Physics of Landau Resonances, Cyclotron Resonances, and Current Generation

Irreversible energy and momentum transfer from waves to particles for tokamak confinement, heating, and control is based on Landau and cyclotron resonances. Above a stochasticity threshold, these interactions can be viewed as a random walk in energy (action) space within the random phase approximation. We present and discuss the quasi-linear theory describing this random walk with a particular emphasis on the interplay between the dynamical picture (electromagnetic forces) and the statistical description (photons emission/absorption). Landau and cyclotron absorptions in tokamaks are thus derived, and the classical theory of current generation in tokamaks is presented in local and nonlocal regimes.