Effect of the plasma inhomogeneity on the nonlinear damping of monochromatic waves

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Abstract
We study the resonant interaction of particles with a monochromatic wave in an inhomogeneous plasma. The effects of the inhomogeneity are represented by a variable phase velocity of the wave. This introduces, in the wave frame, an inertial force due to the non-Galilean transformation of co-ordinates. Asymptotic expressions are obtained for the spatial damping coefficient of the wave in two physically different cases.(i) When the inertial force is greater than the force due to the trapping (strong inhomogeneity case) instead of the null asymptotic behaviour that one obtains in the homogeneous case, the spatial nonlinear damping coefficient behaves asymptotically like the linear Landau damping coefficient.(ii) When the inertial force is lower than the trapping force (weakinhomogeneity case), the spatial nonlinear damping coefficient for short distances is proportional to the ratio of the inertial force to the trapping force. For long distances, this coefficient is proportional to the square of the preceding ratio multiplied by the number of trapping lengths. In both cases, the proportionality coefficient is the linear spatial Landau damping rate.