The acoustic radiation force of Langevin type resulting from the interaction of a high-order Bessel beam with a rigid immovable sphere in an ideal fluid is theoretically investigated. The analysis is based on applying the generalized Rayleigh series used in the near-field acoustic scattering problem to calculate the force. With appropriate selection of specific Bessel beam parameters, results for the rigid sphere unexpectedly reveal a negative radiation force caused by the Lagrangean energy density. Specifically, the negative force on the rigid sphere arises when the kinematic energy density is larger than the potential energy density. This condition provides an impetus for further designing acoustic tweezers operating with high-order Bessel beams of progressive waves for potential applications in particle entrapment and manipulation.