Particle Transport#

Example particle density profile computed for typical solar wind conditions with standard northward IMF, and a 350 inclination of Earth magnetic dipole. The background fields used in this calculation were obtained from the global MHD code BATS-R-US.

The transport of high energy particles in the magnetosphere cannot accurately be described by global MHD models. In that case, it is necessary to study the interaction of individual particles with magnetospheric electric and magnetic fields. There are basically two sources of plasmas particles: the solar wind and the ionosphere, while the primary source of plasma energy is in the solar wind and in the transfer between magnetic energy stored in the magnetosphere and plasma particles. The study of transport covers a wide variety of temporal and spatial scales, and involves such processes as particle kinetics, plasma wave propagation and wave-particle interactions, and global magnetospheric reconfiguration in reaction to changing solar wind conditions.

The framework developed in FDAM is based on a test-particle approach. In this method, large numbers of test-particle-trajectories are followed in time from prescribed initial and/or input conditions, from which averages (primarily mass and energy density) are calculated. The FDAM model allows for time-dependent simulations in which changing conditions in the solar wind are taken account of. Being based on a test-particle approach, the model is not fully self-consistent. In particular, the fields used to integrate particle trajectories are obtained from a macroscopic MHD approximation. They are not affected by the plasma profiles (density, current and stress tensor) through which the particle trajectories are computed.

Ionospheric outflow#

The test particle approach can be used to study the contribution to the magnetospheric plasma associated with particle outflow from the ionosphere. As an example, Figs. 1 and 2 below illustrate how the magnetosphere would be populated with hydrogen ions if such ions were emitted uniformly over the entire ionosphere. These results were calculated with background magnetospheric electric and magnetic fields obtained from the global MHD code BATS-R-US. The solar wind conditions in this case, were assumed to be constant in time, with a purely southward Interplanetary Magnetic Field (IMF) of 5 nT, a solar wind velocity of 300 km/s, and a solar wind hydrogen plasma temperature of 17.23 eV. In this simulation, the Earth magnetic dipole is assumed to be perpendicular to the sun-Earth axis (i.e., there is no dipole tilt). The actual density profile associated with ionospheric outflow depends on the latitudinal and longitudinal outgoing flux distribution at the ionosphere. A detailed comparison with actual observation, or a forecast, of would require using a detailed and accurate ionospheric model.

The simple calculation carried here, based on a constant and uniform outflow, nonetheless reveals some interesting features about the spatial distribution of ions originating from the ionosphere, in the magnetosphere. The majority of the ions emitted tend to form a dense plasma sphere near Earth. These ions are strongly magnetised, and they essentially bounce back and forth along low latitude field lines after being emitted. Some ions, those emitted at higher latitudes, along or near open magnetic field lines, are carried far in the tail region. It is interested to note from Fig. 1, that in the y=0 plane (the plane containing the magnetic axis and the direction sun-Earth), the ions that escape the plasmsphere are transported predominantly in the vicinity of the magnetosheath. There is also a noticeable increase in the density of such ions in the plasmasheath region, tailward, along the sun-Earth direction.

From Fig. 2, we see that in the Z=0 plane the plasma density that results from our assumed uniform ionospheric outflow is much more localised. It is essentially limited to a band extending between 20 Earth radii above and below the sun-Earth axix. The calculated density is also seen to have a marked depletion near that axis.

The results shown here are presented for illustrative purposes only. As mentioned above, detailed comparisons with in situ observations would require the use of a more detailed and physical model for ionospheric outflow. Such comparions, made with different ion species, could also be used to assess the validity of ionospheric outflow models.

Fig. 1.

Fig. 2.