Recent studies have focused on the role of initially weak toroidal magnetic fields embedded in a stellar wind as the agent for collimation in planetary nebulae. In these models, the wind is assumed to be permeated by a helical magnetic field in which the poloidal component falls off faster than the toroidal component. The collimation occurs only after the wind is shocked at large distances from the stellar source. In this paper we reexamine assumptions built into this "magnetized wind-blown bubble" (MWBB) model. We show that a self-consistent study of the model leads to a large parameter regime in which the wind is self-collimated before the shock wave is encountered. We also explore the relation between winds in the MWBB model and those that are produced via magnetocentrifugal processes. We conclude that a more detailed examination of the role of self-collimation is needed in the context of planetary nebula studies.
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