Non-Viscous Transport of Angular Momentum and Non-Linear Model Equations to Remove the Singularities of Optimal Bending Modes in Accretion Disks

Transport of angular momentum in plasma accretion disks with a significant magnetic field (finite β_s=c^2_s/v^2_A) can be produced by singular bending (tri-dimensional) modes^2 at sufficient rates to match the Shakura-Sunyaev viscosity reproducing the luminosity values of a broad class of objects. However, the transport evaluated by the relevant quasilinear theory cannot be represented by an effective viscosity involving a significant dissipation of flow energy into plasma thermal energy. The Doppler shifted frequency of these modes, that corotate locally with the disk, can resonate with the plasma "cusp frequency" at the radii where the flow compressibility, according to the linearized ideal MHD theory, would become singular. Since classical dissipative effects are inadequate to deal with the singularity, a set of model transition equations for the flow compressibility with relevant nonlinear terms is identified to describe the transition across the resonance regions producing significant mode growth rates. ^2B. Coppi and P.S. Coppi, Phys. Rev. Letters 87, 051101-1 (2001)