Interpretation of the finite pressure gradient effects in the reversed shear Alfvén eigenmode theory

Ideal MHD equations employed in the NOVA code are analysed analytically and numerically in order to investigate the role of the pressure gradient on global reversed shear Alfvén eigenmodes (RSAEs) or Alfvén cascades. We confirm both numerically and analytically conclusions obtained earlier using the ideal MHD code NOVA [1] and analytically [10] that the plasma pressure gradient plays a key role in the existence condition and in the dispersion relation for the mode. The effect of the plasma pressure gradient is to shift the mode frequency up at the low part of the RSAE frequency chirp and downshift the mode frequency when the frequency approaches the TAE gap. This finding is contrary to predictions in a recent publication [2], where the pressure gradient is found to be always stabilizing by means of downshifting the RSAE frequency and enhancing its interaction with the continuum. We resolve this discrepancy by showing that neglecting the pressure gradient effect on the plasma equilibrium (modification of the Shafranov shift and the averaged curvature) leads to conclusions at variance with the numerical and analytical results presented here. A new variational approximation of the RSAE is introduced which compares remarkably well with NOVA solutions. With this new approximation we clearly demonstrate the diagnostic potential and limitations of the RSAE frequency measurement for MHD spectroscopy.