On the Second Harmonic Generation through Bell—Plesset Effects in Cylindrical Geometry

Generation of the second harmonic initiated by Bell—Plesset effects in a cylindrical geometry is studied analytically. For an initial single-mode velocity perturbation, the second-order mode-coupling formula is obtained by expanding the perturbation displacement and velocity potential up to the second-order accuracy. It is found that the initially symmetric interface evolves into a significant bubble-spike asymmetric pattern. The second-order solutions clearly show that the amplitude of the spike grows faster than that of the bubble. The temporal evolutions of the amplitudes of the bubble and spike are dependent on the interface velocity V0. The larger interface velocity leads to the smaller amplitude of the perturbation at an arbitrary interface position in a cylindrically convergent geometry.