Enhancement of ionospheric heating effect by chemical release

TL;DR

This paper proposes using chemical releases to enhance the heating effect of electromagnetic waves on the ionosphere by reducing energy absorption.

Contribution

A novel method using SF6 chemical release to create electron density holes and improve ionospheric heating efficiency is proposed.

Findings

Releasing SF6 reduces pump wave absorption in the low ionosphere.

Electron density holes formed by chemical release focus heating beams and enhance heating effects.

Three-dimensional ray tracing confirms improved propagation characteristics in ionospheric holes.

Abstract

The ionosphere can be artificially modified by employing ground-based high-power high-frequency electromagnetic waves to irradiate the ionosphere. This modification is achieved through the nonlinear interaction between the electromagnetic waves and the ionospheric plasma, leading to changes in the physical properties and structure of the ionosphere. The degree of artificial modification of the ionosphere is closely related to the heating energy density of high-frequency pump waves. Due to the high density of neutral constituents in the lower ionosphere and the high frequency of electron-neutral collisions, the energy of heating pump waves will be absorbed and attenuated during the penetration of the low ionosphere, seriously affecting the heating effect. This paper proposes a method to reduce the absorption of ionospheric heating pump waves by releasing electron attachment chemicals into low ionosphere to form a large-scale electron density hole. A model for mitigating pump waves absorption based on SF6 release is established, and the absorption at different frequencies is quantitatively calculated. The propagation characteristics of high-frequency signals in ionospheric holes are studied using a three-dimensional ray tracing method, and the results demonstrate that the chemical release method not only reduces the absorption attenuation of heating pump waves but also forms spherical electron density holes, which exhibit a focusing effect on the heating beam and enhance the heating effect. The results are of great significance for understanding the nonlinear interaction between electromagnetic wave and ionospheric plasma and improving the ionospheric heating efficiency.

Figures

Evolution of the effect of releasing 30 kg SF_6_ at 100 km altitude.Figure 2Evolution of the effect of releasing 30 kg SF_6_ at 120 km altitude.

Electron-neutral component collision frequency profiles.

Variation of incident wave absorption coefficient with altitude (left: 5 MHz, right: 7 MHz).

Variation of incident wave absorption coefficient with altitude (600 s-100 km-30 kg SF_6_, left: 5 MHz, right: 7 MHz).

Variation of incident wave absorption coefficient with altitude (600 s-120 km-30 kg SF_6_, left: 5 MHz, right: 7 MHz).

Propagation process of electromagnetic signals at different frequencies after releasing 30 kg SF_6_ at an altitude of 100 km for 1000 s.Figure 8Propagation process of electromagnetic signals at different frequencies after releasing 30 kg SF_6_ at an altitude of 120 km for 1000 s.

Full text

Introduction

Since the discovery of the Luxembourg Effect^1^ in the 1930s, active modification of the space environment has become a research focus for countries worldwide. Using ground-based radio transmitters, high-power, high-frequency radio waves are emitted into the ionosphere. Through the nonlinear interaction with ionospheric plasma, it excites various parametric instabilities, and then alter the distribution of electron temperature and density in the heated region through processes like thermal convection and diffusion. This, in turn, generates localized structures of electron density irregularities aligned along the geomagnetic field and other nonlinear perturbations that alter the physical properties of the local ionosphere, collectively referred to as “ionospheric heating”^2–7^. In the 1970s, the first ionospheric heating experimental facility was constructed and operated in Platteville, Colorado, USA, yielding a series of remarkable achievements^8^. In view of the characteristics of the ionosphere as a natural plasma laboratory, as well as the potential application of various nonlinear effects observed during ionospheric heating, Western countries, led by the United States, established multiple high-power high-frequency (HF) transmitters to investigate the nonlinear processes involved in ionospheric heating, thereby promoting the development of the ionospheric plasma physics research. These ionospheric heating facilities are predominantly located in high-latitude regions of the Northern Hemisphere, including the Sura heating station constructed by the former Soviet Union^9^, the HIPAS and HAARP stations in Alaska^10,11^, USA, and the Tromsø station in Norway^12,13^. Additionally, there are two stations situated in mid-to-low latitude regions: the Platteville station in Colorado and the Arecibo station in Puerto Rico^14,15^.

The ionospheric plasma is a time-varying medium exhibiting distinct spatiotemporal characteristics, and its heating effects demonstrate features related to solar activity, seasons, and diurnal variations. The ionospheric heating effect is stable during nighttime; however, during the pre-sunrise and midday periods, the effective radiated power reaching the heating altitudes is reduced due to the absorption effects in the low ionosphere. This results in lower trigger efficiency and poorer heating experimental effect^16,17^.

This study addresses the demand for mitigating the absorption effects of high-frequency radio wave heating in the lower ionosphere. A large number of studies and experiments have been carried out on ionospheric hole and electron density irregularities caused by the chemical release^18–21^. However, there are no relevant reports on the use of electrons attachment by chemical release to achieve low ionospheric absorption reduction of heat pump beam. Hence, we propose a method to mitigate the absorption of ionospheric heating pump waves by releasing electron attachment chemicals at low ionospheric altitudes. A model for mitigating ionospheric heating absorption based on SF_6_ release is established, and the absorption of pump waves at different frequencies is quantitatively calculated. The propagation characteristics of high-frequency signals in ionospheric holes are studied using a three-dimensional ray tracing method, and the results demonstrate that the chemical release method not only reduces the absorption attenuation of heating pump waves but also forms spherical electron density holes, which exhibit a focusing effect on the heating beam and enhance the heating effect. The research of this study provides important theoretical support for studying the nonlinear interaction processes between electromagnetic waves and ionospheric plasma and improving the efficiency of ionospheric heating.

The low ionospheric chemical release theory

Ionospheric chemical release refers to the injection of chemicals into ionospheric altitudes using sounding rockets, satellites, and spacecraft, among other launch vehicles. This artificial manipulation modifies the composition and structure of the ionospheric plasma, resulting in significant short-term changes in the ionosphere^22–25^. The release of ionospheric chemicals holds significant importance for the in-depth investigations into the dynamics and coupling mechanisms of the ionospheric system, the study of ionospheric instability excitation mechanisms and processes, and the construction of a new instability theory system.

Chemicals diffusion

In the initial stage of chemical release, under the influence of pressure, the release pushes the surrounding plasma away like a snowplow. This process occurs at supersonic speeds and lasts only a few seconds. Subsequently, the pressure difference rapidly decreases until it becomes comparable to the background pressure. At this point, the released material and the surrounding plasma mix thoroughly and begin to diffuse into space. This diffusion process takes a long time and in which the ionic chemical reaction mainly occurs.

The diffusion equation is expressed as:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{\partial n_{i} }}{\partial t} = D[\frac{{\partial^{2} n_{i} }}{{\partial x^{2} }} + \frac{{\partial^{2} n_{i} }}{{\partial y^{2} }} + \frac{{\partial^{2} n_{i} }}{{\partial z^{2} }}]$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D$$\end{document} is the diffusion coefficient, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n_{i} (x,y,z,t)$$\end{document} is the number density of releases and satisfies \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n_{i} (x,y,z,0) = N_{0} \delta (x,y,z)$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_{0}$$\end{document} is the total number of molecules released.

Considering the release at the beginning of the release as a point source. Under the assumption of a stratified background ionosphere and thermosphere, the diffusion process of the released material can be approximated by the following equation^23^:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{gathered} n_{i} (r,z,t) = \frac{{N_{0} }}{{(4\pi D_{0} t)^{1.5} }}\exp \{ - (z - z_{0} )(\frac{3}{{4H_{\alpha } }} + \frac{1}{{2H_{i} }}) - \alpha t \hfill \\ \begin{array}{*{20}c} {} & {} & {} \\ \end{array} - \frac{{H_{\alpha }^{2} \{ 1 - \exp [ - (z - z_{0} )/(2H_{\alpha } )]\}^{2} }}{{4D_{0} t}} - \frac{{r^{2} \exp [ - (z - z_{0} )/(2H_{\alpha } )]}}{{4D_{0} t}} \hfill \\ \begin{array}{*{20}c} {} & {} & {} \\ \end{array} - (\frac{1}{{H_{\alpha } }} - \frac{1}{{H_{i} }})^{2} \frac{{D_{0} t\exp [(z - z_{0} )/(2H_{\alpha } )]}}{4}\} \hfill \\ \end{gathered}$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n_{i} (r,z,t)$$\end{document} is the density of released material as a function of time t and space (r and z are the radial distance from the point source and the altitude of the ionosphere, respectively), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_{0}$$\end{document} is the altitude of the point of release, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_{0}$$\end{document} is the total number of molecules released, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D_{0}$$\end{document} is the release point diffusion coefficient. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{\alpha } = kT/m_{a} g$$\end{document} is the atmospheric scale altitude and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{i} = kT/m_{i} g$$\end{document} is the released gas scale altitude, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document} is the Boltzmann constant, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T$$\end{document} is the neutral gas temperature, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_{a}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_{i}$$\end{document} are the average molecular weight of the atmosphere and the molecular weight of the released gas, respectively, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g$$\end{document} is the gravitational acceleration, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha t$$\end{document} is the loss term due to chemical reactions.

Chemical reaction of releases with the ionosphere

The main chemical reaction processes of SF_6_ in the ionospheric plasma are shown in Table 1. Among the four equations in Table 1, the reaction efficiency of Eqs. (3) and (4) is very low due to the low O^+^ density at 100 km and 120 km altitude, and they belong to the secondary reactions. In Eqs. (1) and (2), Eq. (2) is more important than Eq. 1, because the reaction coefficient k_2_ of Eq. (2) is much larger than k_1_.Table 1. Reactions stimulated by SF_6_ release in ionosphere^26^.IndexReaction equationReaction rate (cm^3^/s)1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$SF_{6} + e^{ - } \underset{{k_{a} }}{\overset{{k_{1} }}{\longleftrightarrow}}\left( {SF_{6}^{{^{ - } }} } \right)^{*} \mathop{\longrightarrow}\limits^{{k_{b} }}SF_{6}^{ - }$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{gathered} k_{1} = {{2.2 \times 10^{ - 7} } \mathord{\left/ {\vphantom {{2.2 \times 10^{ - 7} } {\left[ {1 + 640\,\exp \left( { - 4770/T} \right)} \right]}}} \right. \kern-0pt} {\left[ {1 + 640\,\exp \left( { - 4770/T} \right)} \right]}} \hfill \\ k_{a} = 4.00 \times 10^{4} \,s^{ - 1} \hfill \\ k_{b} = {{k_{a} } \mathord{\left/ {\vphantom {{k_{a} } {10}}} \right. \kern-0pt} {10}} \hfill \\ \end{gathered}$$\end{document} 2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$SF_{6} + e^{ - } \mathop{\longrightarrow}\limits^{{k_{2} }}SF_{5}^{ - } + F$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{2} = 2.2 \times 10^{ - 7} - k_{1}$$\end{document} 3 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$SF_{6}^{ - } + O^{ + } \mathop{\longrightarrow}\limits^{{k_{5} }}SF_{6} + O^{*}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{5} \approx 5 \times 10^{ - 8}$$\end{document} 4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$SF_{5}^{ - } + O^{ + } \mathop{\longrightarrow}\limits^{{k_{6} }}SF_{6} + O$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{6} \approx k_{5}$$\end{document}

Plasma diffusion

The change in electron density in the release region of ionospheric chemicals disrupts the existing density distribution structure and dynamic equilibrium of charged particles. According to plasma diffusion theory, the transport equation for plasma can be derived as follows^27^:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{gathered} \frac{{\partial n_{p} }}{\partial t} = \sin^{2} I\left( {\frac{\partial D}{{\partial z}}\frac{{\partial n_{p} }}{\partial z} + D\frac{{\partial^{2} n_{p} }}{{\partial z^{2} }} + \frac{{n_{p} }}{{T_{p} }}\frac{\partial D}{{\partial z}}\frac{{\partial T_{p} }}{\partial z} + \frac{D}{{T_{p} }}\frac{{\partial n_{p} }}{\partial z}\frac{{\partial T_{p} }}{\partial z} - \frac{{Dn_{p} }}{{T_{p}^{2} }}\frac{{\partial^{2} T_{P} }}{{\partial z^{2} }} + \frac{{Dn_{p} }}{{T_{P} }}\frac{{\partial^{2} T_{P} }}{{\partial z^{2} }}} \right) \hfill \\ \begin{array}{*{20}c} {} & {} \\ \end{array} + \sin I\cos I\left( {\frac{\partial D}{{\partial z}}\frac{{\partial n_{p} }}{\partial x} + D\frac{{\partial^{2} n_{p} }}{\partial x\partial z}} \right) + \sin I\sin \gamma \left( {\frac{\partial D}{{\partial z}}\frac{{\partial n_{p} }}{\partial y} + D\frac{{\partial^{2} n_{p} }}{\partial y\partial z}} \right) \hfill \\ \begin{array}{*{20}c} {} & {} \\ \end{array} + \sin^{2} I\left( {\frac{{n_{p} }}{{H_{p} }}\frac{\partial D}{{\partial z}} + \frac{D}{{H_{p} }}\frac{{\partial n_{p} }}{\partial z} - \frac{{Dn_{p} }}{{H_{P}^{2} }}\frac{{\partial H_{p} }}{\partial z}} \right) - v_{D} \cdot \sin I\frac{{\partial n_{p} }}{\partial z} \hfill \\ \begin{array}{*{20}c} {} & {} \\ \end{array} + \sin I\cos I\left( {D\frac{{\partial^{2} n_{p} }}{\partial x\partial z} + \frac{D}{{T_{p} }}\frac{{\partial n_{p} }}{\partial x}\frac{{\partial T_{p} }}{\partial z}} \right) + D \cdot \cos^{2} I\frac{{\partial^{2} n_{p} }}{{\partial x^{2} }} + D \cdot \cos I \cdot \sin \gamma \frac{{\partial^{2} n_{p} }}{\partial y\partial x} \hfill \\ \begin{array}{*{20}c} {} & {} \\ \end{array} + \sin I\cos I\left( {\frac{D}{{H_{p} }}\frac{{\partial n_{p} }}{\partial y} - \frac{{Dn_{p} }}{{H_{P}^{2} }}\frac{{\partial H_{p} }}{\partial x}} \right) - v_{D} \cdot \cos I\frac{{\partial n_{p} }}{\partial x} \hfill \\ \begin{array}{*{20}c} {} & {} \\ \end{array} + \sin \gamma \sin I\left( {D\frac{{\partial^{2} n_{p} }}{\partial z\partial y} + \frac{D}{{T_{p} }}\frac{{\partial n_{p} }}{\partial y}\frac{{\partial T_{p} }}{\partial z}} \right) + D \cdot \sin \gamma \cos I\frac{{\partial^{2} n_{p} }}{\partial x\partial y} + D \cdot \sin^{2} \gamma \frac{{\partial^{2} n_{p} }}{{\partial y^{2} }} \hfill \\ \begin{array}{*{20}c} {} & {} \\ \end{array} + \sin \gamma \sin I\left( {\frac{D}{{H_{p} }}\frac{{\partial n_{p} }}{\partial y} - \frac{{Dn_{p} }}{{H_{P}^{2} }}\frac{{\partial H_{p} }}{\partial y}} \right) - v_{D} \cdot \sin \gamma \frac{{\partial n_{p} }}{\partial y} + P_{p} - L_{p} \hfill \\ \end{gathered}$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n_{p}$$\end{document} is the density of ions or electrons; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_{p}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{p}$$\end{document} represent the production and recombination rates of charged particles, respectively. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{p} = L_{0} + \sum\limits_{i = 1}^{M} {\,K_{1i} n_{p} n_{i} }$$\end{document} , where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{0}$$\end{document} is the loss rates of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O^{ + }$$\end{document} reacting with other particles and photochemical reactions, the released neutral gas consists of M species of neutral molecules, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n_{i}$$\end{document} represents the chemical reaction rate between species \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$i$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O^{ + }$$\end{document} ; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{p} = (T_{e} + T_{i} )/2$$\end{document} is the plasma temperature; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{p}$$\end{document} is the plasma scale altitude , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{p} = 2T_{p} k/(m_{p} g)$$\end{document} ; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I$$\end{document} is the magnetic inclination angle, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma$$\end{document} is the magnetic declination Angle; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D$$\end{document} is the effective bipolar diffusion coefficient, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D = (1 + T_{e} /T_{i} )D_{i}$$\end{document} , where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D_{i}$$\end{document} is the ion diffusion coefficient; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_{D}$$\end{document} represents the applied drift velocity (wind speed).

Numerical simulation of ionospheric heating absorption attenuation

Simulation of ionospheric depletion region generation and evolution

In order to study the method of eliminating the absorption of high frequency radio waves in the lower ionosphere by releasing electron-attached chemicals, the background ionosphere generated by IRI2020 model at 12:00 local time on April 15, 2022 in Hainan region was numerically simulated. The ionospheric disturbance effects resulting from the release of 30 kg of SF_6_ at altitudes of 100 km and 120 km were simulated. As shown in Fig. 1 and Fig. 2.Figure 1. Evolution of the effect of releasing 30 kg SF_6_ at 100 km altitude.Figure 2. Evolution of the effect of releasing 30 kg SF_6_ at 120 km altitude.

From the simulation results, it can be observed that the maximum ionospheric hole diameter formed by the release of 30 kg SF_6_ at an altitude of 100 km is approximately 25 km. The maximum ionospheric hole diameter formed by releasing 30 kg SF_6_ at an altitude of 120 km is about 30 km, and the electron density is close to complete depletion. It should be noted that when releasing chemicals at low ionospheric altitudes, the smaller diffusion coefficient of the released material results in smaller ionospheric hole scales, requiring higher control of the release point in space experiments.

Calculation of low ionospheric absorption attenuation for typical time periods

According to the absorption attenuation theory, the total absorption attenuation L of the lower ionosphere can be expressed as^28^:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{L = }}\frac{{e^{2} }}{{2\varepsilon_{0} mcu}}\frac{{n_{e} v}}{{w^{2} + v^{2} }}S$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n_{e}$$\end{document} is the electron density, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon_{0}$$\end{document} is the vacuum permittivity, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c$$\end{document} is the speed of light, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document} is the magnetic permeability, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m$$\end{document} is the electron mass, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$e$$\end{document} is the elementary charge, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v$$\end{document} is the collision frequency, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$w$$\end{document} is the incident wave frequency, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S$$\end{document} is the propagation distance.

The collision frequency \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v$$\end{document} can be expressed as^29^:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v = \frac{{5.45 \times 10^{ - 5} n}}{{T^{3/2} }}$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document} is the neutral component density (cm^−3^) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T$$\end{document} is the temperature.

According to the atmosnrlmsise00 model, the altitude profiles of neutral component density and temperature are calculated. The following seven neutral molecules are considered in the calculation process: He, O, N_2_, O_2_, Ar, H and N. Based on this, the profile of electron-neutral molecule collision frequency is computed, as depicted in Fig. 3.Figure 3. Electron-neutral component collision frequency profiles.

Based on the theory of absorption attenuation in the low ionosphere and the above analyses, the altitude distribution of absorption coefficients at 5 MHz and 7 MHz is calculated as shown in Fig. 4. By integrating the absorption coefficients over altitude, the total absorption attenuation is 4.77 dB for 5 MHz and 2.43 dB for 7 MHz in the altitude range of 40 − 240 km. The maximum absorption altitude varies under different ionospheric backgrounds (different locations, seasons, solar activity) and heating frequencies. To enhance the heating effect using electron-captured material release methods, the release altitude of the material needs to be optimized based on the ionospheric background conditions and heating frequency.Figure 4. Variation of incident wave absorption coefficient with altitude (left: 5 MHz, right: 7 MHz).

Evaluation of absorption elimination effect in the low ionosphere

At an altitude of 100 km, after a time period of 600 s following the release, the total absorption attenuation is calculated to be 1.04 dB for the 5 MHz incident wave and 0.53 dB for the 7 MHz incident wave in the altitude range of 40–240 km. The distribution of absorption attenuation coefficients is illustrated in Fig. 5.Figure 5. Variation of incident wave absorption coefficient with altitude (600 s-100 km-30 kg SF_6_, left: 5 MHz, right: 7 MHz).

At an altitude of 120 km, 600 s after release, using the same calculation method for absorption coefficients as mentioned above, the total absorption of 5 MHz incident wave is calculated to be 4.16 dB, and the total absorption of 7 MHz incident wave is calculated to be 2.12 dB in the range of 40-240 km altitude. The distribution of absorption attenuation coefficients is shown in Fig. 6.Figure 6. Variation of incident wave absorption coefficient with altitude (600 s-120 km-30 kg SF_6_, left: 5 MHz, right: 7 MHz).

Heating antenna 3 dB beamwidth: 19.5/24@5 MHz, 17/21.8@7 MHz. Based on this, the antenna beam diameter at an altitude of 100 km is approximately 35 km@5 MHz and 33 km@7 MHz. At an altitude of 120 km, the antenna beam diameter is approximately 42 km@5 MHz and 40 km@7 MHz. The ionospheric holes created by the release at 100 km have a diameter of approximately 25 km, while at 120 km, the ionospheric holes have a diameter of approximately 30 km. The scale of the ionospheric holes can cover about 70–80% of the heating antenna beam.

Radio wave propagation in the modulated ionosphere

In order to further investigate the impact of the ionospheric depletion structure generated by SF_6_ release on the information transmission link, shortwave ray tracing was conducted to simulate the changes in the propagation path and direction of the shortwave signals at different frequencies after traversing the depletion region. Ray tracing is an effective method for studying the ionospheric wave propagation, especially for radio wave signals above the high frequency band. It can accurately describe the propagation paths of electromagnetic waves^30–32^. In this section, a three-dimensional numerical ray tracing method is used to study the propagation characteristics of shortwave signals in the artificial depletion region.

To further investigate the propagation characteristics of the heating pump wave beam in controlling the ionosphere, based on the half-power beamwidth of the heating pump wave beam, the short-wave ray tracing results of the 4–9 MHz ionospheric heated pump wave at an altitude of 100 km and 120 km with the release of 30 kg of SF_6_ are given in Figs. 7, 8, respectively, at 1000 s after the release.Figure 7. Propagation process of electromagnetic signals at different frequencies after releasing 30 kg SF_6_ at an altitude of 100 km for 1000 s.Figure 8. Propagation process of electromagnetic signals at different frequencies after releasing 30 kg SF_6_ at an altitude of 120 km for 1000 s.

From Figs. 7, 8, it can be observed that by releasing electron attachment chemicals such as SF_6_ at low ionospheric altitudes, a large-scale electron-depleted region is formed, which can cover more than 80% of the heating beam area. This not only reduces the absorption attenuation of the heating pump wave but also, due to the formation of a spherical electron-density hole, the refractive index inside the hole is lower than that of the surrounding plasma. As a result, the heating pump wave beam becomes concentrated in a smaller area, leading to increased heating energy density. This is beneficial for generating a focusing heating effect and enhancing the overall heating efficiency.

Conclusion and discussion

Enhancing the efficiency of ionospheric heating is one of the important research topics in ionospheric heating technology. It is expected that the absorption effect of high-frequency pump wave energy in the low ionosphere can be greatly reduced by releasing neutral gas into the low ionosphere to form ionospheric electron density holes. This paper proposes, for the first time, a method to reduce the absorption of ionospheric heating pump waves by releasing electron attachment chemicals at low ionospheric altitude s to form a large-scale electron density hole. A model for mitigating the absorption of ionospheric heating based on SF_6_ release is established, and the absorption mitigation effects of different frequency pump waves are quantitatively calculated. The propagation characteristics of short-wave signals in ionospheric holes are studied using a three-dimensional ray tracing method, and the results show that the method of releasing electron attachment chemicals not only reduces the absorption attenuation of the heating pump waves but also creates spherical electron density holes that contribute to the generation of a focusing heating effect, thereby enhancing the overall heating efficiency. By combining ionospheric heating and ionospheric chemical release, this study explores approaches and methods to improve the efficiency of ionospheric heating. The results are of great significance for studying the nonlinear interaction between electromagnetic wave and ionospheric plasma and improving the heating efficiency of the ionosphere.

The following conclusions are obtained from theoretical modelling and simulation calculations:

• (1). Releasing SF_6_ gas at an appropriate altitude can significantly reduce the absorption attenuation of high-frequency electromagnetic waves in the low ionosphere by creating ionospheric electron density holes.
• (2). The maximum absorption altitude varies under different ionospheric backgrounds (different locations, seasons, solar activity) and heating frequencies, and the release altitude of the chemical needs to be optimized based on the ionospheric background conditions and heating frequency.
• (3). Due to the small diffusion coefficient of the released chemical, the ionospheric hole scale is small, so it is necessary to control the release location precisely in the space experiment of the low ionospheric chemical release.
• (4). By releasing electron attachment chemicals such as SF6 at low ionospheric altitudes, a large-scale electron-density depletion region is formed. This method reduces the absorption attenuation of the heating pump waves. Additionally, the formation of spherical electron-density hole results in a lower refractive index compared to the surrounding plasma. As a result, the heating pump wave beam becomes concentrated in a smaller area, which can increase the heating energy density. This is beneficial for generating a focusing heating effect and enhancing the overall heating efficiency.