Conservation Laws and Ponderomotive Force for Non-WKB, MHD Waves in the Solar Wind

The interaction of non-WKB Alfvén waves in the Solar Wind was investigated by Heinemann and Olbert (1980), MacGregor and Charbonneau (1994) and others. MacGregor and Charbonneau (1994) investigated non-WKB Alfvén wave driven winds. We discuss both the canonical and physical wave stress energy tensors for non-WKB, MHD waves and the ponderomotive force exerted by the waves on the wind for the case where both compressible (magneto-acoustic type waves) and incompressible waves (Alfvén waves) are present. The equations for the waves include the effects of wave mixing (i.e. the interaction of the waves with each other via gradients in the background flow). Wave mixing is known to be an important element of turbulence theory in the Solar Wind. However, only the wave mixing of Alfvénic type disturbances have been accounted for in present models of Solar Wind turbulence (e.g. Zhou and Matthaeus, 1990), which use Elssässer variables to describe the perturbations. The relationship between the present analysis and nearly incompressible MHD (reduced MHD) is at present unclear. Also unclear is the relationship between the present analysis and theories using wave-mean field interactions (e.g. Grimshaw (1984), Holm (1999)). The analysis is based on a theory for wave and background stress-energy tensors developed by Webb et al. (2004a,b) using a Lagrangian formulation of the total system of waves and background plasma (see e.g. Dewar (1970) for the WKB case). Conservation laws for the total system of waves and background plasma result from application of Noether's theorems relating Lie symmetries of the action to conservation laws.