Kinetic theory of parametric instabilities in magnetized plasmas and its application to analyzing decay waves during the injection of lower hybrid waves

In this paper, a kinetic formalism of parametric decay instabilities (PDI) with electromagnetic waves in magnetized plasmas is compared with its simplified models under the quasi-linear treatment and under the electrostatic limit, as well as a kinetic-fluid hybrid and electrostatic model. Further iteration beyond the quasi-linear approach is shown necessary to deal with the cases of quasi-mode decay; while the kinetic effect and the electromagnetic effect are shown less important in nonlinear coupling physics of PDI during lower hybrid current drive (LHCD) with typical parameters in the scrape-off layer of tokamak plasmas. Therefore, the hybrid electrostatic model can be used in the typical scenarios of LHCD induced PDI provided that the kinetic effect in linear response and the electromagnetic effect in the linear dispersion relation of the pump wave are kept. Also, necessary numerical techniques are applied to address the common problems that usually exist in calculating the nonlinear dispersion relations of PDI. Efforts in physical models and numerical techniques allow us to present detailed investigations of decay channels of the PDI during LHCD. It is shown that the PDI can occur for the decay waves with large refractive index parallel to the static magnetic field (typically and much larger than that of the pump), which are easy to be damped and therefore might be ignored to some extent. Parameter dependencies of the different decay channels are also displayed.