Radiation force of a helicoidal Bessel beam on a sphere

The partial-wave series for the scattering of an acoustic helicoidal Bessel beam by a sphere centered on the axis of the beam is applied to the calculation of the acoustic radiation force by the beam on the sphere in an inviscid fluid. The term "helicoidal" refers to a type of beam having an axial amplitude null and an azimuthal phase gradient. Such a beam is known as an acoustic vortex and only the case of a vortex having a unit magnitude topological charge is considered. There is no monopole contribution to the radiation force. Radiation force examples are computed for a soft sphere, a fixed rigid sphere, a movable rigid sphere, an aluminum sphere in water, and an acrylic sphere in water. Beam parameters are found for the rigid sphere and the aluminum and acrylic cases in which the radiation force is directed opposite the propagation direction of the beam. Negative radiation forces appear to be associated with relatively weak scattering into the backward hemisphere. Some aspects of the low frequency scattering of plane waves and helicoidal Bessel beams are examined for movable rigid spheres.