Random walk of magnetic field lines for different values of the energy range spectral index

An analytical nonlinear description of field-line wandering in partially statistically magnetic systems was proposed recently. In this article the influence of the wave spectrum in the energy range onto field-line random walk is investigated by applying this formulation. It is demonstrated that in all considered cases we clearly obtain a superdiffusive behavior of the field-lines. If the energy range spectral index exceeds unity a free-streaming behavior of the field-lines can be found for all relevant length-scales of turbulence. Since the superdiffusive results obtained for the slab model are exact, it seems that superdiffusion is the normal behavior of field-line wandering.

Ion populations on open field lines within the dayside low-latitude boundary layer: theory and observations during a transient event

We analyze of ion populations observed by the NOAA-12 satellite within dayside auroral transients. The data are matched with an open magnetopause model which allows for the transmission of magnetosheath ions across one or both of the two Alfvén waves which emanate from the magnetopause reconnection site. It also allows for reflection and acceleration of ions of magnetospheric origin by these waves. From the good agreement found between the model and the observations, we propose that the events and the low-latitude boundary precipitation are both on open field lines.

Multiple, discrete arcs on sunward convecting field lines in the 14-15 MLT region

Ionospheric plasma flow measurements and simultaneous observations of thin (∼0.2° invariant latitude (ILAT)), multiple, longitudinally extended auroral arcs of transient nature within 74°-76° ILAT and 1030-1130 UT (∼14-15 MLT) on January 12, 1989, are reported. The auroral structures appeared within the luminous belt of strong 630.0-nm emissions located predominantly on sunward convecting field lines equatorward of the convection reversal boundary as identified by the European Incoherent Scatter UHF radar. The events occurred during a period of several hours quasi-steady solar wind speed (∼ 700 km s−1) and a radially orientated interplanetary magnetic field (IMF) with a weak northward tilt (IMF Bz>0). These typical dayside auroral features are related to previous studies of auroral activity related to the upward region 1 current in the postnoon sector. The discrete auroral events presented here may result from magnetosheath plasma injections into the low-latitude boundary layer (LLBL) and an associated dynamo mechanism. An alternative explanation invokes kinetic Alfvén waves, triggered either by Kelvin-Helmholtz instability at the inner (or outer) edge of the LLBL or by pressure pulse induced magnetopause surface waves.

Tokamak magnetic field lines described by simple maps

The magnetic field line structure in a tokamak can be obtained by direct numerical integration of the field line equations. However, this is a lengthy procedure and the analysis of the solution may be very time-consuming. Otherwise we can use simple two-dimensional, area-preserving maps, obtained either by approximations of the magnetic field line equations, or from dynamical considerations. These maps can be quickly iterated, furnishing solutions that mirror the ones obtained from direct numerical integration, and which are useful when long-term studies of field line behavior are necessary (e.g. in diffusion calculations). In this work we focus on a set of simple tokamak maps for which these advantages are specially pronounced.

Animated feather coats using field lines

The tedious task of manually placing feathers on computer animated objects involves aligning feathers, ensuring that they do not insect each other or penetrate the surface, deforming every feather to match the local surface features, and ensuring that the feather coat is consistent when the underlying object is animated.

We present a technique for generating a feather coat over an object. Feather orientation is specified quickly and easily, feathers are deformed while ensuring collision prevention, and the coat can be animated. We create a vector field in the space surrounding the body object and deform feathers to align with the field lines. The non-intersection property of the field lines ensures that feather intersections are avoided. We provide a formulation of a suitable vector field and demonstrate that it is capable of producing realistic feather coats. The process can easily be integrated into the work-flow of standard modelling and animation processes.

We show examples of feather coat creation on a range of objects, proving that field line based placement of feather coats provides the desired functionality for feather modelling and animation.

Magnetospheric access of solar particles and the configuration of the distant geomagnetic field

The access of 1.2-40 MeV protons and 0.4-1.0 MeV electrons from interplanetary space to the polar cap regions has been investigated with an experiment on board a low altitude, polar orbiting satellite (OG0-4).

A total of 333 quiet time observations of the electron polar cap boundary give a mapping of the boundary between open and closed geomagnetic field lines which is an order of magnitude more comprehensive than previously available.

Persistent features (north/south asymmetries) in the polar cap proton flux, which are established as normal during solar proton events, are shown to be associated with different flux levels on open geomagnetic field lines than on closed field lines. The pole in which these persistent features are observed is strongly correlated to the sector structure of the interplanetary magnetic field and uncorrelated to the north/south component of this field. The features were observed in the north (south) pole during a negative (positive) sector 91% of the time, while the solar field had a southward component only 54% of the time. In addition, changes in the north/south component have no observable effect on the persistent features.

Observations of events associated with co-rotating regions of enhanced proton flux in interplanetary space are used to establish the characteristics of the 1.2 - 40 MeV proton access windows: the access window for low polar latitudes is near the earth, that for one high polar latitude region is ~250 R_⊕ behind the earth, while that for the other high polar latitude region is ~1750 R_⊕ behind the earth. All of the access windows are of approximately the same extent (~120 R_⊕). The following phenomena contribute to persistent polar cap features: limited interplanetary regions of enhanced flux propagating past the earth, radial gradients in the interplanetary flux, and anisotropies in the interplanetary flux.

These results are compared to the particle access predictions of the distant geomagnetic tail configurations proposed by Michel and Dessler, Dungey, and Frank. The data are consistent with neither the model of Michel and Dessler nor that of Dungey. The model of Frank can yield a consistent access window configuration provided the following constraints are satisfied: the merging rate for open field lines at one polar neutral point must be ~5 times that at the other polar neutral point, related to the solar magnetic field configuration in a consistent fashion, the migration time for open field lines to move across the polar cap region must be the same in both poles, and the open field line merging rate at one of the polar neutral points must be at least as large as that required for almost all the open field lines to have merged in 0 (one hour). The possibility of satisfying these constraints is investigated in some detail.

The role played by interplanetary anisotropies in the observation of persistent polar cap features is discussed. Special emphasis is given to the problem of non-adiabatic particle entry through regions where the magnetic field is changing direction. The degree to which such particle entry can be assumed to be nearly adiabatic is related to the particle rigidity, the angle through which the field turns, and the rate at which the field changes direction; this relationship is established for the case of polar cap observations.

Evolution of localized blobs of swirling or buoyant fluid with and without an ambient magnetic field.

We investigate the evolution of localized blobs of swirling or buoyant fluid in an infinite, inviscid, electrically conducting fluid. We consider the three cases of a strong imposed magnetic field, a weak imposed magnetic field, and no magnetic field. For a swirling blob in the absence of a magnetic field, we find, in line with others, that the blob bursts radially outward under the action of the centrifugal force, forming a thin annular vortex sheet. A simple model of this process predicts that the vortex sheet thins exponentially fast and that it moves radially outward with constant velocity. These predictions are verified by high-resolution numerical simulations. When an intense magnetic field is applied, this phenomenon is suppressed, with the energy and angular momentum of the blob now diffusing axially along the magnetic field lines, converting the blob into a columnar structure. For modest or weak magnetic fields, there are elements of both types of behavior, with the radial bursting dominating over axial diffusion for weak fields. However, even when the magnetic field is very weak, the flow structure is quite distinct to that of the nonmagnetic case. In particular, a small but finite magnetic field places a lower bound on the thickness of the annular vortex sheet and produces an annulus of counter-rotating fluid that surrounds the vortex core. The behavior of the buoyant blob is similar. In the absence of a magnetic field, it rapidly develops the mushroomlike shape of a thermal, with a thin vortex sheet at the top and sides of the mushroom. Again, a simple model of this process predicts that the vortex sheet at the top of the thermal thins exponentially fast and rises with constant velocity. These predictions are consistent with earlier numerical simulations. Curiously, however, it is shown that the net vertical momentum associated with the blob increases linearly in time, despite the fact that the vertical velocity at the front of the thermal is constant. As with the swirling blob, an imposed magnetic field inhibits the formation of a vortex sheet. A strong magnetic field completely suppresses the phenomenon, replacing it with an axial diffusion of momentum, while a weak magnetic field allows the sheet to form, but places a lower bound on its thickness. The magnetic field does not, however, change the net vertical momentum of the blob, which always increases linearly with time.

Oscillations in the magnetic field of the solar corona in response to flares near the photosphere

Schrijver, C.J. and Brown, D.S., 2000, Oscillations in the magnetic field of the solar corona in response to flares near the photosphere, Astrophysical Journal, 537, L69-L72. Sponsorship: PPARC

Analytical description of stochastic field-Line wandering in magnetic turbulence

A nonperturbative nonlinear statistical approach is presented to describe turbulent magnetic systems embedded in a uniform mean magnetic field. A general formula in the form of an ordinary differential equation for magnetic field-line wandering (random walk) is derived. By considering the solution of this equation for different limits several new results are obtained. As an example, it is demonstrated that the stochastic wandering of magnetic field-lines in a two-component turbulence model leads to superdiffusive transport, contrary to an existing diffusive picture. The validity of quasilinear theory for field-line wandering is discussed, with respect to different turbulence geometry models, and previous diffusive results are shown to be deduced in appropriate limits.

Detailed analytical investigation of magnetic field line random walk in turbulent plasmas: I. Two-component slab/two-dimensional turbulence

The random displacement of magnetic field lines in the presence of magnetic turbulence in plasmas is investigated from first principles. A two-component (slab/two-dimensional composite) model for the turbulence spectrum is employes. An analytical investigation of the asymptotic behavior of the field-line mean square displacement (FL-MSD) is carried out. It is shown that the magnetic field lines behave superdifusively for every large values of the position variable z, since the FL-MSD sigma varies as sigma similar to z(4/3). An intermediate diffusive regime may also possible exist for finite values of z under conditions which are explicitly determined in terms of the intrinsic turbulent plasma parameters. The superdiffusie asymptotic result is confirmed numerically via an iterative algorithm. The relevance to previous resuslts is discussed.

Detailed analytical investigation of magnetic field line random walk in turbulent plasmas: II. Isotropic turbulence

The random walk of magnetic field lines in the presence of magnetic turbulence in plasmas is investigated from first principles. An isotropic model is employed for the magnetic turbulence spectrum. An analytical investigation of the asymptotic behavior of the field-line mean-square displacement is carried out. in terms of the position variable z. It is shown that varies as similar to z ln z for large distance z. This result corresponds to a superdiffusive behavior of field line wandering. This investigation complements previous work, which relied on a two-component model for the turbulence spectrum. Contrary to that model, quasilinear theory appears to provide an adequate description of the field line random walk for isotropic turbulence.

The influence of the magnetic field on running penumbral waves in the solar chromosphere

We use images of high spatial and temporal resolution, obtained using both ground- and space-based instrumentation, to investigate the role magnetic field inclination angles play in the propagation characteristics of running penumbral waves in the solar chromosphere. Analysis of a near-circular sunspot, close to the center of the solar disk, reveals a smooth rise in oscillatory period as a function of distance from the umbral barycenter. However, in one directional quadrant, corresponding to the north direction, a pronounced kink in the period-distance diagram is found. Utilizing a combination of the inversion of magnetic Stokes vectors and force-free field extrapolations, we attribute this behavior to the cut-off frequency imposed by the magnetic field geometry in this location. A rapid, localized inclination of the magnetic field lines in the north direction results in a faster increase in the dominant periodicity due to an accelerated reduction in the cut-off frequency. For the first time, we reveal how the spatial distribution of dominant wave periods, obtained with one of the highest resolution solar instruments currently available, directly reflects the magnetic geometry of the underlying sunspot, thus opening up a wealth of possibilities in future magnetohydrodynamic seismology studies. In addition, the intrinsic relationships we find between the underlying magnetic field geometries connecting the photosphere to the chromosphere, and the characteristics of running penumbral waves observed in the upper chromosphere, directly supports the interpretation that running penumbral wave phenomena are the chromospheric signature of upwardly propagating magneto-acoustic waves generated in the photosphere.

Suprathermal electron evolution in a Parker spiral magnetic field

Suprathermal electrons (>70 eV) form a small fraction of the total solar wind electron density but serve as valuable tracers of heliospheric magnetic field topology. Their usefulness as tracers of magnetic loops with both feet rooted on the Sun, however, most likely fades as the loops expand beyond some distance owing to scattering. As a first step toward quantifying that distance, we construct an observationally constrained model for the evolution of the suprathermal electron pitch-angle distributions on open field lines. We begin with a near-Sun isotropic distribution moving antisunward along a Parker spiral magnetic field while conserving magnetic moment, resulting in a field-aligned strahl within a few solar radii. Past this point, the distribution undergoes little evolution with heliocentric distance. We then add constant (with heliocentric distance, energy, and pitch angle) ad-hoc pitch-angle scattering. Close to the Sun, pitch-angle focusing still dominates, again resulting in a narrow strahl. Farther from the Sun, however, pitch-angle scattering dominates because focusing is effectively weakened by the increasing angle between the magnetic field direction and intensity gradient, a result of the spiral field. We determine the amount of scattering required to match Ulysses observations of strahl width in the fast solar wind, providing an important tool for inferring the large-scale properties and topologies of field lines in the interplanetary medium. Although the pitch-angle scattering term is independent of energy, time-of-flight effects in the spiral geometry result in an energy dependence of the strahl width that is in the observed sense although weaker in magnitude.

Self-consistent wave-particle interactions in dispersive scale long-period field-line-resonances

Using 1D Vlasov drift-kinetic computer simulations, it is shown that electron trapping in long period standing shear Alfven waves (SAWs) provides an efficient energy sink for wave energy that is much more effective than Landau damping. It is also suggested that the plasma environment of low altitude auroral-zone geomagnetic field lines is more suited to electron acceleration by inertial or kinetic scale Alfven waves. This is due to the self-consistent response of the electron distribution function to SAWs, which must accommodate the low altitude large-scale current system in standing waves. We characterize these effects in terms of the relative magnitude of the wave phase and electron thermal velocities. While particle trapping is shown to be significant across a wide range of plasma temperatures and wave frequencies, we find that electron beam formation in long period waves is more effective in relatively cold plasma.

Reconnection at the high-latitude magnetopause during northward interplanetary magnetic field conditions

The Polar spacecraft had a prolonged encounter with the high-latitude dayside magnetopause on May 29, 1996. This encounter with the magnetopause occurred when the interplanetary magnetic field was directed northward. From the three-dimensional electron and ion distribution functions measured by the Hydra instrument, it has been possible to identify nearly all of the distinct boundary layer regions associated with high-latitude reconnection. The regions that have been identified are (1) the cusp; (2) the magnetopause current layer; (3) magnetosheath field lines that have interconnected in only the Northern Hemisphere; (4) magnetosheath field lines that have interconnected in only the Southern Hemisphere; (5) magnetosheath field lines that have interconnected in both the Northern and Southern Hemispheres; (6) magnetosheath that is disconnected from the terrestrial magnetic field; and (7) high-latitude plasma sheet field lines that are participating in magnetosheath reconnection. Reconnection over this time period was occurring at high latitudes over a broad local-time extent, interconnecting the magnetosheath and lobe and/or plasma sheet field lines in both the Northern and Southern Hemispheres. Newly closed boundary layer field lines were observed as reconnection occur-red first at high latitudes in one hemisphere and then later in the other. These observations establish the location of magnetopause reconnection during these northward interplanetary magnetic field conditions as being at high latitudes, poleward of the cusp, and further reinforce the general interpretation of electron and ion phase space density signatures as indicators of magnetic reconnection and boundary layer formation.