HF-induced airglow at magnetic zenith: theoretical considerations

. Observations of airglow at 630 nm (red line) and 557.7 nm (green line) during HF modiﬁcation experiments at the High Frequency Active Auroral Research Program (HAARP) heating facility are analyzed. We propose a theoretical framework for understanding the generation of Langmuir and ion acoustic waves during magnetic zenith injections. We show that observations of HF-induced airglow in an underdense ionosphere as well as a decrease in the height of the emitting volume are consistent with this scenario. heating facility are presented. Here we focus on observations of the underdense ionosphere, when fo F2 drops below the heating frequency but HF-induced green and red lines at MZ remained. We show that this feature can be understood in terms of the scenario for the generation of strong turbulence at magnetic zenith with the OTSI of upper hybrid waves as the primary source of Langmuir waves.

Observations from the heating facilities at Tromsø ( 69.7 • N, 18.9 • E) and Gakona, Alaska ( 62.4 • N, Correspondence to: E. V. Mishin (evgenii.mishin@hanscom.af.mil) 145.15 • W) show that the HF-induced airglow maximizes during injections toward magnetic zenith (MZ) (Kosch et al., 2002a;Pedersen et al., 2003).The same is true for the intensity of Langmuir waves (Isham et al., 1999) and electron heating (Rietveld et al., 2003;Dhillon and Robinson, 2003) observed by the EISCAT UHF (f 0 =933 MHz) radar.Furthermore, the red line at MZ is excited at extremely low effective radiative power (ERP) P 0 ∼2 MW (Pedersen et al., 2003).The power of ion acoustic waves observed by the EIS-CAT UHF radar was found to be enhanced at, and 6 • to the south of, MZ (Dhillon and Robinson, 2003).
The generation of Langmuir (l) and ion acoustic waves in HF modification experiments is usually explained in terms of the parametric decay (PDI) or oscillating two-stream (OTSI) instabilities of ordinary (o) mode heating waves (Fejer, 1979).However, o-mode waves with incident angles θ 0 outside the Spitze region, θ 0 >θ c , reflect at altitude H mz a few km below the "standard" reflection altitude H 0 , where the local plasma frequency f p (H 0 ) 10 4 √ n e (H 0 ) Hz equals the injected frequency f 0 .Here, θ c =arcsin( f c +f 0 sinχ), f c is the electron gyrofrequency at an altitude of 200 km, n e is the electron density in cm −3 , and χ is the conjugate of the magnetic dip angle.Figure 1 shows a schematic of regions near o-mode reflection at geographic (GZ) and magnetic zenith at Gakona for f 0 =7.8 MHz.
For a heater ERP P 0 =150 MW and distance R=250 km, the wave amplitude is E 0 5.5 and T e =0.1 eV, the HF energy density at the reflection point is It is sufficient to drive the PDI at H 0 (Fejer, 1979) but is not enough for injections toward MZ due to a mismatch of frequencies at H mz and beneath.Gurevich et al. (2002) suggested that decreased plasma densities, within striations generated by heating waves, permit the phase matching necessary for the PDI/OTSI to develop.Istomin and Leyser (2003) showed that electrons can be accelerated by upper hybrid waves trapped inside striations.Changes in the refraction index (self-focusing), caused by striations that form within tens of seconds after turnon, explain some features of the spatial distribution of the E. V. Mishin et al.: HF-induced  HF-induced airglow.Kosch et al. (2002b) showed that the intensity of red-line emissions decreased when the heating frequency approached an electron gyro-harmonic, pointing out the importance of upper hybrid turbulence at MZ.
On the other hand, Langmuir waves at MZ were seen within ∼10 ms (Isham et al., 1999).In 5-s resolution observations made by Dhillon and Robinson (2003), the initial increase in UHF backscatter, characterized by an overshoot, was seen coincident with the heater turn-on.Electron temperatures generally increased at heater turn-on, but the maximum increase occurred several seconds later.Mishin et al. (2004) show that during injections toward magnetic zenith the intensities of the green-line emission gained ∼5 R (Rayleighs) within ∼1 s.This period is dubbed the onset of HF-induced airglow.Time scales 1 s appear too short for significant striations to develop (e.g.Gondarenko et al., 1999).
Striations are generated near the upper hybrid resonance height H uhr , where Vaskov et al., 1981;Lee and Kuo, 1983).Hence, the reflection height of an obliquely-injected heating wave must be at least at the same level.For reflection to occur above H uhr during MZ injections, the inequality f c >f 0 •sinχ must be met.For MZ injections at the HAARP heating facility (χ 14.6 • ), H uhr <H mz if f 0 <f 0 χ 5.4 MHz.However, the strongest airglow occurred at higher f 0 values (Pedersen et al., 2003) and at altitudes well below H 0 and H uhr (Kosch et al., 2002a).Mishin et al. (2004) suggested a scenario for exciting plasma turbulence with subsequent electron heating and acceleration in the HF-illuminated region at MZ.This scenario, depicted in Fig. 2, explores the results of Kuo et al. (1997), who showed that the OTSI can be excited by upper hybrid (uh) waves.In turn, uh-waves are generated through the linear conversion of the o-mode on pre-existing field-aligned irregularities (Wong et al., 1981) or by the parametric decay o→uh + lh (PDI uh o ) (e.g.Istomin and Leyser, 1995); lh stands for lower hybrid waves.
The conversion process occurs at H uhr and has no threshold.PDI uh o develops if E 0 >E 0 uh 1.6 f 2 0 mV/m, provided the corresponding matching conditions are met for x uh =k 2 uh r 2 e <1.Here, r e is the thermal electron gyroradius and k uh is the uh-wave vector.Otherwise, Landau damping of short-scale lower hybrid waves raises the threshold value (Mishin et al., 1997).The rise time of the (primary) uh-wave is τ uh ∼1-3 ms.When the amplitude of the primary uh-wave E uh exceeds ∼10 mV/m, it parametrically decays into lower frequency uh-wave (Zhou et al., 1994).The same is true for subsequently-generated uh-waves.
The OTSI excited by uh-waves produces short-scale, k l >3 −1/2 /r e , Langmuir waves (Kuo et al., 1997).These waves saturate via spectral transfer toward small k l , due to induced scattering by ions (e.g.Zakharov et al., 1976).Depending on the energy density of the uh-turbulence, which depends on the ERP, the induced scattering process may deliver the Langmuir wave energy W l to the region k l →0 (Langmuir condensate) (Zakharov et al., 1976).The dynamics of the Langmuir condensate is defined by the modulational instability and collapse, leading to the establishment of strong (cavitating) Langmuir turbulence (e.g.Zakharov, 1972).This makes the generation of Langmuir turbulence possible within ∼10 ms, consistent with the Isham et al. (1999) observations.
Collisional damping of high-frequency plasma waves is the major source of electron heating.Resonant lh-and lwave-particle interactions accelerate electrons.Based on this scenario, Mishin et al. (2004) developed an explanatory model for the growth of emissions from MZ within the first few seconds after the HF transmitter turn on (airglow onset).The model accounts for the roles played by ambient photoelectrons and dissociative recombination of oxygen ions and shows that heating and acceleration of ambient electrons can explain the observed features of the airglow onset at MZ.
A consistent theory of the HF-induced airglow, accounting for the ion/neutral chemistry, modification of the heated spot, and self-focusing, has yet to be worked out.Pedersen et al. (2003) mentioned that the brightest emissions had a slight tendency to occur very near the critical frequency of the Flayer foF2 , but all emissions cut off sharply at about 0.5 MHz above foF2.
This paper continues our analysis of optical data acquired during the February 2002 campaign at the HAARP heating facility.We focus on intervals when foF2 dropped below the heating frequency, but HF-induced green and red lines at MZ remained.We characterize such events as the HF-induced airglow in an underdense ionosphere and show that this feature can be understood in terms of the above scenario.

Airglow at HAARP in the underdense ionosphere
Figure 3 shows all-sky images of the HF-induced red-and green-line emissions observed from the HAARP site during a long, ∼30 min, pulse that began at 04:32:12 UT on 13 February 2002 (Pedersen et al., 2003).The data show one of the most intense green-line emissions observed at HAARP.During this (twilight) period o-mode waves were injected toward magnetic zenith at f 0 =7.8 MHz and at full power of 940 KW (ERP P 0 165 MW).Exposure durations were 7.5 s.
Figure 4 (top panel) shows the variation of the red-and green-line intensities in the course of the long pulse.The data points are from two red line exposures made at 0 and 24 s after each minute, with one 557.7 nm exposure at 12 s.Simultaneous observations from a digisonde located at the HAARP site showed that the reflection height of a 7.8-MHz o-mode wave at MZ gradually increased from H mz ∼235 to ∼270 km between 04:30 and 04:50 UT.At the same time, the shadow height at the HAARP site increased from ∼230 to ∼300 km following the increasing solar zenith angle and so does the height of the F-peak hmF2.The magnetic conjugate point was sunlit, maintaining a flux of energetic photoelectrons (e.g.Doering et al., 1975;Peterson et al., 1977) above HAARP most of the time.
To account for natural (background) variations, a polynomial fit was made to intensities measured along the magnetic meridian in each all-sky image, with the heated area blocked out.The heater-induced airglow is determined as the difference λ =I λ −b λ between the airglow from the heated volume I λ and the background airglow b λ .During heater-off periods, (off ) λ was less than ∼3-5 and ∼7-10 R for greenand red-line emissions, respectively.This small difference determines the accuracy of heater-induced airglow measurements.
The critical frequency of the F-layer is determined from 5min digisonde observations at the HAARP site.Apparently, foF2 dropped below the transmitter frequency in the course of this pulse.However, the airglow did not diminish.Figure 5 shows that the HF-induced airglow disappeared only at f oF2<f oF2 c f 0 −0.5 MHz.A remark is in order.One can argue that the HAARP digisonde points vertically and the actual foF2 at H mz , that is about 50 km to the south of the local vertical, might be significantly different.However, this is unlikely, for the local geophysical conditions were very quiet.This conjecture is supported by the small difference between the airglow from the heated volume during heater-off periods and the (barely changing) background airglow about 50 km apart.
In addition to Figs. 3 and 5, Fig. 6 shows the results of a survey of all the airglow-events with a 50-R or more enhancement in red line emissions observed on clear-sky nights during the February 2002 optics campaign.Apparently, for f 0 ≥5.8 MHz airglow is enhanced by heating waves until f oF2≥f oF2 c .No enhancements were observed at f oF2<f oF2 c .At f 0 =4.8 and 4.5 MHz the cutoff frequency coincides with f 0 accurate to within ±0.1 MHz, that is within the accuracy of determination of foF2.It is worth mentioning that the difference between f p (H mz (f 0 )) and f 0 =7.8, 6.8, 5.8, and 4.8 MHz is about −0.24, −0.2, −0.17, and −0.14 MHz, respectively.Mishin et al. (2004) emphasized that the scenario in Fig. 2 works at and below the reflection layer H mz , provided that the matching conditions for PDI uh o (e.g.Istomin and Leyser, 1995) are satisfied at local values of x uh =k 2 uh r 2 e <1.During injections toward MZ standing waves do not form, and the heating wave amplitude at the reflection point does not increase relative to that at lower altitudes.Thus, the reflection layer does not stand out as it does for injections within the Spitze region, where the Airy pattern is formed.The ERP and angular width of the HF beam from the HAARP heater depend on the radiated frequency.Roughly, one can estimate P 0 ∝f 2 0 , while the beam has full width at half maximum ∼27 • and ∼15 • N-S at 3.3 MHz and at 7.8 MHz, respectively.For f 0 =7.8, 6.8, 5.8, 4.8, and 4.5 MHz, the free space field of the incident wave from the HAARP heater is E 0 0.25, 0.2, 0.18, 0.15, and 0.14 V/m, that is E 0 >E uh 0 (f 0 ).From the dispersion relation of uh waves

Discussion
x s−1 uh one can readily obtain the value of the uh-wave vector necessary for PDI uh o to occur at a given altitude H (cf. Istomin and Leyser, 1995) This assumes that f 0 is no closer than ∼0.006f c to an electron gyro-harmonic s•f c and x uh <0.5.Here, s is defined by rounding up the f uhr /f c ratio to the nearest integer.Given f c (H mz ) 1.37 MHz at the HAARP site (from the IGRF geomagnetic field model), the heating frequencies amount to f c •5.7, 4.96, 4.23, 3.5, and 3.3, respectively.Apparently,  matching conditions for f 0 =7.8, 6.8, and 5.8 MHz at the reflection height H mz (f 0 ) are satisfied at x * uh (f 0 )<0.5.Importantly, Eq. ( 2) holds well below H mz (f 0 ), that is x * uh →1 at H * (f 0 )=H mz (f 0 )−δH mz (f 0 ).Here, δH mz (f 0 ) amounts to 3.5, 6, and 11.4 km, respectively (the gradient scale-length of a linear plasma density profile of 50 km is assumed).
The volume emission rate (VER) of the red-line emission η r is mainly defined by the electron temperature altitudeprofile (e.g.Mantas and Carlson, 1996;Mishin et al., 2004).It is very sensitive to the distribution of thermal electrons (TEDF), which may strongly deviate from a Maxwellian distribution (MD) due to inelastic collisions with molecular nitrogen N 2 (Mishin et al., 2000).For n e given, the TEDF-MD-deviation decreases with altitude as well as collisional deactivation of the O( 1 D) state.Both effects provide increasing η r (T e ) in the course of the twilight observations (Mishin et al., 2000(Mishin et al., , 2004)).Thus, following H mz , the redline intensity is expected to rise when H mz approaches hmF2 or f oF2→f p (H mz ).
On the other hand, the VER of the green-line emission η g is dominated by suprathermal electrons and increases at lower altitudes (Mishin et al., 2004).Therefore, the greenline intensity is expected to decrease when foF2 approaches f p (H mz ).These conjectures are consistent with data in Figs. 5 and 6.
PDI uh o develops if the dispersion curve (Eq.( 1)) intersects with f 0 at x uh (H )<1.This is possible for f 0 5.8 MHz (4.23f c ) only if f uhr >4.006f c or f p >5.31 MHz.Apparently, the cutoff frequency is ≈f oF2 c .At first glance, the cutoff frequencies for f 0 =7.8 and 6.8 MHz can be roughly defined by the condition x * uh (hmF2, f 0 )∼1.More precisely, one has to account for the second term in Eq. ( 1) that limits f uh (x uh )−f uhr and determines the location of its maximum ∼f 2 c /2f uhr at x uh <1 (e.g.Istomin andLeyser, 1995, 2003).As a result, the cutoff frequencies turn out to be close to f oF2 c f 0 −0.5 MHz.
For f 0 <f χ 0 , that is 4.8 and 4.5 MHz, H mz is located above the upper hybrid resonance layer and Eq. ( 2) can be satisfied at H uhr and by ∼15 km below.In this case we expect striations to grow from H uhr .This process is expected to be most efficient near the maximum of the F-peak (f uhr =f 0 →f oF2), where the vertical plasma density gradient is minimum.Developed striations disguise the plasma density profile thereby making it difficult for PDI uh o and OTSI to develop below H uhr .As the generation of plasma turbulence is prohibited at lower altitudes, the heater-induced airglow is dominated by heating inside striations (Gurevich et al., 2002) and hence must vanish whenever foF2 drops below f 0 .

Conclusion
The results of an ongoing analysis of optical data acquired during the February 2002 campaign at the HAARP heating facility are presented.Here we focus on observations of the underdense ionosphere, when foF2 drops below the heating frequency but HF-induced green and red lines at MZ remained.We show that this feature can be understood in terms of the scenario for the generation of strong turbulence at magnetic zenith with the OTSI of upper hybrid waves as the primary source of Langmuir waves.

Fig. 2 .
Fig. 2. Block-diagram fromMishin et al. (2004) showing energy flow in a model of HF-induced airglow at MZ. Shaded boxes indicate the steps to be worked out.

Fig. 3 .
Fig.3.Heater-induced red-and green-line emissions during the long pulse before (top) and after (bottom) foF2 has dropped below f 0 .Bold circles mark the heated spot at MZ. Bright dots outside the circles are stars.The color bars show the brightness from 0 to 0.48 kR and from 0 to 0.17 kR for the red-and green-line emissions, respectively.

Fig. 4 .Fig. 5 .
Fig. 4. Heater-induced red-and green-line emissions during the long pulse on 13 February 2002.Solid and dashed lines show intensities of the background green (b g ) and (scaled) red (b r ) emissions, respectively.(bottom) The critical frequency of the F-layer above the HAARP site (diamonds); the solid line represents a spline approximation; dashed and dotted lines show the heating frequency and the plasma frequency at H mz , respectively.