On the Balance between Radial and Pitch Angle Diffusion

  • G. Haerendel
Part of the Astrophysics and Space Science Library book series (ASSL, volume 17)


The various attempts to mathematically describe the observed populations of trapped particles can be summarized by the following set of equations expressing conservation of particle number f and energy:
$$\frac{\partial }{{\partial t}}f({x^\mu },t) = \frac{\partial }{{\partial {x^\mu }}}\left( {{D^{\mu v}}\frac{{\partial f}}{{\partial {x^v}}}} \right) - L({x^\mu }) + S({x^\mu })$$
and conservation of electromagnetic wave energy e:
$$\frac{\partial }{{\partial t}}\varepsilon (\omega ,t) = - {\text{div(}}\varepsilon {{\text{v}}_g}{\text{) + 2(}}\gamma {\text{ - }}l{\text{)}}\varepsilon$$
. The variables x μ represent the adiabatic invariants which undergo small fluctuations by either interaction with the electromagnetic wave field or collisions. D μv is the diffusion tensor which so far has been considered mostly for L and pitch angle diffusion. S represents any internal particle source like the neutron albedo decay and L losses due to collisions.


Wave Energy Pitch Angle Flux Tube Particle Flux Proton Flux 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Andronov, A. A. and Trakhtengerts, V. Y.: 1964, Geomag. Aeron. 4, 181.Google Scholar
  2. Cocke, W. J. and Cornwall, J. M.: 1967, J Geophys Res. 72, 2843.ADSCrossRefGoogle Scholar
  3. Cornwall, J. M.: 1966, J. Geophys. Res. 71, 2185.ADSGoogle Scholar
  4. Davis, L. R. and Williamson, J. M.: 1966, in Radiation Trapped in the Earth’s Magnetic Field (ed. by B. M. McCormac), D. Reidel Publishing Company, Dordrecht-Holland, p. 215; also, private communication.Google Scholar
  5. Gendrin, R.: 1968, J. Atmos. Terr. Phys. 30, 1313.ADSCrossRefGoogle Scholar
  6. Haerendel, G.: 1968, in Earth’s Particles and Fields (ed. by B. M. McCormac), Reinhold Publishing Company, New York, p. 171.Google Scholar
  7. Haerendel, G.: 1970, J. Geophys. Res., to be submitted.Google Scholar
  8. Kennel, C. F. and Petschek, H. E.: 1966, J. Geophys. Res. 71, 1.ADSGoogle Scholar
  9. King, J. H.: 1967, NASA Document NASA SP-3024.Google Scholar
  10. Mihalov, J. D. and White, R. S.: 1966, J. Geophys. Res. 71, 39.Google Scholar
  11. Nakada, M. P. and Mead, G. D.: 1965, J. Geophys. Res. 70, 4777.ADSCrossRefGoogle Scholar
  12. Nakada, M. P., Dungey, F. W., and Hess, W. N.: 1965, J. Geophys. Res. 70, 3529.ADSCrossRefGoogle Scholar
  13. Soraas, F. and Davis, L. R.: 1968, GSFC Report X-612-68-328.Google Scholar
  14. Williams, D. J.: 1970, this volume, p. 396.Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1970

Authors and Affiliations

  • G. Haerendel
    • 1
  1. 1.Institut für extraterrestrische PhysikMax-Planck-Institut für Physik und AstrophysikGarching/MunichGermany

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