Low Frequency Collective Motions in Tokamak

Low frequency collective motions play major roles in turbulent transport and also MHD instabilities in tokamaks. In this chapter, we introduce drift waves , shear Alfven waves, wave-particle interactions using fluid and gyro kinetic equations as important collective motions in tokamak . Electrostatic drift waves such as slab drift wave including ion temperature gradient (ITG) drift instability, and toroidal drift waves including ITG and trapped electron mode (TEM) instabilities are introduced in Sect. 5.1. The shear Alfven wave, kinetic Alfven wave and drift Alfven wave are introduced in Sect. 5.2. Classical and modern gyrokinetic theories are introduced in Sect. 5.3. Numerical calculations of toroidal ITG mode, TEM and the electron temperature gradient (ETG) mode based on gyrokinetic theories are described in Sect. 5.4. Columns includes derivation of guiding center Lagrangian, Non-canonical mechanics, Lagrange tensor, and Lie transformation.