Skip to main content

A detector telescope’s pitch angle sampling of magnetospheric particles


A geometrical method developed for a particle detector can be extended for application to the determination of the pitch angle sampling capability of the particle telescope of any orientation and for the parent satellite of any orbital orientation. A unit vector tangent to a dipole geomagnetic field line has been calculated from the dipole magnetic field equations in the geomagnetic coordinate system. Rotation matrices have been used, step-by-step, to align the geomagnetic coordinate frame with the detector coordinate frame. The detector selected in this work has its axis tilted with the local zenith direction. The component of the unit vector in the detector coordinate system is found at an observation point characterized by longitude, latitude, and the geocentric radial distance. Pitch angles are measured with respect to the guiding field direction. The pitch angle sampling factor is used in the calculation of detector response functions to particles of different pitch angles. The sampling efficiency functions are useful to make an absolute comparison of magnetospheric particle fluxes measured by particle telescopes under different solar conditions pertaining to different epochs.


  1. Adel, M. M., Absolute flux comparison of magnetospheric particle, Can. Astronaut. Space J., 2007 (submitted).

    Google Scholar 

  2. Hovestadt, D., B. Hausler, and M. Scholer, Observation of energetic particles at very low altitudes near the geomagnetic equator, Phys. Rev. Lett., 28(20), 1340–1344, 1972.

    Article  Google Scholar 

  3. Miah, M. A., Global Zones of Particle Precipitations, Ph.D. Thesis, Louisiana State University, p. 107, 1988.

    Google Scholar 

  4. Miah, M. A., The ONR-602 Experiment and investigation of particle precipitation near the equator, J. Geomag. Geoelectr., 43, 445–460, 1991a.

    Article  Google Scholar 

  5. Miah, M. A., Observation of Z ≥ 1 particles below 300 km near the geomagnetic equator, J. Geomag. Geoelectr., 43, 461–475, 1991b.

    Article  Google Scholar 

  6. Miah, M. A., Significant variation of proton population in the equatorial thermosphere, Adv. Space Res., 14(9), 229–232, 1994.

    Article  Google Scholar 

  7. Miah, M. A., J. W. Mitchell, and J. P. Wefel, Magnetospheric particle detection efficiency of a conical telescope, Nucl. Instrum. Methods Phys. Res., A281, 622–627, 1989.

    Article  Google Scholar 

  8. Miah, M. A., K. Nagata, T. Kohno, H. Murakami, A. Nakamoto, N. Hasebe, J. Kikuchi, and T. Doke, Spatial and temporal features of 0.64–35 MeV protons in the Space Station environment: EXOS-C observations, J. Geomag. Geoelectr., 44, 591–610, 1992.

    Article  Google Scholar 

  9. Moritz, J., Energetic protons at low equatorial altitudes, Zeitschrift fur Geophysik, 38, 701–717, 1972.

    Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Miah M. Adel.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Adel, M.M. A detector telescope’s pitch angle sampling of magnetospheric particles. Earth Planet Sp 60, 753–761 (2008).

Download citation

Key words

  • Magnetosphere
  • particle telescope
  • pitch angle
  • geomagnetic field
  • rotation matrix
  • satellite orbit
  • efficiency function