Saturation of parametric instabilities in lower hybrid heating of tokamak plasmas

Abstract

A non-linear analysis of parametric instabilities in lower hybrid heating of tokamak plasmas is presented. Harmonic generation of the low frequency mode and its effect on the evolution of the parametric decay of a lower hybrid pump to another lower hybrid wave and a low frequency mode is investigated, and numerical calculations of the relevant wave system are carried out. It is found that the coupling of the low frequency wave to its harmonic may effectively suppress the spatial growth of the primary instability. This may be particularly true at the plasma edge of the tokamak, where electron and ion temperatures are low and the primary instability is strong at high pump intensity. The spectral dependence of the harmonic generation strength is compared with that of the primary instability, and the effect on pump depletion with relevant tokamak parameters is discussed.

Non-linear power conversion by non-resonant parametric decay of the fast wave during ICRF heating

“…However, for the tritium Bernstein mode there is no obvious decay to lower frequency Bernstein waves because of the lack of ion species with lower ion cyclotron frequencies. Second harmonic generation [12] has to be ruled out for the Bernstein waves because the second harmonic wave with a frequency 2w and a wave vector 2 k is a non-resonant and in most cases weakly damped mode. For the quasi-mode, decay is not possible, but coupling to another quasimode at second harmonic is possible.…”

“…(ID (12) where y denotes the primary coupling strength and is given by the integrand in the exponential function of Eq. ( 9), v is the collisional damping decrement of the secondary Bernstein wave and v g ' is the group velocity of that wave.…”