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 subAlfvénic to allow instability while for differential rotation with negative shear also an unstable domain with superAlfvénic rotation exists .
The rotational quenching of the magnetic instability is strongest for magnetic Prandtl number Pm = 1 and becomes much weaker for \mathrm { Pm } \neq 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 superAlfvénic 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 .