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We investigate analytically the magnetic instability in a rotating andelectrically conducting fluid induced by an imposed magnetic field with itsassociated electric current. The short-wavelength approximation is used in thelinear stability analysis, i.e. the length scale of the imposed field is muchlarger than the wavelength of perturbations. The dispersion relationship isderived and then simplified to give the criteria for the onset of the magneticinstability in three cases of imposed field, namely the axial dependence, theradial dependence and the mixed case. The orientation of rotation, imposedfield and imposed current is important for this instability.

Local analysis of the magnetic instability in rotating magneto-hydrodynamics with the short-wavelength approximation