On the theory of MHD winds from a magnetosphere of axisymmetric rotators

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Abstract
The problem of plasma flow in a magnetosphere of an axisymmetric rotator is considered. The equation for a poloidal magnetic field is obtained, taking into account thermal pressure for relativistic plasma. For non-relativistic stellar winds, the gravitational field of the star is also taken into account. The poloidal field is described by the elliptico-hyperbolic equation. The boundary-value problem for this equation is considered from the point of view of the causality principle. It is shown that, along with well-known singularities of equations for plasma motion on the slow and fast magnetosonic and Alfvén surfaces, there is an additional singular surface dividing space into two causally disconnected regions. The condition of regularity of the solution on this surface picks out a unique solution of the problem. It appears that, in the case of a rotating star, the number of singular surfaces exceeds the number of free parameters of the problem. Stationary solutions of the problem, where the plasma flow continuously passes through all singular surfaces, apparently do not exist when the star rotates. Possible discontinuities are discussed.

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