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It has been suggested that magnetic fields play a dynamically-important rolein core-collapse explosions of massive stars. In particular, they may beimportant in the collapsar scenario for gamma-ray bursts (GRB), where thecentral engine is a hyper-accreting black hole or a millisecond magnetar. Thepresent paper is focussed on the magnetar scenario, with a specific emphasis onthe interaction of the magnetar magnetosphere with the infalling stellarenvelope. First, the ``Pulsar-in-a-Cavity'' problem is introduced as a paradigmfor a magnetar inside a collapsing star. The basic set-up of this fundamentalplasma-physics problem is described, outlining its main features, and simpleestimates are derived for the evolution of the magnetic field. In the contextof a collapsing star, it is proposed that, at first, the ram pressure of theinfalling plasma acts to confine the magnetosphere, enabling a gradual build-upof the magnetic pressure. At some point, the growing magnetic pressureovertakes the (decreasing) ram pressure of the gas, resulting in amagnetically-driven explosion. The explosion should be highly anisotropic, asthe hoop-stress of the toroidal field, confined by the surrounding stellarmatter, collimates the magnetically-dominated outflow into two beamedmagnetic-tower jets. This creates a clean narrow channel for the escape ofenergy from the central engine through the star, as required for GRBs. Inaddition, the delayed onset of the collimated-explosion phase can explain theproduction of large quantities of Nickel-56, as suggested by the GRB-Supernovaconnection. Finally, the prospects for numerical simulations of this scenarioare discussed.

Magnetically-dominated jets inside collapsing stars as a model for gamma-ray bursts and supernova explosions