  In order to find an approximate solution to the Vlasov-Maxwell equation
system describing the lower hybrid wave propagation in magnetic confined
plasmas, the use of the WKB method leads to the ray tracing equations. The
Hamiltonian character of the ray tracing equations is investigated analytically
and numerically in order to deduce the physical properties of the wave
propagating without absorption in the confined plasma. The consequences of the
Hamiltonian character of the equations on the travelling wave, in particular,
on the evolution of the parallel wavenumber along the propagation path have
been accounted and the chaotic diffusion of the timeaveraged parallel
wave-number towards higher values has been evaluated. Numerical analysis by
means of a Runge-Kutta based algorithm implemented in a ray tracing code
supplies the analytical considerations. A numerical tool based on the
symplectic integration of the ray trajectories has been developed.
