Other
Scientific paper
Nov 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995phdt........33c&link_type=abstract
Thesis (PH.D.)--MCMASTER UNIVERSITY (CANADA), 1995.Source: Dissertation Abstracts International, Volume: 57-03, Section: B, page
Other
Scientific paper
We investigate the global stability of a differentially rotating fluid shell threaded by magnetic fields to linear perturbations. This system models an accretion disk far from its vertical boundaries. To focus on the direct interaction between the magnetic field and differential rotation, the stability analysis employs an equilibrium model of homogeneous and incompressible fluid which allows these phenomena to be studied in isolation. Depending on the degree of internal pressure support, disks may be either ``thick'' or ``thin'' and both possibilities are considered here. The magnetic field exterior to the fluid has an effect on the radial boundary motion, and we derive the appropriate boundary conditions. The first interaction of interest is the axisymmetric instability of Velikhov and Chandrasekhar. It has both local and global manifestations, the latter of which can be stabilized for all perturbations if and only if the equilibrium magnetic field strength is above a certain threshold value, which we calculate in our model for a wide range of equilibrium parameters. The growth rates of the unstable modes are always less than, but comparable to, the corresponding local growth rates. The former are also considerably higher for free boundaries than for the rigid configurations considered by other authors. The connection between the global and local characters of the instability is fully elucidated. These results are generalized from a purely vertical field to the case when an azimuthal magnetic field is present. In most cases, the azimuthal field tends to stabilize the VC instability, although strong fields (Alfvén speed of order the characteristic rotational speed) are required for complete stabilization. We find an additional strong field instability that arises when the azimuthal Alfvén speed exceeds the characteristic rotational speed. For freely-bounded configurations, this instability resembles the sausage instability for interpenetrating fields in plasma physics. Other interesting interactions appear in the presence of nonaxisymmetric perturbations. The global, dynamical instability of Papaloizou and Pringle, previously known to exist only in non-magnetized models of thick disks, is shown to have a magnetic counterpart. Indeed, this instability grows much more rapidly than in the corresponding hydrodynamic case. There also exist two additional types of unstable modes not present in hydrodynamic disks. The basic instability mechanism for these modes appears to be wave over-reflection between the boundaries and one or more of the singular Alfvén radii that can lie within the shell. These Alfvén resonances have a similar role to the corotation resonance in the purely hydrodynamic disk. We find, as in the axisymmetric case, that highly localized modes are fastest growing; however, they do not exceed the axisymmetric growth rates for any of the system parameters examined. Although all of the instabilities we found grow on the dynamical timescale, they may not be catastrophic to accretion disks. Indeed, the highly localized nature of the fastest growing modes suggests that these modes do not lead to large-scale breakup, but rather serve to ``stir up'' the fluid locally. Thus our results support the oft-mentioned conjecture that these magnetic instabilities could lead to turbulence. The globally unstable modes we found have quite different implications, among them the possibility that large-scale magnetic field generation (which we demonstrate in the linear growth regime) could obviate the need for the α-effect in standard dynamo theory.
No associations
LandOfFree
On The Global Stability of Magnetized Accretion Disks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On The Global Stability of Magnetized Accretion Disks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On The Global Stability of Magnetized Accretion Disks will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1182194