The Correspondence Between Leaky-Box and Diffusion Models of Cosmic-Ray Propagation

The leaky-box model and the attendant concept of path-length distribution of cosmic rays were invented in the mid-1960's. Even though versatile computational packages such as GALPROP and DRAGON with the diffusion approach are now available for analyzing cosmic ray data, the concepts of the leaky-box and path-length distribution continue to be adopted extensively. We show here mathematically that there is a close correspondence between the two approaches: The path-length or resident-time of the leaky-box models are similar to 'impulse response functions' of complex dynamical systems and are intuitively transparent. The results provided by the leaky-box model are valid when used judiciously.