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Possible origins of the magnetic fields of neutron stars include inheritance from the main sequence progenitor and dynamo action at some stage of evolution of progenitor. Inheritance is not sufficient to explain the fields of magnetars. Energetic considerations point to differential rotation in the final stages of core collapse process as the most likely source of field generation, at least for magnetars. A runaway phase of exponential growth is needed to achieve sufficient field amplification during relevant phase of core collapse; it can probably be provided by a some form of magnetorotational instability. Once formed in core collapse, the field is in danger of decaying again by magnetic instabilities. The evolution of a magnetic field in a newly formed neutron star is discussed, with emphasis on the existence of stable equilibrium configurations as end products of this evolution, and the role of magnetic helicity in their existence. [ABSTRACT FROM AUTHOR]

Many main-sequence stars exhibit extensive radiative zones. Some of these may rotate differentially and have large-scale meridional circulations, while the solar radiative core rotates rigidly. We are concerned with three topics: The generation of magnetic fields by a dynamo effect of these large-scale motions, the stability of differential rotation if magnetic fields are present initially, and the formation of the solar tachocline being a thin transition layer from rigid solar-core rotation to differential rotation of the outer convective shell. We conclude that dynamo-generation of magnetic fields is unlikely in stellar radiative envelopes. This finding supports the view that the fields of magnetic Ap stars are fossil. If they do exist from the beginning of the stellar life, they will make a differential rotation unstable if the angular velocity decreases with axis distance. This is the magneto-rotational instability. It is found that the time-scale of turning a differential rotation into a rigid one is about 10–100 million years. In the solar radiative core, the angular velocity gradient is positive and the magneto-rotational instability is not found. Nevertheless, magnetic fields will suppress differential rotation by the Lorentz force and reduce the transition between the differentially rotating outer convection zone and the core to a very thin layer. The field strength of the poloidal core magnetic field has to be of the order of 10 G in order to produce the solar tachocline thickness. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]