Asymptotic analysis of lower hybrid wave propagation in tokamaks

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Abstract
An asymptotic analysis of the lower hybrid wave propagation in toroidal geometry is presented which relies on the difference in magnitude between the parallel and perpendicular wave vectors when the wave frequency is of the order of the ion plasma frequency. Using the method of matched asymptotic expansions, the equation for the radial position of the ray is solved and the effects of the toroidal corrections are discussed. Moreover, the equation for the parallel wave vector is derived and analytically solved by using a multiple scale analysis. The latter solution is asymptotically matched to a local exact solution near the plasma edge where the multiple scale analysis breaks down. The result of the asymptotic analytical treatment is compared with the findings of a numerical integration of the starting set of equations. Finally, using the previous results, the equation for the variation of the electric field amplitude along the trajectory is analytically solved.