  Geostrophic jets propagating as Alfv\'en waves are shown to arise ina rapidly
rotating spherical shell permeated by a magnetic field among the transient
motions set up by an impulsive rotation of the inner core. These axially
invariant motions evolve on a time-scale which is short compared to the
magnetic diffusion time. The numerical study is taken as illustrative of a more
general point: on such a fast time-scale the dimensionless number appropriate
to compare the rotation and magnetic forces is independent of the magnetic
diffusivity in contrast with the often used Elsasser number. Extension of the
analysis to non-axisymmetrical motions is supported by published studies of
dynamo models and magnetic instabilities.
