The effect of equilibrium poloidal flow and pressure gradient on the m/n = 2/1 (m is the poloidal mode number and n is the toroidal mode number) tearing mode instability for tokamak plasmas is investigated. Based on the condition of p ≠ 0 (p is plasma pressure), the radial part of the motion equation is derived and approximately solved for large poloidal mode numbers (m). By solving partial differential equations (Whittaker equation) containing second order singularity, the tearing mode stability index Δ' is obtained. It is shown that the effect of equilibrium poloidal flow and pressure gradient has an adverse effect on the tearing mode instability when the pressure gradient is nonzero. The poloidal equilibrium flow with pressure perturbation partially reduces the stability of the classical tearing mode. But the larger pressure gradient in a certain poloidal flow velocity range can abate the adverse influence of equilibrium poloidal flow and pressure gradient. The numerical results do also indicate that the derivative of pressure gradient has a significant influence on the determination of the instability region of the poloidal flow with pressure perturbation.
Geodesic acoustic modes and zonal flows in rotating large-aspect-ratio tokamak plasmas