Analysis of the Chaotic Behavior of the Lower Hybrid Wave Propagation in Magnetised Plasma by Hamiltonian Theory

Abstract

Abstract:The Hamiltonian character of the ray tracing equations describing the propagation of the Lower Hybrid Wave (LHW) in a magnetic confined plasma device (tokamak) is investigated in order to study the evolution of the parallel wave number along the propagation path. The chaotic diffusion of the "time-averaged" parallel wave number at higher values (with respect to that launched by the antenna at the plasma edge) has been evaluated, in order to find an explanation of the filling of the spectral gap (Fisch, 1987) by "Hamiltonian chaos" in the Lower Hybrid Current Drive (LHCD) experiments (Fisch, 1978). The present work shows that the increase of the parallel wave number n due to toroidal effects, in the case of the typical plasma parameters of the Frascati Tokamak Upgrade (FTU) experiment, is insufficient to explain the filling of the spectral gap, and the consequent current drive and another mechanism must come into play to justify the wave absorption by Landau damping. Analytical calculations have been supplemented by a numerical algorithm based on the symplectic integration of the ray equations implemented in a ray tracing code, in order to preserve exactly the symplectic character of a Hamiltonian flow.

Structure-preserving electromagnetic–kinetic simulations of lower hybrid-wave injection and current drive

“…For years, a wide variety of simulation methods based on different theoretical models have been constructed to address different aspects of LHW problems. Examples include Fokker-Planck code that solves the Fokker-Planck equation to obtain the steady-state distribution function and current generation [11,12], ray-tracing or beam-tracing code based on the Wentzel-Kramers-Brillouin (WKB) approximation [13,14] that solves the propagation of the LHW, and full-wave code that solves the Maxwell equations using plasma currents to describe the propagation and mode structure of waves. Usually, different simulation approaches are combined to investigate LHW physics.…”

Nonlinear lower hybrid wave equations in collisional tokamak plasmas

“…Indeed, as a result of the LH propagation in the presence of magnetic shear, the poloidal components are produced by the scattering project in the parallel direction. However, the geometrical effects might be not be sufficient to bridge the spectral-gap problem [36,50] and the experimental study performed in [21] suggested a leading role of PI in this context. Concerning the density limit in the LH current drive, the effects of ionization and resistive losses [51] as well as the LH scattering off density fluctuations have been invoked as a possible explanation [52][53][54][55][56][57].…”