universe Review The Generation of ULF/ELF/VLF Waves in the Ionosphere by Modulated Heating Zhe Guo 1,2 , Hanxian Fang 1,* and Farideh Honary 2 1 College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China; [email protected] 2 Department of Physics, Lancaster University, Lancaster LA1 4YB, UK; [email protected] * Correspondence: [email protected] Abstract: One of the most important effects of ionospheric modification by high power, high fre- quency (HF) waves is the generation of ultra low frequency/extremely low frequency/very low frequency (ULF/ELF/VLF) waves by modulated heating. This paper reviews the scientific achieve- ments of the past five decades regarding the main mechanisms of excitation of ULF/ELF/VLF waves and discusses their characteristics, such as their electrojet dependency, the location of the source region, continuous and discontinuous waves, the number of HF arrays, and the suitable range of the modulation frequency for different proposed mechanisms. Finally, the outlook for future research in this area is presented. Keywords: powerful HF waves; ULF/ELF/VLF waves; modulated heating; ionospheric heating 1. Introduction Ultra low frequency (ULF, below 3 Hz)/extremely low frequency (ELF, 3-3000 Hz)/very low frequency (VLF, 3–30 kHz) [1] waves are important not only for the navigation, commu- Citation: Guo, Z.; Fang, H.; Honary, nication, and detection of underground targets, but also for the precipitation of energetic F. The Generation of ULF/ELF/VLF electrons in radiation belts, in order to protect astronauts and spacecrafts operating in Waves in the Ionosphere by these regions [2]. This is because, firstly, ULF/ELF/VLF waves can travel thousands Modulated Heating. Universe 2021, 7, of kilometers in the Earth-ionospheric waveguide. Secondly, ULF/ELF/VLF waves can 29. https://doi.org/10.3390/ propagate upwards, into the magnetosphere. The magnetosphere is a large, natural plasma universe7020029 laboratory that is filled with a large number of high-energy electrons. The energy of these Received: 17 December 2020 high-energy electrons ranges from about ~100 keV to several MeV, and electrons with a Accepted: 26 January 2021 higher energy (>2 MeV) are called “relativistic electrons” or “killer electrons”, which can Published: 29 January 2021 damage or even “kill” satellites. These “killer electrons” can be precipitated through the process of wave-particle interactions with ULF/ELF/VLF waves. This effect is of great Publisher’s Note: MDPI stays neutral practical significance with regards to eliminating the natural radiation belts or artificial with regard to jurisdictional claims in radiation belts caused by high-altitude nuclear explosions [3–5]. However, there are some published maps and institutional affil- disadvantages of directly transmitting ULF/ELF/VLF waves by ground-based antenna iations. arrays, such as the very large floor space, poor flexibility, low radiation efficiency, and high costs of use and maintenance, so there are difficulties in building such antenna arrays [6,7]. For example, the US Navy’s VLF antenna (as shown in Figure1) consists of 26 towers and the height of each is 850 to 1000 ft. Moreover, the power of 18 MW consumed by the Copyright: © 2021 by the authors. antenna is obtained from a dedicated power plant [8]. Furthermore, in the 1960s, the US Licensee MDPI, Basel, Switzerland. Navy devised a plan to build an ELF antenna called Project Sanguine, which would have This article is an open access article taken up 41 percent of the area of Wisconsin, but this project never came to fruition, mainly distributed under the terms and due to its overwhelming cost and the potential environmental impact [9]. Based on the conditions of the Creative Commons above reasons, alternate methods are in demand. Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Universe 2021, 7, 29. https://doi.org/10.3390/universe7020029 https://www.mdpi.com/journal/universe Universe 2021, 7, 29 2 of 18 Universe 2020, 6, x FOR PEER REVIEW 2 of 17 FigureFigure 1. Very 1. Very low frequencylow frequency (VLF) antenna (VLF) ofantenna the US Navy. of the US Navy. IonosphericIonospheric heating heating by high by power, high high power, frequency high (HF,frequency 3–30 MHz) (HF, [10 3-30] radio MHz) waves [10] radio waves is a method of artificially modifying the ionosphere by transmitting high frequency radio is a method of artificially modifying the ionosphere by transmitting high frequency radio waves that can interact with ionospheric plasma and excite a series of non-linear physical processes.waves that The studycan interact of ionospheric with heatingionospheric by high plasma power high and frequency excite a radioseries waves of non-linear is physical anprocesses. interdisciplinary The study field of of radio ionospheric wave propagation, heating space by high science, power and plasma high frequency physics. It radio waves is hasan always interdisciplinary been an important field research of radio direction wave ofpropagation, space physics andspace radio science, physics. and The plasma physics. theoreticalIt has always study of been ionospheric an important heating includes research two direction kinds of non-linear of space effects: physics (1) Theand radio physics. thermal effect dominated by Ohmic heating and (2) parametric instability and electron accelerationThe theoretical due to the study electric of waveionospheric field. heating includes two kinds of non-linear effects: 1) TheIonospheric thermal effect modulated dominated heating by by high Ohmic power heating HF waves and is carried 2) parametric out by transmitting instability and electron HFacceleration waves modulated due byto ULF/ELF/VLFthe electric wave waves field. into the ionosphere, so that the ionosphere radiatesIonospheric expected ULF/ELF/VLF modulated waves heating under by ahigh series powe of non-linearr HF waves effects. is carried With the out by transmit- continuous improvement of theoretical and experimental research, modulated heating has becometing HF one waves of the mostmodulated significant by applications ULF/ELF/VLF of ionospheric waves into heating, the consistingionosphere, of a so that the iono- seriessphere of modulation radiates methodsexpected based ULF/ELF/VLF on different mechanisms. waves un Streltsovder a series et al. [ 11of] reviewednon-linear effects. With thethe various continuous modulation improvement methods and of providedtheoretical an excellentand experimental summary of research, experimental modulated heating andhas theoretical become investigationsone of the most regarding significant the different applicat ULF/ELF/VLFions of ionospheric wave generation heating, consisting of mechanisms.a series of Thismodulation review paper methods is focused based on theon characteristicsdifferent mechanisms. of each modulation Streltsov et al. [11] re- method and discusses topics that have not been covered in previous reviews, such as theviewed controversy the various of Beat Wavemodulation Modulation methods and the and new provided theory of Thermal an excellent Cubic Non-summary of experi- Linearity.mental Inand particular, theoretical the characteristics investigations of various regarding modulation the different methods are ULF/ELF/VLF summarized wave genera- andtion compared mechanisms. and two This possible review methods paper for is resolving focused theon controversythe characteristics of Beat Wave of each modulation Modulationmethod and are proposed.discusses topics that have not been covered in previous reviews, such as the The idea of generating ULF/ELF/VLF waves by ionospheric modulated heating was firstcontroversy proposed by of Willis Beat and Wave Davis Modulation [12], and was soon and tested the new successfully theory for of the Thermal first time Cubic by Non-Linear- Getmantsevity. In particular, et al. [13]. Itsthe basic characteristics principle is that of the va highrious frequency, modulation high power methods transmitter are summarized and “heater”compared is switched and two on and possible off with methods the frequency for resolving of the desired the ULF/ELF/VLFcontroversy of waves, Beat Wave Modula- givingtion riseare toproposed. increases and decreases of the local electron temperature with the modulation frequency.The Such idea periodic of generating changes in ULF/ELF/VLF the electron temperature waves cause by ionospheric corresponding modulated changes heating was in the electron density and conductivity, generating the modulation current. In the presence offirst an electrojet proposed in the by ionosphere, Willis and the Davis modulated [12], current and wa enhancess soon the tested current successfully and radiates for the first time theby low Getmantsev frequency signalet al. [13]. (as shown Its basic in Figure principle2[ 14]). is Thisthat methodthe high is frequency, called Amplitude high power transmit- ter “heater” is switched on and off with the frequency of the desired ULF/ELF/VLF waves, giving rise to increases and decreases of the local electron temperature with the modulation frequency. Such periodic changes in the electron temperature cause corresponding changes in the electron density and conductivity, generating the modulation current. In the presence of an electrojet in the ionosphere, the modulated current enhances the current and radiates the low frequency signal (as shown in Figure 2 [14]). This method is called Amplitude Mod- ulation (AM). Several other modulation methods that have the same