Plasma pressure effect on Alfvén cascade eigenmodes

Tokamak plasmas with reversed magnetic shear are prone to the excitation of Alfvén cascade (AC) eigenmodes by energetic particles. These modes exhibit a quasiperiodic pattern of predominantly upward frequency sweeping. Observations also reveal that the AC spectral lines sometimes bend at low frequencies, which is a significant deviation from the shear Alfvén wave dispersion relation. This paper shows that the underlying reasons for such bending are the finite pressure of the plasma and the geodesic curvature that precludes shear Alfvén perturbations from being strictly incompressible. In addition to the geodesic effect, there are two other pressure effects on shear Alfvén waves, which are the convection in the presence of an equilibrium pressure gradient and the toroidicity-induced coupling between shear Alfvén waves and acoustic modes. An analytical treatment of the problem enables a parametric comparison of all three mechanisms. The key distinction between the geodesic compressibility and the acoustic coupling is that geodesic compression occurs without plasma displacement along the magnetic-field lines. As a result, the mode phase velocity is greater than the ion thermal velocity even in an isothermal plasma, which allows the mode to avoid a strong ion Landau damping. Plasma temperature diagnostics via magnetohydrodynamic spectroscopy employing the low-frequency part of the ACs is suggested.