Perturbation analysis of beta-induced Alfvén eigenmode in toroidally rotating tokamak plasmas

Abstract The effects of equilibrium toroidal rotation flow (ETRF) and finite parallel wavenumber (FPWN) on beta-induced Alfvén eigenmode (BAE) in tokamak plasmas are investigated within the ideal magnetohydrodynamic framework. Both ETRF and FPWN increase the BAE frequency, with FPWN contributing a finite upshift and ETRF leading to a stronger increase with increasing toroidal Mach number M T . In the poloidal magnetic field perturbation δB θ , the fundamental component with poloidal mode number m 0 is primarily induced by FPWN, with its amplitude proportional to the FPWN parameter n ∥ , whereas the m 0 ±1 sidebands contain contributions from the inverse aspect ratio ϵ , FPWN, and finite plasma beta β , defined as the ratio of plasma pressure to magnetic pressure. At zero rotation, the ratios | δB θ , m 0 ±1 / δB θ , m 0 | can be of order unity for n ∥ <0 with n ∥ O( ϵ ), and both increase with ϵ in this range. For n ∥ >0 in the same ordering range, the m 0 −1 sideband remains relatively weak, and the two m 0 ±1 sidebands are not simultaneously comparable to the m 0 component. For the representative negative values of n ∥ considered, as M T increases from zero, | δB θ , m 0 +1 / δB θ , m 0 | first decreases slightly and then increases, whereas | δB θ , m 0 −1 / δB θ , m 0 | decreases throughout the M T range considered. With increasing M T , | δB θ , m 0 +2 / δB θ , m 0 | passes through a shallow minimum at low M T before increasing, while | δB θ , m 0 −2 / δB θ , m 0 | increases throughout the M T range considered. Under strong ETRF, the m 0 ±2 sidebands induced by finite β can become comparable in magnitude to the m 0 component.