  The potential of the nonaxisymmetric magnetic instability to transport
angular momentum and to mix chemicals is probed considering the stability of a
nearly uniform toroidal field between conducting cylinders with different
rotation rates. The fluid between the cylinders is assumed as incompressible
and to be of uniform density. With a linear theory the neutral-stability maps
for m=1 are computed. Rigid rotation must be subAlfvenic to allow instability
while for differential rotation with negative shear also an unstable domain
with superAlfvenic rotation exists. The rotational quenching of the magnetic
instability is strongest for magnetic Prandtl number Pm=1 and becomes much
weaker for Pm unequal 1. The effective angular momentum transport by the
instability is directed outwards(inwards) for subrotation(superrotation). The
resulting magnetic-induced eddy viscosities exceed the microscopic values by
factors of 10-100. This is only true for superAlfvenic flows; in the
strong-field limit the values remain much smaller. The same instability also
quenches concentration gradients of chemicals by its nonmagnetic fluctuations.
The corresponding diffusion coefficient remains always smaller than the
magnetic-generated eddy viscosity. A Schmidt number of order 30 is found as the
ratio of the effective viscosity and the diffusion coefficient. The magnetic
instability transports much more angular momentum than that it mixes chemicals.
