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A unified linear theory that includes forced reconnection as a particular case of Alfvén resonance is presented. We consider a generalized Taylor problem in which a sheared magnetic field is subject to a time-dependent boundary perturbation oscillating at frequency ω0. By analyzing the asymptotic time response of the system, the theory demonstrates that the Alfvén resonance is due to the residues at the resonant poles, in the complex frequency plane, introduced by the boundary perturbation. Alfvén resonance transitions towards forced reconnection, described by the constant-psi regime for (normalized) times t≫S1/3, when the forcing frequency of the boundary perturbation is ω0≪S−1/3, allowing the coupling of the Alfvén resonances across the neutral line with the reconnecting mode, as originally suggested in Uberoi and Zweibel, (1999). Additionally, it is shown that even if forced reconnection develops for finite, albeit small, frequencies, the reconnection rate and reconnected flux are strongly reduced for frequencies ω0≫S−3/5.

The steady-state confinement, beta limit, and divertor heat load are among the most concerned issues for toroidal confinement of fusion plasmas. In this work, we show that the negative triangularity tokamak has promising prospects to address these issues. We first demonstrate that the negative triangularity tokamak generates the filed line rotation transform more effectively. This brings bright prospects for the advanced steady-state tokamak scenario. Given this, the MHD stability and equilibrium confinement of negative triangularity tokamak are investigated. We point out that the negative triangularity configuration with a broad pressure profile is indeed more unstable for low-n magnetohydrodynamic modes than the positive triangularity case so that the H-mode confinement can hardly be achieved in this configuration, where n is the toroidal mode number. Nevertheless, we found that the negative triangularity configuration with high bootstrap current fraction, high poloidal beta, and peaked pressure profiles can achieve higher normalized beta for low-n modes than the positive triangularity case. In a certain parameter domain, the normalized beta can reach about twice the extended Troyon limit, while the same computation indicates that the positive triangularity configuration is indeed constrained by the Troyon limit. This shows that the negative triangularity tokamaks are not only favorable for divertor design to avoid the edge localized modes but also can have promising prospects for advanced steady-state confinement of fusion plasmas in high beta.