The Magnetorotational Instability in a Collisionless Plasma

We consider the linear axisymmetric stability of a differentially rotatingcollisionless plasma in the presence of a weak magnetic field; we restrict ouranalysis to wavelengths much larger than the proton Larmor radius. This is thekinetic version of the magnetorotational instability explored extensively asmechanism for magnetic field amplification and angular momentum transport inaccretion disks. The kinetic calculation is appropriate for hot accretion flowsonto compact objects and for the growth of very weak magnetic fields, where thecollisional mean free path is larger than the wavelength of the unstable modes.We show that the kinetic instability criterion is the same as in MHD, namelythat the angular velocity decrease outwards. However, nearly every mode has alinear kinetic growth rate that differs from its MHD counterpart. The kineticgrowth rates also depend explicitly on beta, i.e., on the ratio of the gaspressure to the pressure of the seed magnetic field. For beta ~ 1 the kineticgrowth rates are similar to the MHD growth rates while for beta >> 1 theydiffer significantly. For beta >> 1, the fastest growing mode has a growth rateof sqrt{3} Omega for a Keplerian disk, larger than its MHD counterpart; thereare also many modes whose growth rates are negligible, < beta^{-1/2} Omega <

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