We revisit the modal analysis of small perturbations in Keplerian ideal gas flows with a constant vertical magnetic field leading to magnetorotational instability (MRI) using the nonlocal approach. In the general case, MRI modes are described by a Schrödinger-like differential equation with some effective potential, including 'repulsive' (1/r²) and 'attractive' (−1/rr³) terms, and are quantized. In shallow potentials, there are no stationary 'energy levels.' In thin Keplerian accretion discs, the perturbation wavelengths λ =2π /k_z are smaller than the disc semi-thickness h only in 'deep' potential wells. We find that there is a critical magnetic field for the MRI to develop. The instability arises for magnetic fields below this critical value. In thin accretion discs, at low background Alfvén velocity c_A≪ (c_A)_cr, the MRI instability increment ω is suppressed compared to the value obtained in the local perturbation analysis, ω ≈ −√3ic_Ak_z. We also investigate for the first time the case of a radially variable background magnetic field.

Keywords: magnetorotational instability, accretion discs PACS: 95.30.Qd, 97.10.Gz (all) DOI: 10.3367/UFNe.2023.09.039554 URL: https://ufn.ru/en/articles/2023/12/f/ 001172931200005 2-s2.0-85183001473 2023PhyU...66.1262S Citation: Shakura N I, Postnov K A, Kolesnikov D A, Lipunova G V "Magnetorotational instability in Keplerian disks: a nonlocal approach" Phys. Usp. 66 1262–1276 (2023) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Received: 16th, December 2022, revised: 21st, September 2023, accepted: 22nd, September 2023 Оригинал: Шакура Н И, Постнов К А, Колесников Д А, Липунова Г В «Магниторотационная неустойчивость в кеплеровских дисках: нелокальный подход» УФН 193 1340–1355 (2023); DOI: 10.3367/UFNr.2023.09.039554