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The production of acoustical vortices-based potential wells for particle trapping is not only restricted to the use of a Laguerre-Gaussian beam. Other useful types of vortex beams include an r-vortex beam, a non-diffracting high-order Bessel and Bessel-Gauss beam, a fractional (diffracting) highorder Bessel beam, a non-diffracting high-order Bessel beam of fractional type α, and a hypergeometric beam to name a few. Representative types of vortex beams are chosen here, but the examples are not exhaustive and additional categories of vortex beams may be reported and investigated. Expressions for the incident acoustic pressure field of various vortex beams are provided. The results should assist in the development of a multitude of vortex-based potential-well models for particle entrapment and manipulation.