TH/P5-10 · Development Of Theory Of Reversed-Shear Alfven Eigenmodes
S.V. Konovalov1), A.B. Mikhailovskii1), E. A. Kovalishen1)3), T. Ozeki2), T. Takizuka2), M.S. Shirokov1)
1) Institute of Nuclear Fusion, RRC "Kurchatov Institute", Moscow, Russian Federation
2) Naka Fusion Research Establishment, Japan Atomic Energy Research Institute, Naka-machi, Naka-gun, Ibaraki-ken, Japan
3) Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow Region, Russia
Abstract: New magnetohydrodynamic (MHD) phenomena with upward frequency- sweeping named Alfvén Cascades (ACs) were revealed recently on JT-60U and JET in discharges with non-monotonic safety factor (reversed magnetic shear, (RS)) and significant population of the hot ions. The first theoretical description of ACs was given in paper [Berk et al., Phys. Rev. Lett. 87, 185002 (2001)], where radial localization of Alfvén Eigenmode (AE) was provided by the non-resonant response of hot ion population. Another mode localizing toroidal MHD effect was considered by Breizman et al. [Phys. Plasmas 10, 3649 (2003)]. In the present report we extend the theory of AE in RS tokamak plasmas (RSAE) by incorporating the effect of thermal plasma density gradient taken from theory of cylindrical Global Alfvén Eigenmodes (GAE) and kinetic (finite ion Larmor radius) effects from theory of Kinetic Toroidicity induced Alfvén Eigenmodes (KTAE). It is shown that the localization effect of thermal plasma density gradient on AC mode can be stronger than the toroidal MHD effect as squared aspect ratio. Thus, the Alfvén Cascade modes can be theoretically demonstrated in cylindrical geometry approximation. Then the role of thermal plasma density gradient can be dominant if the localization effect of density gradient of large orbit hot ions is sufficiently weak. The mode localization effect considered in the present report can be essential only if the thermal plasma density gradient is not too small. It is localizing for the mode numbers satisfying the condition q(min) > m/n. Then ACs correspond to the "sub-Alfvén" modes. In the opposite condition, q(min) < m/n, this effect is delocalizing. Then to provide AC eigenmodes existence other localizing mechanisms should be considered. The shift of the localization region of the eigenmodes and the eigenfrequency shift caused by the thermal plasma density gradient were found to be sufficiently small. Taking into account the finite ion Larmor radius (kinetic) effects in Alfvén mode equation allows us to predict a new branches of these modes called the Kinetic Reversed-Shear Alfvén Eigenmodes (KRSAEs). These modes are shown to posses the features of Alfvén Cascades even for homogeneous thermal plasma density in cylindrical geometry approximation.
Keywords: Alfvén eigenmodes, reversed shear, TAE instabilities,