Investigation of ionospheric stimulated Brillouin scatter generated at pump frequencies near electron gyroharmonics



[1] Stimulated Electromagnetic Emissions (SEEs), secondary electromagnetic waves excited by high power electromagnetic waves transmitted into the ionosphere, produced by the Magnetized Stimulated Brillouin Scatter (MSBS) process are investigated. Data from four recent research campaigns at the High Frequency Active Auroral Research Program (HAARP) facility is presented in this work. These experiments have provided additional quantitative interpretation of the SEE spectrum produced by MSBS to yield diagnostic measurements of the electron temperature and ion composition in the heated ionosphere. SEE spectral emission lines corresponding to ion acoustic (IA) and electrostatic ion cyclotron (EIC) mode excitation were observed with a shift in frequency up to a few tens of Hz from the pump frequency for heating near the third harmonic of the electron gyrofrequency 3fce. The threshold of each emission line has been measured by changing the pump wave power. The excitation threshold of IA and EIC emission lines originating at the reflection and upper hybrid altitudes is measured for various beam angles relative to the magnetic field. Variation of strength of MSBS emission lines with pump frequency relative to 3fce and 4fce is also studied. A full wave solution has been used to estimate the amplitude of the electric field at the interaction altitude. The estimated instability threshold using the theoretical model is compared with the threshold of MSBS lines in the experiment and possible diagnostic information for the background ionospheric plasma is discussed. Simultaneous formation of artificial field-aligned irregularities (FAIs) and suppression of the MSBS process is investigated. This technique can be used to estimate the growth time of artificial FAIs which may result in determination of plasma waves and physical process involved in the formation of FAIs.

1 Introduction

[2] Interaction of a high power electromagnetic wave transmitted from the ground with local plasma in the ionosphere has been used as a powerful remote sensing tool for the modified ionospheric environment. Stimulated Electromagnetic Emissions (SEE) induced by the pump wave can be detected by ground receivers. SEE is believed to be produced locally by parametric instability processes in the plasma involving the pump field which may decay into electrostatic (ES) and electromagnetic (EM) waves [Leyser, 2001]. The generated EM wave propagates back to the Earth and can be detected by SEE receivers. Viable parametric instability processes were proposed by Stubbe et al. [1984]. A wide variety of electrostatic and electromagnetic waves may be produced during the SEE generation process [Leyser, 2001]. The SEE spectral sidebands were found to depend on a number of ionospheric parameters in addition to the heater wave characteristics. It was later postulated that the sidebands in the SEE spectrum should develop in the altitude region where the pump frequency f0 is near the local plasma frequency (reflection altitude) or where f0 is near the local upper hybrid (UH) frequency. Use of high-frequency heating experiments has been extended in recent years and used extensively to investigate the charged dust layers in the mesosphere [Chilson et al., 2000; Havnes et al., 2003; Mahmoudian et al., 2011; Mahmoudian and Scales, 2012; Mahmoudian and Scales, 2013].

[3] Thide et al. [1982] discovered stimulated electromagnetic emissions and first viable parametric instability processes were proposed by Stubbe et al. [1984]. Leyser [2001] extended the theory and very detailed review of previous works. Frolov et al. [2001] and Sergeev et al. [2006] investigated the dependence of the SEE spectra on the relation between f0 and nfce in a wide f0 range. Thide et al. [2005] and Kotov et al. [2007] studied the competition between reflection-altitude-related and UH-related SEE features. The role of field-aligned irregularities (FAI) for different features was studied by Norin et al. [2008]. Grach [1985] and Grach et al. [1998] observed the role of the FAI in SEE (Broad Continuum feature) generation for the first time. Carozzi et al. [2002], Kotov et al. [2008], and Grach et al. [2008] performed a fine study of f0 and nfce with fast f0 sweep near nfce. It should be also noted that recent experiments at HAARP has lead to the first observation of Stimulated Ion Bernstien Scatter (SIBS) near the second and third electron gyrofrequency [Bernhardt et al., 2011; Scales et al., 2011; Samimi et al., 2013; Mahmoudian et al., 2013, Fu et al., 2013]. Furthermore, the SIBS feature has been recently observed simultaneously with the artificial airglow [Mahmoudian et al., 2013]. The first unique narrowband emissions ordered near the hydrogen ion (H+) gyrofrequency (fcH) in the stimulated electromagnetic emission spectrum when the transmitter is tuned near the second electron gyroharmonic frequency (2fce) during ionospheric modification experiments was observed by Bordikar et al.[2013a], (M. R. Bordikar et al., Impact of active geomagnetic conditions on stimulated radiation during ionospheric second electron gyroharmonic heating, submitted to Journal of Geophysical Research, 2013b). The implications of these new observations are new possibilities for characterizing proton precipitation events during ionospheric heating experiments.

[4] The High Frequency Active Auroral Research Program (HAARP) heating facility in Gakone, Alaska, has opened the door to investigate parametric decay instabilities that have higher pump threshold power such as stimulated Brillouin Scatter (SBS) that appears with emission lines at much narrower bandwidths relative to the pump frequency [Norin et al., 2009; Bernhardt et al., 2010]. Stimulated Brillouin Scatter (SBS) is a strong SEE mode involving a direct parametric decay of the pump wave into an ES and a secondary EM wave that sometimes could be as strong as the HF pump [Bernhardt et al., 2010]. SBS has been studied in laboratory plasma experiments by the interaction of high power lasers with plasmas. This parametric decay instability has been studied in theory, and excited ion acoustic and EM waves have been observed in laboratory experiments [Kruer, 1988; Eliezer, 2002]. The term Magnetized Stimulated Brillioun Scatter (MSBS), as will be used in this work, was introduced to describe SBS which may exhibit both electrostatic ion cyclotron EIC as well as ion acoustic IA low-frequency decay modes due to propagation in the magnetized ionospheric plasma. It should be also noted that recent experiments at HAARP have lead to the first observation of Stimulated Ion Bernstien Scatter (SIBS) near the second and third electron gyrofrequency [Bernhardt et al., 2011; Mahmoudian et al., 2013]. Furthermore, the SIBS feature has been recently observed simultaneously with the artificial airglow [Mahmoudian et al., 2013].

[5] Historically, attempts to investigate the Stimulated Brillioun Scatter (SBS) process in the ionosphere date back to theoretical and experimental investigations of Dysthe et al. [1977], Fejer [1977], and Fejer et al. [1978] after Dysthe et al. [1977] predicted the possibility of exceeding the threshold for SBS in ionospheric experiments. Stenflo [2004] provides a brief review with historical perspective and relevance of these early works. The SBS instability in a magnetized ionospheric plasma excited by high power HF wave-ionospheric experiments was observed in the SEE spectrum for the first time at the High Frequency Active Auroral Research Program (HAARP) facility by Norin et al. [2009] and Bernhardt et al.[2009, 2010]. It has been shown that an ordinary mode electromagnetic wave can decay into an electrostatic wave and a scattered electromagnetic wave by a process called Magnetized Stimulated Brillouin Scatter (MSBS). Depending on the angle between the wave normal direction and the background magnetic field vector, the excited electrostatic wave could be either Ion Acoustic (IA) or Electrostatic Ion Cyclotron (EIC). In fact, enhanced electron temperature in the modified ionosphere by the pump wave excites the naturally existing IA waves typically heavily damped by Landau damping as a result of TeTi. Therefore, IA emission lines are expected to be seen in spectra due to the enhanced electron temperature and for small propagation angle relative to the magnetic zenith. EIC lines can be excited with oblique propagation angles [Bernhardt et al., 2010]. It is of interest to note that potentially useful characteristics of the EIC waves including ion velocity distributions, collisional effects, and dynamical variation of electron temperature predicted by earlier works [e.g., Panchenko et al., 1985; Stenflo, 1989; Scales and Xi, 2000] have yet to be investigated carefully and should be the subject of future experimental study.

[6] The excited daughter (downshifted) electromagnetic wave, in the MSBS process in the interaction region, which could be the reflection altitude where refractive index goes to zero or UH resonance altitude, appear in the SEE spectrum as spectral lines offset from the pump frequency. Stimulated Brillouin scatter produces extremely strong SEE emissions up to 10 dB below the HF pump amplitude in comparison with other SEE lines which are usually weaker than the pump by about 40 dB. The received SEE spectral lines originating from the UH and reflection regions are distinguished by their offset frequencies. The SBS emission originating near the reflection altitude has a downshifted peak (SBS−1 or narrow peak (NP)) frequency of about 15 Hz. The SBS emission from the upper-hybrid region has a downshifted peak (SBS−2 or 2NP) frequency of about 30 Hz. While the downshifted emission lines are produced by the upgoing pump wave, the upshifted emission lines have been interpreted as being due to a four-wave interaction involving the scattered downgoing pump EM wave [Bernhardt et al., 2009, 2010]. Both SBS lines can have weaker upshifted peaks with the same magnitude frequency offsets [Norin et al., 2009; Bernhardt et al., 2009, 2010].

[7] The primary purpose of this paper is to extend the work of Norin et al. [2009] and Bernhardt et al.[2009, 2011] by providing more experimental observations and theory of Magnetized Stimulated Brillouin Scatter (MSBS). The results of matching condition and ray tracing are discussed in the first section. Then, solution of wave equation and an estimation of electric field amplitude near the interaction region are provided. New measurements of MSBS for pump frequency variation near 3fce, beam angle, and amplitude of pump power variation are presented that were not explored in the previous works. Finally, a conclusion is provided.

2 MSBS Instability Growth Rate

[8] Threshold fields for each mode are dependent on the propagation angle in the plasma. The conditions for growth of IA waves are more favorable than EIC waves in the modified ionosphere over HAARP. The EM pump wave elevates the electron temperature so TeTi and the IA waves are not subject to strong Landau damping. The electrostatic wave number is equal to twice the EM wave number which becomes small near the EM wave reflection altitude. Finally, at HAARP, the beam of the EM wave is tilted up the magnetic field line, so the transverse component of the EIC vector is small. In summary, the MSBS preferentially yields IA waves over EIC waves. The MSBS instability threshold is controlled by the strength of the pump wave and the rate of the ion collisional damping.

[9] A simplified expression for the ratio of the EIC and IA growth rates using the assumption |kLCIA|≪Ωci can be written as [Bernhardt et al., 2010]:

display math(1)

where θ is the angle between the wave normal direction and background magnetic field where the maximum amplitude of the standing wave of the EM pump occurs and kL is low-frequency wave number. CIA denotes the ion sound speed.

[10] Another theoretical model of MSBS was developed by Shukla and Stenflo [2010] assuming that the square of the pump wave frequency is much larger than the square of the (radian) electron gyrofrequency Ωce. Considering the IA wave excited by the MSBS instability with assumptions of ω≪Ωci and kzk, the maximum growth rate of IA waves is given by [Shukla and Stenflo, 2010]:

display math(2)

where inline image, CIA is the ion sound speed, u0=eE0/meω0 is the oscillation velocity, ωo is the (radian) pump frequency, E0 is the pump electric field, and ωpi denotes the (radian) ion plasma frequency. It has been shown for ωci that maximum growth rate for EIC waves also can be written as [Shukla and Stenflo, 2010]:

display math(3)

where k is the perpendicular wave number and kz is the parallel wave number to the magnetic field. The IA growth rate in this case also is greater than the EIC growth at smaller angle relative to magnetic field which validates the analytical expressions of IA and EIC growth rate given by Bernhardt et al. [2010]. According to Figure 1, Bernhardt's model predicts that EIC growth rate should exceed IA growth rate for θ0>45° while Stenflo and Shukla's model predicts the same trend for θ0>37°. This figure shows the transition between IA and EIC wave excitation as a function of propagation angle relative to B. Ion acoustic waves grow much faster than EIC waves for propagation angle close to magnetic zenith. For propagation at larger angles and nearly perpendicular to B, the EIC mode is dominant. Therefore, considering the Bernhardt model approximation that the square of the pump wave frequency is much larger than the square of the electron gyrofrequency and the approximation by Stenflo and Shukla that the pump wave frequency may be near the electron gyrofrequency, the two models estimate the angle in the same range. It should be noted that a more general dispersion relation of MSBS has been derived by Brodin and Stenflo [2013] which have potential to alleviate limitations of the two models for calculations near gyroharmonics that would be used for future investigation. The dispersion relation is stated in Appendix A.

Figure 1.

Ratio of MSBS EIC to IA parametric decay growth rates for varying wave normal angle. Note that EIC waves dominate at wave normal angles close to perpendicular to the magnetic field.

3 Ray Racing and Wave Matching Conditions for MSBS

[11] The Hamilton's equations for raypaths using the refractive index in a magnetized plasma are given by Yeh and Liu [1972] and Budden [1985]. These equations were solved numerically for propagation in the measured ionosphere over the HAARP transmitter. When the HF beam is tilted off magnetic zenith, the wave normal angle relative to the magnetic field direction will vary with altitude. Ray tracing in the anisotropic plasma can provide both the wave number magnitude k0 and the wave normal angle θ. The magnetic zenith (MZ) path starts out along the magnetic field direction with a propagation angle of zero. This angle stays near zero except within a few kilometers below the plasma resonance altitude where the angle becomes 90° at reflection. The wave propagation angle θ at the upper hybrid resonance altitude is 12° for the upgoing MZ ray. The ray propagates horizontally for about 10 km with a wave normal nearly perpendicular to B. The ray returns to Earth with a 28° angle relative to B. The observations of upshifted MSBS lines indicate the presence of EM waves with simultaneous upward and downward propagation along the same field-aligned path.

[12] According to the matching condition, the IA wave mode is limited to frequencies less than the ion gyrofrequency fci while the EIC mode is found for frequencies just above fci. The energy and momentum conservation requires that the wave frequency and propagation direction satisfy these expressions:

display math(4)
display math(5)

where k0, kS, and kL denote the wave numbers for the upward electromagnetic pump, scattered electromagnetic wave, and IA/EIC waves, respectively [Kruer, 1988; Eliezer, 2002]. It should be noted that ks, k0, and kL describe propagation directions. The downshifted emission lines are a result of interaction of the pump wave with plasma below the reflection altitude. The upward propagating EM pump generates downshifted MSBS lines with frequency less than the pump (ωs=ω0ωL) as it loses energy through the parametric decay instability. The weakened upward propagating pump due to this interaction below the plasma resonance altitude will reflect near where the refractive index goes to zero. This downward wave interacts with low-frequency IA waves excited through previous interaction and generates a secondary upward scattered electromagnetic wave with wave vector kS+=k0+kL at frequency ωS+=ω0+ωL. This scattered wave also reflects back and produces an upshifted spectral line in the spectra. Since this mode is generated by a weaker pump wave, upshifted emission lines are expected to be weaker than downshifted spectral lines. Because the scattered and pump EM wave frequencies are almost equal, the matching conditions equation is well approximated by letting ks=−k0, so kL=2k0. The frequency of low-frequency products ωLis given by [Bernhardt et al., 2010]:

display math(6)

where + sign represents the EIC wave and − sign denotes the IA wave. The computed matching conditions for the HAARP experimental parameters and two propagation angles with respect to magnetic field are shown in Figure 2b based on the numerical solution of equation (6). The angle θ is between the wave normal direction and the background magnetic field vector and it satisfies BkL=|B||kL|cosθ. The IA wave is limited to frequencies less than the longitudinal component (fcicos(θ)) of the ion cyclotron frequency. Figure 2b illustrates that O Mode can excite the IA wave and EIC at both upper hybrid (UH) and reflection altitudes. The generated IA wave at the reflection altitude is expected to be near 10 Hz and the IA emission originated at the upper hybrid altitude has frequency of about 20–30 Hz. The EIC wave excited at the reflection and upper hybrid altitude also has a frequency just above fci. As can be seen, increasing the electric field angle at the reflection altitude from 14° to 42° reduces the frequency of excited IA waves and also increases the EIC frequency, however, to a lesser degree. It turns out that increasing CIA also has a similar effect as the electric field angle on the frequency of the excited modes.

Figure 2.

(a) Raypaths for wave propagation at magnetic zenith and vertical. Raypath 5.6 MHz is calculated for foF2= 6.125 MHz. (b) Generalized SBS matching conditions for O-Mode electromagnetic waves at 4.1 MHz for an ionosphere with an ion sound speed of 1600 m/s and an ion gyrofrequency fci= 49.6 Hz propagating at an angle of 14.5° with respect to magnetic field direction.

[13] A solution of the wave equation described in Appendix B is shown in Figure 3 for the three components of electric field for altitude range 172–177 km. The numerical solution starts at altitude 172.4 km with an upward propagating wave with a transverse electric field of 1.2 V/m corresponding to 1 GW ERP (effective radiated power) at 4.5 MHz in the ionosphere neglecting any D region absorption. As the pump wave approaches the plasma resonance altitude where the pump frequency 4.5 MHz equals the plasma frequency, the amplitude of the transverse component Ey increases to 3 V/m while the amplitude of the other transverse component drops to 0.5 V/m. The vertical/longitudinal electric field has the largest amplitude of ∼ 200 V/m only a few tens of meters below the plasma resonance altitude. Such a strong electric field can strongly modify the plasma and the linear dispersion relation used to derive the matching condition is no longer valid in this region. For the simulation illustrated in Figure 3, the peak electric fields near the UH resonance altitude are (Ex, Ey, Ez)=(1.6, 1.9, 2.3) V/m. Considering the use of the WKB approximation, this model may somewhat overestimate the calculated amplitude of electric field at the interaction altitude in comparison with full simulation models [Eliasson et al., 2012].

Figure 3.

Computed transverse and longitudinal electric fields produced by the 4.5 MHz HAARP transmitter. The maximum electric field is found in the longitudinal component Ez= 200 V/m just below the plasma resonance at 177.74 km altitude where the local plasma frequency is 4.48 MHz.

4 Experimental Observations of MSBS

[14] We present data from five different experiments performed on 25 October 2008, 18–23 July 2010, 19–27 July 2010, 24 July 2011, and 5–9 August 2012 at the HAARP facility (geographical coordinates 62.39°N, 145.15°W). The effective radiated power was 1 GW, which exceeds the capability of all other similar HF facilities. A large dynamic range HF receiver was set up at HAARP to record Stimulated Electromagnetic Emissions (SEE). The reflected EM signal was measured using a digital receiving system that sampled the HF signals from a 30 m folded-dipole antenna at a rate of 250 kHz.

[15] The HF radio waves had O-mode polarization and the pump beam direction was alternated between the geomagnetic zenith (MZ), (202° azimuth, 14° zenith) up to 202° azimuth, 28° zenith. The beam was transmitted in a continuous or quasi-continuous wave mode (for example, 30 s on, 30 s off) for up to 2 h per experiment. The recorded time series were analyzed by applying a fast Fourier transform with a Blackmann window, corresponding to 0.8 s, revealing sideband emissions in the frequency domain with a resolution of 1.25 Hz for 2008 campaign data. All other SEE data shown in this paper have frequency resolution less than 1 Hz.

[16] Observations of Magnetized Stimulated Brillouin Scatter (MSBS) were obtained with HAARP by tuning the transmitter near the third harmonic of the electron gyrofrequency 3fce. In the previous study by Bernhardt et al. [2010], it has been shown that excited electrostatic waves through the MSBS process in the ionosphere, either IA or EIC waves, depend on the value of θ0 (angle between the wave vector and magnetic field) at the interaction altitude. Although the theoretical calculation suggests the excitation of MSBS process with X-mode pump wave, it should be noted no IA or EIC emission lines was observed during X-mode heating.

[17] Figure 4 illustrates an SEE spectrum immediately after the turn-on of the HAARP transmitter at 4.1 MHz for O-mode polarization. This figure represents the effect of angular variation on the excitation of EIC emission line associated with MSBS. The data were taken during the 2011 campaign. The HF signal data were acquired with the Australian developed GBox-5 receiver that digitizes a 250 kHz band around the pump frequency for digital signal processing to produce the SEE spectra. The spectrum for a full power beam pointed at three different zenith angles ZA= 0°, 7°, and 14° with azimuth angle 202° is shown. The spectrum shows the upshifted and downshifted IA emission lines excited at reflection altitude at frequency around 10 Hz. In this case for the beam offset from the MZ by 0° and 7°, only IA emission lines appear in the spectrum and when the beam was tilted more to 14° a strong EIC line is produced at 51 Hz. It has been shown that fci at 225 km altitude over HAARP is estimated to be 49 Hz. This is consistent with the previous observation of MSBS [Bernhardt et al., 2010] that a stronger excitation of EIC spectral lines are observed at larger angles with respect to the MZ. The 120 Hz lines are produced by power ripple in the transmitter power system. As mentioned before, the upshifted IA lines are the result of scatter by the reflected pump wave from the IA waves to produce an upgoing, upshifted EM wave that reflects in the ionosphere and is received on the ground.

Figure 4.

Narrowband SEE spectra showing IA spectral lines when the beam offset from the magnetic zenith is 0° and 7°, and when the beam is tilted more to 14°, a strong EIC line is produced.

[18] A more extensive study on MSBS excited at 3fce was conducted during the 2012 campaign at HAARP. According to the ionogram data, the altitude of HF reflection was around 230 km during this experiment. The International Geomagnetic Reference Field (IGRF) model provided the magnetic field strength and direction in the upper atmosphere over HAARP. The magnetic field near the HF reflection altitude is estimated to be |B|=5.082×10−5 Tesla which results in 3fce approximately 4.28 MHz. Figure 5 shows SEE spectra for the experiment carried out on 12 August 2012 from 4:30 UT to 5:30 UT. The transmitter was pointed at ZA=18°, AZ=202° and operated with O-mode polarization at full power alternating between 30 s at full power and 30 s off to allow recovery from artificially induced effects. The transmitter frequency stepped through 3fce from 4.25 MHz to 4.31 MHz in 20 kHz steps every other “on” period to compare effects away and near 3fce. The frequency resolution 200 kHz used in the experiment does not allow us to study the variation of MSBS emission lines with pump frequency near 3fcein detail and is the subject of future investigation. As can be seen, the upshifted IA emission line almost disappears at 4.31 MHz and the strength of the downshifted IA emission lines drop about 20 dB. Increasing the pump frequency toward the gyroharmonic also shifts the SBS−1 line from −9 Hz to −12 Hz while the SBS+1 stays almost at the same frequency.

Figure 5.

Experimental observations of IA emission lines associated with MSBS when the heater frequency was tuned to frequencies near 3fce, 4.25 MHz, 4.27 MHz, 4.29 MHz, and 4.31 MHz and heating cycle was 30 s. MSBS weakens as the pump approaches 3fce.

[19] The 2010 campaign at HAARP aimed at measuring the threshold of EIC and IA emission lines for the first time. Variation of the spectrum with transmitter power for three values of power is illustrated in Figure 6. The previous study by Bernhardt et al. [2010] has shown that EIC lines have much smaller growth than IA lines. Therefore, in order to estimate the threshold for the EIC emission lines, the experiment was conducted for three transmitter powers 3.6 MW (ERP≈ 1 GW), 2.9 MW (ERP≈ 800 MW), and 1.9 MW (ERP≈ 520 MW). The pump wave frequency was at 4.18 MHz and 4.1 MHz and transmitter beam was pointed 14° off the MZ. The EIC emission line can be clearly seen in the spectra of Figure 6a for pump power 3.6 MW around 52 Hz downshifted from the pump. This frequency is consistent with the frequency range predicted by the matching condition in the first section and shows that both IA and EIC lines are produced by the interaction at the reflection altitude. This figure shows that reduction of the pump power may bring the pump amplitude at the reflection altitude below the EIC mode threshold which is necessary for the MSBS process and turn off the EIC instability. This happens when the pump power reduces to 2.9 MW (ERP≈ 800 MW) where the strength of the EIC line drops significantly relative to the full power case. No EIC line is observed for pump power 1.9 MW (ERP≈ 520 MW). As can be seen, the strength of the IA emission line does not change by reducing the power amplitude from 3.6 MW to 1.9 MW which indicates that the IA waves have much larger growth rate than EIC waves. To measure the threshold of IA lines, another experiment with fine power step at lower amplitude was carried out that will be presented shortly. Figure 6b shows the same behavior for the pump frequency 4.1 MHz. This case also shows a similar behavior with Figure 6a and the EIC line almost disappears by reducing the pump power to 2.9 MW. Reducing the power amplitude to 1.9 MW in this case makes the upshifted IA line very weak.

Figure 6.

Variation of EIC line with the pump power (a) f= 4.18 MHz and (b) 4.1 MHz. The figure validates theoretical predictions that EIC has higher threshold.

[20] The pump power reduced in 3 dB steps in order to measure the threshold for the excitation of IA lines is shown in Figure 7. The MSBS experiment on 19 July 2010 used a power beam at magnetic zenith, vertical, and ZA=−14° with pump power varying from 3.6 MW (ERP≈ 1 GW) to 0.11 MW (ERP≈ 30 MW). Figure 7a shows the power spectrum of IA emission lines with pump power for the beam pointed at magnetic zenith and the spectra illustrates a pair of weak upshifted MSBS lines (anti-Stokes lines) and two stronger downshifted MSBS lines. The past theoretical works on the stimulated Brillouin spectra in an unmagnetized plasma by Kruer [1988] and Eliezer[2002] have also predicted that a stronger downshifted IA lined should be produced. All the IA SBS lines presented in this investigation show stronger downshifted lines than upshifted lines. Figures 7a and 7b show that when the pump beam was directed vertically and toward MZ SBS±1 and SBS±2 emission lines appear symmetrically around f0 with frequency shifts ∼10 Hz and ∼26 Hz, respectively. The downshifted SBS−1 is well developed in most spectra but the upshifted SBS+1 cannot always be identified. It turns out that the downshifted lines have the lowest threshold among the IA emission lines. When the HF beam was pointed toward the magnetic zenith, spectra shows two set of lines. One set is near 27 Hz which represents excited IA waves due to the interaction at the UH altitude and there is a second set of lines near 10 Hz that corresponds to the interaction at the reflection altitude. This is in agreement with the wave matching condition and theory presented in the section 3. The SBS−1 line has a frequency offset 11.4 Hz from the pump and SBS±2 are located at 26.7 Hz and 29 Hz from the pump wave. Upshifted lines are weaker than the Stokes lines which is consistent with the theory and represents the weak interaction of the reflected wave with the local plasma at the UH and reflection altitudes. It turns out that the lowest power for the observation of SBS+1 line is about 1.8 MW (ERP≈ 500 MW) and SBS±2 lines disappear from the spectra by reducing the pump power to a value less than 0.45 MW (ERP≈ 125 MW). Spectra for the beam pointed at vertical are illustrated in Figure 7b which shows the same trend as Figure 7a. The SBS+1 line has the lowest threshold and only appears for 3.6 MW (ERP≈ 1 GW) pump power. SBS±2 lines are weaker in comparison with MZ, but they have almost the same threshold of about 0.4 MW (ERP≈ 110 MW).

Figure 7.

Spectra of scattered electromagnetic waves from the HAARP transmitter operating at 4.5 MHz for the pump beam angles at (a) magnetic zenith, (b) vertical, and (c) ZA=−14° (antimagnetic zenith) and pump power variation from 0.1 MW to 3.6 MW in 3 dB steps. All the data were taken within a 1 h period on 20 July 2010. The downshifted lines are also called the Stokes lines, downshifted SBS− lines or the downshifted narrow peaks (NP−). The upshifted lines are similarly called the anti-Stokes lines, upshifted SBS+ lines or the upshifted narrow peaks (NP+).

[21] To get a better estimation of the threshold of MSBS processes including both IA and EIC lines, a new experiment was designed and carried out on 24 July 2011. The transmitter was operated with 4 min on and 1 min off cycles. The power increased from 0.1 MW (ERP≈ 27 MW) to 3.6 MW (ERP≈ 1 GW) in 210 s and 35 steps, and set at full power with 3.6 MW for 30 s. The beam was tilted from magnetic zenith to 15° off with 3° increments to excite both IA and EIC emission lines. The measured threshold of MSBS emission lines is similar to the previous experiments in which the pump power was increased in 3 dB steps every on and “off” period. The upshifted IA emission lines have a power threshold near 1 MW and EIC emission line appears in the spectra when the amplitude of the pump power exceeds 3 MW. The dynamic spectra recorded for a pump beam at (ZA = 18° and AZ = 202°) (1 GW ERP) at 4.2 MHz is illustrated in Figure 8c, and pump power is increased from 0.1 MW to 3.6 MW. Figures 8a and 8b shows the time snapshots of Figure 8c. As can be seen in Figure 8b, EIC line appears in the spectra when the pump power exceeds 3 MW. After a transient produced by the HAARP transmitter at turn-on, the SEE spectra shows the central pump line, two MSBS lines around the pump at 10 Hz which correspond to the excited IA lines near the reflection altitude. IA lines appear in the spectra when pump power exceeds 1.15 MW (ERP≈ 320 MW) around t=60 s after pump turn-on. When the power exceeds 2.9 MW (ERP≈ 800 MW) at t=170 s, a strong emission line appears in the spectra at 50 Hz as a result of excited EIC wave.

Figure 8.

Spectrogram of the Magnetized Stimulated Brillouin Scatter lines for a pump wave beam offset 14° from the magnetic field direction. This figure is showing the difference in threshold power of IA and EIC lines as the transmitter power is varied from 0.1 MW to 3.6 MW during the period shown.

[22] As stated earlier, another relevant process for excitation of SEE during the MSBS line generation involves mode conversion of the O-Mode EM pump wave into an upper hybrid wave. This upper hybrid wave undergoes parametric decay into a lower frequency upper hybrid wave and a lower hybrid wave. The daughter UH wave mode converts on field-aligned irregularities into an O-Mode electromagnetic wave which is received on the ground as a downshifted maximum (DM) SEE line [Stubbe et al., 1984; Leyser et al., 1994]. The side-by-side spectrograms in Figure 9 for the full power beam at 3.6 MW show the disappearance of the MSBS line relative to the subsequent appearance of the field-aligned irregularity and downshifted upper hybrid line (DM). Weaker lines at 120 and 180 Hz are produced by power-line harmonics in the pump transmissions as illustrated by the vertical lines in the spectra of Figure 9(left). The fast narrow continuum (FNC) is a smooth, downshifted feature seen immediately after pump start [Leyser, 2001]. The 8 kHz offset of the DM from the pump frequency is consistent with an estimated lower hybrid frequency of 8.18 kHz. This feature narrows to less than 5 kHz when the DM starts to appear. The spectral features below the dashed line in Figure 9 are formed without field-aligned irregularities (FAI). Above the dashed line, the effects of FAI, especially in the UH resonance region, are important.

Figure 9.

Low- and medium-frequency spectrograms of the SEE emissions around the 5.8 MHz carrier. The SBS−1 starts at pump turn-on and disappears after 12 s. The fast narrow continuum (FNC) broadens a few seconds after turn-on and then decays in width after 12 s. The downshifted maximum (DM) starts to appear soon after the SBS−1 has vanished.

[23] The temporal variations in the peak amplitude of the MSBS lines are shown in Figure 10 where the dB power scale has been chosen to make average received pump power about 0 dB. The MSBS line (NP) appears immediately after the pump turn-on at 21:35:30 UT. The MSBS line decays for 11 s at a rate of 1.14 dB/s. At 21:35:41, the NP or SBS−1 line power drops by 30 dB vanishing from the spectra. Past this time, the spectrum is composed of the upshifted continuum and power-line harmonics in the pump wave. The DM power starts to increase at 21:35:42, 12 s after turn-on. During this whole process, the average received pump power stays at about 0 dB.

Figure 10.

Time history of the reflected pump amplitude, the downshifted SBS line, and downshifted maximum DM after turn-on of the 5.8 MHz pump. The average pump power shows no systematic drop but the narrow peak (NP) associated with the SBS instability decays and then precipitously drops. The drop occurs just before the DM power begins to increase.

5 Discussion

[24] According to the raypath for vertical beam shown in Figures 2a and 7, a weak interaction is expected for the reflected wave at UH and reflection altitude. Therefore, upshifted emission lines are expected to be absent or very weak in spectra in comparison with MZ pump heating. It should be noted that both Stokes and anti-Stokes lines are effectively excited when the low-frequency ES waves (in this case, IA and EIC waves) have frequency offset much smaller than growth rate. Therefore, not observing the upshifted EIC emission line in the spectra could be due to the fact that EIC growth rate is comparable to fEIC. This is the subject of future work. As expected from theory, increasing the angle between wave normal and magnetic field line reduces the growth rate of IA lines and increases the threshold. As the result, no IA emission line originating from the UH altitude is seen and the SBS−1 line has a threshold about 1.9 MW. It should be noted that naturally existing IA waves damp out in the ambient ionosphere as the result of ion Landau damping but this can be neglected if TeTi[Ichimaru, 1973]. In the ionospheric modification experiment using the HAARP HF transmitter, it is assumed that the electron temperature is much larger than the ion temperature, so ion Landau damping can be neglected. For MSBS, the theory shows that the growth rate for the EIC waves is much lower than the growth rate for the IA waves in the plasma near the reflection or upper hybrid altitudes [Bernhardt et al., 2009, 2010]. The spectrum was experimentally found to be highly dependent on the proximity of the pump frequency to the harmonics of the electron cyclotron frequency fce which has not been investigated by current theory. To study this effect on the MSBS generated in the ionosphere, a pump frequency near third harmonic of the electron cyclotron frequency 3fce was employed in the experiment. As can be seen in Figure 7a, the SBS+1 line originated at the reflection altitude exists in the spectra even for pump powers as low as 0.1 MW. This is consistent with the calculations of electric field amplitude presented in section 3, since electric field amplitude increases by a factor of 5 at the UH altitude while the enhancement of the order 100 may occur near the reflection altitude.

[25] According to Kruer [1988], the nonlinear dispersion relation of MSBS may be written in the form:

display math(7)

where γ0 is the maximum growth rate of the scattered wave, γi the ion Landau damping rate of the IA wave, and γs the collisional damping. For the threshold (where γ=0), the dispersion relation will be simplified to inline image. γs can be written as inline image, where νen is the electron-neutral collision frequency. For the current calculations νen≈1 kHz. Assuming TeTiand long wavelengths, ion Landau damping can be approximated as inline image. Using equation (2) in (7), it turns out that according to the theory, E0 needed to excite the IA mode is of order 1 V/m. The measured threshold power for SBS instability during the experiment on average is about 1 MW which leads to the electric field amplitude threshold E0 of tens of V/m near the interaction altitude. This difference could be as a result of calculating the growth rate for homogeneous plasma. Therefore, including plasma inhomogeneity into calculations may give a much better approximation of the threshold [e.g., Rosenbluth, 1972].

[26] At the UH layer, the parametric process producing the Downshifted Maximum (DM) may occur as well as MSBS leading to SEE. To reiterate, the process postulated to produce the DM is as follows. The EM pump field is converted into an UH wave and FAI first, then UH wave acts as a pump field for generation of a LH wave and another UH wave through a parametric decay process [Grach, 1985; Grach et al., 1998]. The second UH wave is shifted below the pump field by the LH frequency (8 kHz). The second UH wave is scattered into another EM wave (nonlinear beat currents) and observed on the ground as the DM [Stubbe et al., 1984; Leyser et al., 1994; Grach et al., 2008]. Before field-aligned irregularities FAI form, DM lines are prevented in the spectrum and SBS lines dominate. After FAIs form, the pump wave may be depleted in the UH region and there may not be sufficient electromagnetic pump power near the reflection altitude for SBS although DM generation is allowed due to the presence of FAIs. The experimental observations presented in this paper illustrate the transition between a strong SBS-1 line and a weaker DM1 emission. This transition is abrupt for the SBS instability indicating that there is a threshold for excitation and maintenance of the SBS instability. Proximity of the pump frequency to 4fce could be a possibility of the slow DM development.

6 Conclusions

[27] The generalized Magnetized Stimulated Brillouin Scatter (MSBS) was studied with both theory and ionospheric heating experiment. A dispersion relation of MSBS, wave matching condition, and ray tracing was employed to investigate the required conditions for excitation of MSBS instability in the modified ionospheric plasma. The theory predicts a beam angle dependence for the excitation of the IA and EIC lines of MSBS. For propagation at small angles to the magnetic field, the IA lines grow much faster than the EIC lines, and EIC lines are excited when the transmitter beam is titled off MZ. Variations of IA and EIC emission lines with pump wave frequency sweeping near the 3fce and beam angle were examined during 2010, 2011, and 2012 campaigns at HAARP. Tuning the pump frequency to frequencies close the gyroharmonic also weakens the MSBS process. Experimental observations show good agreement with theoretical calculations. The threshold of each emission line was measured in two ways by stepping and sweeping the amplitude of the pump wave that gives an estimation of the electric field at the interaction altitude needed to derive each mode. The measured threshold using both approaches show that the EIC line has a higher threshold than the IA line which is consistent with the theoretical predictions. Upshifted emission lines are weaker. The EIC line excited at the UH altitude has threshold ∼3 MW (ERP≈ 830 MW), and the IA line excited at the same altitude grows above the noise level when the amplitude of the pump power exceeds 0.5 MW (ERP≈ 140 MW). It has been observed that the pump beam pointed at angles close to MZ only produces IA lines, tilting the beam to angles larger than 14° relative to MZ can excite EIC lines which is in agreement with theory developed by Bernhardt et al. [2010]. Simultaneous development of the downshifted maximum DM produced by artificial FAI and decay of MSBS from the electromagnetic pump field was observed which allowed the growth time of the formation of the FAIs to be measured. The sensitivity of IA and EIC lines with different parameters was investigated in this work to get a better estimation of electron temperature and ion composition using emission lines produced by the MSBS process.

Appendix A: Derivation of the Governing Equations of MSBS Dispersion Relation

[28] Using the electromagnetic wave equations derived from the Maxwell equations, the electric field for the initial pump wave gives the equation for the ordinary mode and extraordinary mode as:

display math(A1)

where Fp is the pump wave function, ωp is the plasma frequency, z is altitude, p denotes the pump wave along the propagation path, c is the speed of light, and inline image is the ordinary and extraordinary refractive index, respectively, based on the Appleton-Hartree formula. The scattered EM wave at ωS is driven by the pump wave electric fields Ep and the EIC/IA fluctuations in the ion density at ωL±. The wave equation for the scattered EM component becomes

display math(A2)

where inline image is z component of ion velocity. The mixing between the pump wave and the low-frequency ion wave in the left side of equation (A2) can provide both the downshifted Stokes mode at frequency ωS=ωpωL and the upshifted anti-Stokes mode at frequency ωAS=ωp+ωL. The mixing of two electromagnetic waves provides the source for low-frequency electrostatic wave equations that describe the ion acoustic and electrostatic ion cyclotron waves. This mixing is the result of the effects of the gradient of the radiation pressure or ponderomotive force as derived later in this section for a magnetized electron plasma.

[29] Consider a single electron acting under the nonlinear influence of the electromagnetic fields just described. The ponderomotive force of a single particle in an electromagnetic field has been derived for unmagnetized plasma by Schmidt [1966], Chen [1984], and Eliezer [2002] and for magnetized plasma that is warm, spatially dispersive, nonstationary, and inhomogeneous by Lee and Parks [1983]. A comparison of single particle and fluid approaches to this derivation is discussed by Vaclivik et al. [1986]. In this paper, where the phase velocities of the high-frequency pump EM waves are much larger than thermal velocities of the electrons and ions in the plasma, the single particle method will be used.

[30] The nonlinear ponderomotive force couples the pump wave into the scattered electromagnetic waves. The low-frequency wave equation using the single particle approach for a magnetized plasma and assuming small density and velocity fluctuation can be written as [Bernhardt et al., 2010]:

display math(A3)

where ET is the total electric field including pump and scattered electric field, inline image, and Ω=eB/m. The low-frequency electrostatic and scattered electromagnetic waves grow together with the energy supplied by the pump wave amplitude inline image. Damping of the SBS mode is specified by ion-neutral collisions in Ui=1−iνi/ωL± and the electron-neutral collisions. Additional damping of the ion acoustic wave occurs with ion Landau damping but this can be neglected if TeTi[Ichimaru, 1973].

[31] The coupled set of low- and high-frequency wave equations (A1)(A3) provides a complete description of the SBS instability in a magnetized plasma that leads to the growth rate for the MSBS [Bernhardt et al., 2010]. The ratio of EIC growth rate γL+ to IA acoustic growth rate γLis given by:

display math(A4)

where Ωiz is the ion gyrovector transverse to the electromagnetic wave vector. The instability occurs at the characteristic electrostatic frequency that is a normal mode. ωL± is the undamped mode frequency and with the ± signs representing the two roots for the EIC and IA modes, respectively, above and below the ion gyrofrequency.

[32] For small wave numbers such that kL≪Ωi/CIAor for propagation at small angle to the magnetic field, equation (A4) is much less than unity, the IA wave (L−) grows much faster than the EIC wave (L+).

[33] As an alternative, the general MSBS dispersion relation can be written as follows [Brodin and Stenflo, 2013]:

display math(A5)

where χe(ω,k) and χi(ω,k) are the standard low-frequency electron and ion susceptibilities for ion acoustic and electrostatic ion cyclotron waves, ω and k are the frequency and wave vector, and k0 is the wave vector of the high-frequency electromagnetic pump wave. u0=eE0/meω0 is the electron quiver velocity of the pump with the electric field E0 and the frequency. ϕrepresents the angle between the low-frequency sidebands and u0 and vg=k0c2/ω0. Numerical calculations of equation (A5) are beyond the scope of this work and are the subject of future investigations.

Appendix B: The Electromagnetic Pump in the Ionosphere and Dispersion Relation

[34] For vertical propagation in a horizontally stratified plasma layer, the second-order differential equation for O- and X-mode waves can be written like equation (A1).

[35] The refractive index for these modes is given by [Budden, 1985]:

display math(B1)

where inline image, Yce/ω, and wave polarization is given by [Yeh and Liu, 1972]:

display math(B2)

[36] inline image denotes collisional loss between electrons and ions and νen is electron-neutral collision frequency. Finite difference approximations are used for solving equation (B1) numerically. The boundary conditions above and below the resonance altitude are specified by the WKB approximation.

[37] The relationships between the electric field components of the wave and the function F(O,X)(z) for Oand X mode are given by [Yeh and Liu, 1972]:

display math(B3)
display math(B4)

with the magnetic field B in the y-z plane, RP(X) is the extraordinary mode polarization, and inline imageis the ordinary and extraordinary mode longitudinal polarization for the pump wave. Details on the derivation are given by Yeh and Liu [1972, equations 5.17.11 and 5.17.12] and Budden [1985]. The longitudinal polarization inline image is the ratio Ez/Ex of the longitudinal to northward fields. The electric field component along the direction of the magnetic field is given by E(z)=Ez(z)cosθEy(z)sinθ, where θis again the complement of the magnetic dip angle. Excellent descriptions of these features are provided by Budden[1966, 1985], Yeh and Liu [1972], and Lundborg and Thide[1985, 1986]. In terms of refractive index, the polarizations for both the O- and X-mode waves are the following [Yeh and Liu, 1972]:

display math(B5)
display math(B6)

[38] For SBS, the largest interactions occur near the O-Mode reflection altitude where Xe→1 and the Quasi-longitudinal (QL) conditions do not apply. For this reason, the QL approximation is not employed for simplifications in this work. Near the X-Mode reflection altitude where Xe=1−Ye, the transverse (Ex(X), Ey(X)) electric field amplitudes become large but the longitudinal Ez(X) may remain small.


[39] This work was supported by the National Science Foundation.