On the equation of transport for cosmic-ray particles in the interplanetary region

Astronomy and Astrophysics – Astrophysics

Scientific paper

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Cosmic Rays, Interplanetary Space, Particle Motion, Transport Properties, Adiabatic Conditions, Continuity Equation, Differential Equations, Energy Transfer, Liouville Equations, Momentum Transfer

Scientific paper

Two alternative derivations of the well-known transport equation for cosmic-ray particles in interplanetary space are presented. The first derivation involves a continuity equation for the cosmic rays that takes into account particle streaming and energy changes; the second is based on the ensemble-averaged Liouville equation for cosmic-ray propagation in the stochastic interplanetary magnetic field. Both derivations are carried out by using particle position and time in a frame of reference fixed in the solar system and by specifying the particle momentum relative to the local solar-wind frame of reference. It is shown that the mean temporal rate of change in particle momentum in the fixed frame depends on the particle number-density gradient. The adiabatic deceleration rate is derived on the basis of the betatron deceleration process and the inverse Fermi effect.

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