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The characteristics of traditional acoustic vortices (AVs) were verified by the cross-sectional axisymmetric pressure distributions with perfect phase spirals around the center pressure null. In order to generate a non-axisymmetric pressure distribution, the concept of power-exponent-phase was first introduced into the formation of AV beams, named "power-exponent-phase acoustic vortices (PAVs)" in this paper. Based on a ring-array of sector transducers, the helical distribution of the low-pressure valley in cross-sections of PAVs, which enables particles to move from a distant position to the center low-potential well along a certain spiral passageway, was proved theoretically. The particle manipulation behavior for PAVs with a power order of 2 is numerically modeled and experimentally confirmed. The results show that PAVs with a non-axisymmetric spiral pressure distribution can be used to realize the directional transport of particles in an enlarged scope, suggesting prospective application potential in biomedical engineering. [ABSTRACT FROM AUTHOR]