Theory of selfrefraction effect of intensive focused acoustical beams

The theory of selfrefraction of nonlinear acoustical beams is developed based on some exact and approximate analytical equations and solutions. The system of base equations in geometrical acoustics approximation is sequentially derived from Khokhlov-Zabolotskaya equation for nonlinear focused acoustical beams. The generalized method of extended characteristics allows to set up the simplified closed equation for ray convergence on the beam axis for the most interesting case of small diffraction, when large amplitudes in the focal area are observed. The exact solution is derived in particular case. For the common case of wave parameters there are suggested some analytical approximations and numerical solution. The amplitude dependencies on longitudinal and transversal distances and other wave parameters are obtained. It is shown that at the axis of gaussian beam in the focal area the local minimum of amplitude can be formed. Some initial transversal beamforms, such as gaussian, and initial phase modulation as parabolic or sinusoidal are analyzed.