Effects of pressure gradient on existence of Alfvén cascade modes in reversed shear tokamak plasmas

It is shown analytically that pressure gradient effects are favorable to the existence of Alfvén cascade (AC) modes in a tokamak plasma with reversed shear. What is crucial for obtaining the improved existence criterion of ACs is the averaged normal curvature. This term depends on the Shafranov shift, which contains a pressure gradient term that at sufficiently low frequency causes a cancellation in the mode existence criterion of all terms quadratic in the pressure gradient. The favorable criterion is then found to be proportional to the product of the pressure gradient and the inverse aspect ratio. Near the rational surface, there is one-to-one correspondence between Mercier stability and the AC mode existence. When the averaged curvature is favorable to Mercier modes, it is also favorable to the existence of AC. However, at higher frequencies the α2 term can be unfavorable to mode existence. We show that when α>3ϵ, that as qmin decreases from m∕n, the cascade mode can easily satisfy its existence criterion at lower frequencies, but the existence criterion will fail before the frequency reaches the toroidal Alfvén eigenmode (TAE) gap, which occurs when qmin approaches (m−1∕2)∕n.