PPPL-3843 is available in <a href="PPPL-3843.pdf">pdf</a> format (844 KB).

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<b>Transition from Collisionless to Collisional MRI</b>
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<b>Authors:</b> Prateek Sharma, Gregory W. Hammett, and Eliot Quataert

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<b>Date of PPPL Report:</b> July 2003
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<b>Submitted to:</b> Astrophysical Journal


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Recent calculations by Quataert et al. (2002) found that the growth rates of the magnetorotational instability (MRI) in a collisionless plasma can differ significantly from those calculated using MHD. This can be important in hot accretion flows around compact objects. In this paper, we study the transition from the collisionless kinetic regime to the collisional MHD regime, mapping out the dependence of the MRI growth rate on collisionality. A kinetic closure scheme for a magnetized plasma is used that includes the effect of collisions via a BGK operator. The transition to MHD occurs as the mean free path becomes short compared to the parallel wavelength 2<font face = "symbol">p</font face = "symbol">/k<sub>||</sub>. In the weak magnetic field regime where the Alfv&#233;n and MRI frequencies <font face = "symbol">w</font face = "symbol"> are small compared to the sound wave frequency k<sub>||</sub>c<sub>0</sub>, the dynamics are still effectively collisionless even if <font face = "symbol">w</font face = "symbol"> << <font face = "symbol">n</font face = "symbol">, so long as the collision frequency <font face = "symbol">n</font face = "symbol"> << k<sub>||</sub>c<sub>0</sub>; for an accretion flow this requires <font face = "symbol">n</font face = "symbol"> less than or approximately equal to <font face = "symbol">Wb</font face = "symbol"><sup>1/2</sup>. The low collisionality regime not only modifies the MRI growth rate, but also introduces collisionless Landau or Barnes damping of long wavelength modes, which may be important for the nonlinear saturation of the MRI.





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