A Three Dimensional Alfvenic Pulse in a Transversely Inhomogeneous Medium

Interaction of incompressible and compressible MHD fluctuations on a one-dimensional plasma inhomogeneity, transverse to the magnetic field, is considered in the three-dimensional regime. An initially incompressible (Alfvenic) MHD fluctuation generates, by linear coupling, compressible (magnetoacoustic) fluctuations. In the initial stage of the interaction, the efficiency of the coupling is enhanced by phase mixing of the incompressible mode. In the developed stage of phase mixing, the interaction saturates and both incompressible and compressible fluctuations approach a new quasi-stationary state. The saturation levels of density fluctuations and incompressible fluctionations tend to become equal as the linear coupling strength increases. The results obtained provide a necessary basis for further studies of MHD weak turbulence in the solar wind. In the solar context, the interaction of Alfven and magnetoacoustic modes in the three-dimensional regime of phase mixing suggests an efficient mechanism for conversion of incompressible perturbations to compressible perturbations. The latter are subject to more efficient dissipation by collisional or collisionless mechanisms. This makes the results obtained relevant to the problem of the heating of open coronal structures