Modified Fermi Mechanism for the Acceleration of Cosmic Rays

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Abstract
Fermi's treatments of the acceleration of cosmic rays are generalized by including the statistical fluctuations in the number of accelerating and decelerating interactions of a particle with a varying magnetic field. This alone does not greatly change the result, a power-law energy spectrum still being obtained. However, interactions, not considered by Fermi, in which the average energy change is zero may now contribute much, or all, of the acceleration. In particular, in his second model, where the galactic magnetic field is roughly uniform along the spiral arm of the galaxy, standing hydromagnetic waves now accelerate and decelerate particles by "betatron" collisions. To get the observed energy spectrum requires rms gas velocities of 10 km/sec in oscillations whose extensions normal to and parallel to the field are of order 1 and 7 light years, respectively. The observed near-isotropy of cosmic rays may be explained by inhomogeneities in the magnetic field of scale small compared to the helix radius. These can be numerous enough to produce near-isotropy without being so numerous that the particle is less likely to diffuse to the end of the spiral arm than to make a nuclear collision. It is speculated that, because of the statistical effects, fluctuating stellar magnetic fields may accelerate a few particles in a small-scale version of Fermi's first model and thus solve the injection problem.