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Magnetospheric Models and Trajectory Computations

  • Conference paper
Cosmic Rays and Earth

Part of the book series: Space Sciences Series of ISSI ((SSSI,volume 10))

Abstract

The calculation of particle trajectories in the Earth’s magnetic field has been a subject of interest since the time of Störmer. The fundamental problem is that the trajectory-tracing process involves using mathematical equations that have ‘no solution in closed form’. This difficulty has forced researchers to use the ‘brute force’ technique of numerical integration of many individual trajectories to ascertain the behavior of trajectory families or groups. As the power of computers has improved over the decades, the numerical 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 direction in space of various cosmic ray anisotropies. Unfortunately, cutoff rigidities are not simple parameters due to the chaotic behavior of the cosmic-ray trajectories in the cosmic ray penumbral region. As the computational problem becomes more manageable, there is still the issue of the accuracy of the magnetic field models. Over the decades, magnetic field models of increasing complexity have been developed and utilized. The accuracy of trajectory calculations employing contemporary magnetic field models is sufficient that cosmic ray experiments can be designed on the basis of trajectory calculations. However, the Earth’s magnetosphere is dynamic and the most widely used magnetospheric models currently available are static. This means that the greatest uncertainly in the application of charged particle trajectories occurs at low energies.

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Authors and Affiliations

  1. Air Force Research Laboratory, Space Vehicles Directorate, Bedford, MA, 01731, USA

    D. F. Smart & M. A. Shea

  2. Physikalisches Institut, CH-3012, Bern, Switzerland

    E. O. Flückiger

  3. Air Force Research Laboratory (VSBS), Space Vehicles Directorate, 29 Randolph Road, Bedford, MA, 01731, USA

    D. F. Smart

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  1. D. F. Smart
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  2. M. A. Shea
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  3. E. O. Flückiger
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Editors and Affiliations

  1. Bartol Research Institute, University of Delaware, 19716, Newark, DE, USA

    J. W. Bieber  & P. Evenson  & 

  2. Institute of Terrestrial Magnetism, Ionosphere, and Radiowave Propagation (IZMIRAN), 142092, Troitsk, Moscow regime, Russia

    E. Eroshenko

  3. Solar-Terrestrial Research, National Science Foundation, 22230, Arlington, VA, USA

    P. Evenson

  4. Physikalisches Institut, Universität Bern, CH-3012, Bern, Switzerland

    E. O. Flückiger

  5. International Space Science Institute, CH-3012, Bern, Switzerland

    R. Kallenbach

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Smart, D.F., Shea, M.A., Flückiger, E.O. (2000). Magnetospheric Models and Trajectory Computations. In: Bieber, J.W., Eroshenko, E., Evenson, P., Flückiger, E.O., Kallenbach, R. (eds) Cosmic Rays and Earth. Space Sciences Series of ISSI, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1187-6_15

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  • DOI: https://doi.org/10.1007/978-94-017-1187-6_15

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