Global Asymptotic Solutions for Non-relativistic Mhd Jets and Winds

We present general and global analytical solutions, valid from pole to equator, for the asymptotic structure of non-relativistic, rotating, stationary, axisymmetric, polytropic, unconfined, perfect MHD winds. The standard five lagrangian first integrals along field lines are assumed known. The asymptotic structure of such winds consists of field-regions virtually devoid of poloidal current. We show that an Hamilton-Jacobi equation, or equivalently a Grad-Shafranov equation, gives the asymptotic structure in the field regions. These field regions are bordered by current-carrying boundary layers around the polar axis and near null magnetic surfaces. Current closure is achieved in a number of separate cells bordered by null surfaces. The solution is given in the form of matched asymptotics separately valid outside and inside these boundary layers. The polar boundary layer is pressure-supported against the pinching Observatoire, Université Louis Pasteur, 11 Rue de l’Université, 67000 Strasbourg, France Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218 Department of Physics and Astronomy, Homewood Campus, The Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218 Visiting Scientist at Space Telescope Science Institute and Department of Physics and Astronomy, Johns Hopkins University