The main focus of our space science group is ionospheric and magnetospheric physics. We investigate ionized gas in the planetary environments in the Solar System by means of theory, simulation and data analysis.
The magnetospheric plasma is collisionless and hot, while the ionospheric plasma is cold and strongly affected by collisions with the neutral atmosphere. Consequently, plasma studies usually require different methods in the two mediums. However, these two regions are strongly coupled, and because the magnetic field has a strong influence on charge particles, ionospheric and magnetospheric processes are naturally organized with respect to the magnetic field. It is then convenient to organize data and to develop simulation models in coordinate systems aligned with the magnetic field.
This was the reason why we decided to define magnetic field coordinates for a realistic geomagnetic field  as well as for the magnetic field of some of the outer planets [1,2]. These coordinates are based on Euler potentials, following the method we present in , and have been useful to study numerous plasma properties:
The ionospheric dynamo is the major source of electric fields and currents in the low- and mid-latitudes ionosphere. The process is similar to the generation of current when a conducting wire is moved through the field of a magnet. In the ionosphere, ions and electrons (created by the solar radiation) are differently moved through the Earth magnetic field by thermospheric winds (also created by the solar radiation through heating).
Models of this process have been developed for almost 50 years, with Baker and Martyn  providing the first model. However, these models have usually reduced the geomagnetic field to a dipole.
In case of the Earth, the departures of the magnetic field from dipolar configuration at ionospheric altitudes can exceed 50 % at some geographical locations. Because ionospheric electrodynamics is affected by these distortions, we have developed a model to simulate the ionospheric dynamo in a realistic field model of the Earth main field, the International Geomagnetic Reference Field (IGRF).
The resulting code, the Prairie View Dynamo Code (PVDC), allows separating the longitudinal variations from the Universal Time variations of any electrodynamics quantity (electric fields and potential, ion drifts, electric currents, Birkeland currents, and related magnetic perturbations). The following results have been published :
The Universal Time/longitudinal variability of the ionospheric current, which features a vortex in each hemisphere, can be seen in the 24-hours animation. The time shift between the north and south focus is reproduced on the Figure below for equinox conditions.
Figure: Time shift between the foci of the North and South hemisphere current vortices.
Panel A: With a dipole field aligned with the Earth rotation axis, there is no time shift, because the two hemispheres are exactly symmetric in the model. With a tilted dipole, a sinus-like variation of the time shift is simulated. With the IGRF model, a variation more similar to the one observed on Sq (Sq is an estimated ionospheric current modeled from records of ground magnetic variations) is finally obtained.
Panel B: Our IGRF results are compared with the few results reported by previous modelers, who also included longitudinal variations in the dynamo system.
The guiding center motion approach has been widely used in plasma physics. It consists in replacing the particle motion with the motion of the center of gyration of the particle. The gyration being separated from the motion of the particle, a magnetic moment Mg related to the gyration is associated to the guiding center.
It has been noticed that the guiding center wobbles about the guiding field line, and that this wobbling can be separated from the guiding field line motion. Thus, a new approach to represent particle's motion has been developed [4 9]: a particle motion is considered like a drifting string-like entity, with mass, charge and gyromagnetic moment distributed along the guiding field line, plus a wobble magnetic moment Mw.
The wobbling of the guiding center has been noted before. Northrop [1963, pp35], in an addendum, remarks that the guiding center "travels in roughly a helix about the field line, just as the particle does. However, it can be shown that the radius of the helix is one order of ε smaller than the radius of the particle helix." Consequently, the smaller helix (i.e. the wobbling) has been ignored. However, we show  that the magnetic moments Mg and Mw, associated with the gyromotion and the wobbling respectively, are of the same order of magnitude. The reason is that Mw is obtained by integration along the path of the guiding center.
When one considers calculating the electric current in a collisionless plasma, the advantage of the new approach is easy to notice.
With the "guiding center", the current provided by one species of particles is:
With the "guiding field line", it is:
where n is the density of guiding field line with a drift Vd .
Eqs. (1) and (2) give the same current but have to be integrated over the density of guiding center for (1), and over the density of guiding field line for (2).
To compute the current density parallel to the magnetic field from (1), an expansion of the equilibrium Vlasov equation in the particle adiabatic parameter is required, because the zero order distribution function gives no parallel current.
With (2), such expansion is not needed and the zero order distribution function, e.g., a maxwellian, can be used to calculate the parallel current.References:
Northrop, T. G., The adiabatic motion of charged particles, Interscience Publishers, 1963.
Because satellite-based radiometers have revealed continuous changes in the total solar irradiance and its spectral distribution since 1978 [e.g., Willson and Mordvinov, 2003], the constancy of the Sun is not assumed anymore. Understanding the variability of the Sun has important implications for both terrestrial and space climatology, but presents a formidable challenge. Sun and Earth are complex dynamic systems, which are linked through radiation, particles, and magnetic fields.
The open solar magnetic flux is one solar characteristic that is believed to have an influence Earth's climate. A doubling of this flux during the 20th century has been inferred by Lockwood et al.  and has been linked to a corresponding rise in Earth's surface temperature during the last 100 years [Lockwood and Stamper, 1999]. Empirical models of the magnetic flux also show a large increase in the 20th century [Solanki, 2000].
These reports have engendered controversy, leading to a series of papers in the October 2002 issue of the Journal of Geophysical Research. In particular, there is no evidence for an increase in the solar flux after ~1955 [e.g., Arge et al., 2002, Richardson et al., 2002, Kotov and Kotova, 2001]. This absence of an increase in the recent data has raised questions about the reality of the reported increase prior to 1955. The doubt has been substantiated by one of us , who used polar cap geomagnetic fields to found no long-term trend in the solar wind electric field between 1926 and 2001.
The ensuing contradictions suggest that the aa index is not uniformly calibrated, since Lockwood et al.  results are based on aa and their method is sound.
To exploit the long time-series of geomagnetic variations available, new indices are being proposed , that will separate the influence of solar wind speed and the interplanetary magnetic field.
The solar wind flowing outward from the Sun interacts with Earth’s magnetic field to confine and compress the magnetic field on the day side and form a wake or tail downstream of Earth. This is Earth’s “magnetosphere”. The Earth’s magnetic field confines a plasma. The plasma is a completely ionized, electrically neutral, collisionless gas consisting of solar-wind protons, atmospheric oxygen ions, and electrons. The plasma behaves as an ideal gas with specific entropy, s = PV5/3, where P = nkT is the plasma pressure, and V is the flux-tube volume, . The differential drifts between the plasma’s ions and electrons result in electrical currents which couple to Earth’s ionosphere. Normally, earthward transport in the magnetic tail is weak. However, during geomagnetic storms and substorms, magnetic reconnection occurs in the middle portion of the magnetic tail which substantially reduces the specific entropy of flux tubes. These flux tubes of reduced specific entropy, or “bubbles”, rapidly interchange with flux tubes of larger specific entropy. This results in the rapid transport of energetic plasma and magnetic flux toward Earth. These low-specific-entropy bubbles preferentially deposit their energetic plasma and magnetic flux near Earth and determine the electrical coupling of the magnetosphere with the Earth’s ionosphere.
We have introduced a method to obtain the specific entropy of flux tubes from single-satellite measurements of the plasma and magnetic field. We confirm that rapid Earthward transport of plasma and magnetic flux occurs as flux tubes of reduced specific entropy (“bubbles”). Quantitative determination of the specific entropy of flux tubes is critical for the understanding, modeling, and eventual prediction of space-weather events that affect power grids, communication, navigation, as well as radiation exposure to humans and satellite assets.
Wolf, R. A., V. Kumar, F. R. Toffoletto, G. M. Erickson, A. M. Savoie, C. X. Chen, and C. L. Lemon (2006), Estimating local plasma sheet PV5/3 from single-spacecraft measurements, J. Geophys. Res., 111, A12218, doi:10.1029/2006JA012010
This project is supported by NASA under grant NNG06GH72G to Prairie View A&M University. Geotail magnetic field and plasma data were provided by T. Nagai, H. Hayakawa, and T. Mukai through DARTS at the Institute of Space and Astronautical Science (ISAS) in Japan.