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We propose a different formulation of the problem of magnetically driven outflows when the magnetic field has only a toroidal component. The absence of a poloidal component (and therefore of poloidal magnetic flux surfaces) makes the present formulation different from the usual Grad--Shafranov one. We show that the toroidal magnetic field alone is very efficient in accelerating and collimating outflows (jets) from accretion disks (the important factor is not rotation). This suggests an alternative driving mechanism to the centrifugal driving of Blandford \& Payne (1982). We obtain solutions which, at large distances, are the same with solutions of the Grad--Shafranov problem.
We also discus the physical meaning of the so called `modified' fast magnetosonic surface (or limiting characteristic), a critical surface which appears beyond the usual fast magnetosonic critical surface in 2-D MHD flow problems. Our formalism is also applied to describe analytically the time dependent problem.
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