A simulation study of 630 nm and 557.7 nm airglow variations due to dissociative recombination and thermal electrons by high‐power HF heating

One of the important effects of the ionospheric modification by high‐power waves is the airglow enhancement. Both the thermal electrons and the dissociation recombination contribute to generate the airglow emissions during HF heating. However, the relative importance of the airglow emission induced by dissociative recombination and thermal electrons has been rarely investigated. In this study, we carry out a simulation study on the airglow produced by high‐power HF heating at nighttime associated with dissociative recombination and thermal electrons. SAMI2 (Sami2 is Another Model of the Ionosphere) is employed to simulate the ionospheric variations during the HF heating. The main conclusions from this study are as follows: (1) For the airglow induced by dissociative recombination, both 630.0 nm and 557.7 nm emissions show a decrease at the heating wave reflection height during the heating period, while when the heating is turned off, an increase is shown at lower altitudes. The reduction of airglow during the heating is caused by the rapid increase of electron temperature and the diffusion of plasmas dominates the after‐heating airglow enhancement. (2) 630.0 nm emission due to thermal electrons is greatly enhanced at the wave reflection height, indicating that thermal electrons play a major role in exciting 630.0 nm emission. For the 557.7 nm emission, the excitation threshold (4.17 eV) is too high for thermal electrons. (3) The combined effect of dissociative recombination and thermal electrons could be the possible reason for the observed X‐mode (extraordinary mode) suppression of 630.0 nm airglow during O‐mode (ordinary mode) enhancement.


Introduction
Strong airglow enhancements have been observed during highpower HF heating since 1970s (Biondi et al., 1970;Sipler et al., 1974;Bernhardt et al., 1988;Brändström et al., 1999;Djuth et al., 2005;Gustavsson et al., 2005;Kosch et al., 2005;Holma et al., 2006). The red and green line emissions (630.0 and 557.7 nm) of atomic oxygen are among the most prominent features during the HF heating experiments. The natural 630.0 nm and 557.7 nm airglow in the ionosphere is produced by the excitation through dissociative recombination of oxygen molecule ions by collision with electrons (e.g., Peterson et al., 1966;Bates, 1992).
The greatly enhanced airglow observed during the heating experiments has been suggested to be caused by the accelerated elec-trons (Perkins and Kaw, 1971;Weinstock and Bezzerides, 1974;Weinstock and Sleeper, 1975;Gurevich et al., 1985) and the thermal electrons (Mantas, 1994;Mantas and Carlson, 1996). The theory of accelerated electrons suggested that the enhanced excitation of O( 1 D) is due to a non-thermal electron distribution in the energy range above 2 eV. The source of this distribution is the acceleration of electrons by Langmuir turbulence (Gordon and Carlson, 1974;Meltz and Perkins, 1974;Gurevich et al., 1985;Bernhardt et al., 1989).
The other hypothesis is that the red-line airglow is caused by direct excitation of oxygen atoms by collision with thermal electrons through the high energy tail of a Maxwellian electron distribution. Mantas (1994) suggested that the thermal electron excitation of the O( 1 D) state is sufficient to explain the 630.0 nm emission intensity observed during the ionosphere heating experiments. Later, Mishin et al. (2000) suggested that the Maxwellian electron distribution should be corrected for the effects of N 2 inelastic collisions.
Although the airglow variations during HF heating were widely examined, the comparison of the airglow emission induced by dissociative recombination and thermal electrons has rarely been investigated. In this work, we mainly focus on the 630.0 nm and 557.7 nm airglow caused by dissociative recombination reaction and thermal electrons. We utilize SAMI2 (Sami2 is Another Model of the Ionosphere) to simulate the ionospheric variations during the HF heating by including an additional heating source, with a time step of 30 seconds. Based on the model, we present the comparison of the spatial and temporal variations of airglow emission induced by the dissociative recombination and thermal electrons. The thermal electrons effect under the condition of non-Maxwellian electron distribution is also discussed.

Heating Model
In this study, we use the ionospheric model SAMI2 (Huba et al., 2000) to conduct heating simulations with a realistic ionosphere. SAMI2 solves plasma continuity, momentum, and energy equations to provide plasma densities and temperatures. The plasma field-aligned motion along a magnetic flux tube and the motion across the flux tube via E×B drift are considered in the model. The neutral species are specified using the Mass Spectrometer Incoherent Scatter model (MSIS00) and the Horizontal Wind Model (HWM93). SAMI2 (together with the 3D version SAMI3) has been used in a number of simulation studies of ionospheric artificial heating (e.g., Wu TW et al., 2012;Zawdie et al., 2013Zawdie et al., , 2015Zawdie and Huba, 2014). Similar to Wu TW et al. (2012), we add a source term (Q RF ) in the electron temperature equation. The modified electron temperature equation is The second term on the left-hand side is the heat conduction term, κ e is the parallel electron thermal conductance, k is the Boltzmann constant, and b s is the component of the magnetic field in the field line direction. The other heating/cooling terms on the right-hand side of equation (1) are associated with electronneutral collisions (Q en ), electron-ion collisions (Q ei ), and photoelectron heating (Q phe ). Q RF is the heating term, which is represented by a Gaussian-shaped source: where is the total heating rate per electron in K/s, z is the altitude, and θ is the latitude. z 0 and θ 0 are the center altitude and latitude of the heating location and Δz and Δθ stand for the altitudinal and latitudinal extent of the heating region. In this study, we set the total heating rate to be 1000 K/s, which is suggested in previous studies using the SURA heater (Milikh et al., 2010a). The location of the HF heater is set at Arecibo, Puerto Rico (18.3°N, 66.7°W, 28°N magnetic latitude). HF heating begins at 01:00 LT and lasts for 5 min. In this study, Δz=10 km and Δθ=0.05°, which are the same as Wu TW et al. (2012). The pump frequency is 5 MHz, corresponding to the wave reflection height of 282 km and electron density of 3.1×10 5 cm -3 above Arecibo Observatory at 01:00 LT. The wave reflection height is below the F region peak height of about 300 km.

Airglow Model
The 630 To estimate the airglow induced by dissociative recombination, we use the airglow model proposed by Vlasov et al. (2005), which includes the effects of molecular ions. The volume emission rate (VER) of red-and green-line emission are given by the formulae where β is the yield of the N( 2 D) atoms in the reaction between NO + and electron; γ O is the rate coefficient of the deactivation of N( 2 D) atoms by atomic oxygen; γ D is the rate coefficient of reaction between N( 2 D) and O 2 ; k 1 , k 2 , and k 3 are the rate coefficient of O( 1 D) quenching by N 2 , O 2 , and O, respectively; A 1D and A 2D are the O( 1 D)->O( 3 P) transition coefficients; A 1S and A 2S are the O( 1 S) ->O( 1 D) transition coefficients. The parameters and reactions are described in detail in Vlasov et al. (2005).
During the HF heating, the excited oxygen state O( 1 D) could be generated through the impact of thermal electrons: where e * denotes the electrons with energy greater than 1.96 eV. For the 557.7 nm airglow, the threshold energy of O( 1 S) state is 4.17 eV. In this study, we use the airglow model proposed in Mantas (1994) and Gurevich and Milikh (1997) to calculate the airglow excited by thermal electrons: Here and are respectively the excitation rates of O( 1 D) and O( 1 S), which are defined as Finally, the integrated airglow intensity can be expressed as The main purpose of this work is to investigate the relative effect of dissociative recombination and thermal electrons on airglow. We run SAMI2 simulation in the meridional plane of Arecibo under the following geophysical conditions: F 10.7 =100, Ap=4, and day of year = 130. Electron density, electron temperature and the calculated airglow without HF heating are subtracted for each grid point and time step to show the heating induced perturbations. Figure 1 shows the perturbations of electron temperature and density at the end time of HF heating (01:05 LT) as a function of latitude and altitude. As given in Figure 1a, after 5 min of heating, electron temperature shows a large enhancement, with fieldaligned striations extending from 150 km to above 500 km. Electron temperature reaches maximum at the heating center region, about 2100 K above the ambient temperature. As shown in Figure 1b, a density depletion of about 1×10 5 cm -3 can be seen at the heating center region, while electron density has an increase above and below the heating center region. This structure is possibly associated with the large thermal pressure due to the absorption of heating waves at the wave reflection height. Plasma tends to diffuse along the field line under the force of the pressure gradient. Note that the electron density perturbation is asymmetric on the two sides of the heating center region along the field line. The altitude above the heating center exhibits a higher density increase than the lower altitudes, which is probably due to the low diffusion coefficient as well as the high recombination rate at low altitudes. Such field-aligned density ducts have been observed by the Detection of Electro-Magnetic Emissions Transmitted from Earthquake Regions (DEMETER) and Defense Meteorological Satellite Program (DMSP) satellites routinely in the topside ionosphere during ionospheric modification experiments at the High Frequency Active Auroral Research Program (HAARP) and SURA heating facilities (Milikh et al., 2008(Milikh et al., , 2010bRapoport et al., 2010;Fallen et al., 2011).

Results and Discussions
Figure 2 presents temporal variations of electron temperature and density along the magnetic field line. The zero time represents the start of artificial heating, and thus the heating ends at 5 min. Electron temperature greatly enhances during the heating period and rapidly depletes in 1-2 minutes. For electron density, as heating starts, a density cavity forms along with the density enhancement on both sides. Different from the electron temperature changes, due to the large time constant of diffusion transport process, the electron density takes more than 30 min to recover to the preconditions. The variations of electron temperature and density by HFpump heating are confirmed by previous studies (e.g., Hansen et al., 1989;Milikh et al., 2010aMilikh et al., , 2010bMilikh et al., , 2012. When the heating has been turned off for 2 min (01:07 LT), the airglow shows an increase at a lower altitude than the heating center, which is in contrast with the airglow change during the heating period. The change of the 557.7 nm airglow is similar to that of the 630.0 nm airglow with a smaller perturbation of about 0.7 cm -3 s -1 .
The above simulation shows that the airglow decreases when the transmitter was turned on while increases when the transmitter was turned off. This behavior is usually prominent when the heater was run with extraordinary mode (X-mode) polarization (Biondi et al., 1970;Sipler and Biondi, 1972). The X-mode polarization wave collisionally heats the plasma without parametric excitation of electrostatic waves (Bernhardt et al., 1988). As shown by equations (4) and (5), the volume emission rate of airglow is mainly dominated by the dissociative recombination coefficient α and electron density (α is approximately proportional to T e -0.6 ). Consequently, when the electron temperature increases significantly  during the heating period, X-mode heating suppresses the airglow intensity by reducing the recombination coefficient. This suppression of the natural airglow is usually masked by collisional excitation during O-mode heating. When the heating is terminated, the electron temperature rapidly depletes to unperturbed condition; however, the electron density change could last for a long time. Therefore, the airglow perturbation is mainly dominated by the variations of electron density when the heater is turned off. Electrons at the heating region are transported to lower altitudes along the field line (Figure 1b), and thus the airglow enhances at a lower height. Note that a weak depletion at 01:07 LT also occurs at the wave reflection region because of the  Then, we take the thermal electrons into account to investigate the enhanced airglow during the ordinary mode (O-mode) heating. Figure 4 shows the changes of volume emission rate due to thermal electrons as a function of geographic latitude and altitude. Strong 630.0 nm airglow increase can be noted at the heating time of 1 min (01:01 LT). As the HF heating continues, the volume emission rate of red-line airglow increases up to 50 cm -3 s -1 at 01:04 LT. After the heating is turned off in the bottom panel, the airglow enhancement is depleted. For the green-line airglow, the variation of volume emission rate due to the thermal electron is much smaller than that caused by the recombination effect, indicating that the thermal electrons induced 557.7 nm airglow is weak. This is associated with the high threshold energy (4.17 eV) for the excitation of O( 1 S).
The temporal variations of airglow along the heated magnetic field line are displayed in Figure 5. Both the red-line and greenline airglows decrease during the heating, but increase when the heating is turned off. The strongest reduction happens when the heating is turned on and the strongest enhancement occurs at 2 min after the heating is terminated. The magnitude of green-line airglow changes is much smaller than that of the red-line airglow. For the 630.0 nm airglow induced by thermal electrons in the bottom panel, the volume emission rate largely enhances at the reflection height as the heating starts and disappears in 1 min after heating is turned off. The volume emission rate of the red-line air-glow reaches 50 cm -3 s -1 when the HF heating is absent. As compared with Figure 5b, the green-line airglow due to thermal electrons in Figure 5d is negligible, although it shows a slight increase during heating period.
In Figure 6, the variations of airglow intensity integrated by the volume emission rate are shown. The recombination associated red-line airglow intensity has a decrease of 20 Rayleighs (R) during the heating period and has an increase up to 10 R after 2 min as the heating is switched off. The airglow intensity induced by the thermal electrons strongly increases and peaks with a value of 270 R when the heating is terminated. After that, the airglow rapidly recovers to the precondition level in about 1 min. As compared with the red-line airglow, the green-line intensity is much smaller. The 557.7 nm airglow intensity caused by the recombination effect shows a similar variation as the red-line airglow but with smaller magnitude. The maximum reduction and enhancement are 4 R and 2 R, respectively. The intensity of green-line airglow caused by thermal electrons is almost negligible. Gustavsson et al. (2009) presented an interesting observation of 630 nm emission from HAARP heater with simultaneous transmission in X and O-mode. They firstly reported the additional transmission of X-mode significantly suppressed the enhancement of O-mode 630.0 nm enhancement. This result is consistent with our calculations and might be associated with the combined effect of dissociative recombination and thermal electrons. Here it should be pointed out that the integrated airglow intensity is calculated along the magnetic field, and thus it may be overestimated. Over the years, strong enhancement of optical emissions from states with excitation threshold higher than 1.96 eV of O( 1 D) has been observed. These emissions involve 557.7 nm (with excita-tion threshold energy of 4.17 eV) (e.g., Bernhardt et al., 1989;Gustavsson et al., 2002), 660.0 nm (9 eV) (Djuth et al., 1999) et al., 2001;Holma et al., 2006). From our simulation results of the green-line airglow, the theory of thermal electrons is unable to explain the emissions with excitation threshold energy of 4.17 eV or higher. The suprathermal electrons, which have been suggested to be accelerated by Langmuir turbulence or the upper hybrid plasma turbulence, are a widely accepted theory for these emissions (e.g., Grach, 1999;Mishin et al., 2005;Gurevich, 2007). The relative contributions of accelerated electrons, thermal electrons and dissociative recombination to the airglow require further investigation.
Despite of the strong red-line airglow enhancement, Sergienko et al. (2000) shows that the thermal electron theory significantly overestimates the observed emission intensity. Mishin et al. (2000) and Gustavsson et al. (2004) further proposed that the collisions between N 2 and electrons lead to a strong depletion from the Maxwellian electron distribution in the high energy range. Consequently, this depletion results in a reduction of O( 1 D) state and airglow intensity. Next, we carry out a simple sensitivity analysis of airglow due to deviations from the Maxwellian electron distribution. The standard Maxwellian electron energy distribution is where T is the electron temperature, k is the Boltzmann constant, and E is the electron energy. Through solving the one dimensional Vlasov equation for ionospheric F-region conditions during high-power HF-heating, Wang JG et al. (1997) found that the energy distribution of suprathermal electrons induced by HF heating could be modeled by a power law. Vlasov et al. (2004) found that the electron energy distribution in the energy range of 2-3 eV can deviate significantly from a Maxwellian distribution due to the impact of N 2 vibrational excitation. In this study, the effect of deviation from the Maxwellian electron energy distribution on the airglow intensity is tested using the combination of the results from Wang JG et al. (1997) and Vlasov et al. (2004). The non-Maxwellian electron energy distribution F NM is expressed as where R=1.2, E'=E-2 eV and E' av =0.5 eV. Figure 7 shows the comparison of Maxwellian and non-Maxwellian electron energy distributions at the electron temperature of 4000 K. The non-Maxwellian electron energy distribution function F NM (E) is lower than the pure thermal one F M (E) in the energy range between 2 eV and 3 eV, but higher in the energy range greater than 3 eV. The simulated airglow difference between Maxwellian and non-Maxwellian electron energy is shown in Figure 8. The volume emission rate of red-line airglow under the modified non-Maxwellian electron distribution is about 6 cm -3 s -1 lower than the pure thermal case at around 300 km. The depletion in the energy range between 2-3 eV of Maxwellian electron distribution causes a smaller airglow intensity than the pure thermal model. This test sup-ports the assumption in Sergienko et al. (2000) that the inelastic collisions between N 2 and electrons lead to an overestimation of the airglow intensity in the pure thermal theory. In addition, the present calculation does not consider excitation of O( 1 D) and O( 1 S) through collisions with other excited species, such as N 2 rotational and vibrational states. The non-Maxwellian component with energies of 20 eV may produce many excited species that can also contribute to excite O( 1 D) and O( 1 S) through collisions (e.g., Rees, 1963;Banks et al., 1974) and thus the results in this study might be influenced.

Conclusions
In this study, we present the simulation results of the heating effect on 630.0 nm and 557.7 nm airglow based on SAMI2. We mainly focus on the comparison of airglow caused by the dissociative recombination reaction and thermal electrons during the nighttime. The main results are summarized as follows: (1) The intensities of both 630.0 nm and 557.7 nm airglow in-  duced by the dissociative recombination show a decrease during the heating and increase after the heating is turned off. The intensity perturbation of the 630.0 nm airglow is about 15 R larger than that of 557.7 nm airglow.
(2) The volume emission rate of airglow due to dissociative recombination shows significant altitudinal and temporal distributions. During the heating period, the reduction of recombination coefficient, which is caused by the increase of electron temperature, leads to a decrease of airglow at the wave reflection height. When the heating is turned off, the field-aligned downward diffusion of electron dominates the airglow variation and enhances the airglow at lower altitudes.
(3) During the heating period, 630.0 nm emission is greatly enhanced by 260 R at wave reflection height due to thermal electrons, indicating that the thermal process plays a major role in causing 630.0 nm emission. The enhancement rapidly depletes in 1 min after the heating is turned off. The 557.7 nm emission induced by thermal electrons is nearly unchanged because of the high excitation threshold energy (4.17eV) of O( 1 S). The theory of accelerated electron could probably explain the observed greenline enhancement.