电离层涡旋加热波的传播特性理论分析

涡旋波加热是目前电离层加热试验技术研究的一个热点，但主要侧重于试验现象的分析和解释，对涡旋加热波传播特性及空间场分布特性的讨论很少.文章从菲涅耳衍射理论出发，利用厄米-高斯模和拉盖尔-高斯模的相互转换关系，对电离层涡旋加热波在自由空间的传播特性进行了理论分析，推导了其解析表达式.结果表明涡旋电磁波在传播时，可保持自身表达形式的不变性.依据解析表达式，仿真分析了涡旋波空间幅相分布与拉盖尔-高斯模阶数的关系，给出了涡旋场峰值波束指向的求解方法和公式.这些结论为利用涡旋波深入开展电离层加热研究，实现可控的涡旋加热场空间分布提供了一定的理论指导.

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 HermitianGaussian 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.