Self-consistent solutions are presented, in which cosmic rays are confined by Alfvén waves which are dissipated through a cascade involving sound waves. There are solutions in which Fermi acceleration of particles by the Alfvén waves can reduce or even invert the adiabatic energy losses associated with motion down density gradients. For galactic parameters, such acceleration does not occur, but a very high degree of confinement is predicted, with particles of energy less than some tens of GeV being restricted to stream less quickly than |~ 50\,km s⁻¹| (twice the Alfvén speed).
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John Skilling (1975) studied this question.