In this paper we describe the mutual interaction between Alfv¿n waves and a multicomponent plasma (such as the solar wind) consisting of various ion species streaming differentially with speeds ui along the ambient radial magnetic field. It is shown that the wave adiabatic invariant discovered by Isenberg and Hollweg (1982) for this multi-ion system can be case in the form of the conservation of wave action flux in which the ''intrinsic'' frequency &ohgr;m, say, is simply the ratio between the mean squared Doppler-shifted frequency and the mean Doppler-shifted frequency both of which being weighted according to the mass density abundance of the various streaming ions. The existence of the invariant permits the self-consistent formulation of steady flows in a multi-ion system (such as the solar wind in which alpha particles are placed on the same footing as protons and not treated simply as test particles) subject not only to the coupling effect of an electric field or Coulomb friction but also to Alfv¿n wave forces, which also bind the system together. This type of coupling arises essentially because variations in the Alfv¿n wave pressure p&ohgr;, or wave energy density E&ohgr;, are related to variations in the local hydrodynamic properties of the multi-ion plasma flow in such a way as to conserve the wave action flux.

Furthermore, if the composite multi-ion system were subject to slow modulations of the medium in time as well as gradual variations in space, the Alfv¿n wave amplitude would be governed by a conservation equation for the wave action variable. This wave action equation enables us to investigate the properties of long-wavelength/low-frequency sound waves in a multi-ion system subject to short-wavelength/high-frequency Alfv¿n wave forces, as well as the usual electrical coupling. It is important to carry out such an investigation since it is the condition for stationary sound waves in such a system that yields the appropriate generalization of the idea of a sonic point for a multi-ion flow, thereby providing a physical framework within which the sonic critical curves may be discussed and analyzed. We have carried this out in the simplest case of extremely sub-Alfv¿nic flow in order to illustrate its importance in the context of the initial acceleration of the solar wind plasma and to clarify the nature of possible streaming instabilities. Finally, in the ethos of the JWKB analysis developed here or by using the variational approach [Dewar, 1970; Whitham, 1974>, it follows that similar wave action conservation equations hold for magnetoacoustic waves in multi-ion plasmas.