The evolution of the periodic bottle beam generated by a gradient axicon system is described by a novel method based on the ray-tracing.The transverse intensity distributions of the Bottle beam in propagation are simulated by using the irradiance map function of optical simulation software.It is shown that the region of generating the periodic bottle beam can be controlled by changing the two cone angles of the axicon.The small-size bottle beam can be generated by using the gradient axicon syste...