Hydromagnetic Waves and the Acceleration of Cosmic Rays

The large amounts of energy necessary for the acceleration of cosmic rays throughout the galaxy introduces a serious transport problem. The hydrodynamic and hydromagnetic equations are investigated from the viewpoint of energy propagation. It is shown that, with the galactic model of Fermi and Chandrasekhar, the observed motions of the interstellar gas reduce to hydromagnetic waves, which are, as it turns out, the most effective means of energy transport. A consideration of the interaction of charged particles with hydromagnetic waves shows that it is the fluid velocity, and not the wave velocity, that is responsible for the acceleration of cosmic rays by Fermi's mechanism. We calculate the the dissipation of hydromagnetic waves in the interstellar medium, and the variation of amplitude and wavelength of such waves with changes in density and large-scale field intensity. It is then shown that the galaxy is no more than one percent efficient in the acceleration of cosmic rays because of the tremendous viscous losses in the interstellar medium, and that there is no hydromagnetic mechanism that can convert the observed large-scale low-velocity fluctuations in the interstellar medium to the required small-scale high-velocity motions.