A pressure-gradient-driven tokamak "resistive magnetohydrodynamic" instability in the banana-plateau collisionality regime

The moment equation approach to neoclassical processes is used to derive the linearized electrostatic perturbed flows, currents, and resistive MHD-like equations for a tokamak plasma. The new features of the resultant "neoclassical magnetohydrodynamics," which requires a multiple length scale analysis for the parallel eigenfunction, but is valid in the experimentally relevant banana-plateau regime of collisionality, are: (1) a global Ohm's law that includes a fluctuating bootstrap current resulting from the "parallel" electron viscous damping (at rate μ_e) of the poloidal flow due to the perturbed radial pressure gradient; (2) reduction of the curvature effects to their flux surface average because Pfirsch-Schlüter currents cancel out the lowest-order geodesic curvature effects: (3) an increased polarization drift contribution with B^-2, replaced by B_⊖^-2, where B_⊖ is the poloidal magnetic field component. An electrostatic eigenmode equation is determined from ▽·J̃=0. For the unstable fluid-like eigenmodes, the new viscous damping effects dominate (by ε^-3/2) over the curvature effects, but the growth rates still scale roughly like resistive-g or resistive-ballooning modes, γ_μτ_Α∼ n^2/3S_N^1/3β_T^2/3(μ _e/ν_e)^1/3. Diamagnetic drift frequency corrections to these new modes are also discussed.