to magnetic energy, the plasma-beta is negligible. Despite the widespread use of this assumption observations, models, and theoretical considerations show that beta is of the order of a few percent to more than 10%, and thus not small. We investigate what consequences this has for the reliability of extrapolation results. We use basic concepts starting with the force and the energy balance to infer relations between plasma-beta and free magnetic energy, to study the direction of currents in the corona with respect to the magnetic field, and to estimate the errors in the free magnetic energy by neglecting effects of the plasma (beta<<1). A comparison with a 3D MHD model supports our basic considerations. If plasma-beta is of the order of the relative free energy (the ratio of the free magnetic energy to the total magnetic energy) then the pressure gradient can balance the Lorentz force. This is the case in the solar corona, and therefore the currents are not properly described. In particular the error in terms of magnetic energy by neglecting the plasma is of the order of the free magnetic energy, so that the latter can not be reliably determined by an extrapolation. While a force-free extrapolation might capture the magnetic structure and connectivity of the coronal magnetic field, the derived currents and free magnetic energy are not reliable. Thus quantitative results of extrapolations on the location and amount of heating in the corona (through current dissipation) and on the energy storage of the magnetic field (e.g. for eruptive events) are limited.

Momentum transfer from solar wind to interplanetary field enhancements inferred from magnetic field draping signatures

Abstract: Characterized by a cusp-shaped enhancement in the magnetic field strength, the magnetic structure in the solar wind, called an interplanetary field enhancement (IFE), has been investigated since its discovery. To understand its three-dimensional magnetic field geometry, we study an IFE detected by five spacecraft simultaneously. Field lines are seen draping around in the upstream region and rotating in the ambient convection electric field direction in the downstream region. Earlier studies suggest that IFEs are created when the solar wind accelerates newly formed dust clouds. Both signatures found in our study support this hypothesis: the field line draping is caused by dust-solar wind momentum exchange, while the field line rotation is a typical signature of dusty plasma pickup. The force that exchanges the momentum is approximately 106 N. This study illustrates the nature of the interaction between two flowing plasmas of very different mass-to-charge ratio.

A modified Equivalent Source Dipole method to model partially distributed magnetic field measurements, with application to Mercury

Abstract: Hermean magnetic field measurements acquired over the northern hemisphere by the MErcury Surface Space ENvironment GEochemistry, and Ranging (MESSENGER) spacecraft provide crucial information on the magnetic field of the planet. We develop a new method, the Time Dependent Equivalent Source Dipole, to model a planetary magnetic field and its secular variation over a limited spatial region. Tests with synthetic data distributed on regular grids as well as at spacecraft positions show that our modeled magnetic field can be upward or downward continued in an altitude range of −300 to 1460 km for regular grids and in a narrower range of 10 to 970 km for spacecraft positions. They also show that the method is not sensitive to a very weak secular variation along MESSENGER orbits. We then model the magnetic field of Mercury during the first four individual sidereal days as measured by MESSENGER using the modified Equivalent Source Dipoles scheme and excluding the secular variation terms. We find a dominantly zonal field with small-scale nonaxisymmetric features corotating with the Sun in the Mercury Body Fixed system and repeating under similar local time, suggestive of external origin. When modeling the field during one complete solar day, these small-scale features decrease and the field becomes more axisymmetric. The lack of any coherent nonaxisymmetric feature recovered by our method, which was designed to allow for such small-scale structures, provides strong evidence for the large-scale and close-to-axisymmetry structure of the internal magnetic field of Mercury.

Influence of Non-Potential Coronal Magnetic Topology on Solar-Wind Models

Abstract: By comparing a magneto-frictional model of the low-coronal magnetic-field to a potential-field source-surface model, we investigate the possible impact of non-potential magnetic structure on empirical solar-wind models. These empirical models (such as Wang–Sheeley–Arge) estimate the distribution of solar-wind speed solely from the magnetic-field structure in the low corona. Our models are computed in a domain between the solar surface and 2.5 solar radii, and they are extended to 0.1 AU using a Schatten current-sheet model. The non-potential field has a more complex magnetic skeleton and quasi-separatrix structures than the potential field, leading to different sub-structure in the solar-wind speed proxies. It contains twisted magnetic structures that can perturb the separatrix surfaces traced down from the base of the heliospheric current sheet. A significant difference between the models is the greater amount of open magnetic flux in the non-potential model. Using existing empirical formulae this leads to higher predicted wind speeds for two reasons: partly because magnetic-flux tubes expand less rapidly with height, but more importantly because more open-field lines are further from coronal-hole boundaries.

Effects of large-scale non-axisymmetric perturbations in the mean-field solar dynamo

Abstract: We explore a response of a non-linear non-axisymmetric mean-field solar dynamo model to shallow non-axisymmetric perturbations. After a relaxation period the amplitude of the non-axisymmetric field depends on the initial condition, helicity conservation, and the depth of perturbation. It is found that a perturbation which is anchored at r=0.9R has a profound effect on the dynamo process, producing a transient magnetic cycle of the axisymmetric magnetic field, if it is initiated at the growing phase of the cycle. The non-symmetric with respect to the equator perturbation results in a hemispheric asymmetry of the magnetic activity. The evolution of the axisymmetric and non-axisymmetric field depends on the turbulent magnetic Reynolds number R_m. In the range of R_m=10^{4-6} the evolution returns to the normal course in the next cycle, in which the non-axisymmetric field is generated due to a non-linear alpha-effect and magnetic buoyancy. In the stationary state the large-scale magnetic field demonstrates a phenomenon of "active longitudes" with cyclic 180 degree "flip-flop" changes of the large-scale magnetic field orientation. The flip-flop effect is known from observations of solar and stellar magnetic cycles. However this effect disappears in the model which includes the meridional circulation pattern determined by helioseismology. The rotation rate of the non-axisymmetric field components varies during the relaxation period, and carries important information about the dynamo process.

Spatial Spectra of the Geomagnetic Field in the Observations and Geodynamo Models

Abstract: The correlation coefficients of the geomagnetic field on different spatial scales are estimated for the observations since 1590 and for a three-dimensional spherical-shell geodynamo model. It is shown that in the latter case, despite the presence of the geomagnetic reversals, the correlation of the magnetic field on different scales is low. The time behavior of the magnetic dipole is correlated to the evolution of the integral magnetic energy in the liquid core, whereas the dependence of the behavior of the integral kinetic energy on the magnetic field evolution is weak. Two-dimensional spectra of the magnetic field, velocity field, and cross-helicity in the liquid core of the Earth are presented.

Observational Estimate of Magnetic Field and Geodynamo Parameters under the Surface of the Earth's Core

Abstract: For the first time, estimates (averaged in latitude and longitude) of the radial derivatives of the vortex magnetic field hidden directly under the surface of the Earth’s core were obtained on the basis of contemporary determinations of the electric conductivity and systematic observations of the geomagnetic dipole evolution, as well as Faraday’s and Ohm’s laws. This allows one to formulate the simplest, ‘almost dipole” model of the vortex field under the core surface and to estimate a characteristic scale of the field measurements, which determines the depth of the adequacy area of the proposed simplest model. According to this estimate, the spatial size of the field (around 60 km) is an order of magnitude less than its typical size, following from an extrapolation of the observable field to the mantle–core boundary. This agrees well with the modern theory of hydromagnetic dynamos of planets, making it possible to refine the typical values of the magnetic field, the convection rate, and specific power, together with other geodynamo parameters, on the basis of known scaling laws and observations. The proposed new approach to determining the surface characteristics of the vortex magnetic field hidden in the interior of a physical object from the observed evolution of the potential field may be used for both astrophysical and engineering objects with an inaccessible current system.

Torsional oscillations of neutron stars with highly tangled magnetic fields

Abstract: To determine the frequencies of magnetic oscillations in neutron stars with highly tangled magnetic fields, we derive the perturbation equations. We assume that the field strength of the global magnetic structure is so small that such fields are negligible compared with tangled fields, which may still be far from a realistic configuration. Then, we systematically examine the spectra of the magnetic oscillations, as varying the magnetic field strength and stellar mass. The frequencies without crust elasticity are completely proportional to the strength of the magnetic field, whose proportionality constant depends strongly on the stellar mass. On the other hand, the oscillation spectra with crust elasticity become more complicated, where the frequencies even for weak magnetic fields are different from the crustal torsional oscillations without magnetic fields. For discussing spectra, the critical field strength can play an important role, and it is determined in such a way that the shear velocity is equivalent to the Alfv\'{e}n velocity at the crust basis. Additionally, we find that the effect of the crust elasticity can be seen strongly in the fundamental oscillations with a lower harmonic index, $\ell$. Unlike the stellar models with a pure dipole magnetic field, we also find that the spectra with highly tangled magnetic fields become discrete, where one can expect many of the eigenfrequencies. Maybe these frequencies could be detected after the violent phenomena breaking the global magnetic field structure.

Bounce‐ and MLT‐averaged diffusion coefficients in a physics‐based magnetic field geometry obtained from RAM‐SCB for the 17 March 2013 storm

Abstract: Local acceleration via whistler wave and particle interaction plays a significant role in particle dynamics in the radiation belt. In this work we explore gyroresonant wave-particle interaction and quasi-linear diffusion in different magnetic field configurations related to the 17 March 2013 storm. We consider the Earth's magnetic dipole field as a reference and compare the results against nondipole field configurations corresponding to quiet and stormy conditions. The latter are obtained with the ring current-atmosphere interactions model with a self-consistent magnetic field (RAM-SCB), a code that models the Earth's ring current and provides a realistic modeling of the Earth's magnetic field. By applying quasi-linear theory, the bounce- and Magnetic Local Time (MLT)-averaged electron pitch angle, mixed-term, and energy diffusion coefficients are calculated for each magnetic field configuration. For radiation belt (∼1 MeV) and ring current (∼100 keV) electrons, it is shown that at some MLTs the bounce-averaged diffusion coefficients become rather insensitive to the details of the magnetic field configuration, while at other MLTs storm conditions can expand the range of equatorial pitch angles where gyroresonant diffusion occurs and significantly enhance the diffusion rates. When MLT average is performed at drift shell L=4.25 (a good approximation to drift average), the diffusion coefficients become quite independent of the magnetic field configuration for relativistic electrons, while the opposite is true for lower energy electrons. These results suggest that, at least for the 17 March 2013 storm and for L≲4.25, the commonly adopted dipole approximation of the Earth's magnetic field can be safely used for radiation belt electrons, while a realistic modeling of the magnetic field configuration is necessary to describe adequately the diffusion rates of ring current electrons.

A statistical study of the low-altitude ionospheric magnetic fields over the north pole of Venus

Abstract: Examination of Venus Express (VEX) low-altitude ionospheric magnetic field measurements during solar minimum has revealed the presence of strong magnetic fields at low altitudes over the north pole of Venus. A total of 77 events with strong magnetic fields as VEX crossed the northern polar region were identified between July 2008 and October 2009. These events all have strong horizontal fields, slowly varying with position. Using the superposed epoch method, we find that the averaged peak field is about 45 nT, which is well above the average ambient ionospheric field of 20 nT, with a full width at half maximum duration of 32 s, equivalent to a width of about 300 km. Considering the field orientation preference and spacecraft trajectory geometry, we conclude that these strong fields are found over the northern hemisphere with an occurrence frequency of more than 33% during solar minimum. They do not show a preference for any particular interplanetary magnetic field (IMF) orientation. However, they are found over the geographic pole more often when the interplanetary field is in the Venus orbital plane than when it is perpendicular to the orbital plane of Venus. The structures were found most frequently in the −E hemisphere, determined from the IMF orientation. The enhanced magnetic field is mainly quasi perpendicular to solar wind flow direction, and it is suggested that these structures form in the low-altitude collisional ionosphere where the diffusion and convection times are long.

Simulating astrophysical magnetic fields with smoothed particle magnetohydrodynamics

Abstract: Numerical methods to improve the treatment of magnetic fields in smoothed field magnetohydrodynamics (SPMHD) are developed and tested. A mixed hyperbolic/parabolic scheme is developed which "cleans" divergence error from the magnetic field. The method introduces a scalar field which is coupled to the magnetic field. A conservative form for the hyperbolic equations is obtained by first defining the energy content of the new field, then using it in the discretised Lagrangian to obtain equations which manifestly conserve energy. This is shown to require conjugate first derivative operators in the SPMHD cleaning equations. Average divergence error is shown to be an order of magnitude lower for all test cases considered, and allows for the stable simulation of the gravitational collapse of magnetised molecular cloud cores. The effectiveness of the cleaning may be improved by explicitly increasing the hyperbolic wave speed or by cycling the cleaning equations between timesteps. In the latter, it is possible to achieve DivB=0 in SPMHD. The method is adapted to work with a velocity field, demonstrating that it can reduce density variations in weakly compressible SPH simulations by a factor of 2. A switch to reduce dissipation of the magnetic field from artificial resistivity is developed. Discontinuities in the magnetic field are located by monitoring jumps in the gradient of the magnetic field at the resolution scale relative to the magnitude of the magnetic field. This yields a simple yet robust method to reduce dissipation away from shocked regions. Compared to the existing switch in the literature, this leads to sharper shock profiles in shocktube tests, lower overall dissipation of magnetic energy, and importantly, is able to capture magnetic shocks in the highly super-Alfvenic regime. These numerical methods are compared against grid-based MHD methods by comparison of the small-scale dynamo amplification of a magnetic field in driven, isothermal, supersonic turbulence. We use the SPMHD code, Phantom, and the grid-based code, Flash. We find that the growth rate of Flash is largely insensitive to the numerical resolution, whereas Phantom shows a resolution dependence that arises from the scaling of the numerical dissipation terms. The saturation level of the magnetic energy in both codes is about 2-4% of the mean kinetic energy, increasing with higher magnetic Reynolds numbers. Phantom requires lower resolution to saturate at the same energy level as Flash. The time-averaged saturated magnetic spectra have a similar shape between the two methods, though Phantom contains twice as much energy on large scales. Both codes have PDFs of magnetic field strength that are log-normal, which become lopsided as the magnetic field saturates. We find encouraging agreement between grid- and particle methods for ideal MHD, concluding that SPMHD is able to reliably simulate the small-scale dynamo amplification of magnetic fields. We note that quantitative agreement on growth rates can only be achieved by including explicit, physical terms for viscosity and resistivity, because those are the terms that primarily control the growth rate and saturation level of the turbulent dynamo.

Numerical simulations of sheared magnetic lines at the solar null line

Abstract: Aims. We perform numerical simulations of sheared magnetic lines at the magnetic null line configuration of two magnetic arcades that are settled in a gravitationally stratified and magnetically confined solar corona. Methods. We developed a general analytical model of a 2.5D solar atmospheric structure. As a particular application of this model, we adopted it for the curved magnetic field lines with an inverted Y shape that compose the null line above two magnetic arcades, which are embedded in the solar atmosphere that is specified by the realistic temperature distribution. The physical system is described by 2.5D magnetohydrodynamic equations that are numerically solved by the FLASH code. Results. The magnetic field line shearing, implemented about 200 km below the transition region, results in Alfven and magnetoacoustic waves that are able to penetrate solar coronal regions above the magnetic null line. As a result of the coupling of these waves, partial reflection from the transition region and scattering from inhomogeneous regions the Alfven waves experience fast attenuation on time scales comparable to their wave periods, and the physical system relaxes in time. The attenuation time grows with the large amplitude and characteristic growing time of the shearing. Conclusions. By having chosen a di erent magnetic flux function, the analytical model we devised can be adopted to derive equilibrium conditions for a diversity of 2.5D magnetic structures in the solar atmosphere.

A Magnetic Field Separation Technique for a Scaled Model Ship through an Earth’s Magnetic Field Simulator

Abstract: This paper presents an experimental technique to accurately separate a permanent magnetic field and an induced one from the total magnetic fields generated by a steel ship, through compensating for the Earth’s magnetic field. To achieve this, an Earth’s magnetic field simulator was constructed at a non-magnetic laboratory, and the field separation technique was developed, which consisted of five stages. The proposed method was tested with a scaled model ship, and its permanent and induced magnetic fields were successfully extracted from the magnetic field created by the ship. Finally, based on the separated permanent magnetic field data, the permanent magnetization distribution on the hull was predicted by solving an inverse problem. Accordingly, the permanent magnetic fields generated by the ship can easily be calculated at any depth of water.

Significance of Polarization Charges and Isomagnetic Surface in Magnetohydrodynamics

Abstract: From the frozen-in field lines concept, a highly conducting fluid can move freely along, but not traverse to, magnetic field lines. We discuss this topic and find that in the study of the frozen-in field lines concept, the effects of inductive and capacitive reactance have been omitted. When admitted, the relationships among the motional electromotive field, the induced electric field, the eddy electric current, and the magnetic field becomes clearer. We emphasize the importance of isomagnetic surfaces and polarization charges, and show analytically that whether a conducting fluid can freely traverse magnetic field lines or not depends solely on the magnetic gradient along the path of the fluid. If a fluid does not change its density distribution and shape (can be regarded as a quasi-rigid body) and moves along isomagnetic surface, it can freely traverse magnetic field lines without any magnetic drag, no matter how strong the magnetic field is. Besides theoretical analysis, we also present experimental results to support our analysis. The main purpose of this work is to correct a fallacy among some astrophysicists.