On the Saturation of the Magnetorotational Instability via Parasitic Modes

TY - JOUR

T1 - On the Saturation of the Magnetorotational Instability via Parasitic Modes

AU - Pessah, Martin Elias

AU - Goodman, Jeremy

PY - 2009/6/10

Y1 - 2009/6/10

N2 - We investigate the stability of incompressible, exact, non-ideal magnetorotational (MRI) modes against parasitic instabilities. Both Kelvin-Helmholtz and tearing-mode parasitic instabilities may occur in the dissipative regimes accessible to current numerical simulations. We suppose that a primary MRI mode saturates at an amplitude such that its fastest parasite has a growth rate comparable to its own. The predicted alpha parameter then depends critically on whether the fastest primary and parasitic modes fit within the computational domain and whether non-axisymmetric parasitic modes are allowed. Hence even simulations that resolve viscous and resistive scales may not saturate properly unless the numerical domain is large enough to allow the free evolution of both MRI and parasitic modes. To minimally satisfy these requirements in simulations with vertical background fields, the vertical extent of the domain should accommodate the fastest growing MRI mode while the radial and azimuthal extents must be twice as large. The fastest parasites have horizontal wavelengths roughly twice as long as the vertical wavelength of the primary.

AB - We investigate the stability of incompressible, exact, non-ideal magnetorotational (MRI) modes against parasitic instabilities. Both Kelvin-Helmholtz and tearing-mode parasitic instabilities may occur in the dissipative regimes accessible to current numerical simulations. We suppose that a primary MRI mode saturates at an amplitude such that its fastest parasite has a growth rate comparable to its own. The predicted alpha parameter then depends critically on whether the fastest primary and parasitic modes fit within the computational domain and whether non-axisymmetric parasitic modes are allowed. Hence even simulations that resolve viscous and resistive scales may not saturate properly unless the numerical domain is large enough to allow the free evolution of both MRI and parasitic modes. To minimally satisfy these requirements in simulations with vertical background fields, the vertical extent of the domain should accommodate the fastest growing MRI mode while the radial and azimuthal extents must be twice as large. The fastest parasites have horizontal wavelengths roughly twice as long as the vertical wavelength of the primary.

KW - astro-ph.HE

U2 - 10.1088/0004-637X/698/1/L72

DO - 10.1088/0004-637X/698/1/L72

M3 - Journal article

SN - 0067-0049

SN - 1538-4357

SN - 1538-4365

VL - 698

SP - L72-L76

JO - Astrophysical Journal Letters

JF - Astrophysical Journal Letters

IS - 1

ER -