The Hubble Space Telescope (HST) has revealed the existence of multiple, regularly spaced, and faint concentric shells around some planetary nebulae. Here we present two- (and a half) dimensional magnetohydrodynamic numerical simulations of the effects of a solar-like magnetic cycle, with periodic polarity inversions, in the slow wind of an asymptotic giant branch (AGB) star. The stellar wind is modeled with a steady mass-loss at constant velocity. This simple version of a solar-like cycle, without mass-loss variations, is able to reproduce many properties of the observed concentric rings. The shells are formed by pressure oscillations, which drive compressions in the magnetized wind. These pressure oscillations are due to periodic variations in the field intensity. The periodicity of the shells, then, is simply a half of the magnetic cycle since each shell is formed when the magnetic pressure goes to zero during the polarity inversion. As a consequence of the steady mass-loss rate, the density of the shells scales as r-2, and their surface brightness has a steeper drop-off, as observed in the shells of NGC 6543, the best documented case of these HST rings. Deviations from sphericity can be generated by changing the strength of the magnetic field. For sufficiently strong fields, a series of symmetric and equidistant blobs are formed at the polar axis, resembling the ones observed in He 2-90. These blobs are originated by magnetic collimation within the expanding AGB wind.
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