Nonlinear analysis of lower hybrid by many-body techniques

Abstract

In some recent experiments, intense ion heating has been observed. This heating has been attributed to the excitation of the lower hybrid in the inhomogeneous magnetoactive plasma. The level of turbulence is observed to be quite high, but the lower hybrid instability is seen to saturate after growing initially. This thesis deals with the development of a consistent theory for the experimentally observed facts. A nonlinear saturation of this lower hybrid excitation at high ion temperatures is considered. First of all, the possibility of such an instability is investigated and the linear non-resonant growth rate is interpreted as due to an interaction between a negative energy mode and a positive energy mode, after showing mathematically that both kinds of waves do exist. By employing many-body techniques, nonlinear interactions between the modes excited in the plasma, such as: (a) forward scattering of positive and negative energy modes, through the creation or annihilation of the positive-negative energy wave doublet; (b) vertex renormalization of two-mode coupling are calculated. It is found that as the waves grow, an attractive potential develops, which becomes responsible for cutting down the linear growth rate. Further, the resonant wave-particle interaction is considered for a finite wave vector parallel to the external magnetic field (q?), along with the other processes. Thereafter we deal with the case when q? = 0 and show that a resonant interaction between waves and particles is still possible, if one takes into account the perturbation on the particle trajectories brought about by the plasmon field. This interaction is otherwise impossible. The renormalized energy of the particle is obtained by Many-Body Techniques. However, only at higher levels of the wave energy this interaction appears to come into the picture. The calculations with q? = 0, along with the other nonlinear interactions, show a good agreement with the experimental results of Alexeff et al. (1971), Hirose and Alexeff (1972a,b) and Kovpik et al. (1972).