  We perform the first magnetohydrodynamical simulations of tidal disruptions
of stars by supermassive black holes. We consider stars with both tangled and
ordered magnetic fields, for both grazing and deeply disruptive encounters.
When the star survives disruption, we find its magnetic field amplifies by a
factor of up to twenty, but see no evidence for the a self-sustaining dynamo
that would yield arbitrary field growth. For stars that do not survive, and
within the tidal debris streams produced in partial disruptions, we find that
the component of the magnetic field parallel to the direction of stretching
along the debris stream only decreases slightly with time, eventually resulting
in a stream where the magnetic pressure is in equipartition with the gas. Our
results suggest that the returning gas in most (if not all) stellar tidal
disruptions is already highly magnetized by the time it returns to the black
hole.
