Theoretical analysis of propagation characteristics of ionospheric vortex heating waves

Vortex beam heating is a research hotspot in ionospheric heating experimental technique. The existing research work focuses on the analysis and interpretation of experimental phenomena, while there are few discussions about the propagation characteristics and spatial distribution characteristics of vortex heating waves. Based on the Fresnel diffraction theory, the propagation characteristics of vortex beam are analyzed and analytical expression is deduced using the reciprocal conversion between Hermitian-Gaussian mode and Laguerre-Gaussian mode. The invariance of the expression form of vortex beam propagating in free space is proved. Then, the relationship between vortex field distribution and the order of Laguerre-Gaussian mode is studied, and the solving method and formula of peak power direction are derived, which can play a guiding role in achieving the controllable spatial distribution of vortex heating field. The research provides some theoretical guidance for the further study of ionospheric heating with vortex beam.