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

Abstract

We investigate analytically the magnetic instability in a rotating and electrically conducting fluid induced by an imposed magnetic field with its associated electric current. The short-wavelength approximation is used in the linear stability analysis, i.e. the length scale of the imposed field is much larger than the wavelength of perturbations. The dispersion relationship is derived and then simplified to give the criteria for the onset of the magnetic instability in three cases of imposed field, namely, the axial dependence, the radial dependence and the mixed case. The orientation of rotation, imposed field and imposed current is important for this instability.

Keywords:

• Magnetohydrodynamics
• Instability

Acknowledgements

The motivation of this calculation was illuminated by the talk with Prof. Günther Rüdiger about the paper (Sreenivasan and Jones 2011) during my visit to Astrophysical Institute Potsdam. An anonymous referee pointed out that the radial dependence of background field would be more interesting to astrophysicists. I am financially supported by the project SPP1488 of the program PlanetMag of Deutsche Forschungsgemeinschaft (DFG).