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**Session 85 - Cataclysmic Variables and Accretion Disks.**

*Oral session, Wednesday, January 15*

*Harbour A, *

## [85.02] Magnetic Shearing Instabilities in Accretion Disks

*D. B. Curran, E. Vishniac (Univ. of Texas)*
We examine the growth of the Velikhov-Chandrasekhar instability
for an azimuthal field in a thin accretion disk. We assume
periodic vertical boundary conditions and look for modes that
vanish far from the corotation radius, thereby eliminating any
dependence on artificial boundaries. In an inviscid and
perfectly conducting fluid there are no solutions which are
properly localized. If we modify the force equations to include
radial diffusion, then we obtain a sixth order equation in the
radial velocity, with solutions that contain a local
instability. We obtain a similar result using magnetic
resistivity instead. Finally we using both a
diffusion coefficient and magnetic resistivity and
gives a tenth order differential equation in u_r with
reasonable asymptotic limits. The well behaved solutions
include modes with arbitrarily large growth rates, but these
modes have a negligible effect on transport.
\vskip .1in
We explore parameter space and look at the growth rate of instabilities
contained within the disk. We found that the critical quantity in the
final result is the ratio of the diffusion coefficient to the resistivity.
We try various values of this quantity to determine which range of this
ratio gives the largest transport effects. This involves actually
integrating the modified force equations, changing Døver \eta then
looking at the growth rates as a function of frequency. We conclude
that the instability is formally nonlinear in the absence of resistivity
or viscosity, but one can produce linear instabilities when includes
diffusion, resistivity or both diffusion and resistivity into the force
equations.

**Program
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