大功率电波加热电离层中热自聚焦不稳定性的理论研究和数值模拟

Theoretical analysis and numerical simulation of thermal self-focusing instability caused by powerful HF radio waves used in ionospheric heating experiments

本文首先从电子密度及电子温度的输运方程和考虑自作用时的电磁波波动方程出发,利用简正模展开的方法推导出泵波在反射区域激发出热自聚焦不稳定性（thermal self-focusing instabilities,TSFI）所需电场阈值以及其增长率的完整数学表达式,并估算了TSFI激发阈值及所对应的有效辐射功率（ERP）的量级.随后利用三维垂直加热的理论模型,结合国际参考电离层（IRI-2012）和中性大气模型（MSIS-E-00）给出的背景参数,数值模拟了大功率高频泵波加热电离层时泵波反射区域电子密度及电子温度因TSFI而产生的变化及发展的过程,并对比分析了不同背景参数对较热效果的影响.结果表明：当高频泵波的加热阈值达到或超过百毫伏每米的量级时,即可激发TSFI,发展出大尺度电子密度及温度不均匀体,这些不均匀体内的密度耗空约为4%~10%,而电子温度剧烈增长,到达背景温度值的1.6~2.1倍;且在相当的加热条件下,背景电子温度越低、电子密度越小,加热效果越显著;电子密度及电子温度的扰动幅度随着加热时间的推移而逐渐减小,即扰动逐渐趋于饱和,且电子温度要快于电子密度达到饱和状态.本文还对泵波反射高度处的电子密度及电子温度变化率进行采样并求得其功率谱密度,分析结果表明：TSFI发展出的大尺度不均匀体满足幂律谱结构,谱指数随着加热的进行逐渐趋于稳定,白天与夜间的幂律谱指数区别不大,但电子密度与电子温度的幂律谱有所区别.

Thermal self-focusing effect（TSFI）is an important mechanism for large scale fieldaligned density irregularities generated when powerful HF radio waves incident on the ionosphere.The detailed analysis and accurate simulation of it is meaningful for the study of various non-linear phenomenon generated in ionospheric modulation experiments.The numerical simulation results can also provide some theoretical reference for the ionospheric modulation experiments that may be carried out in our country in the future.Firstly,the mathematical expressions for the excitation threshold value and the growth rate of TSFI are derived by the normal mode expansion approach which couples the transport equations of electron temperature and plasma density and the equation describing wave propagation,and with the adoption of the International Reference Ionosphere（IRI-2012）model and the neutral atmospheric model（MSIS-E-00）as background parameters.Secondly,a threedimensional numerical model for vertical heating of the ionosphere by powerful high-frequency radio waves is presented,and the disturbances of electron density and electron temperature in the pump wave reflection region under different heating conditions are simulated and analyzed in detail.Finally,the electron density and electron temperature fluctuations at the reflection height are evaluated and the corresponding power spectra are computed and analyzed.The calculation shows that TSFI may occur when the heating threshold of HF pump waves reaches or exceeds the magnitude of 100 mV/m,which is consistent with the estimation of classical theory.When the powerful HF pump waves incident to the ionosphere,large-scale fieldaligned irregularities（FAI）are developed near the reflection area of it due to the TSFI.The simulation results show that：1.Lots of density striations with 4% ~10% density depletions formed near the pump wave reflection area and the electron temperature inside the depletions has a strong enhancement which can reach 1.6~2.1times of the background value.2.The heating effects become even stronger for lower background electron temperature and density.3.The perturbation amplitude of electron temperature and density decreases with time and gradually becomes saturated,the time scale of which for electron temperature is much faster than that for electron density.The analysis results of the power spectra of the electron density and electron temperature fluctuations show that：1.The large-scale irregularities caused by TSFI meet the power-law spectrum,but do not approach the stage of turbulence.2.The spectral index gradually stabilizes as the heating continues.3.The difference between the power-law spectral index during the daytime and nighttime is small,but the spectrum of electron density and temperature differs much to each other.The three-dimensional numerical model for ionospheric vertical heating presented in our paper is utilized for simulating the self-consistent development of the density and temperature perturbations due to the TSFI in the pump wave reflection region.The formation and evolution of the irregularities in the daytime and night show marked differences.The simulation results obtained in this paper can be compared with the observation data obtained in the ionospheric modulation experiments probably carried out in the future,in order to verify the accuracy of our results.