  The analysis using the partial-wave series expansion (PWSE) method in
spherical coordinates is extended to evaluate the acoustic radiation force
experienced by rigid oblate and prolate spheroids centered on the axis of wave
propagation of high-order Bessel vortex beams composed of progressive, standing
and quasi-standing waves, respectively. A coupled system of linear equations is
derived after applying the Neumann boundary condition for an immovable surface
in a non-viscous fluid, and solved numerically by matrix inversion after
performing a single numerical integration procedure. The system of linear
equations depends on the partial-wave index n and the order of the Bessel
vortex beam m using truncated but converging PWSEs in the least-squares sense.
Numerical results for the radiation force function, which is the radiation
force per unit energy density and unit cross-sectional surface, are computed
with particular emphasis on the amplitude ratio describing the transition from
the progressive to the pure standing waves cases, the aspect ratio (i.e., the
ratio of the major axis over the minor axis of the spheroid), the half-cone
angle and order of the Bessel vortex beam, as well as the dimensionless size
parameter. A generalized expression for the radiation force function is derived
for cases encompassing the progressive, standing and quasi-standing waves of
Bessel vortex beams. This expression can be reduced to other types of
beams/waves such as the zeroth-order Bessel non-vortex beam or the infinite
plane wave case by appropriate selection of the beam parameters. The results
for progressive waves reveal a tractor beam behavior, characterized by the
emergence of an attractive pulling force acting in opposite direction of wave
propagation. Moreover, the transition to the quasi-standing and pure standing
wave cases shows the acoustical tweezers behavior in dual-beam Bessel vortex
beams.
