Showing papers on "Dipole model of the Earth's magnetic field published in 2000"

A new precise measurement of the coronal magnetic field strength

Abstract: Magnetism dominates the structure and dynamics of the solar corona. Current theories suggest that it may also be responsible for coronal heating. Despite the importance of the magnetic field in the physics of the corona and despite the tremendous progress made recently in the remote sensing of solar magnetic fields, reliable measurements of the coronal magnetic field strength and orientation do not exist. This is largely due to the weakness of coronal magnetic fields, previously estimated to be on the order of 10 G, and the difficulty associated with observing the extremely faint solar corona emission. Using a very sensitive infrared spectropolarimeter to observe the strong near-infrared coronal emission line Fe XIII λ10747 above active regions, we have succeeded in measuring the weak Stokes V circular polarization profiles resulting from the longitudinal Zeeman effect of the magnetic field of the solar corona. From these measurements, we infer field strengths of 10 and 33 G from two active regions at heights of h = 0.12 R☉ and h = 0.15 R☉, respectively. We expect that this measurement technique will allow, in the near future, the routine precise measurement of the coronal magnetic field strength with application to many critical problems in solar coronal physics.

Mean field model for the formation of filament channels on the sun

Abstract: The coronal magnetic field is subject to random footpoint motions that cause small-scale twisting and braiding of field lines. We present a mean field theory describing the effects of such small-scale twists on the large-scale coronal field. This theory assumes that the coronal field is force free, with electric currents flowing parallel or antiparallel to magnetic field lines. Random footpoint motions are described in terms of diffusion of the mean magnetic field at the photosphere. The appropriate mean field equations are derived, and a numerical method for solving these equations in three dimensions is presented. Preliminary results obtained with this method are also presented. In particular the formation of filament channels is studied. Filament channels are regions where the coronal magnetic field is strongly aligned with the underlying polarity inversion line in the photosphere. It is found that magnetic flux cancellation plays an important role in the formation of such channels. Various models of the coronal field are presented, including some in which the axial field is assumed to originate from below the photosphere. The models reproduce many of the observed features of filament channels, but the observed hemisphere pattern of dextral and sinistral channels remains a mystery.

Earth's Core and the Geodynamo

Abstract: Earth's magnetic field is generated by fluid motion in the liquid iron core. Details of how this occurs are now emerging from numerical simulations that achieve a self-sustaining magnetic field. Early results predict a dominant dipole field outside the core, and some models even reproduce magnetic reversals. The simulations also show how different patterns of flow can produce similar external fields. Efforts to distinguish between the various possibilities appeal to observations of the time-dependent behavior of the field. Important constraints will come from geological records of the magnetic field in the past.

A global MHD solar wind model with WKB Alfvén waves: Comparison with Ulysses data

Abstract: We use a steady state global axisymmetric MHD model to reproduce quantitatively the Ulysses observations during its first fast latitude traversal in 1994–1995. In particular, we are able to account for the transformation of a surface dipole magnetic field near the Sun into the configuration observed at large heliocentric distances. The MHD equations are solved by combining a time relaxation numerical technique with a marching-along-radius method. We assume that Alfven waves, propagating outward from the Sun, provide additional heating and acceleration to the flow. Only solutions with waves reproduce the plasma parameters observed in the high-latitude fast solar wind. We show that the meridional distribution of solar wind plasma and magnetic field parameters is dominated by two processes. First, inside ∼24 R⊙ both the plasma velocity and magnetic field relax toward a latitude-independent profile outside the equatorial current sheet (where magnetic forces dominate over thermal and wave gradient forces). Second, outside ∼24 R⊙ there is another meridional redistribution due to a poleward thermal pressure gradient that produces a slight poleward gradient in the radial velocity and an equatorward gradient in the radial component of the magnetic field. We reproduce the observed bimodal structure and morphology of both fast and slow wind and show that computed parameters are generally in agreement with both in situ data and conditions inferred to be characteristic of the solar corona.

Cosmological magnetic fields from primordial helicity

Abstract: Primordial magnetic fields may account for all or part of the fields observed in galaxies. We consider the evolution of the magnetic fields created by pseudoscalar effects in the early universe. Such processes can create force-free fields of maximal helicity; we show that for such a field magnetic energy inverse cascades to larger scales than it would have solely by flux freezing and cosmic expansion. For fields generated at the electroweak phase transition, we find that the predicted wavelength today can in principle be as large as 10 kpc, and the field strength can be as large as 10^{-10} G.

Solar wind control of the polar cusp at high altitude

Abstract: The POLAR mission is ideally suited to study the high-altitude polar cusp. Polar magnetometer data, together with electron and ion measurements from the Hydra and Toroidal Imaging Mass-Angle Spectrograph (Timas) instruments from March 1996 to December 1997, have been used to identify 459 polar cusp crossings. These crossings are used to study the statistical behavior of the cusp location and its dependence on the solar wind conditions. We find that the invariant latitude of the center of the cusp varies from 70° to 86° as solar wind conditions change and the magnetic local time of the footprints of the cusp magnetic field lines extends from 0800 to 1600 MLT, the cusp being slightly wider for increasing solar wind dynamic pressure. The average latitude of the center of the cusp is at 80.3° invariant latitude at noon and decreases to 78.7° at 0800 and 1600 MLT. The cusp also appears to thicken slightly in invariant latitude with increasing dynamic pressure. The center of the cusp moves equatorward with increasingly southward interplanetary magnetic field (IMF) to 73° invariant latitude for a 10 nT southward IMF. The cusp moves only slightly for northward IMF. This motion is consistent with erosion of dayside magnetic flux for southward IMF but little or no erosion for northward IMF. The cusp is also somewhat wider in invariant latitude with increasingly northward IMF. Consistent with low-altitude observations, we find that there is a clear MLT shift due to the IMF By for strongly southward IMF. We interpret the motion of the local time of the cusp for southward IMF as a shift of the reconnection site away from the noon meridian when the IMF is not due southward.

The Generation of Magnetic Fields through Driven Turbulence

Abstract: We have tested the ability of driven turbulence to generate magnetic field structure from a weak uniform field using three-dimensional numerical simulations of incompressible turbulence. We used a pseudospectral code with a numerical resolution of up to 1443 collocation points. We find that the magnetic fields are amplified through field line stretching at a rate proportional to the difference between the velocity and the magnetic field strength times a constant. Equipartition between the kinetic and magnetic energy densities occurs at a scale somewhat smaller than the kinetic energy peak. Above the equipartition scale the velocity structure is, as expected, nearly isotropic. The magnetic field structure at these scales is uncertain, but the field correlation function is very weak. At the equipartition scale the magnetic fields show only a moderate degree of anisotropy, so the typical radius of curvature of field lines is comparable to the typical perpendicular scale for field reversal. In other words, there are few field reversals within eddies at the equipartition scale and no fine-grained series of reversals at smaller scales. At scales below the equipartition scale, both velocity and magnetic structures are anisotropic; the eddies are stretched along the local magnetic field lines, and the magnetic energy dominates the kinetic energy on the same scale by a factor that increases at higher wavenumbers. We do not show a scale-free inertial range, but the power spectra are a function of resolution and/or the imposed viscosity and resistivity. Our results are consistent with the emergence of a scale-free inertial range at higher Reynolds numbers.

Disk Formation by AGB Winds in Dipole Magnetic Fields

Abstract: We present a simple, robust mechanism by which an isolated star can produce an equatorial disk. The mechanism requires that the star have a simple dipole magnetic field on the surface and an isotropic wind acceleration mechanism. The wind couples to the field, stretching it until the field lines become mostly radial and oppositely directed above and below the magnetic equator, as occurs in the solar wind. The interaction between the wind plasma and magnetic field near the star produces a steady outflow in which magnetic forces direct plasma toward the equator, constructing a disk. In the context of a slow (10 km/s) outflow (10^{-5} M_sun/yr) from an AGB star, MHD simulations demonstrate that a dense equatorial disk will be produced for dipole field strengths of only a few Gauss on the surface of the star. A disk formed by this model can be dynamically important for the shaping of Planetary Nebulae.

Stability and equilibrium of emerged magnetic flux

Abstract: We analyse stability and equilibrium of a unipolar large-scale magnetic field pervading a plane horizontal subphotospheric layer with the possible implications for sunspots in mind. Eddy diffusivity is applied to account for the effects of the small-scale convective turbulence. Diffusivity quenching by magnetic field results in a secondary large-scale instability. A linear stability analysis is performed to define the marginal stability boundary in parametric space and the unstable mode structure. The nonlinear dynamics of the unstable modes are followed numerically. The original state of a uniform vertical magnetic field is transformed via the instability into the nonlinear dynamical equilibrium with a highly intermittant distribution of the magnetic field. Magnetic flux is concentrated in a relatively small area surrounded by an almost field-free region. The role of the fluid motion in the hydromagnetic equilibrium is emphasized. Although the relevance of the instability to the process of sunspot formation is rather questionable, the resulting equilibrium structures are similar to mature spots in their thermal and magnetic properties. Also, the simulated flow structure agrees with helioseismic tomography results.

Can the Earth's magnetic field be simulated in the laboratory?

Abstract: Today it is generally accepted that the Earth's magnetic field, as well as that of many other planets, is generated by buoyancy driven convection in the electrically conducting liquid cores of these rotating celestial bodies. The conversion of mechanical energy into electromagnetic energy is known as the dynamo effect. In contrast to technical dynamos, which utilize the rotational motion of a complex arrangement of wire coils and other materials of different electrical and magnetic properties, the geodynamo is based on a freely developing spiral flow in a practically homogeneous, electrically conducting liquid core domain, and is therefore termed a homogeneous dynamo. This report outlines some fundamental properties of the Earth's magnetic field. The structure of the spiral flow in the liquid interior of planets is explained with the help of some model experiments in rapidly rotating spherical shells, which were carried out by Busse and Carrigan (1974). Based on the main ideas of electromagnetism it is shown that spiral motion in well-conducting fluids, like liquid metals, can amplify seed magnetic fields to generate dynamo action. Starting from the conjectured flow structure in the Earth's interior, a conceptional and engineering design is described for a laboratory dynamo experiment. Some details of the construction of the test facility and first experimental results are presented and discussed.

Magnetic field depressions in the solar wind

Abstract: Depressions in the interplanetary magnetic field strength occur on a wide range of temporal scales, starting with magnetic holes with a duration of several seconds and extending to larger-scale structures of more than 30 min duration. Using the magnetic field measurements of the Ulysses spacecraft, we quantify the statistical significance of the occurrence rate of depressions in the magnetic field compared to a lognormal distribution. On this basis we introduce measures for the length and depth of magnetic depressions. There is a weak indication for a change in the character of the length distribution at 20–40 s in the high-speed solar wind. An analysis of 115 depressions with a length > 2 min showed that (1) they are bounded by tangential discontinuities in 78% of all cases, (2) normals to the structure boundaries have no strong orientation with respect to background field or global geometry, and (3) an increased proton temperature anisotropy is the only bulk ion parameter correlating with the depressions.

A new model for the topology of magnetic clouds in the solar wind

Abstract: We present a model that describes the topology of a magnetic cloud. The model relates the magnetic field vector and current density of the cloud without assuming the force-free condition. Fitting the model to the experimental data we obtain the current density, the attitude of the axis and the relative closest-approach distance between the spacecraft and the cloud axis. In this paper, several magnetic clouds of 1997 are analyzed. The results indicate that the topology presented in this paper explains the magnetic field inside a MC better than force-free models. A current density of the order of 10−12 C m−2 s−1 is obtained in the fitting of all the events.

Extrapolation of the solar magnetic field within the potential-field approximation from full-disk magnetograms

Abstract: This paper is concerned with the Laplace boundary-value problem with the directional derivative, corresponding to the specific nature of measurements of the longitudinal component of the photospheric magnetic field. Boundary conditions are specified by a distribution on the sphere of projection of the magnetic field vector unto a given direction. It is shown that the solution of this problem exists in the form of a spherical harmonic expansion, and uniqueness of this solution is proved. A conceptual sketch of numerical determination of the harmonic series coefficients is given. The field of application of the method is analyzed having regard to the peculiarities of actual data. Finally, we present differences in results derived from extrapolating the magnetic field from a synoptic map and a full-disk magnetogram.

Shear Alfvén waves on stretched magnetic field lines near midnight in Earth's magnetosphere

Abstract: The spectrum of toroidal standing shear Alfven waves (SAWs) is derived for a stretched magnetic field line geometry that is approximated by the Tsyganenko 96 magnetic field model. The model is applied to field lines near the midnight meridional plane. It is demonstrated that the fundamental mode frequency for typical ambient parameters of Earth's magnetosphere is in the 1–4 mHz range. This frequency is in agreement with the measured frequency of magnetospheric field line resonances, and is up to an order of magnitude smaller than for a dipolar magnetic field. We conclude that stretching of Earth's magnetic field offers a possible explanation for anomalously low frequency SAWs observed within diffuse auroral emission (Hβ) produced by energetic proton precipitation in the inner plasma sheet.

Two‐dimensional MHD simulation of the solar wind interaction with magnetic field anomalies on the surface of the Moon

Abstract: Two-dimensional magnetohydrodynamic simulations of the solar wind interaction with the magnetized regions on the surface of the Moon suggest “mini-magnetospheres” can form around the regions on the Moon when the magnetic anomaly field strength is above 10 nT at 100 km above the surface (for a surface field strength of 290 nT) and when the solar wind ion density is below 40 cm−3, with typical observations placing anomalous magnetic field strengths around 2 nT at 100 km above the surface. The results suggest that not only can a bow shock and magnetopause form around the small anomalies, but their position and shape can change dramatically with changes in the solar wind conditions. A switch from southward to northward interplanetary magnetic field (IMF) causes the size of the mini-magnetosphere to increase by 90% and the magnetic field at various positions inside the bow shock to increase by a factor of 10. In addition to affecting the stand-off distance, changes in the IMF can also cause the mini-magnetosphere to go from very round to flat and elongated. The scale size of the mini-magnetospheres is 100 km for the range of typical solar wind conditions and the surface magnetic field strengths measured by Lunar Prospector. A stagnation point inside the shock region also exists for several solar wind conditions.

Interplanetary magnetic clouds: Sources, properties, modeling, and geomagnetic relationship

Abstract: We present a review of interplanetary magnetic clouds, whose structures are usually those of very large magnetic flux ropes (of ∼ 1/4 AU diameter at 1 AU) possessing intense axial magnetic fields and relatively cool internal proton plasma. The review covers the clouds' solar sources, their average solar wind characteristics (based primarily on IMP-8, ISEE 3, and WIND spacecraft data), their interactions with the Earth's magnetosphere, and their tendency (about 1/2 the time) to drive interplanetary shock waves and under what conditions. The clouds are analyzed according to a force free, cylindrically symmetric, flux rope model, which provides fundamental cloud properties, such as cross-sectional size, axial attitude, axial field intensity, and field handedness, as well as the spacecraft's closest approach distance, and a quantitative means of evaluating the quality of the model's fit to field data. All of these and other relevant quantities are reviewed statistically for many clouds from both the active and quiet parts of the solar cycle and the results compared. A natural by-product of cloud modeling is the ability to estimate the axial magnetic flux carried by the cloud. Such an estimate can be compared to an estimate of the solar source flux for a candidate region on the Sun for a check of flux consistency and a confirmation of the specific cloud-source relationship. Using a carefully chosen subset of WIND magnetic clouds, a profile of a generic cloud in terms of scalar quantities (field intensity, density, speed, proton thermal speed, and proton plasma beta) is produced and discussed. One of the most dramatic consequences of magnetic clouds arises from their interaction with Earth's magnetosphere, since there is a high probability of this coupling causing geomagnetic storms, one of the elements of space weather.

Titan's magnetic wake: Atmospheric or magnetospheric interaction

Abstract: We compare the magnetic field topology in the Titan wake to an idealized picture of magnetic field lines draping about a conductive nonmagnetic obstacle. It is shown that in the inner part of the wake the magnetic field picture differs significantly from that expected for an idealized draping: The transverse magnetic field component rotates by 90° as compared with the direction of the upstream transverse magnetic field. Another difference is the existence of a deep magnetic field minima separating the inner and outer parts of the wake. Transverse magnetic field rotation can be explained neither by temporal changes in the upstream magnetic field nor by reconnection processes in the wake. We find that this behavior of the transverse magnetic field can be explained at least qualitatively if one assumes the existence of a small intrinsic magnetic field of Titan. An effective magnetic dipole of 1021 G cm3 can account for the observed topology of the Titan magnetic wake. The origin of this field may be related to a residual magnetization of Titan's crust or to induction in a conducting ionosphere of the satellite. We present results of MHD simulations which support the above theoretical conclusion.

Distribution of magnetic flux on the solar surface and low-degree p-modes

Abstract: The frequencies of solar p-modes are known to change over the solar cycle. There is also recent evidence that the relation between frequency shift of low-degree modes and magnetic flux or other activity indicators differs between the rising and falling phases of the solar cycle, leading to a hysteresis in such diagrams. We consider the influence of the changing large-scale surface distribution of the magnetic flux on low-degree (l≤3) p-mode frequencies. To that end, we use time-dependent models of the magnetic flux distribution and study the ensuing frequency shifts of modes with different order and degree as a function of time. The resulting curves are periodic functions (in simple cases just sine curves) shifted in time by different amounts for the different modes. We show how this may easily lead to hysteresis cycles comparable to those observed. Our models suggest that high-latitude fields are necessary to produce a significant difference in hysteresis between odd- and even-degree modes. Only magnetic field distributions within a small parameter range are consistent with the observations by Jimenez-Reyes et al. Observations of p-mode frequency shifts are therefore capable of providing an additional diagnostic of the magnetic field near the solar poles. The magnetic distribution that is consistent with the p-mode observations also appears reasonable compared with direct measurements of the magnetic field.

The large-scale solar magnetic field and 11-year activity cycles

Abstract: Magnetic Hα synoptic maps of the Sun for 1915–1999 are analyzed and the intensities of spherical harmonics of the large-scale solar magnetic field computed. The possibility of using these Hα maps as a database for investigations of long-term variations of solar activity is demonstrated. As an example, the magnetic-field polarity distribution for the Hα maps and the analogous polarity distribution for the magnetographic maps of the Stanford observatory for 1975–1999 are compared. An activity index A(t) is introduced for the large-scale magnetic field, which is the sum of the magnetic-moment intensities for the dipole and octupole components. The 11-year cycle of the large-scale solar magnetic field leads the 11-year sunspot cycle by, on average, 5.5 years. It is concluded that the observed weak large-scale solar magnetic field is not the product of the decay of strong active-region fields. Based on the new data, the level of the current (23rd) solar-activity cycle and some aspects of solar-cycle theory are discussed.

Mean Field Theory Interpretation of Solar Polarity Reversal

Abstract: A mechanism of the polarity reversal of the solar magnetic field is explored on the basis of the mean field or turbulent dynamo theory. In the low-latitude region of the convective zone, the toroidal magnetic field, which is the origin of sunspots, is generated by the rotational motion of fluids, with the turbulent cross helicity as the intermediary. This field generates the poloidal field of dipole type through the alpha or turbulent helicity effect. The latter, in turn, contributes to the annihilation of the turbulent cross helicity, resulting in the decay of the toroidal magnetic field. This process indicates less room for the occurrence of the fully developed poloidal field in the low-latitude region and paves the way for the polarity reversal through the change of the sign of the turbulent cross helicity. A simple model mimicking the periodic polarity reversal is presented, and the relationship of the reversal period to the ratio of the poloidal to toroidal fields is given. The meridional-flow velocity at the solar surface is estimated, giving a result consistent with observations.

Elusive Magnetic Structures in the Sun and Solar-Type Stars

Abstract: The magnetic structures of the Sun are very inhomogeneous, with irregularities smaller than the smallest sizes that we resolve from Earth. Such irregularities are not properly accounted for by standard magnetic field diagnostic techniques. We have identified a quantitatively important bias that has remained unnoticed hitherto. Intense magnetic fields embedded in inhomogeneous magnetic structures produce little light and easily escape detection. These elusive magnetic fields, which cheat standard observing techniques, seem to be common. We estimate that they carry at least half of the solar magnetic flux. Should the bias be so severe, it would cast doubts on the present interpretation of many solar magnetic phenomena. Since magnetic field measurements in solar-type stars reproduce solar methods, they are liable to the same systematic errors.

Dynamical investigation of three‐dimensional reconnection in quasi‐separatrix layers in a boundary‐driven magnetic field

Abstract: Quasi-separatrix layers are regions in space where the mapping of field line connectivity changes especially rapidly. These layers have been suggested as special locations in three-dimensional magnetic fields that may host magnetic reconnection. Previous investigations have been analytical and have taken different simplifying assumptions to investigate the problem. This paper takes a numerical approach to investigate the dynamical properties of quasi-separatrix layers. The magnetic topology is stressed using drivers suggested by the analytical investigations but modified to fit the adopted boundary conditions. The experiments show that current does accumulate at specific locations in the numerical domain. The current magnitude and location depend strongly on the profile of the imposed driver, and they are found to be generated by the changes in field line parts imposed by the driving. They are therefore the manifestation of free magnetic energy in the perturbed magnetic field. After the stressing of the field has stopped, it is found that the plasma pressure is able to balance the Lorentz force of the stressed magnetic field and prevent a continued growth of the current amplitude in the current layers. Field-line changes are produced in the experiments that include magnetic resistivity. The reconnection takes place at locations where the electric field component along the magnetic field is large. The changes in field-line connectivity initiate flow velocities across the magnetic field lines at only a small fraction of the local Alfven velocity.

Response above a plane-conducting earth to a pulsed vertical magnetic dipole at the surface

Abstract: A theoretical study of the pulsed electromagnetic radiation from a vertical magnetic dipole placed on a plane-conducting earth is presented. The application of a Laplace transformation in time and a Fourier transformation in the two orthogonal, horizontal, spatial components leads, under consideration of initial, boundary, and transition conditions, to an integral representation of the solution of the wave equation in frequency space. A modified Cagniard method is then used to derive closed-form expressions for the magnetic Hertz vector anywhere above the conducting earth. The method is used to perform numeric calculations of the magnetic Hertz vector, for different source-receiver distances, as well as different values of the earth's conductivity and permittivity. PACS Nos.: 41.20Jb, 42.25Bs, 42.25Gy, 44.05+e

Grand minima in a buoyancy-driven solar dynamo

Abstract: Numerical simulations of a 2D mean-field model are presented which show that grand minima, typical for the long- term behaviour of solar magnetic activity, can be produced by a dynamo that features an alpha effect based on the buoyancy instability of magnetic fluxtubes. The buoyancy-driven alpha effect functions only if the magnetic field strength exceeds a minimal value necessary for instability. It opens the possibil- ity of dynamo action within the solar overshoot layer, where a strong magnetic field, B 10 5 G, is thought to be stored. The existence of a magnetic threshold for dynamo action can lead to interruptions of the magnetic cycle, similar to the grand minima of solar activity. Transitions across the instability threshold are triggered by magnetic-flux injections from the convection zone. This is modelled by allowing for a small-scale kinematic alpha effect in the convection zone, and convective downdrafts that penetrate the overshoot layer.

Exact solutions for internally induced magnetization in a shell

Abstract: Summary We analyse the external magnetic field generated by a spheroidal shell of constant susceptibility when it is magnetized by an internal magnetic field of arbitrary complexity. The analysis is relevant to the generation of the Earth’s crustal magnetic field by the internal core field. We find an analytical expression for such a crustal field that is expressed in an oblate spheroidal coordinate system, valid for arbitrary flattening, shell thickness and susceptibility. Our exact calculation takes into account magnetization due to the magnetic field of the crust itself, generating an external field that depends on terms both linear and non-linear in the susceptibility. Each spheroidal harmonic coefficient of the external field is generated by and proportional to the same coefficient in the expansion of the inducing field. The terms linear in the susceptibility are generated by the flattening of the Earth, and would otherwise vanish (by Runcorn’s theorem) in the spherical case. For a geophysically relevant model, the crustal field is weak, generated primarily by the non-linear terms, and dominated by long wavelengths.

Magnetic models of slowly rotating magnetic Ap stars: aligned magnetic and rotation axes

Abstract: As a result of major surveys carried out during the past decade by Mathys and collaborators, we now have mea- surements with full phase coverage of several magnetic field moments, including the mean longitudinal field B', the mean field modulus Bs, and in most cases the mean quadratic field Bmq and mean crossover field Bxover, for a sample of 24 chem- ically peculiar magnetic (Ap) stars. This represents an increase of a factor of order five in the stellar sample with data of this quality, compared to the situation a decade ago. We exploit this dataset to derive general and statistical prop- erties of the stars in the sample, as follows. First, we fit the avail- able field moment observations assuming a simple, axisymmet- ric multipole magnetic field expansion (with dipole, quadrupole, and octupole components) over each stellar surface. We show that this representation, though not exact, gives an adequate description of the available data for all the stars in this sam- ple, although the fit parameters are in many cases not unique. We find that many of the stars require an important quadrupole and/or octupole field component to satisfy the observations, and that some (usually small) deviations from our assumed axisym- metric field distributions are certainly present. We examine the inclination i (0 i 90) of the rotation axis to the line of sight and the obliquity (0 90) of the magnetic field with respect to the rotation axis, and show that the stars with periods of the order of a month or longer have systematically small values of : slowly rotating magnetic stars generally have their magnetic and rotation axes aligned to within about 20 , unlike the short period magnetic Ap stars, in which is usually large. This is a qualitatively new result, and one which is very important for efforts to understand the evolution of magnetic fields and angular momentum in the magnetic Ap stars.