AG_56.05.13_HAO_SHUJI_finalonline:Layout 6 ANNALS OF GEOPHYSICS, 56, 5, 2013, A0566; doi:10.4401/ag-6308 A0566 Influences of the state of ionospheric background on ionospheric heating effects Hao Shuji1, Li Qingliang2, Che haiqin2, Yang Jutao2, Yan Yubo2, Wu Zhensen1,*, Xu Zhenwen2 1 Xidian University, Department of Physics, Xi’an, China 2 China Research Institute of Radiowave Propagation, Qingdao, China ABSTRACT According to the well-performed ionospheric heating experiments at Arecibo in the low latitudes as well as at Tromsø in the high latitudes, the large-scale modification effects are simulated under an assumption of equivalent conditions, i.e., with the same effective radiative power and the same ratio of the heating frequency fHF to the critical frequency of ionospheric F region foF2. The findings are extensively exploited to ver- ify the validation of our model by comparison to the experimental results. Further, a detailed study is carried out on the influences of the back- ground electron density gradient as well as the ratio of fHF to foF2 on heating effects. Conclusions are drawn as follows: under certain condi- tions, a smaller electron density gradient of background ionospheric F re- gion leads to a better ionospheric heating effect; during over-dense heating, the heating effects are enhanced if the ratio of fHF to foF2 increases, which is slightly limited by the resultant elevation of the reflection height. How- ever, there might be a better ratio range with small values of the ratio of fHF to foF2, e.g., [0.5, 0.7] in the current study. Finally, we analyzed how to select heating parameters efficiently under adverse conditions so to ob- tain relatively effective results. 1. Introduction As an active ionospheric research, modification of the ionosphere by powerful high frequency (HF) waves is to date of great scientific interest and rapidly devel- oped in the last several decades since they provide an effective tool for investigations of the Earth environ- ment as well as for understanding various plasma phe- nomena. The heating experiments were successfully performed firstly at Platteville, Colorado [Utlaut 1970], almost simultaneously at Arecibo [Gordon and Showen et al. 1971], in the early 1970s, and subsequently at other ionospheric heating facilities such as Tromsø, SURA, HAARP (The High Frequency Active Auroral Research Program) and SPEAR (Space Plasma Explo- ration by Active Radar). A wide variety of fascinating phenomena are observed, some of which are associated with the development of parametric instabilities and ionospheric turbulence, including enhancement of electron temperature [Mantas et al. 1981], generation of plasma oscillations and field-aligned irregularities [Rietveld et al. 2003, Tereshchenko et al. 2006, Wright and Dhillon 2009], excitation of artificial radio and op- tical emission [Frolov et al. 1999, Pedersen and Carlson 2001, Kosch et al. 2007]. Among the main phenomena, renewed attention is paid to the wave-plasma interac- tion process leading to nonlinear density perturbations at different scales. Large-scale (kilometer size) irregu- larities are best interpreted in terms of thermally driven self-focusing of the incident HF electromagnetic wave [Duncan and Sheerin 1985]. Small-scale (meter size) field-aligned striations are generally explained as differ- ential plasma heating from enhanced Langmuir wave collisional dissipation or HF scatter from the induced plasma oscillations [Blagoveshchenskaya et al. 1995]. Concerning the nature and origin of Langmuir wave, a popular view is the theory of thermal parametric (resonant) instability developed at the upper hybrid res- onance altitude [Das and Fejer 1979]. Only the O-mode propagating in the vertical or nearly vertical direction reaches the resonance region, and the X-mode is al- ways reflected from the region lying below the reso- nance one. In the previous heating experiments, field-aligned irregularities, electron density and anom- alous absorption all occurred only during O-mode heating [Robinson et al. 1998]. Recently experimental evidence of the excitation of strong small-scale field- aligned irregularities was presented due to an X-mode HF pump wave radiated in the direction of magnetic zenith [Blagoveshchenskaya et al. 2011]. In most of studies, the HF-induced electron den- sity profile modification is observed only by a few per- cent. Xu et al. [2009] presented evidence of a density Article history Received February 21, 2013; accepted June 11, 2013. Subject classification: Ionospheric heating, Ionospheric background, Heating effects, Heating parameters, Electron density gradient. depletion by 4-10% with the heating facility at Tromsø with an effective radiated power Perf = 90 MW and heating frequency fHF = 4.04 MHz. Isham et al. [1987] reported a decrease of electron density by 3-5% using the heating facility at Arecibo with Perf = 100 MW and fHF = 5.1 MHz. Duncan et al. [1988] first reported di- rect observations of large electron-density depletions of about 30% with Perf = 60 MW and fHF = 3.175 MHz. Such large depletions were observed reproducibly only after local midnight in the winter ionosphere for ionos- pheric densities critical only for the lowest pump fre- quency available at Arecibo. The state of the background ionosphere is found to be an important factor influ- encing the observed effects. The resultant heating ef- fects and their magnitudes may be different due to discrepancies of ionospheric background and heating parameter settings in specific research processes. Therefore, researchers undertook a series of the- oretical investigations by simulation of the factors in- fluencing the strength of ionospheric heating effects. The basic theory of ionospheric heating was system- atically discussed by Gurevich [1978] who used a set of continuity equation, momentum equation and energy equation. Shoucri et al. [1984] considered the depen- dences of heating effects on Perf and fHF, respectively. Hansen et al. [1992] modeled the large-scale HF-in- duced ionospheric modifications reported by Duncan et al. [1988]. Mingaleva and Mingalev [1997] and Min- galeva et al. [2008] investigated the range of values for fHF to get the best heating effects in mid- or low-lati- tude regions, it is fHF ≈ 0.8 ~ 0.86 foF2 during the day, and fHF ≈ 0.9 ~ 0.96 foF2 at night. In order to perform a detailed study on diversities of heating effects in different areas, an investigation is carried out on the influences of the background elec- tron density gradient as well as the ratio of fHF to foF2 on heating effects in Section 2. Then our final conclu- sions and proposals for future work are presented in Section 3. A theoretical model of ionospheric heating will be built in Appendix A. 2. Analysis of simulation results 2.1. Comparion of simulations with experimental results In order to verify the numerical model described in Appendix A, simulation parameters are selected to be the same with those in the heating experiments listed in Table 1. Density depletions and temperature enhance- ments are found at the reflection height for both cases at Arecibo as well as at Tromsø. In our simulation, the den- sity depletions N1/N0 are about 3.4% at Arecibo. The maximum temperature in the depletions increases about 28.4% which is consistent with the experimental results at 20-30%. For the case at Tromsø, we found the density depletion up to 6.12% and the temperature en- hancement reaching 70.6% which also are in accordance with the measured enhancement of 60-120%. 2.2. Analysis of factors influencing heating effects In the F-region, the heating effects have a close re- lationship with energy absorption via various electron heating channels. Besides the linear Ohmic heating process, the various nonlinear processes with different thresholds, characteristic times, and saturation mecha- nisms may also be excited, depending on the incident power and the state of background ionosphere [Duncan et al. 1988]. Thus, with the values of the pump frequency and Perf selected, the geomagnetic dip and the state of ionospheric background (mainly described by the elec- tron densities and their gradients) have a remarkable im- pact on heating effects (variation of electron density), which will be dealt with in Section 2.2 separately. 2.2.1. Influences of Perf and the dip angle on heating effects Influences of system’s Perf and the geomagnetic dip on heating effects have already been specified in the pre- vious calculations, which will be briefly discussed here. We hence compare the results of heating experiments performed at Tromsø and Arecibo (see Table 1) and find that the two experiments were carried out under differ- HAO SHUJI ET AL. 2 site geographic coordinate fHF (MHz) foF2 (MHz) fHF/foF2 h0 (km) Te1/Te0 at h0 N1/N0 at h0 Arecibo 68.8°W, 18.3°N 5.1 7.44 0.69 200 20% ~ 30% 3% ~ 5% Tromsø 19.2°E, 69.6°N 4.04 4.99 0.81 217 60% ~ 120% 4% ~ 12% Table 1. Parameters of the heating experiments carried out at Arecibo [Isham et al. 1987] and Tromsø [Xu et al. 2009], where h0 refers to the reflection height of HF radio wave in the ionosphere. 3 ent heating conditions (e.g., different Perf and fHF/foF2), leading to different heating effects. In order to study the influence of Perf and fHF/foF2 on the heating effects and compare the difference of the heating effects under the same conditions at different radar sites, we theoretically simulate the heating effects assuming the same heating conditions (i.e., Perf = 100 MW and fHF/foF2 = 0.81) at Tromsø, Arecibo, and Guangzhou. Under the equiva- lent conditions with Perf = 100 MW and fHF/foF2 = 0.81 during daytime, heating effects are simulated for the cases at Tromsø, Arecibo, and Guangzhou (113°E, 22°N), respectively. The background parameters de- rived from the IRI and MSIS model at Tromsø and Arecibo are the same as those mentioned in Section 2.1. The relative variation profiles of electron density are plotted in Figure 1. Heating effects are found to be quite comparable between Arecibo and Guangzhou, with density depletions of 4.20% and 4.27%, respectively. However, the effects are appreciably stronger at Tromsø with a density depletion of 6.47%. Comparison between the simulations above in Sec- tion 2.1 and the results shown in Figure 1 indicates that when the reflection altitude h0 remains invariable, the increase of fHF/foF2 = 0.81 or Perf of the heating sys- tem leads to an enhancement of heating effects. For ex- ample, with fHF/foF2 increased from 0.69 to 0.81 at Arecibo, the density depletion ranges from 3.4% to 4.2%; with the Perf enhanced from 90 MW to 100 MW at Tromsø, the depth of electron density depletions in- creases slightly from 6.12% to 6.47%. It must be pointed out that the numerical com- parisons of the density modification at different loca- tions have limited guiding significance. The regional difference between high- and mid-latitudes and the time difference at similar latitudes are not taken into account. The ionospheric heating experiments were easily car- ried out after sunset at Arecibo but mainly done during daytime at Tromsø for lack of high enough electron density during night [Rietveld et al. 2002]. At Arecibo, the large depletions were observed reproducibly even after local midnight in the winter ionosphere. 2.2.2. Influences of the electron density gradients on heating effects In order to study the impact of electron density gradients on the density modification in ionospheric heating experiments, we select different background density profiles deduced from two ionograms illus- trated in Figure 2 at different times of a day and keep the other parameters fixed in our simulation. The den- sity profiles are labeled as density mode A and B (both derived from Guangzhou ionospheric observatory of CRIRP; Ionogram A and B were deduced at 15:31 LT in October 5, 2010, and 16:13 LT in October 17, 2010, re- spectively), respectively, as shown in Figure 3. The rel- ative variations of electron density with height caused by heating are shown Figure 4. The reflection height of HF radio wave h0 is about 243 km for the selected density models shown in Fig- ure 2. From Figure 3. We can see ∇NA<∇NB for the case of h > h0 and ∇NA>∇NB for h < h0. As illustrated in Fig- ure 4, a larger density gradient leads to a smaller density depletion and temperature increment, which implies that the density gradient is an adverse factor for ionos- pheric heating experiments. The interpretation can be more easily understood in terms of electron density scale height H [White and THE INFLUENCE FACTORS OF HEATING EFFECTS Figure 1. Comparisons of relative variation profiles of electron den- sity at Arecibo, Tromsø and Guangzhou under equivalent conditions with Perf = 100 MW and fHF/foF2 = 0.81 indicated in the insert. Figure 2. The selected background ionograms (the critical fre- quencies of ionograms A and B are 16.6 MHzand 15.2 MHz, re- spectively; in order to derive an entire electron density profiles of O-mode and X-mode from ionogram A, extend the ionogram traces reasonably using extrapolation). Chen 1974], which is inversely proportional to ∇N (1) The electric field of O-mode near the reflection al- titude behaves as a standing wave and undergoes an am- plitude swelling. The swelling factor of the incident power density just below the reflection height [Kantor 1972] is (2) The standing wave pattern near the reflection height has a significant relationship with the possible excitation of parametric processes and thus the HF wave energy absorption. Under certain conditions, anomalous absorption will play an important role. A smaller electron density gradient, which means a larger swelling factor, will lead to a larger heating effect. 2.2.3. Influences of the ratio of fHF to foF2 to on heat- ing effects The background ionosphere is controlled by solar activity and its critical frequencies vary in a large range in a day, especially during high solar activity. As a com- parison, the heating parameters can remain constant in certain periods due to limits of heating conditions or experimental setup. In order to investigate the influence of the ratio of fHF to foF2 on heating effects and com- pare results under different conditions, we do the sim- ulations as follows: (1) assume fHF as a constant and set foF2 different values in a day; (2) keep foF2 as a con- stant and change fHF. Here the heating effects at Guangzhou with Perf = 200 MW are simulated. fHF is equal to 6.5 MHz and foF2 ranges from 7 MHz to 15.5 MHz in the first case while foF2 remains fixed at 15.2 MHz and fHF ranges from 6 MHz to 15 MHz in the sec- ond case. The results are plotted in Figure 5 and Figure 6 respectively. The electron density depletion N1/N0 and tem- perature increment Te1/Te0 has a close relationship with the ratio of fHF to foF2 (see Figure 5). The critical frequency foF2 is inclined to change quickly in a day but the HF frequency fHF remains constant and smaller than foF2 all the time. The heating effects are getting better as fHF/foF2 approaches to 1. As foF2 increases (hence the ratio fHF/foF2 decreases), the reflection height h0 firstly shows a drop until fHF/foF2 = 0.65 and then shows a rise. They influence heating effects to- gether, resulting in an appreciable density disturbance under the condition of low fHF/foF2, as shown by the local maximum at fHF/foF2 ≈ 0.65. These findings are quite helpful for the selection of fHF. A similar result can be found more clearly in Fig- ure 6, where a maximum of N1/N0 occurs when HAO SHUJI ET AL. 4 Figure 3. The selected background electron density profiles de- duced from two measured ionograms (Figure 2). Figure 4. Relative variation profiles of electron density (left) and electron temperature (right) caused by heating with different background density gradients. H f f Z Np 2 2 1 2 2 = -c m .A c H7 2 /1 3~ = ` j (a) (b) 5 fHF/foF2 ranges form 0.5 to 0.7. When foF2 is constant, the reflection height and fHF/foF2 varies in phase with fHF. Their increases have a positive and a negative im- pact on heating effects, respectively. Unlike the first case shown in Figure 5, the reflection height shown in Fig- ure 6 covers a larger range and thus has a more effective impact on variations of electron density. With fHF/foF2 less than 0.5, the reflection height plays a dominant role and the increase of fHF leads to a decrease of N1/N0. As fHF increases up to a certain value fHF/foF2 becomes dominant and N1/N0 begins increasing. With a further increase of fHF/foF2 larger than 0.7, the reflection THE INFLUENCE FACTORS OF HEATING EFFECTS Figure 5. Influences of the ratio of fHF to foF2 on heating effects with a constant fHF and different values of foF2. The solid line with aster- isks represents the density depletion N1/N0 (left) and temperature increment Te1/Te0 (right), the broken line with squares represents h0. Figure 6. Same as Figure 5. but for a constant foF2 (=15.2MHz) and different values of fHF. Figure 7. Relative variation profiles of electron temperature and density caused by heating with different values of ratio fHF/foF2. The ob- servations are indicated with asterisks and the fitted curve with solid line. (a) Density depletion (a) Density depletion (b) Density depletion (b) Temperature increment (b) Temperature increment (a) Temperature increment height shows its dominance on heating effects again. The temperature increment shows a similar trend. The results imply that there might be a better ratio range with small values of the ratio of fHF to foF2, which is supported further by an experimental exam- ple. I.e., the experiment study of influences of the ratio of fHF to foF2 on heating effects was conducted using the EISCAT facility on August 17, 2009. The facility ra- diated O-mode waves at the frequency fHF =4.04 MHz with Perf = 120 MW in the following mode: 8-min ra- diation 4-min pause in the experiment. The results (the electron temperature) were dealt with using average value of each period, which are shown in Figure 7. When the value fHF/foF2 is small, the variation of the electron temperature is small, when fHF is close to foF2, the variation of the electron temperature is relatively large, but meanwhile there is a peak at fHF/foF2 = 0.74. The electron density perturbation shows a similar trend.The experimental result shows that there was a better ratio range with a small fHF/foF2, which can be used during the ionospheric heating to obtain relatively effective results. 3. Conclusions In this paper, we have simulated the heating effects in the low- and high-latitude under the equivalent con- ditions stemming from the well-known ionospheric heating experiments at Arecibo as well as at Tromsø, respectively. The findings have been extensively ex- ploited to verify the validation of our model by com- parison to the experimental results. Further, the analysis has been carried out on the influences of the dip angle, the background electron density gradient and the ratio fHF/foF2 on heating effects. Finally we come to draw the following conclusions: (1) Under certain conditions, a smaller electron density gradient of background ionospheric F region leads to a better ionospheric heating effect. When the background electron density suffers a rapid change, the altered gradient affects heating effects. (2) During over-dense heating, the heating effects are enhanced if the ratio of fHF to foF2 increases, which is slightly limited by the resultant elevation of the re- flection height. However, there might be a better ratio range with small values of the ratio fHF to foF2, e.g., [0.5, 0.7] in the current study. According to the simulation results in the paper, several measures can be taken to improve heating ef- fects under unfavorable background conditions. When the height of ionospheric F region rises up, we may in- crease the Perf of the heating facilities to increase the in- cident power density of the heated volume. When the ionospheric critical frequency shifts rapidly, we may make use of a short duty cycle and switch pump fre- quencies swiftly. If the capacity of the available heating system is limited, we may choose matched times with low ionospheric height, critical frequencies or gradient of electron density to obtain relatively effective results. We considered the influences of the ratio fHF/foF2 and the reflection height together which have been neg- lected by the previous theoretical investigations. Dur- ing the experiments, especially at noon during high solar activity, unfavorable background conditions are often encountered without choice, in which we can ad- just heating parameters adaptively. Acknowledgements. We are grateful to Li Qiang for useful suggestions. The authors are appreciated to the EISCAT Scientific Association. EISCAT is an international association supported by China (CRIRP), Finland (SA), Japan (NIPR and STEL), Norway (NFR), Sweden (VR) and the United Kingdom (NERC). This work is supported by the NSFC with grant No. 41004065. References Banks, P.M., and G. Kockarts (1972). Aeronomy, part B, Academic Press, NewYork. Blagoveshchenskaya, N.F., A.D. Andreev et al. (1995). Ionospheric wave processes during HF heating ex- periments, Adv. Space Res, 15 (12), 45-48. Blagoveshchenskaya, N., F. Borisova et al. (2011). The effects of modification of a high-latitude ionosphere by high-power HF radio waves. Part 1. Results of multi-instrument ground-based observations, Ra- diophysics and Quantum Electronics, 53 (9), 512-531. Das, A.C., and J.A. Fejer (1979). Resonance Instability of Small-Scale Field-Aligned Irregularities, J. Geo- phys. Res, 84 (A11), 6701-6704. Duncan, L.M., and J.P. Sheerin (1985). High-Resolution Studies of the HF Ionospheric Modification Inter- action Region, J. Geophys. Res, 90 (A9), 8371-8376. Duncan, L.M., J.P. Sheerin et al. (1988). Observations of Ionospheric Cavities Generated by High-Power Radio Waves, Phys. Rev. Lett, 61 (2), 239-242. Frolov, V., L. Kagan et al. (1999). Review of features of stimulated electromagnetic emission (see): Recent results obtained at the SURA heating facility, Radio- physics and Quantum Electronics, 42 (7), 557-561. Gordon, W.E., R. Showen et al. (1971). Ionospheric Heating at Arecibo: First Tests, J. Geophys. Res., 76 (31), 7808-7813. Gurevich, A V. (1978). Nonlinear Phenomena in the Ionosphere, Springer, Berlin. Gustavsson, B., M.T. Rietveld et al. (2010). Rise and fall of electron temperatures: Ohmic heating of ionos- pheric electrons from underdense HF radio wave pumping, J. Geophys. Res, 115 (A12), A12332. Hansen, J.D. (1990). Large-scale ionospheric modifca- HAO SHUJI ET AL. 6 7 tion by high-power radio waves: theory and obser- vation, PhD, University of California, Los Angeles. Hansen, J.D., G.J. Morales et al. (1992). Large-Scale HF- Induced Ionospheric Modifications: Theory and Modeling, J. Geophys. Res, 97 (A11), 17019-17032. Hinkel, D., M. Shoucri et al. (1992). Modeling of HF prop- agation and heating in the ionosphere, Final Tech- nical Report, TRW space and technology group. Isham, B., W. Birkmayer et al. (1987). Observations of Small-Scale Plasma Density Depletions in Arecibo HF Heating Experiments, J. Geophys. Res, 92 (A5), 4629-4637. Kantor, I.J. (1972). Plasma waves induced by HF radio waves, PhD, Rice University. Kosch, M.J., T. Pedersen et al. (2007). Artificial optical emissions in the high-latitude thermosphere in- duced by powerful radio waves: An observational review, Adv. Space Res, 40 (3), 365-376. Mantas, G.P., H.C. Carlson Jr. et al. (1981). Thermal Re- sponse of the F Region Ionosphere in Artificial Modification Experiments by HF Radio Waves, J. Geophys. Res, 86 (A2), 561-574. Meltz, G., L.H. Holway Jr. et al. (1974). Ionospheric heating by powerful radio waves, Radio Science, 9 (11), 1049-1063. Mingaleva, G.I., and V.S. Mingalev (1997). Response of the convecting high-latitude F layer to a powerful HF wave, Ann. Geophysicae, 15 (10), 1291-1300. Mingaleva, G.I., V.S. Mingalev et al. (2008). Model Pre- diction of the Most Effective Frequency for the Large-Scale Modification of the Midlatitude Ionos- pheric F2 Layer by Powerful HF Radiowaves, Geo- magn. Aéron, 48 (1), 66-74. Pavlov, A.V. (1998). New electron energy transfer rates for vibrational excitation of N2, Ann. Geophysicae, 16 (2), 176-182. Pavlov, A.V., and K.A. Berrington (1999). Cooling rate of thermal electrons by electron impact excitation of fine structure levels of atomic oxygen, Ann. Geo- physicae, 17 (7), 919-924. Pedersen, T.R., and H.C. Carlson (2001). First observa- tions of HF heater-produced airglow at the High Frequency Active Auroral Research Program facil- ity: Thermal excitation and spatial structuring, Radio Science, 36 (5), 1013-1026. Rietveld, M.T., B. Isham et al. (2002). HF-Pump- induced parametric instabilities in the auroral E-re- gion, Adv. Space Res, 29 (9), 1363-1368. Rietveld, M.T., M.J. Kosch et al. (2003). Ionospheric electron heating, optical emissions, and striations in- duced by powerful HF radio waves at high latitudes: Aspect angle dependence, J. Geophys. Res, 108 (A4), 1141. Rishbeth, H., and O.K. Garriott (1969). Introduction to ionospheric physics, Academic Press, New York. Robinson, T.R., A. Stocker et al. (1998). First CUTLASS- EISCAT heating results, Adv. Space Res. 21 (5), 663- 666. Shoucri, M.M., G.J. Morales et al. (1984). Ohmic Heat- ing of the Polar F Region by HF Pulses, J. Geophys. Res., 89 (A5), 2907-2917. Tereshchenko, E.D., B.Z. Khudukon et al. (2006). The relationship between small-scale and large-scale ionospheric electron density irregularities generated by powerful HF electromagnetic waves at high lati- tudes, Ann. Geophysicae, 24 (11), 2901-2909. Utlaut, W.F. (1970). An Ionospheric Modification Ex- periment Using Very High Power, High Frequency Transmission, J. Geophys. Res, 75 (31), 6402-6405. White, P.B., and F.F. Chen (1974). Amplification and ab- soption of electromagnetic waves in overdense plas- mas, Plasma Physics, 16, 565-587. Wright, D.M., R.S. Dhillon et al. (2009). Excitation thresholds of field-aligned irregularities and associ- ated ionospheric hysteresis at very high latitudes ob- served using SPEAR-induced HF radar backscatter, Ann. Geophysicae, 27 (7), 2623-2631. Xu Bin, Wu Jun, Wu Jian and Wu Zhensen et al. (2009). Observations of the heating experiments in polar winter ionosphere, Chinese J. Geophys., 52 (2), 322- 341 (in English). *Corresponding author: Wu Zhensen, Xidian University, Department of Physics, Xi’an, China; email: wuzhs@mail.xidian.edu.cn. © 2013 by the Istituto Nazionale di Geofisica e Vulcanologia. All rights reserved. THE INFLUENCE FACTORS OF HEATING EFFECTS Appendix A: Theoretical model According to the basic theory of ionospheric heat- ing, microscopic modification of the electron temper- ature and density in the F region can be modeled by fluid equations [Meltz et al. 1974, Gurevich 1978]. The three physical equations involved in our simulation model are the momentum equation, the continuity equation and the energy equation. A.1. The momentum equation Considering four species of singly charged ions and electron (O+, NO+, O2 +, e) and neglecting the iner- tia term, the momentum equation can be written as follows: (A1) where the subscripts a,b refer to the different types of charged particles (O+, NO+, O2 +, e), n the neutral parti- cles. pa = nakbTa is the pressure of species a, and Na, ma, Ta, va are density, mass, temperature and drift ve- locity, respectively. g is the acceleration of gravity and kb is Boltzmann’s constant. The collisional rate oan and oab represent collisions of species a with neutral parti- cles and species b, respectively. Summing Equation (A1) over the charged species, the collisional terms among charged particles are deleted completely, and the elec- tromagnetic force terms vanish with the hypotheses of quasi-neutrality and ambipolar diffusion. Introducing a mass-weighted ionic collisional term MIyIn [Hinkel et al. 1992] and the diffusion coefficient D (A2) and assuming the three species ions have the identical temperature Ti then the momentum equation in the di- rection of the geomagnetic field can be written as (A3) where yen and yIn are collisional frequencies of electron and ions with neutral particles, respectively, and I is the geomagnetic dip. A.2. The continuity equation The main ion constituent in the F-region is atomic O+, which does not recombine with electrons directly [Rishbeth and Garriot 1969]. Instead, O+ undergoes an ion-atom interchange reaction with neutral particles (mainly N2 and O2) and the resultant molecular ions com- bine with electrons, known as the b-type recombination, which has no dependence on electron temperature (A4) When ignoring the density variations of N2, O2 and O+ during the heating process, the enhancement of electron temperature has little effect on the produc- tion of NO+ and O2 +. Therefore, the continuity equa- tion takes the form: (A5) where k1 = 4.2×10 −7(300/Te ) 0.85 cm3/s and k2 = 1.6×10−7(300/Te ) 0.55 cm3/s are dissociative recombi- nation coefficients, Q0 is electron production rate in the equilibrium state (∂/∂t = 0) without external electric fields. A.3. The energy equation The energy equation can be written as follows: (A6) Equation (A6) is a time-dependent expression for electron temperature including the effects of convec- tion, compression, conduction, heat production and loss. The left terms are the change rate of electron en- ergy, the convection, and compression rate. The first term on the right side is the heat conduction rate. The heat conduction across the magnetic field can be ig- nored and the parallel thermal conductivity Ke [Banks and Kockarts 1972] is (A7) where, Nn represents the densities of neutral particles and the transfer cross-section of mean momentum for corresponding neutral particles [Banks and Kockarts 1972]. A complete theoretical description of the absorp- tion of the HF wave SHF involves ohmic heating due to deviative absorption, linear mode conversion to electro- static waves, parametric processes and Langmuir col- lapse, and the slow-down of super thermal electrons accelerated by the mode-converted waves. The exact amount of energy deposited in the ionospheric electrons in this region is therefore difficult to calculate accurately from first principles. Here following the simple absorp- tion model proposed by Hansen [Hansen 1990], we uti- HAO SHUJI ET AL. 8 , v v cos N D N k T T N m g N Ie b e i e n e e d = - + + +a a a ^ h8 B/ ,vt N Q k N k N N NNO O e e 0 1 2 e e2 $ 2 2 d= - + -+ +^ ^h h . . eV cm s K K T N N Q T 1 3 22 10 7 7 10 e e e e / n n 4 2 5 5 2 1 1 1 # # $ $ $ = + - - - D^ h/ 0 v v v v v E B g v v p N q q N m N m N mn n #d- + + - - - - - - = ! a a a a a a a a a a a a a a b a b b a^ ^h h/ ,M n n D m Mm 1 1 I In i n i e i n I Ini e e y y y y = = + ^ h/ O N N N, O O O O N N , O O OO O O e e 2 2 2 2 " " " " + + + + + + + + + + + + + - + - . v vk N t T N T N T T k K S S L 2 3 b e e e e e e e e e e b HF 0 d d d d 2 2 + =+ + + -^ h 8 B 9 lize a Gaussian profile placed near the reflection layer. S0 and L are the electron heating rate from other sources (mainly the solar radiation) and electron cool- ing rate, respectively. It is widely accepted that the dom- inant electron cooling processes involve elastic collisions between electrons and neutrals, rotational and vibrational excitation of molecular species, fine structure transitions in atomic oxygen, and collisions between electrons and ions. The updated estimates of inelastic cross sections associated with cooling rate cal- culations can be found [Pavlov 1998, Pavlov and Berrington 1999, Gustavsson et al. 2010]. Electron and ion temperatures in the background ionosphere are specified with the IRI-2012 model, and the atmosphere density and temperature are derived from the MSIS-90 model. In our calculations the time step is 0.01 second and the space step is 1/sinI km. The simulation processes are as follows: solve Equation (A3) to calculate ve according to the background parameters (Te0, Ne0, etc.); calculate variations of electron temper- ature Te1 in the Equation (A6) and then update Te0 and the recombination and loss rates; obtain variations of electron density Ne1 with Equation (A5), then update Ne0 and the corresponding terms; finish the current cal- culation loop and step into the next loop until the end of heating. The subscript e in electron density will be omitted for convenience. 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