We consider the linear axisymmetric stability of a differentially rotating collisionless plasma in the presence of a weak magnetic field ; we restrict our analysis to wavelengths much larger than the proton Larmor radius .
This is the kinetic version of the magnetorotational instability explored extensively as mechanism for magnetic field amplification and angular momentum transport in accretion disks .
The kinetic calculation is appropriate for hot accretion flows onto compact objects and for the growth of very weak magnetic fields , where the collisional 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 , namely that the angular velocity decrease outwards .
However , nearly every mode has a linear kinetic growth rate that differs from its MHD counterpart .
The kinetic growth rates also depend explicitly on \beta , i.e. , on the ratio of the gas pressure to the pressure of the seed magnetic field .
For \beta \sim 1 the kinetic growth rates are similar to the MHD growth rates while for \beta \gg 1 they differ significantly .
For \beta \gg 1 , the fastest growing mode has a growth rate \approx \sqrt { 3 } \Omega for a Keplerian disk , larger than its MHD counterpart ; there are also many modes whose growth rates are negligible , { { { { \mathrel { \mathchoice { \vbox { \offinterlineskip \halign { \cr } $ \displaystyle \hfil < $% \cr$ \displaystyle \hfil \sim$ } } } { \vbox { \offinterlineskip \halign { \cr } $ \textstyle% \hfil < $ \cr$ \textstyle \hfil \sim$ } } } { \vbox { \offinterlineskip \halign { \cr } $% \scriptstyle \hfil < $ \cr$ \scriptstyle \hfil \sim$ } } } { \vbox { \offinterlineskip% \halign { \cr } $ \scriptscriptstyle \hfil < $ \cr$ \scriptscriptstyle \hfil \sim$ } } } } % \beta ^ { -1 / 2 } \Omega \ll \Omega .
We provide a detailed physical interpretation of these results and show that gas pressure forces , rather than just magnetic forces , are central to the behavior of the magnetorotational instability in a collisionless plasma .
We also discuss the astrophysical implications of our analysis .

Subject Headings : accretion , accretion disks ; instabilities ; plasmas