The Strength and Structure of the Coronal Magnetic Field

I discuss a method for determining the strength and spatial structure of the coronal magnetic field by observations of the Faraday rotation of a radio galaxy which is in conjunction with the Sun. Given a knowledge of the plasma density in the outer corona, and the magnetic field sector structure (both independently available), the strength of the coronal field can be determined, as well as the magnitude of spatial variations on scales of 1000 km to several solar radii. Such knowledge is crucial for testing computational models of the solar corona, which are prominently featured in this meeting. Results are presented from observations with the Very Large Array radio telescope of the radio galaxy 3C228 on August 16, 2003, when the line of sight to the source was at heliocentic distances of 7.1−6.2R _⊙. The observations are consistent with a coronal magnetic field which is proportional to the inverse square of the distance in the range 6 ≤ r ≤ 10R _⊙, and has a value of 39 mG at 6.2R _⊙. The Faraday rotation is uniform across the source, indicating an absence of strong plasma inhomogeneity on spatial scales up to 35,000 km.     

Time-implicit simulation of particle-fluid systems

This paper presents one-dimensional particle-fluid hybrid simulations in which the strongly collisional components of the plasma (e.g., ions and thermal electrons with ν_cfΔt > 1) are treated as fluids and the weakly collisional components (e.g., energetic electrons with ν_cpΔt ≪ 1) are treated as particles. Here ν_cf denotes the fluid ion and electron collision frequencies, ν_cp is the energetic particle collision frequency and Δt is the time step. Collisions between particle and fluid components are treated by a Monte-Carlo method and mass transfers between the particle and fluid electron components are governed by collision frequency thresholds. The field is computed implicitly to allow time steps with Ω_p Δt > 1 (Ω_p: plasma frequency).     

Effects of Superthermal Particles on Waves in Magnetized Space Plasmas

Distributions with excess numbers of superthermal particles are common in space environments. They are well modelled by the isotropic kappa distribution, or, where magnetic effects are important, the kappa-Maxwellian. This paper presents a review of some studies of electrostatic and electromagnetic waves in such plasmas, based on the associated generalized plasma dispersion functions, Z _κ and Z _κM. In particular, the effects of low values of κ are considered, i.e. strongly accelerated distribution functions. Recently the full susceptibility tensor for oblique propagation of electromagnetic waves in a kappa-Maxwellian magnetoplasma has been established and has been applied to the study of whistler waves.     

Non-linear resonant excitation of whistler mode waves in the Earth's ionosphere

We examine the resonant non-linear interaction in the Earth's ionosphere of two powerful high frequency radio beams with frequencies f ₁ and f ₂ (both larger than the plasma frequency at F2_max) and wave numbers k ₁ and k ₂ such that a whistler mode wave can be excited with a frequency f ₃ = f ₁ — f ₂ and a wave number k ₃ = k ₁ – k ₂. The feasibility of an effective ground based installation, sited at low latitudes, is discussed and the field strength of the wave emerging from a 10 km wide ionospheric region illuminated by the beams is evaluated for a range of transmitted frequencies, beam orientations and plasma frequencies in the interaction region. It is suggested that the longitude dependence of the enhancement of VLF noise bands detected by the Ariel 3 satellite may be due to a non-linear interaction of this type between any two or more medium wavelength signals from areas where there is a high concentration of commercial broadcasting stations, such as the NE region of the U.S.A.     

The Effects of Transverse Magnetic Field and Density Variations on the Particle Energy Spectra in a Reconnecting 3D Current Sheet

Electron and proton acceleration by a super-Dreicer electric field is further investigated in a non-neutral reconnecting current sheet (RCS) with a variable plasma density. The tangential B _z and transverse magnetic field components B _x are assumed to vary with the distances x and z from the X nullpoint linearly and exponentially, respectively; the longitudinal component (a ‘guiding field’) is accepted constant. Particles are found to gain a bulk of their energy in a thin region close to the X nullpoint where the RCS density increases with z exponentially with the index λ and the tangential magnetic field B _x also increases with z exponentially with the index α. For the RCS with a constant density (λ = 0), the variations of the tangential magnetic field lead to particle power-law energy spectra with the spectral indices γ₁ being dependent on the exponent α as: for protons and for electrons in a strong guiding field (β > 10⁻²) and for electrons in a moderate or weak guiding field (β > 10⁻⁴). For the RCS with an exponential density increase in the vicinity of the X nullpoint (λ≥ 0) there is a further increase of the resulting spectral indices γ that depends on the density exponent index λ as for protons and for electrons in weaker guiding fields and as for electrons in stronger guiding fields. These dependencies can explain a wide variety (1.5–10) of particle spectral indices observed in solar flares by the variations of a magnetic field topology and physical conditions in a reconnecting region. This can be used as a diagnostic tool for the investigation of the RCS dynamics from the accelerated particle spectra found from hard X-ray and microwave emission.     

Mercury’s Surface Composition and Character as Measured by Ground-Based Observations

Mercury’s surface is thought to be covered with highly space-weathered silicate material. The regolith is composed of material accumulated during the time of planetary formation, and subsequently from comets, meteorites, and the Sun. Ground-based observations indicate a heterogeneous surface composition with SiO₂ content ranging from 39 to 57 wt%. Visible and near-infrared spectra, multi-spectral imaging, and modeling indicate expanses of feldspathic, well-comminuted surface with some smooth regions that are likely to be magmatic in origin with many widely distributed crystalline impact ejecta rays and blocky deposits. Pyroxene spectral signatures have been recorded at four locations. Although highly space weathered, there is little evidence for the conversion of FeO to nanophase metallic iron particles (npFe⁰), or “iron blebs,” as at the Moon. Near- and mid-infrared spectroscopy indicate clino- and ortho-pyroxene are present at different locations. There is some evidence for no- or low-iron alkali basalts and feldspathoids. All evidence, including microwave studies, point to a low iron and low titanium surface. There may be a link between the surface and the exosphere that may be diagnostic of the true crustal composition of Mercury. A structural global dichotomy exists with a huge basin on the side not imaged by Mariner 10. This paper briefly describes the implications for this dichotomy on the magnetic field and the 3 : 2 spin : orbit coupling. All other points made above are detailed here with an account of the observations, the analysis of the observations, and theoretical modeling, where appropriate, that supports the stated conclusions.     

Modelling of the electromagnetic field in the interplanetary space and in the Earth's magnetosphere

A magnetohydrodynamic model of the solar wind flow is constructed using a kinematic approach. It is shown that a phenomenological conductivity of the solar wind plasma plays a key role in the forming of the interplanetary magnetic field (IMF) component normal to the ecliptic plane. This component is mostly important for the magnetospheric dynamics which is controlled by the solar wind electric field. A simple analytical solution for the problem of the solar wind flow past the magnetosphere is presented. In this approach the magnetopause and the Earth's bow shock are approximated by the paraboloids of revolution. Superposition of the effects of the bulk solar wind plasma motion and the magnetic field diffusion results in an incomplete screening of the IMF by the magnetopause. It is shown that the normal to the magnetopause component of the solar wind magnetic field and the tangential component of the electric field penetrated into the magnetosphere are determined by the quarter square of the magnetic Reynolds number. In final, a dynamic model of the magnetospheric magnetic field is constructed. This model can describe the magnetosphere in the course of the severe magnetic storm. The conditions under which the magnetospheric magnetic flux structure is unstable and can drive the magnetospheric substorm are discussed. The model calculations are compared with the observational data for September 24–26, 1998 magnetic storm (Dst _min=−205 nT) and substorm occurred at 02:30 UT on January 10, 1997. This revised version was published online in August 2006 with corrections to the Cover Date.     

Fast Dust in the Heliosphere

The dynamics of dust particles in the solar system is dominated by solar gravity, by solar radiation pressure, or by electromagnetic interaction of charged dust grains with the interplanetary magnetic field. For micron-sized or bigger dust particles solar gravity leads to speeds of about 30 to 40 km s^–1 at the Earths distance. Smaller particles that are generated close to the Sun and for which radiation pressure is dominant (the ratio of radiation pressure force over gravity F _rad/F _grav is generally termed ) are driven out of the solar system on hyperbolic orbits. Such a flow of -meteoroids has been observed by the Pioneer 8, 9 and Ulysses spaceprobes. Dust particles in interplanetary space are electrically charged to typically +5 V by the photo effect from solar UV radiation. The dust detector on Cassini for the first time measured the dust charge directly. The dynamics of dust particles smaller than about 0.1 m is dominated by the electromagnetic interaction with the ambient magnetic field. Effects of the solar wind magnetic field on interstellar grains passing through the solar system have been observed. Nanometer sized dust stream particles have been found which were accelerated by Jupiters magnetic field to speeds of about 300 km s^–1.     

Locations of Atmospheric Photoelectron Energy Peaks Within the Mars Environment

By identifying peaks in the photoelectron spectrum produced by photoionization of CO₂ in the Martian atmosphere, we have conducted a pilot study to determine the locations of these photoelectrons in the space around Mars. The significant result of this study is that these photoelectrons populate a region around Mars bounded externally by the magnetic pileup boundary, and internally by the lowest altitude of our measurements (∼250 km) on the dayside and by a cylinder of approximately the planetary radius on the nightside. It is particularly noteworthy that the photoelectrons on the nightside are observed from the terminator plane tailward to a distance of ∼3 R _M, the Mars Express apoapsis. The presence of the atmospherically generated photoelectrons on the nightside of Mars may be explained by direct magnetic field line connection between the nightside observation locations and the Martian dayside ionosphere. Thus the characteristic photoelectron peaks may be used as tracers of magnetic field lines for the study of the magnetic field configuration and particle transport in the Martian environment.     

The Origin of Mercury’s Internal Magnetic Field

Mariner 10 measurements proved the existence of a large-scale internal magnetic field on Mercury. The observed field amplitude, however, is too weak to be compatible with typical convective planetary dynamos. The Lorentz force based on an extrapolation of Mariner 10 data to the dynamo region is 10⁻⁴ times smaller than the Coriolis force. This is at odds with the idea that planetary dynamos are thought to work in the so-called magnetostrophic regime, where Coriolis force and Lorentz force should be of comparable magnitude. Recent convective dynamo simulations reviewed here seem to resolve this caveat. We show that the available convective power indeed suffices to drive a magnetostrophic dynamo even when the heat flow though Mercury’s core–mantle boundary is subadiabatic, as suggested by thermal evolution models. Two possible causes are analyzed that could explain why the observations do not reflect a stronger internal field. First, toroidal magnetic fields can be strong but are confined to the conductive core, and second, the observations do not resolve potentially strong small-scale contributions. We review different dynamo simulations that promote either or both effects by (1) strongly driving convection, (2) assuming a particularly small inner core, or (3) assuming a very large inner core. These models still fall somewhat short of explaining the low amplitude of Mariner 10 observations, but the incorporation of an additional effect helps to reach this goal: The subadiabatic heat flow through Mercury’s core–mantle boundary may cause the outer part of the core to be stably stratified, which would largely exclude convective motions in this region. The magnetic field, which is small scale, strong, and very time dependent in the lower convective part of the core, must diffuse through the stagnant layer. Here, the electromagnetic skin effect filters out the more rapidly varying high-order contributions and mainly leaves behind the weaker and slower varying dipole and quadrupole components (Christensen in Nature 444:1056–1058, 2006). Messenger and BepiColombo data will allow us to discriminate between the various models in terms of the magnetic fields spatial structure, its degree of axisymmetry, and its secular variation.     

Alfvén waves in the context of solar-like star formation: accretion columns and disks

In this work we examine the damping of Alfvén waves as a source of plasma heating in disks and magnetic funnels of young solar like stars, the T Tauri stars. We apply four different damping mechanisms in this study: viscous-resistive, collisional, nonlinear and turbulent, exploring a wide range of wave frequencies, from 10⁻⁵Ω_i to 10⁻¹Ω_i (where Ω_i is the ion-cyclotron frequency). The results show that Alfvénic heating can increase the ionization rate of accretion disks and elevate the temperature of magnetic funnels of T Tauri stars opening possibilities to explain some observational features of these objects. This revised version was published online in August 2006 with corrections to the Cover Date.     

Multidimensional particle codes: Their capabilities and limitations

Increasing the number of dimensions calls for significant changes in simulation techniques. Demand on computer time and space increases by orders of magnitude and hardware development affects the feasibility. Gridless and Fokker-Planck codes are possible in ID, but one needs grids and PIC codes in 2D and 3D. This imposes limits on Debye lengths, particle size and spacing, and on resolution. Non-spectral (local) E-M codes also suffer a Courant restriction on δt, in addition to the usual ω_p δt restriction. Spectral methods therefore have an advantage; they also permit convenient filtering, particle shaping and control of resolution. 2D and codes are well advanced and documented (4,5). 3D codes are in their infancy. Data management, rather than physics or numerical analysis, becomes the major problem (10). Machine-independent 3D codes are too limited in resolution and speed. Parallelism helps greatly but makes the 3D codes machine-dependent. A present-day limit is attempted in a 2*128**3 grid code for CRAYs which process ∼ 5 million particles in ∼ 2 minutes per time step. Layering is employed to break up the 3D problem into many 2D problems. Fields and particles are packed and buffered in and out of core. Diagnostics are limited by the large volume of information accumulated in a run. Results of runs with 3D codes have tended to show that the third dimension, treated as “ignorable” in 2D simulations, should not have been ignored. With the next generation of highly parallel multiprocessors (which, however, call for the abandonment of spectral and implicit methods) one may hope to do very realistic 3D simulations.     

Early results from ISEE-1 electric field measurements

The double probe, floating potential instrumentation on ISEE-1 is producing reliable direct measurements of the ambient DC electric field at the bow shock, at the magnetopause, and throughout the magnetosheath, tail plasma sheet and plasmasphere. In the solar wind and in middle latitude regions of the magnetosphere spacecraft sheath fields obscure the ambient field under low plasma flux conditions such that valid measurements are confined to periods of moderately intense flux. Initial results show: (a) that the DC electric field is enhanced by roughly a factor of two in a narrow region at the front, increasing B, edge of the bow shock, (b) that scale lengths for large changes in E at the sub-solar magnetopause are considerably shorter than scale lengths associated with the magnetic structure of the magnetopause, and (c) that the transverse distribution of B-aligned E-fields between the outer magnetosphere and ionospheric levels must be highly complex to account for the random turbulent appearance of the magnetospheric fields and the lack of corresponding time-space variations at ionospheric levels. Spike-like, non-oscillatory, fields lasting <0.2 s are occasionally seen at the bow shock and at the magnetopause and also intermittently appear in magnetosheath and plasma sheet regions under highly variable field conditions. These suggest the existence of field phenomena occurring over dimensions comparable to the probe separation and c/_pe (the characteristic electron cyclotron radius) where _pe is the electron plasma frequency.     

The Magnetometer Instrument on MESSENGER

The Magnetometer (MAG) on the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) mission is a low-noise, tri-axial, fluxgate instrument with its sensor mounted on a 3.6-m-long boom. The boom was deployed on March 8, 2005. The primary MAG science objectives are to determine the structure of Mercury’s intrinsic magnetic field and infer its origin. Mariner 10 observations indicate a planetary moment in the range 170 to 350 nT R _M³ (where R _M is Mercury’s mean radius). The uncertainties in the dipole moment are associated with the Mariner 10 trajectory and variability of the measured field. By orbiting Mercury, MESSENGER will significantly improve the determination of dipole and higher-order moments. The latter are essential to understanding the thermal history of the planet. MAG has a coarse range, ±51,300 nT full scale (1.6-nT resolution), for pre-flight testing, and a fine range, ±1,530 nT full scale (0.047-nT resolution), for Mercury operation. A magnetic cleanliness program was followed to minimize variable and static spacecraft-generated fields at the sensor. Observations during and after boom deployment indicate that the fixed residual field is less than a few nT at the location of the sensor, and initial observations indicate that the variable field is below 0.05 nT at least above about 3 Hz. Analog signals from the three axes are low-pass filtered (10-Hz cutoff) and sampled simultaneously by three 20-bit analog-to-digital converters every 50 ms. To accommodate variable telemetry rates, MAG provides 11 output rates from 0.01 s⁻¹ to 20 s⁻¹. Continuous measurement of fluctuations is provided with a digital 1–10 Hz bandpass filter. This fluctuation level is used to trigger high-time-resolution sampling in eight-minute segments to record events of interest when continuous high-rate sampling is not possible. The MAG instrument will provide accurate characterization of the intrinsic planetary field, magnetospheric structure, and dynamics of Mercury’s solar wind interaction.     

Cross Field Diffusion of Cosmic Rays in a Two-Dimensional Magnetic Field Turbulence

Cross field diffusion of energetic particles (cosmic rays) in a two-dimensional static magnetic field turbulence is studied performing test particle simulations. Qualitatively different diffusion processes are observed depending on the ratio of Larmor radius (ρ) to the correlation length (λ) of the magnetic field fluctuations. The diffusion is found to be composed of several regimes with distinct statistical properties, which can be characterized using Levy statistics. This revised version was published online in August 2006 with corrections to the Cover Date.     

Coupling between the outer magnetosphere and the high-latitude ionosphere

The coupling between the ionosphere and the outer magnetosphere depends on the topology of the geomagnetic field. Some aspects of the closed and open magnetospheric models are briefly discussed.The assumption that the geomagnetic field lines are equipotentials is critisized both on observational and on theoretical grounds. Measurements of H Doppler profiles, of precipitating particles above the ionosphere, and of charged particle densities in the magnetosphere indicate the existence of electric fields, E_\\, parallel with the magnetic field.Two different models of E_\\ are considered. Both models violate the condition of frozen-in magnetic fields. In one of them there are occasional transient electric field impulses along the field lines which cause precipitation splashes. The other model invokes electrostatic fields which vanish occasionally due to instabilities. This gives rise to precipitation splashes of about equal numbers of ions and electrons.The latter model seems to be favoured by known satellite data concerning the pitch angle distributions of electrons above the ionosphere.It is suggested that electric fields in space should be measured by satellites and rockets. Expected values of the fields in different regions of space are given.     

Experimental Aspects of Mid-Frequency Pulsations (f≈10–100 mHz) in the Southern Polar Cap

We review the results obtained in the frequency range of Pc3 (22-100 mHz) and Pc4 (7-22 mHz) pulsations at Italian Antarctic stations in the southern polar cap (“Mario Zucchelli”, at Terra Nova Bay, TNB, 80^˚.S; “Concordia”, the Italian/French base at Dome C, DMC, 89^˚.S). The absence of a midnight enhancement in the pulsation power suggests a negligible substorm influence at extreme latitudes, while the sharp noon enhancement, which appears only at TNB, is determined by the closer proximity of the station to cusp related phenomena. The relationship between the frequency of the band-limited signals and the interplanetary magnetic field strength, the cone angle influence, and the higher correlation of the Pc3 power with the solar wind speed in the morning hours suggest a global scenario in which upstream waves would be mainly responsible for the mid-frequency activity in the polar cap. However, the polarization pattern is odd with respect to the predictions for tailward propagating modes.     

Review of the CIV phenomenon

Alfvén's Critical Ionization Velocity (CIV) phenomenon is reviewed, with the main emphasis on comparisons between experimental and theoretical results. The review covers (1) the velocity measurements in laboratory experiments, (2) the effect of wall interaction, (3) the experimental and theoretical limits to the magnetic field strength and the neutral density, (4) ionospheric release experiments, (5) theoretical models for electron energization in comparison to experimental results, and (6) CIV models. All laboratory investigations of the CIV are found to obey the three following simple rules of thumb: (1) if the magnetic field is so strong that V _A > 3V ₀, and if there is enough neutral gas that the Townsend condition is fulfilled, then the CIV effect occurs, (2) when it occurs, the threshold velocity (or E/B value) is within ± 50% of Alfvén's proposed value V _c , and (3) for weaker magnetic fields, the effect gradually becomes irreproducible or weak and disappears altogether for V _A < V ₀. The theoretical understanding of the process has grown rapidly during the last decade, mainly due to the introduction of computer simulation models which have to a large degree confirmed and extended earlier analytical theories. The CIV mechanism is not due to one single plasma process, but to several different mechanisms which are applicable in different parameter regimes and geometries. The computer simulations have shown that in order to understand the mechanism properly it is necessary to consider a large number of interlocking collisional and plasma processes. The theoretical development has reached the stage where it should be possible to adapt computer simulation models to specific experiments and predict ionization rates, plasma flow velocities, E/B values, particle distributions, and wave spectra. Such models should for the first time provide a really firm basis for extrapolations of the CIV process to space applications.     

Study of magnetospheric dynamics using energetic solar particles

Information can be obtained from energetic particle measurements through the chemical composition, energy spectrum, directional anisotropy, temporal and spatial intensity variations. This is equivalent to saying that there is a distribution functionf _k(p,r,t) wherek corresponds to thekth particle species of momentump at positionr and timet.Particle transport is described by the Boltzmann equation, and because the densities are generally low in the case of cosmic rays or energetic solar flare particles, collective transport effects can be neglected. In the absence of magnetospheric motion it is relatively easy to treat the problems of particle transport as simple propagation of charged particles in a stationary magnetic field configuration using, for instance, trajectory calculations in model fields. The method here is to use correlated measurements of the particle distribution at two points along a dynamic trajectory, and in this way to learn something about the geomagnetic field. This approach provides a good basis from which to study magnetospheric dynamics. If the magnetosphere moves, large scale electric fields, turbulent electromagnetic fields and sources and sinks affect the propagation of energetic particles considerably. These effects change the distribution functionf _k(p,r,t) and can thus be detected.In this paper, we shall show the importance of the single particle approximation (trajectories in a reference field) in forming the basis of our understanding of the quiet-time penetration of cosmic rays into the magnetosphere, we shall consider the steady dynamics such as wave-particle inter-action and field line reconnection, which is believed to exist nearly all the time, and finally we shall review the work which has been done in the much more complex and less well-understood field of impulsive dynamics such as geomagnetic storms and substorms. This last topic is only just beginning to be investigated in detail, and it is hoped that the study of impulsive dynamics, using energetic particles, may be as successful as the study of the quiet magnetosphere and the steady dynamics.     

Time-Dependent 2d Model Compared with Observations During the 1974 Mini Cycle

The 1974 mini-cycle is a medium term cosmic ray modulation event with about one year duration. It occurred in an A>0 epoch of solar magnetic polarity during conditions of low activity, but with an increase in the latitudinal extent of the heliospheric current sheet (tilt angle α) and the magnitude B of the heliospheric magnetic field. This cosmic ray decrease can be used to test the hypothesis that such large scale decreases (mini cycles) may be caused primarily by a combination of changes in α and B. For this purpose a fully time-dependent 2D model of solar modulation is used, which includes the effects of global and current sheet drifts, and anisotropic perpendicular diffusion. Such models have been used successfully to describe the proton energy spectrum as well as the radial and latitudinal gradients near 1 AU. Comparison of the model solutions with the observed decrease for 1.8 GV protons allows us to study the combined influence of variable drift and diffusion effects throughout the event. This revised version was published online in August 2006 with corrections to the Cover Date.