Origin and Dynamics of Cosmic Rays

As a consequence of our inability to observe directly the origin of a cosmic-ray particle, we begin the development with a discussion of the limitations within which we can construct a cosmic-ray accelerator mechanism. We find that we are allowed only the betatron effect and the Fermi mechanism. We review some of the many variations of these mechanisms which are to be found in the literature. Then it is shown that trains of oppositely moving hydromagnetic waves of large amplitude and with sharp crests can accomplish large and continued particle accelerations which are adequate to maintain the observed galactic cosmic-ray field. The large acceleration arises as a consequence of the simple fact that each wave tends to sweep up the cosmic-ray particles before it, so that head-on collisions of particles with waves are much more common than overtaking collisions. It is pointed out that the sharp crests of the waves are a natural consequence of the observed supersonic mass motions. Therefore, the acceleration by oppositely moving waves does not depend upon any special wave form, and we suggest that it is the naturally occuring acceleration process.By treating the cosmic rays as a gas with relativistic thermal motions, it is shown that the cosmic-ray gas is effectively coupled to the motions of the ordinary matter both parallel and perpendicular to the magnetic field. Thus the effective speed of sound must be computed in the composite cosmic-ray and ordinary gas. It is noted that with this composite speed of sound the irregular mass motions in the galactic disk and halo are approximately Mach one. It is suggested that this represents a general dynamic balance to be found in all sufficiently active regions of space, and explains how it is that we often observe prolonged mass motions in the galaxy and in stellar atmospheres which would otherwise be computed to be highly supersonic and dissipative. The dynamic balance comes about from the fact that increased cosmic-ray density would reduce the effective Mach number below one, allowing the sharp crests of the hydromagnetic waves to degenerate, and thereby halting the production of comsic-ray particles.