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Title: Magnetorotational Instability: Nonmodal Growth and the Relationship of Global Modes to the Shearing Box

We study the magnetorotational instability (MRI) (Balbus & Hawley 1998) using non-modal stability techniques.Despite the spectral instability of many forms of the MRI, this proves to be a natural method of analysis that is well-suited to deal with the non-self-adjoint nature of the linear MRI equations. We find that the fastest growing linear MRI structures on both local and global domains can look very diff erent to the eigenmodes, invariably resembling waves shearing with the background flow (shear waves). In addition, such structures can grow many times faster than the least stable eigenmode over long time periods, and be localized in a completely di fferent region of space. These ideas lead – for both axisymmetric and non-axisymmetric modes – to a natural connection between the global MRI and the local shearing box approximation. By illustrating that the fastest growing global structure is well described by the ordinary diff erential equations (ODEs) governing a single shear wave, we find that the shearing box is a very sensible approximation for the linear MRI, contrary to many previous claims. Since the shear wave ODEs are most naturally understood using non-modal analysis techniques, we conclude by analyzing local MRI growth over finite time-scales usingmore » these methods. The strong growth over a wide range of wave-numbers suggests that non-modal linear physics could be of fundamental importance in MRI turbulence (Squire & Bhattacharjee 2014).« less
Authors:
 [1]
  1. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Publication Date:
OSTI Identifier:
1179780
Report Number(s):
PPPL--5051
DOE Contract Number:
DE-AC02-09CH11466
Resource Type:
Technical Report
Research Org:
Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
Sponsoring Org:
USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)
Contributing Orgs:
1 Max Planck/Princeton Center for Plasma Physics, Department of Astrophysical Sciences and Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543, USA 2 Princeton Center for Heliospheric Physics, Department of Astrophysical Sciences and Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543, USA
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY Astrophysics; Magnetic fields; MHD Instability; Accretron Disks