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In order to find an approximate solution to the Vlasov-Maxwell equationsystem describing the lower hybrid wave propagation in magnetic confinedplasmas, the use of the WKB method leads to the ray tracing equations. TheHamiltonian character of the ray tracing equations is investigated analyticallyand numerically in order to deduce the physical properties of the wavepropagating without absorption in the confined plasma. The consequences of theHamiltonian character of the equations on the travelling wave, in particular,on the evolution of the parallel wavenumber along the propagation path havebeen accounted and the chaotic diffusion of the timeaveraged parallelwave-number towards higher values has been evaluated. Numerical analysis bymeans of a Runge-Kutta based algorithm implemented in a ray tracing codesupplies the analytical considerations. A numerical tool based on thesymplectic integration of the ray trajectories has been developed.

Study of lower hybrid wave propagation in ionized gas by Hamiltonian theory