Alfvén continuum and high-frequency eigenmodes in optimized stellarators

An equation of shear Alfvén eigenmodes (AE) in optimized stellarators of Wendelstein line (Helias configurations) is derived. The metric tensor coefficients, which are contained in this equation, are calculated analytically. Two numerical codes are developed: the first one, COBRA (COntinuum BRanches of Alfvén waves), is intended for the investigation of the structure of Alfvén continuum; the second, BOA (Branches Of Alfvén modes), solves the eigenvalue problem. The family of possible gaps in Alfvén continuum of a Helias configuration is obtained. It is predicted that there exist gaps which arise due to or are strongly affected by the variation of the shape of the plasma cross section along the large azimuth of the torus. In such gaps, discrete eigenmodes, namely, helicity-induced eigenmodes (HAE21) and mirror-induced eigenmodes (MAE) are found. It is shown that plasma inhomogeneity may suppress the AEs with a wide region of localization.