Abstract
To realize the magnetorotational instability (MRI) with liquid metals such as gallium in the laboratory, one needs Reynolds numbers exceeding 10 7 (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 perfectconducting cylinders with Rout =2 Rin = 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 1 demonstrates the existence of the MRI in the laboratory.
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