On the Propagation of Galactic Cosmic Rays

Recent observations of cosmic ray composition imply that the average amount of interstellar matter traversed by the cosmic rays before escaping from the Galaxy decreases as their energy increases. These observations are reviewed in Chapter 1 together with other relevant observations of the cosmic ray composition, spectrum and anisotropy.
In Chapter 2 theories on the origin and propagation of galactic cosmic rays are reviewed in the ligjit of the data presented in the first chapter. Models in which they are confined to the Galaxy by diffusion in the irregular galactic magnetic field experience difficulty in accounting for their slow leakage rate out of the Galaxy, in which observations indicate that they remain confined for an average time of about a million years. However, since the energy densities of the cosmic rays and the galactic magnetic field are similar, it is logical to expect that the field cannot influence the propagation of the cosmic rays without itself undergoing change. In Chapter 3 the effect of the cosmic rays on the field is discussed. A net streaming motion of the cosmic rays causes hydromagnetic waves to form in the field, which have a wavelength of the order of the cosmic ray gyro-radius. These waves in turn scatter the cosmic rays of corresponding gyro-radius, thereby reducing their streaming speed.
This process is used in Chapter 4 to explain the long residence time, the energy-dependent path length and the low observed anisotropy of galactic cosmic rays. The hydromagnetic waves formed by the streaming cosmic rays have to compete against damping processes in the interstellar medium. The dominant linear damping process is that due to collisions between the charged particles moving with the wave and the neutral particles of the interstellar medium. The waves can only begin to form when the damping rate due to this process becomes smaller than their growth rate, that is at heights above the galactic plane where the neutral hydrogen density is low enough. Skilling's analysis of the scattering process is used to obtain an expression for the height at which waves resonating with cosmic rays of a particular rigidity begin to form. As the wave growth rate varies as the density of resonant cosmic rays, it decreases as the cosmic ray energy increases. Therefore higher energy cosmic rays can only encounter resonant waves at greater heights above the galactic plane, where the density of neutral hydrogen is smaller. The onset of the waves at their respective heights above the galactic plane produces a reflecting boundary which prevents free diffusion out of the Galaxy.
Once the waves have grown to a finite amplitude, non-linear -damping processes become important. The waves which scatter the cosmic rays become degraded into other modes which are rapidly damped. Wentzel's analysis is used to investigate the effects of non-linear damping, after showing that it is equivalent to Skilling's analysis in the absence of non-linear damping. Under steady-state conditions, this process causes the net cosmic ray streaming speed through the waves to increase steeply with energy. As a result, higher energy cosmic rays can escape from the Galaxy more readily than those of lower energy. The energy-dependence of their residence time in the Galaxy can account for the observed decrease in path length with increasing energy.
The effect of this confinement process on the spectrum of cosmic ray electrons is investigated in the first half of Chapter 5» The electrons experience the same decrease in residence time with energy as do the other cosmic ray species. The effect of this is to reduce the overall change in their spectral index which is expected when their residence time is similar to their timescale of energy loss due to synchrotron emission and the inverse Gompton effect. This may be the reason why no change of order unity in the spectral index has been detected above 50 GeV .
The hydromagnetic waves which confine the cosmic rays to the Galaxy do not themselves produce compression of the interstellar medium. But the modes into which they decay by non-linear processes are compressive, and would therefore produce irregularities in the interstellar electron density with a length scale short compared to that which is expected from normal interstellar motions. The scattering of electromagnetic radiation from pulsars is discussed in the second half of Chapter 5, where it is suggested that these compressive modes may be responsible for the observed broadening of the pulses with increasing wavelength.
As a background for further study, the coupling between hydromagnetic wave modes is outlined in Chapter 6. The equations describing a MHD plasma are expanded to third order to obtain the wave-wave transition rates, and the results are interpreted in terms of collisions between plasmons.