The magnetorotational instability of MHD Taylor--Couette flows

G. Rüdiger - M. Schultz

Astrophysikalisches Institut Potsdam, D14467 Potsdam, Germany

Abstract
To realize the magnetorotational instability (MRI) with liquid metals such as gallium in the laboratory, one needs Reynolds numbers exceeding 10⁷ (due to their small magnetic Prandtl number \Pm), which seems to be out of the current technical possibilities. We have shown that in the presence of combined axial and azimutal magnetic fields (`helical' fields) a new solution beyond the Rayleigh limit appears, which for small magnetic Prandtl numbers does not depend on \Pm. The critical Reynolds number is reduced to O(10^3...4), which does not make any technical difficulty. For liquid gallium between the perfect-conducting cylinders with R_out = 2 R_in=8 cm the necessary axial magnetic field is  ∼ 100 Gauss and the axial current, which produces the azimutal field, must have  ∼ 3000 Amp. The critical rotation rate of the inner cylinder is then less than 1 Hz. The gallium Taylor-Couette experiment PROMISE (``PotsdamROssendorfMagneticInStabilityExperiment"