Showing papers on "Dipole model of the Earth's magnetic field published in 2010"

Fast torsional waves and strong magnetic field within the Earth’s core

Abstract: The magnetic field inside the Earth's fluid and electrically conducting outer core cannot be directly probed. The root-mean-squared (r.m.s.) intensity for the resolved part of the radial magnetic field at the core-mantle boundary is 0.3mT, but further assumptions are needed to infer the strength of the field inside the core. Recent diagnostics obtained from numerical geodynamo models indicate that the magnitude of the dipole field at the surface of a fluid dynamo is about ten times weaker than the r.m.s. field strength in its interior, which would yield an intensity of the order of several millitesla within the Earth's core. However, a 60-year signal found in the variation in the length of day has long been associated with magneto-hydrodynamic torsional waves carried by a much weaker internal field. According to these studies, the r.m.s. strength of the field in the cylindrical radial direction (calculated for all length scales) is only 0.2mT, a figure even smaller than the r.m.s. strength of the large-scale (spherical harmonic degree n<=13) field visible at the core-mantle boundary. Here we reconcile numerical geodynamo models with studies of geostrophic motions in the Earth's core that rely on geomagnetic data. From an ensemble inversion of core flow models, we find a torsional wave recurring every six years, the angular momentum of which accounts well for both the phase and the amplitude of the six-year signal for change in length of day detected over the second half of the twentieth century. It takes about four years for the wave to propagate throughout the fluid outer core, and this travel time translates into a slowness for Alfven waves that corresponds to a r.m.s. field strength in the cylindrical radial direction of approximately 2mT. Assuming isotropy, this yields a r.m.s. field strength of 4mT inside the Earth's core.

Equation of state of a dense and magnetized fermion system

Abstract: The equation of state of a system of fermions in a uniform magnetic field is obtained in terms of the thermodynamic quantities of the theory by using functional methods. It is shown that the breaking of the O(3) rotational symmetry by the magnetic field results in a pressure anisotropy, which leads to the distinction between longitudinal- and transverse-to-the-field pressures. A criterion to find the threshold field at which the asymmetric regime becomes significant is discussed. This threshold magnetic field is shown to be the same as the one required for the pure field contribution to the energy and pressures to be of the same order as the matter contribution. A graphical representation of the field-dependent anisotropic equation of state of the fermion system is given. Estimates of the upper limit for the inner magnetic field in self-bound stars, as well as in gravitationally bound stars with inhomogeneous distributions of mass and magnetic fields, are also found.

The Magnetic Field of Mercury

Abstract: The magnetic field strength of Mercury at the planet’s surface is approximately 1% that of Earth’s surface field. This comparatively low field strength presents a number of challenges, both theoretically to understand how it is generated and observationally to distinguish the internal field from that due to the solar wind interaction. Conversely, the small field also means that Mercury offers an important opportunity to advance our understanding both of planetary magnetic field generation and magnetosphere-solar wind interactions. The observations from the Mariner 10 magnetometer in 1974 and 1975, and the MESSENGER Magnetometer and plasma instruments during the probe’s first two flybys of Mercury on 14 January and 6 October 2008, provide the basis for our current knowledge of the internal field. The external field arising from the interaction of the magnetosphere with the solar wind is more prominent near Mercury than for any other magnetized planet in the Solar System, and particular attention is therefore paid to indications in the observations of deficiencies in our understanding of the external field. The second MESSENGER flyby occurred over the opposite hemisphere from the other flybys, and these newest data constrain the tilt of the planetary moment from the planet’s spin axis to be less than 5°. Considered as a dipole field, the moment is in the range 240 to 270 nT-R M 3 , where R M is Mercury’s radius. Multipole solutions for the planetary field yield a smaller dipole term, 180 to 220 nT-R M 3 , and higher-order terms that together yield an equatorial surface field from 250 to 290 nT. From the spatial distribution of the fit residuals, the equatorial data are seen to reflect a weaker northward field and a strongly radial field, neither of which can be explained by a centered-dipole matched to the field measured near the pole by Mariner 10. This disparity is a major factor controlling the higher-order terms in the multipole solutions. The residuals are not largest close to the planet, and when considered in magnetospheric coordinates the residuals indicate the presence of a cross-tail current extending to within 0.5R M altitude on the nightside. A near-tail current with a density of 0.1 μA/m2 could account for the low field intensities recorded near the equator. In addition, the MESSENGER flybys include the first plasma observations from Mercury and demonstrate that solar wind plasma is present at low altitudes, below 500 km. Although we can be confident in the dipole-only moment estimates, the data in hand remain subject to ambiguities for distinguishing internal from external contributions. The anticipated observations from orbit at Mercury, first from MESSENGER beginning in March 2011 and later from the dual-spacecraft BepiColombo mission, will be essential to elucidate the higher-order structure in the magnetic field of Mercury that will reveal the telltale signatures of the physics responsible for its generation.

Modelling the Galactic magnetic field on the plane in two dimensions

Abstract: We present a method for parametric modelling of the physical components of the Galaxy's magnetized interstellar medium, simulating the observables and mapping out the likelihood space using a Markov Chain Monte Carlo analysis. We then demonstrate it using total and polarized synchrotron emission data as well as rotation measures of extragalactic sources. With these three data sets, we define and study three components of the magnetic field: the large-scale coherent field, the small-scale isotropic random field and the ordered field. In this first paper, we use only data along the Galactic plane and test a simple two-dimensional (2D) logarithmic spiral model for the magnetic field that includes a compression and a shearing of the random component giving rise to an ordered component. We demonstrate with simulations that the method can indeed constrain multiple parameters yielding measures of, for example, the ratios of the magnetic field components. Though subject to uncertainties in thermal and cosmic ray electron densities and depending on our particular model parametrization, our preliminary analysis shows that the coherent component is a small fraction of the total magnetic field and an ordered component comparable in strength to the isotropic random component is required to explain the polarization fraction of synchrotron emission. We outline further work to extend this type of analysis to study the magnetic spiral arm structure, the details of the turbulence as well as the 3D structure of the magnetic field.

An ellipsoidal harmonic representation of Earth's lithospheric magnetic field to degree and order 720

Abstract: [1] While high-degree models of the Earth's gravity potential have been inferred from measurements for more than a decade, corresponding geomagnetic models are difficult to produce. The primary challenge lies in the estimation of the magnetic potential, which is not completely determined by available field intensity measurements and cannot be computed by direct integration. Described here is the methodology behind the third generation of the National Geophysical Data Center's degree 720 magnetic model. Key issues are (1) the ellipsoidal harmonic representation of the magnetic potential, (2) the reduction of ambiguities by a suitable penalty function, and (3) the use of an iterative method to estimate the model coefficients. The NGDC-720 model provides the lithospheric magnetic field vector at any desired location and altitude close to and above the Earth's surface. Anticipated uses are in geological and tectonic studies of the lithosphere, as a local correction for magnetic navigation and heading systems, and the calibration of ground, marine, airborne, and spaceborne magnetometers. The NGDC-720 model is available at http://geomag.org/models/ngdc720.html and for long-term archive at http://earthref.org/cgi-bin/er.cgi?s=erda.cgi?n=989.

Saturn's internal planetary magnetic field

Abstract: [1] A model of Saturn's internal planetary magnetic field based on data from the Cassini prime mission has been derived. In the absence of a determination of the rotation rate, the model is constrained to be axisymmetric. Non-axisymmetric models for a range of plausible planetary rotation periods have also been derived and we evaluate upper limits on the asymmetry of the internal magnetic field based on those models. We investigate whether a maximum in the non-axisymmetric magnetic field can be identified at a particular rotation rate thus providing insight into the rotation rate of the planet's interior. No such peak can unambiguously be identified. An axisymmetric octupole model is adequate to fit the data and addition of higher order terms does not improve the goodness of fit. The largest value of the dipole tilt obtained from non-axisymmetric models (<0.1°) confirm the high degree of symmetry of Saturn's magnetic field.

Tidal dissipation and the strength of the Earth’s internal magnetic field

Abstract: Magnetic fields at the Earth's surface represent only a fraction of the field inside the core. The strength and structure of the internal field are poorly known, yet the details are important for our understanding of the geodynamo. Here I obtain an indirect estimate for the field strength from measurements of tidal dissipation. Tidally driven flow in the Earth's liquid core develops internal shear layers, which distort the internal magnetic field and generate electric currents. Ohmic losses damp the tidal motions and produce detectable signatures in the Earth's nutations. Previously reported evidence of anomalous dissipation in nutations can be explained with a core-averaged field of 2.5 mT, eliminating the need for high fluid viscosity or a stronger magnetic field at the inner-core boundary. Estimates for the internal field constrain the power required for the geodynamo.

Dependence of pitch‐angle scattering rates and loss timescales on the magnetic field model

Abstract: [1] Radiation belt diffusion codes require, as inputs, precomputed scattering rates, which are currently bounce-averaged in the dipole magnetic field. We present the results of computations of the bounce-averaged quasi-linear pitch-angle diffusion coefficients of relativistic electrons for various distances and two MLT in the Tsyganenko 89c magnetic field model. The coefficients were computed for quiet and storm-time conditions. We compare scattering rates bounce-averaged in a non-dipole field model with those in the dipole field. We demonstrate that on the day side the effects of taking into account a realistic magnetic field are negligible at distances less than six Earth radii. On the night side diffusion coefficients may significantly depend on the assumed field model. Pitch-angle scattering rates calculated in the non-dipole field can explain the often observed night-side chorus induced precipitation. The physical explanation for the changes of pitch-angle scattering rates with the field model is presented and discussed.

Solar parity issue with flux-transport dynamo

Abstract: We investigated the dependence of the solar magnetic parity between the hemispheres on two important parameters, the turbulent diffusivity and the meridional flow, by means of axisymmetric kinematic dynamo simulations based on the flux-transport dynamo model. It is known that the coupling of the magnetic field between hemispheres due to turbulent diffusivity is an important factor for the solar parity issue, but the detailed criterion for the generation of the dipole field has not been investigated. Our conclusions are as follows. (1) The stronger diffusivity near the surface is more likely to cause the magnetic field to be a dipole. (2) The thinner layer of the strong diffusivity near the surface is also more apt to generate a dipolar magnetic field. (3) The faster meridional flow is more prone to cause the magnetic field to be a quadrupole, i.e., symmetric about the equator. These results show that turbulent diffusivity and meridional flow are crucial for the configuration of the solar global magnetic field.

Solar wind influence on Pc4 and Pc5 ULF wave activity in the inner magnetosphere

Abstract: [1] Abundant evidence has shown that ULF wave activity measured at geosynchronous orbit is well correlated with solar wind parameters, such as the solar wind velocity and dynamic pressure. However, many of the past studies were based on magnetic field measurements near the equatorial plane and thus could not unambiguously describe ULF waves, as magnetic field oscillations in the fundamental toroidal mode have a node at the magnetic equator. In this study, we use, for the first time, simultaneous electric and magnetic field measurements by Time History of Events and Macroscale Interactions during Substorms satellites throughout the inner magnetosphere to statistically examine the correlation between ULF wave activity in the inner magnetosphere and the solar wind parameters: velocity, dynamic pressure, and variation in dynamic pressure. On the basis of electric field observations from August 2007 to May 2009, we found that, among the three parameters, the solar wind velocity has the strongest correlation with the daily averaged Pc4 and 5 wave magnitude in 4 ∼ 9 RE. For example, the correlation coefficient of δEr (the square root of the integrated power spectral density of the radial component of the electric field) in the Pc5 frequency range with the solar wind dynamic pressure is 0.35; with the dynamic pressure variation, it is 0.42; and with the solar wind velocity, it is 0.55. However, using only magnetic field observations, the variation in dynamic pressure is best correlated, with correlation coefficients of δBr (the square root of the integrated power spectral density of the radial component of the magnetic field) with the dynamic pressure being 0.59, with the dynamic pressure variation being 0.63 and with the solar wind velocity being 0.53. We suggest that this difference arises because toroidal and poloidal mode pulsations are not detected with the same effectiveness in the electric field and the magnetic field near the magnetic equator and/or because of the presence of broadband ULF noise. We further suggest that either directly measured or flow-derived electric field measurements are better suited in the study of the relationship between wave power of fundamental field line resonance (i.e., in Pc5 frequency range) and solar wind conditions.

The Magnetic Field at the Inner Boundary of the Heliosphere Around Solar Minimum

Abstract: STEREO A and B observations of the radial magnetic field between 1 January 2007 and 31 October 2008 show significant evidence that in the heliosphere, the ambient radial magnetic field component with any dynamic effects removed is uniformly distributed. Based on this monopolar nature of the ambient heliospheric field we find that the surface beyond which the magnetic fields are in the monopolar configuration must be spherical, and this spherical surface can be defined as the inner boundary of the heliosphere that separates the monopole-dominated heliospheric magnetic field from the multipole-dominated coronal magnetic field. By using the radial variation of the coronal helmet streamers belts and the horizontal current – current sheet – source surface model we find that the spherical inner boundary of the heliosphere should be located around 14 solar radii near solar minimum phase.

A nonpotential model for the Sun's open magnetic flux

Abstract: [1] Measurements of the interplanetary magnetic field (IMF) over several solar cycles do not agree with computed values of open magnetic flux from potential field extrapolations. The discrepancy becomes greater around solar maximum in each cycle when the IMF can be twice as strong as predicted by the potential field model. Here we demonstrate that this discrepancy may be resolved by allowing for electric currents in the low corona (below 2.5R⊙). We present a quasi-static numerical model of the large-scale coronal magnetic evolution, which systematically produces these currents through flux emergence and shearing by surface motions. The open flux is increased by 75%–85% at solar maximum, but only 25% at solar minimum, bringing it in line with estimates from IMF measurements. The additional open flux in the nonpotential model arises through inflation of the magnetic field by electric currents, with superimposed fluctuations due to coronal mass ejections. The latter are modeled by the self-consistent ejection of twisted magnetic flux ropes.

Modelling the Earth’s core magnetic field under flow constraints

Abstract: Two recent magnetic field models, GRIMM and xCHAOS, describe core field accelerations with similar behavior up to Spherical Harmonic (SH) degree 5, but which differ significantly for higher degrees. These discrepancies, due to different approaches in smoothing rapid time variations of the core field, have strong implications for the interpretation of the secular variation. Furthermore, the amount of smoothing applied to the highest SH degrees is essentially the modeler’s choice. We therefore investigate new ways of regularizing core magnetic field models. Here we propose to constrain field models to be consistent with the frozen flux induction equation by co-estimating a core magnetic field model and a flow model at the top of the outer core. The flow model is required to have smooth spatial and temporal behavior. The implementation of such constraints and their effects on a magnetic field model built from one year of CHAMP satellite and observatory data, are presented. In particular, it is shown that the chosen constraints are efficient and can be used to build reliable core magnetic field secular variation and acceleration model components.

Galileo constraints on the secular variation of the Jovian magnetic field

Abstract: [1] The variations of the terrestrial magnetic field place important constraints on the behavior of the fluid in the Earth's magnetic dynamo. Jupiter is currently the only other planet for which magnetic measurements exist over a sufficiently long baseline to enable a study of the secular variation of the field to be undertaken. The average magnetic moment during the Galileo epoch was 4.334 ± 0.010 Gauss RJ3 or 1.584 ± 0.004 × 1020 Tm3. The tilt angle of the dipole was 9.71° ± 0.05°. We examine both the change in the magnetic field during the period in which Galileo operated in Jovian orbit and the change in the field between the initial observations with Pioneer 11 and the Galileo epoch. Neither approach definitively identifies secular change in the Jovian field but rather puts a limit on that rate of change. The only significant change is associated with the current imprecision of the International Astronomical Union-defined System III period.

Nonlinear force-free modelling: influence of inaccuracies in the measured magnetic vector

Abstract: Context. Solar magnetic fields are regularly extrapolated into the corona starting from photospheric magnetic measurements that can be affected by significant uncertainty. Aims. We study how inaccuracies introduced into the maps of the photospheric magnetic vector by the inversion of ideal and noisy Stokes parameters influence the extrapolation of nonlinear force-free magnetic fields. Methods. We compute nonlinear force-free magnetic fields based on simulated vector magnetograms, by the inversion of Stokes profiles that were computed by a 3-D radiation MHD simulation snapshot. These extrapolations are compared with extrapolations that originate directly in the field in the MHD simulations, which is our reference. We investigate how line formation and instrumental effects such as noise, limited spatial resolution, and the effect of employing a filter instrument influence the resulting magnetic field structure. The comparison is performed qualitatively by visually inspecting the magnetic field distribution and quantitatively by different metrics. Results. The reconstructed field is most accurate if ideal Stokes data are inverted and becomes less accurate if instrumental effects and noise are included. The results demonstrate that the nonlinear force-free field extrapolation method tested here is relatively insensitive to the effects of noise in measured polarization spectra at levels consistent with present-day instruments. Conclusions. Our results show that we can reconstruct the coronal magnetic field as a nonlinear force-free field from realistic photospheric measurements with an accuracy of a few percent, at least in the absence of sunspots.

Magnetic Component Model for Planar Structures Based on Transmission Lines

Abstract: Magnetic component models are quite complex if they take into consideration the variation of the field distribution in a three-dimensional (3-D) space. However, if the field distribution can be assumed to be one-dimensional (1-D), the magnetic component models can be drastically simplified because it is feasible to obtain accurate analytical expressions based on the solution of the Maxwell equations for a 1-D field distribution. The field distribution in magnetic components can be assumed to be 1-D when the field depends on one of its coordinates and the dependence on the other coordinates is negligible. Therefore, classical 1-D models have to be modified in order to be applied to planar transformers because their magnetic field vector has a constant direction, but its magnitude is not constant along that direction. This paper presents a 1-D model for planar magnetic transformers. Some comparisons between 2-D approaches and the proposed 1-D model have been carried out in order to show the accuracy of the proposed method.

The role of magnetic handedness in magnetic cloud propagation

Abstract: . We investigate the propagation of magnetic clouds (MCs) through the inner heliosphere using 2.5-D ideal magnetohydrodynamic (MHD) simulations. A numerical solution is obtained on a spherical grid, either in a meridional plane or in an equatorial plane, by using a Roe-type approximate Riemann solver in the frame of a finite volume approach. The structured background solar wind is simulated for a solar activity minimum phase. In the frame of MC propagation, special emphasis is placed on the role of the initial magnetic handedness of the MC's force-free magnetic field because this parameter strongly influences the efficiency of magnetic reconnection between the MC's magnetic field and the interplanetary magnetic field. Magnetic clouds with an axis oriented perpendicular to the equatorial plane develop into an elliptic shape, and the ellipse drifts into azimuthal direction. A new feature seen in our simulations is an additional tilt of the ellipse with respect to the direction of propagation as a direct consequence of magnetic reconnection. During propagation in a meridional plane, the initial circular cross section develops a concave-outward shape. Depending on the initial handedness, the cloud's magnetic field may reconnect along its backside flanks to the ambient interplanetary magnetic field (IMF), thereby losing magnetic flux to the IMF. Such a process in combination with a structured ambient solar wind has never been analyzed in detail before. Furthermore, we address the topics of force-free magnetic field conservation and the development of equatorward flows ahead of a concave-outward shaped MC. Detailed profiles are presented for the radial evolution of magnetoplasma and geometrical parameters. The principal features seen in our MHD simulations are in good agreement with in-situ measurements performed by spacecraft. The 2.5-D studies presented here may serve as a basis under more simple geometrical conditions to understand more complicated effects seen in 3-D simulations.

Why are relativistic electrons persistently quiet at geosynchronous orbit in 2009

Abstract: [1] Relativistic electrons at geosynchronous orbit (GEO) were persistently quiet in 2009 for almost a whole year. The solar wind speed, which has been known as a primary parameter controlling the outer belt electrons, was very slow in 2009 as expected and at a comparably low level as of 1997 when we did not observe such a persistently quiet condition. Since the interplanetary magnetic field (IMF) was quite different between 1997 and 2009, the difference in IMF is a possible cause of the difference in the electron flux levels, providing an important clue to understand the complex source and loss process of relativistic electrons at GEO. We suggest that the extremely weak IMF of the very slow solar wind plays an essential role in diminishing the source processes themselves associated with magnetic storms and substorms, and in turn to suppress the relativistic electron flux at GEO over the time scale of a year, as an inevitable consequence of extremely weak open magnetic field of the Sun associated with the extremely weak current solar minimum.

A photospheric bright point model

Abstract: Aims. A magneto-hydrostatic model is constructed with spectropolarimetric properties close to those of solar photospheric magnetic bright points. Methods. Results of solar radiative magneto-convection simulations are used to produce the spatial structure of the vertical component of the magnetic field. The horizontal component of magnetic field is reconstructed using the self-similarity condition, while the magneto-hydrostatic equilibrium condition is applied to the standard photospheric model with the magnetic field embedded. Partial ionisation processes are found to be necessary for reconstructing the correct temperature structure of the model. Results. The structures obtained are in good agreement with observational data. By combining the realistic structure of the magnetic field with the temperature structure of the quiet solar photosphere, the continuum formation level above the equipartition layer can be found. Preliminary results are shown of wave propagation through this magnetic structure. The observational consequences of the oscillations are examined in continuum intensity and in the Fe I 6302 A magnetically sensitive line.

Statistical study of low‐frequency magnetic field fluctuations near Venus under the different interplanetary magnetic field orientations

Abstract: [1] The magnetic field fluctuations near Venus are investigated in the frequency range 0.03–0.3 Hz on the basis of the measurements observed by Venus Express from April 2006 to December 2008. The data are sorted by the angle between interplanetary magnetic field (IMF) and solar wind flow. The spatial distributions of fluctuation properties under the different IMF orientations are presented and a comparative study is performed. In the mantle and tail regions, the magnetic field is fairly quiet and the fluctuations are almost linearly polarized. There are two possible sources for the fluctuations in the magnetosheath: convection from the upstream foreshock and local generation. When the IMF is nearly perpendicular to the solar wind flow, the fluctuations in the magnetosheath are mainly generated locally by an ion cyclotron instability due to planetary ion pickup. The wave intensity is relatively low and the transverse component is dominant. The waves are left-handed, elliptically polarized, and propagating parallel to the mean magnetic field. When the IMF is nearly aligned to the solar wind flow, foreshock waves are convected into the magnetosheath. The fluctuations in the magnetosheath become more intensive. Their polarization properties are very mixed and there is no clear tendency. It indicates that the waves convected from the foreshock may be the mixture of multiple wave types and incoherent noise.

Magnetic reversals in a simple model of magnetohydrodynamics.

Abstract: We study a simple magnetohydrodynamical approach in which hydrodynamics and MHD turbulence are coupled in a shell model, with given dynamo constraints in the large scales. We consider the case of a low Prandtl number fluid for which the inertial range of the velocity field is much wider than that of the magnetic field. Random reversals of the magnetic field are observed and it shown that the magnetic field has a nontrivial evolution--linked to the nature of the hydrodynamics turbulence.

Reproducing spacecraft measurements of magnetic correlations in the solar wind

Abstract: Analytical models for magnetic turbulence are an important ingredient in the theory of field line wandering and cosmic ray diffusion. In previous investigations, a so-called slab/2D model has been used. In the present article, we develop a more general analytical model for magnetic turbulence. This model is then compared with solar wind observations. We investigate numerically the possibility to explain the maltese cross structure of the correlation function of solar wind turbulence with this model.

Derivation of characteristics of the relation between geomagnetic and geoelectric variation fields from the surface impedance for a two-layer earth

Abstract: The surface impedance is defined to give the ratio between horizontal geoelectric and geomagnetic variation fields at the earth’s surface in the frequency domain. Studying the properties of the surface impedance enables conclusions about the corresponding relation between the surface electric and magnetic variation fields in the time domain. In particular, it is possible to perform an investigation about assumptions that lead to a proportionality between the geoelectric field and the time derivative of the geomagnetic field and about situations that make the electric field and the variations of the magnetic field proportional. The results are directly applicable to the research of geomagnetically induced currents (GIC) driven by the geoelectric field in technological networks at the earth’s surface. Thus, the main objective of this paper is not in traditional magnetotellurics but in studies of ground effects of space weather. We use a two-layer earth model, which is simple enough to have a precise analytic formula for the surface impedance. It is shown in this paper that a poorly-conducting upper layer above a highly-conducting bottom is favourable to the electric field (and GIC) being proportional to the magnetic time derivative at the earth’s surface whereas a thin highly-conducting upper layer above a less-conducting bottom results in a surface electric field (and GIC) proportional to magnetic variations.

A dynamo cascade interpretation of the geomagnetic dipole decrease

Abstract: SUMMARY We propose a spectral transfer model for the secular variation of the geomagnetic core field to explain the simultaneous decrease in dipole field intensity and the increase in non-dipole field intensity from 1840 to the present in terms of a dynamo cascade process. The main assumption of this model is that magnetic energy is transferred between adjacent spherical harmonic degrees in the Mauersberger–Lowes spectrum of the geomagnetic field. The key parameters are a set of coefficients that indicate the rate and direction of magnetic energy transfer through the spectrum. Applying the spectral transfer model to the historical period, we find that the quadrupole family of the core field can be characterized by a persistent inverse magnetic energy cascade from higher towards lower spherical harmonics. In the dipole family of the core field, we find cascade behaviour generally from lower to higher spherical harmonics, consistent with axial dipole decrease, but with a high level of time variability that correlates with variations in the dipole family intensity. During time intervals when the dipole family intensity rapidly decreases, energy appears to cascade towards higher spherical harmonics, beyond the limit of the observable part of the core field spectrum. During time intervals when the dipole family intensity is nearly constant, a more limited forward cascade appears to trap energy at intermediate spherical harmonics. Similar fluctuations in the rate and direction of spectral transfer are also seen in the Mauersberger–Lowes spectrum of a numerical dynamo model during a dipole decrease event that led to a polarity excursion. We discuss the possibility of this scenario for the current geomagnetic dipole decrease.

On the scaling properties of anisotropy of interplanetary magnetic turbulent fluctuations

Abstract: The anisotropic character of interplanetary magnetic-field turbulence has been studied through the analysis of Cluster data. The full tensor of the mixed second-order structure functions has been used to quatitatively measure the degree of anisotropy and its effect on small-scale turbulence. Three different regions of the near-Earth space have been studied, namely the solar wind, the Earth's foreshock and magnetosheath. While in the undisturbed solar wind the observed strong anisotropy is mainly due to the large-scale magnetic field, near the magnetosphere other sources of anisotropy influence the magnetic-field properties.

On the definition and calculation of a generalised McIlwain parameter

Abstract: The L parameter, which indicates the distance where a magnetic field line crosses the equatorial plane, is defined only for an aligned magnetic dipole field. For a re- alistic planetary magnetic field, however, neither a definition nor a method to calculate this parameter are available so far. We therefore extent the definition of the McIlwain parameter for an arbitrary planetary magnetic field and numerically cal- culate it for the actual geomagnetic field. In order to do so, we first calculate the Earth's magnetic field for 2008 with the IGRF model. To motivate a proper definition for a general L parameter, each component of this field will be illustrated and discussed. In a second step, we present four possible definitions for the L parameter and discuss their properties and differences with respect to the question in how far they reflect the field geometry. We contrast our method with the traditional derivation of the L parameter employing numeri- cal simulations of the cut-off rigidities of energetic particles and an empirical relation between the latter and L.