Hydromagnetic Waves Excited by Slowly Streaming Cosmic Rays

Cosmic rays streaming along a magnetic field generate hydromagnetic waves with a wide range in 0, the angle between the field and the direction of wave propagation. An expansion in terms of VA! (c cos 0) <<1, where VA is the Alfvén speed, is used to show that such waves are not influenced by mix- ing with electrostatic wave modes and that they are generated when the mean velocity of the cosmic rays exceeds (approximately) VA/COS 0. The growth rate of the unstable waves is greater than the rate at which cosmic rays escape the galactic disk