Interaction of an Acoustical Quasi-Gaussian Beam With a Rigid Sphere: Linear Axial Scattering, Instantaneous Force, and Time-Averaged Radiation Force

This work focuses on the interaction of an acoustical quasi-Gaussian beam centered on a rigid immovable sphere, during which at least three physical phenomena arise-the (axial) acoustic scattering, the instantaneous force, and the time-averaged radiation force-which are investigated here. The quasi-Gaussian beam is an exact solution of the source-free Helmholtz wave equation and is characterized by an arbitrary waist, w(0), and a diffraction convergence length known as the Rayleigh range, z(R). Specialized formulations for the scattering and the instantaneous force function, as well as the (time-averaged) radiation force function, are provided. Numerical computations illustrate the variations of the backscattering form function, the instantaneous force function, and the (time-averaged) radiation force function versus the dimensionless frequency ka (where k is the wave number and a is the radius of the sphere); the results show significant differences from the plane wave limit when the dimensionless beam waist parameter kw(0) < 25. The radiation force function may be used to calibrate high-frequency transducers operating with this type of beam. Furthermore, the theoretical analysis can be readily extended to the case of other types of spheres (i.e., elastic, viscoelastic, shells, and coated spheres and shells), providing that their appropriate scattering coefficients are used.