Magnetospheric models and trajectory computations

The calculation of particle trajectories in the Earth's magnetic field has been a subject of interest since the time of Stormer. The fundamental probl em is that the trajectory-tracing process involves using mathematical equat ions that have `no solution in closed form'. This difficulty has forced res earchers to use the `brute force' technique of numerical integration of man y individual trajectories to ascertain the behavior of trajectory families or groups. As the power of computers has improved over the decades, the num erical integration procedure has grown more tractable and while the problem is still formidable, thousands of trajectories can be computed without the expenditure of excessive resources. As particle trajectories are computed and the characteristics analyzed we can determine the cutoff rigidity of a specific location and viewing direction and direction and deduce the direct ion in space of various cosmic ray anisotropies. Unfortunately, cutoff rigi dities are not simple parameters due to the chaotic behavior of the cosmic- ray trajectories in the cosmic ray penumbral region. As the computational p roblem becomes more manageable, there is still the issue of the accuracy of the magnetic field models. Over the decades, magnetic field models of incr easing complexity have been developed and utilized. The accuracy of traject ory calculations employing contemporary magnetic field models is sufficient that cosmic ray experiments can be designed on the basis of trajectory cal culations. However, the Earth's magnetosphere is dynamic and the most widel y used magnetospheric models currently available are static. This means tha t the greatest uncertainly in the application of charged particle trajector ies occurs at low energies.