Narrowband Stimulated Radiation during Ionospheric Heating Experiments: Recent Observations, Theory, and Modeling

Abstract

Ground-based transmission of high-power high frequency (HF) radio waves into the Earth’s ionosphere produces a plethora of physical phenomena that result from complex nonlinear processes. This field has commonly been referred to as ionospheric heating or ionospheric modification in pertinent literature, and it has a long, rich history dating back at least to the 1960s. The phenomenon induced by the interaction of a radio wave and ionospheric plasma may serve as a laboratory for investigating fundamental phenomena as well as facilitate ionospheric diagnostics. This chapter will concentrate on a specific phenomenon which is stimulated secondary radiation that exists in the frequency band typically within about 1 KHz of the transmit frequency. This narrowband stimulated radiation has been studied extensively over the past decade or so at the High Frequency Active Auroral Research Program (HAARP) Facility in Gakona, Alaska. HAARP’s unprecedented capabilities in terms of maximum power, transmit beam and frequency agility, have resulted in discovery of several new nonlinear ionospheric phenomena that may be leveraged for new diagnostics by using the narrowband stimulated radiation spectrum. This chapter will provide a synopsis of the most recent observations, theory, and advanced computational modeling and provide a future outlook on possibilities for future avenues of investigation.

1. Introduction

When a high-power high frequency (HF) radio wave, also typically referred to a pump wave, is injected into, and interacts with the Earth’s ionosphere, experiments commonly referred to as ionospheric heating experiments, a plethora of physical processes occur [1]. One of these processes is secondary radiation, produced in the ionosphere, called Stimulated Electromagnetic Emissions (SEEs) which are observed by ground-based receivers typically within 100 km of the ground-based high power ionospheric heating facility. The possibility of generating SEEs during ionospheric heating experiments was theoretically proposed in the late 1970’s and SEEs were first observed using the heater at the facility now called the European Incoherent Scatter Radar (EISCAT) heating facility as reported in the early 1980’s [2]. Since then, SEEs have been developed into a useful diagnostic for ionospheric parameters as well as the nonlinear processes produced during heating by using the spectral line characteristics and their temporal evolution [3]. SEEs along with other diagnostics probing the heated region such as optics, coherent and incoherent radar scatter, GPS scintillation measurements, and in situ satellite measurements can form an even more effective diagnostic suite for analyzing the ionosphere during these experiments. The spectrum of physical processes occurring during ionospheric heating include electron acceleration, airglow, production of a relatively broad spatial scale of ionospheric irregularities as well as secondary radiation, that is, SEEs. SEEs spectral lines studied in the past occur within a frequency bandwidth of approximately ±100 kHz around the pump wave frequency ${\omega }_0$ which typically ranges from 2 to 8 MHz. An effective radiated power (ERP) of 100’s of MW to 1 GW is usually available from the pump wave. The ionospheric interaction typically occurs in the altitude range of 150–250 km. The interaction of the pump wave with the ionosphere may occur strongly at the reflection altitude where the pump frequency is near the local electron plasma frequency ${\omega }_0\approx {\omega }_{\mathit{pe}}$ or the upper hybrid (UH) layer where the pump frequency is near the plasma upper hybrid resonance frequency ${\omega }_0\approx {\omega }_{\mathit{uh}}=\sqrt{{\omega }_{\mathit{pe}}^2+{\mathrm{\Omega }}_{\mathit{ce}}^2}$ where ${\mathrm{\Omega }}_{\mathit{ce}}\approx 1.4$MHz is the electron gyrofrequency. The upper hybrid layer is roughly 5 km or so below the reflection altitude. Many heating facilities such as EISCAT are in polar regions where the geomagnetic field $B_0$ is nearly vertical which implies that there are very prominent and important SEEs spectral lines produced at the upper hybrid layer. As will be discussed later, this is related to the orientation of the pump wave electric field being nearly perpendicular to $B_0$ at the upper hybrid layer and nearly parallel to $B_0$ near the reflection height. Also, it is well known that there are important changes to the spectral lines when ${\omega }_0$ is swept through harmonics of the electron gyrofrequency ${n\mathrm{\Omega }}_{\mathit{ce}}$ where for the observations discussed in detail in Section 2, $n=2,3$ [3].

Since 2010, a host of newly discovered phenomena associated with SEEs have been observed and studied at the High Frequency Active Auroral Research Program (HAARP) facility in Gakona, Alaska [4, 5] which is the focus of this chapter. HAARP is arguably the most powerful and versatile ionospheric heating facility presently. Its higher effective radiated power (ERP), more agile frequency and antenna array beam sweeping capabilities have opened new doors for experimental investigation of SEEs. Most of the investigations conducted at HAARP since 2010 have concentrated on SEEs within ±1 kHz of the pump wave frequency ${\omega }_0$, and often this radiation is observed within 100 Hz and even 10 Hz of ${\omega }_0$. Several authors have termed the SEEs within ±100 kHz of ${\omega }_0$ wideband SEEs (WSEEs) and the more recent observations within ±1 kHz of ${\omega }_0$, narrowband SEEs (NSEEs). This later terminology will be used in the discussions here. Recent work at HAARP has also focused on the generation of SEEs near twice the pump frequency, that is, 2${\omega }_0$, a process known as second harmonic generation (SHG). The motivation behind these SHG investigations is two-fold. The first is to leverage the longstanding and validated techniques and theory from studies of Laser Plasma Interactions (LPI) to derive diagnostics of ionospheric plasma and the second is the presentation of an avenue to study SHG in magnetized plasmas on timescales possibly not available in LPI. Since the concentration of this chapter is on narrowband SEEs near ${\omega }_0$ and $2{\omega }_0$, the former is referred to as PW-NSEEs and the latter SH-NSEEs, for clarity of distinction. “PW” and “SH” are respectively abbreviations for pump wave and second harmonic [6].

The nonlinear physical processes believed to initiate the generation of SEEs are parametric instabilities involving coupling of the pump electromagnetic wave into ionospheric plasma waves that can be either electromagnetic or electrostatic [7]. One of the simplest forms of a parametric instability relevant to SEEs is the three-wave parametric decay in which the pump wave decays into two downshifted sideband waves. These three waves are related by frequency and wavenumber matching conditions in which the pump wave frequency and wavenumber (${\omega }_0$, $k_0)$ is equal to the sum of the frequency and wavenumber of the high frequency (${\omega }_1$, $k_1)$ and low frequency (${\omega }_2$, $k_2)$ decay sidebands (often an electrostatic wave), i.e.

$${\omega }_0={\omega }_1+{\omega }_2$$E1

$$k_0=k_1+k_2$$E2

The frequency shift between the pump frequency and the downshifted high frequency sideband, $\mathrm{\Delta }\omega ={\omega }_0-{\omega }_1={\omega }_2$, can be shown, through parametric instability theory, to depend on properties of the heated ionospheric plasma and therefore form the basis for diagnostic information. The temporal evolution of the high frequency sideband can also be used for diagnostic information. This evolution typically results from more strongly nonlinear processes, and comparison with nonlinear plasma simulation models can provide further possibilities for diagnostic information.

It is particularly important that the electric field vector of the pump wave on the ray path is nearly perpendicular to the geomagnetic field at the UH layer and nearly parallel near the reflection altitude for the experiments to be discussed. The pump electric field vector direction determines which wave modes participate in the parametric instability. For instance, at the UH layer, ionospheric plasma wave modes that propagate perpendicular to the geomagnetic field are expected to be involved in the parametric decay. High frequency decay modes in this case may be upper hybrid (UH) and electron Bernstein (EB) modes and low frequency wave modes may include lower hybrid (LH), ion Bernstein (IB), and highly oblique ion acoustic (IA). Interactions at the reflection altitude may include high frequency Langmuir waves (LW), a.k.a. electron plasma waves, and low frequency ion acoustic (IA) and oblique electrostatic ion cyclotron (EIC) waves since all these waves propagate with significant wave vector component along $B_0$. Knowledge of these wave modes will be important for interpreting the observations as well as utilizing the spectral line frequency shifts for diagnostic purposes using parametric instability theory. Since there are other nonlinear processes associated with the parametric instability such as strong turbulence development and electron heating, computational plasma modeling can be important for interpreting temporal evolution of the frequency sidebands and their association with various nonlinear ionospheric irregularity development. Therefore, the two tools, theory and modeling are critical for development of NSEE into a viable ionospheric diagnostic.

The organization of this chapter is as follows. First, recent observations of NSEE spectral lines at the HAARP facility will be discussed as well as some ancillary diagnostics. Next theoretical plasma physics concepts to explain the new SEE spectral lines will be discussed. This will largely be consideration of parametric decay instability theory. Growth rates and frequency shifts $\mathrm{\Delta }\omega$ will be discussed and their dependence on ionospheric parameters that may provide diagnostic information. This will be followed by a discussion of nonlinear plasma simulations to provide deeper insight for linking specific NSEE spectral lines to nonlinear processes in the ionosphere such as electron acceleration and strong turbulence development. Finally, a summary and future outlook and opportunities will be provided.

2. Observations

All the observations discussed in this section were made using transmissions from the High Frequency Active Auroral Research Program (HAARP) facility in Gakona, Alaska, with location site (62.39° N, 145.15° W). The observations here were reported during the period roughly between 2010 and 2021. The maximum HAARP ERP used was 1 GW with the pump power variation depending on the experiment and O-mode polarization was used. The HAARP transmitter has approximately a 30 dB gain. The SEE signals were typically received with a 30 m folded dipole antenna located roughly 10 km from the transmitter site at the Riverview Inn. The antennas were connected to high sensitivity wideband software defined radio reviewers. The receiver shifts the frequency of the acquired signal by the transmit (pump) frequency ${\omega }_0$by mixing, and sampling it at 250 kHz. The acquired in-phase and quadrature-phase (I and Q) data are post-processed by utilizing Blackman windowing and then fast Fourier transformed (FFT) to obtain spectrograms of the received signal. The frequency resolution of the spectra was in the range of approximately 1–4 Hz depending on the experiment. The magnetic zenith direction is 14⁰, that is, near vertical, with the HAARP antenna beam pointed at or near magnetic zenith with azimuth near 200⁰ which was shown to provide good NSEE observations for most experiments. The HAARP transmitter frequency ${\omega }_0$was typically frequency stepped within approximately ±100 kHz of $2{\mathrm{\Omega }}_{\mathit{ce}}\approx$ 2.8 MHz and $3{\mathrm{\Omega }}_{\mathit{ce}}\approx$ 4.2 MHz to provide strong interactions at the upper hybrid layer as well as interaction at the reflection altitude. The receivers measured the NSEE signals near ${\omega }_0$ and also near 2 ${\omega }_0$ for considering second harmonic generation. Figure 1 shows a diagram of a typical experimental set up.

Figure 1.

A typical experimental set up to measure NSEE using transmissions from the HAARP facility. The transmitted signal produces nonlinear processes in the ionosphere between the upper hybrid layer and reflection altitude. These nonlinear processes produce secondary radiation (NSEE) observed on the ground with frequency sidebands near ${\omega }_0$and $2{\omega }_0$that may be used for diagnostic information on the heated ionosphere.

2.1 Stimulated Brillouin scatter

The first key discovery in NSEE was Stimulated Brillouin Scatter (SBS). The first observations were reported by Norin et al. [8] and soon after by [9, 10]. The latter work provided more detailed theoretical analysis that was in relatively good agreement with the behavior during the experiments. Although SBS had been studied relatively extensively within the Laser Plasma Interaction (LPI) community for several decades, a key difference was the importance of the geomagnetic field $B_0$ during the ionospheric heating experiments which produced new spectral lines. Also since there were pump wave interactions at both the upper hybrid and reflection altitudes, there were spectral lines believed to be associated with both interaction altitudes. The primary spectral lines observed during ionospheric heating experiments are associated with ion acoustic (IA) and electrostatic ion cyclotron (EIC) low frequency decay wave modes. The former is more prominent and produces a sideband typically shifted below ${\omega }_0$by roughly 10 Hz for interaction at the reflection altitude [10]. Sidebands shifted below the pump by several 10’s of Hz can be argued to result from interaction at the upper hybrid layer by consideration of wave matching conditions. Upshifted sidebands could also be accounted for by wave mixing of the upwards and downwards going waves. Since the shift of the IA sideband below the pump is related to the ion acoustic frequency, which depends on temperature, it was proposed that SBS could be used as an important temperature diagnostic and there has been recent progress in this area by using comparisons with temperature measurements using Incoherent Scatter Radar (ISR) [11]. The SBS IA spectral line has also been replicated at the European Incoherent Scatter Radar (EISCAT) facility near Tromso Norway [12]. Another important feature of the IA decay line is that it can often be comparable or even larger than the pump spectral line as was noticed in the early reports. Nonlinear computer simulations show that this is consistent with the behavior of nonlinear development of the SBS parametric decay instability. Several related characteristics and phenomena are discussed in Section 4.1.

The second important SBS line was discovered by Bernhardt et al. [9] guided by the early theoretical calculations. The EIC spectral line shift is near the $O^{+}$ cyclotron (or gyro) frequency ${\mathrm{\Omega }}_{\mathit{cO}}$ ≈ 50 Hz. Note $O^{+}$ is the dominant ion species in the interaction region. In general, obliquely propagating EIC waves only exist in a magnetized plasma at frequencies slightly above the ion gyrofrequency ${\mathrm{\Omega }}_{\mathit{ci}}$ and therefore the presence of this spectral line has resulted in SBS in the ionospheric plasma being referred to Magnetized SBS (MSBS). Since in general, ${\mathrm{\Omega }}_{\mathit{ci}}$ depends on the ion mass, i.e., ${\mathrm{\Omega }}_{\mathit{ci}}=\mathit{eB}/m_i$ where e and $m_i$ are the unit electron charge and ion mass, the importance of this spectral line to ionospheric mass spectrometry measurements was recognized. Further details will be discussed in Section 2.2.

The EIC spectral line was observed to be present when the HAARP transmit antenna beam angle was at least a few degrees off the magnetic zenith angle of 14⁰ which allows the pump electric field vector to couple more effectively to the obliquely propagating EIC waves. This will be discussed in more detail in Section 3.1. Also, the EIC line requires a much higher pump power to excite. Typically, this spectral line is observed only when the pump power is above several 100 MW ERP which is considerably more than the IA spectral line which may be observed for a pump power of less than 100 MW ERP.

Figure 2 shows observations of SBS proposed to be produced near the reflection height by using ray tracing calculations [13]. The left panel shows variation of the HAARP beam angle from magnetic zenith to 7° and 14° off magnetic zenith using 1 GW ERP. The IA spectral line can be seen to be shifted by roughly 10 Hz below the pump frequency of 4.1 MHz ($\approx 3{\mathrm{\Omega }}_{\mathit{ce}})$ and is consistent with generation at the reflection altitude. As the beam angle is increased off magnetic zenith by 14°, the EIC spectral line can be seen to appear albeit at a much lower amplitude than the IA line. The frequency shift is near ${\mathrm{\Omega }}_{\mathit{cO}}$ ≈ 50 Hz. An upshifted IA spectral line can also be observed and is explained due to mixing of upwards and downward propagating wave modes [13]. The right panel shows SBS observations with varying pump power from 520 through 800 MW, to 1 GW with the HAARP antenna beam angle being 14° off magnetic zenith. It can be seen that considerably more pump power is necessary to excite the EIC spectral line, relative to the IA line, which begins to be observed above 800 MW power for these observations.

Figure 2.

Frequency spectra of stimulated Brillouin scatter (SBS) observed during ionospheric heating experiments. Two primary spectral lines exist, the ion acoustic (IA) and the electrostatic ion cyclotron (EIC). The EIC has a higher power threshold and is present for high pump powers and/or off magnetic zenith pumping. Adapted from [13].

Increasing the pump power of course produces more strongly nonlinear processes in the ionosphere. Therefore, it is helpful to consider the impact of increasing pump power on the NSEE spectral line characteristics. Variation i n spectral lines between low and high pump power may potentially provide useful diagnostic information. A study of the IA spectral line characteristic variation with pump power has been made by Yellu et al. [14]. Figure 3 shows NSEE spectra for a relatively low (∼150 MW) transmit power and high (∼280 MW) transmit power. The antenna beam angle was along magnetic zenith and ${\omega }_0\approx 3{\mathrm{\Omega }}_{\mathit{ce}}\approx$ 4.32 MHz. The lower power case shows a relatively distinct SBS IA line shifted below ${\omega }_0$ by roughly 9 Hz and the spectral bandwidth is roughly 5 Hz. This is consistent with the observations shown earlier in Figure 2. Along with a considerably larger sideband spectral power, the higher power case shows a broadened line which, upon careful examination, can be described as a cascade of individual SBS IA lines. The bandwidth in the high-power case is roughly 14 Hz. Yellu et al. [14] suggests that this behavior for high power results from development of strong ion acoustic turbulence in which the backscattered EM wave decay product of an SBS instability acts as a pump to initiate a successive SBS instability. Such strongly turbulent processes can be studied in detail using nonlinear plasma simulations as will be discussed in Section 4.1.

Figure 3.

Variation of IA SBS spectral line with pump power. Lower 150 MW transmit power (left) and higher 280 MW transmit power (right). Higher power produces a broader bandwidth spectral line which is expected to be linked to strong IA turbulence. Adapted from [14].

2.2 Ion gyroharmonic spectral lines

As was discussed in the previous section, a prominent SBS line is the EIC line which is shifted from ${\omega }_0$ by the $O^{+}$ gyrofrequency ${\mathrm{\Omega }}_{\mathit{cO}}$. As the pump frequency is swept very near a multiple of the electron gyrofrequency ${\omega }_0\approx {n\mathrm{\Omega }}_{\mathit{ce}}$another class of NSEE spectral lines shifted by multiples of ${\mathrm{\Omega }}_{\mathit{cO}}$, that is, $∆\omega \approx n{\mathrm{\Omega }}_{\mathit{cO}}$, are observed. These were originally reported by Bernhardt et al. [15] with considerable observations, theory, and computer plasma modeling to follow [16, 17, 18, 19]. This section will provide a brief summary of these NSEE spectral line observations. These NSEE spectral lines are proposed to be produced near the upper hybrid layer since it has been known that a strong pump interaction exists for ${\omega }_0\approx {n\mathrm{\Omega }}_{\mathit{ce}}$ which may produce ionospheric Artificial Field Aligned Irregularities (AFAIs) which are important for production of SEE spectral lines [3]. Also Fu et al. [19] has observed the transition from SBS in the previous section to these ion gyroharmonic spectral lines when ${\omega }_0$ is stepped within a few 10’s of kHz of $2{\mathrm{\Omega }}_{\mathit{ce}}$. These NSEE spectral lines involve ion Bernstein (IB) low frequency decay wave modes. IB modes propagate nearly perpendicular to the magnetic field as so-called plasma flute mode waves [7]. They are harmonically ordered by ${\mathrm{\Omega }}_{\mathit{ci}}$ in a hot plasma. The EIC wave can be considered as a specific type of IB wave that propagates considerably more obliquely to the magnetic field. These NSEE spectral lines were originally termed Stimulated Ion Bernstein Emissions (SIBE) [15] and later Stimulated Ion Bernstein Scatter (SIBS) due to the possible connection to SBS as demonstrated by Fu et al. [19]. For consistency with the later works, the term SIBS will be used here as necessary. These spectral line shifts of course depend on ion mass and therefore information is available on the ion species present in the heating interaction region as will be discussed.

2.2.1 Oxygen spectral lines

Since the dominant ion species at the pump interaction altitude is atomic oxygen, $O^{+}$, it is expected that the most common ion gyroharmonic spectral lines observed will be associated with $O^{+}$ and this is the case. An example of these spectral lines are observed in the left panel of Figure 4. These observations are at a pump power of 1 GW ERP and ${\omega }_0\approx 2{\mathrm{\Omega }}_{\mathit{ce}}\approx 2.8$MHz. The HAARP antenna beam is pointed along the magnetic zenith 14°. It can be observed that unlike the SBS EIC line which just exhibits a single spectral line shifted below ${\omega }_0$ by ${\mathrm{\Omega }}_{\mathit{cO}}\approx 50$ Hz, there are many harmonics shifted below ordered by $n{\mathrm{\Omega }}_{\mathit{cO}}$ with some harmonics shifted above ${\omega }_0$ as well. These observations show 9 or so harmonics, however, other observations have shown 20 to 30 harmonics or more. The larger the number of harmonics has been shown to be linked to strong bulk heating of electrons across the magnetic field as will be discussed in Section 4.2. Also, the downshifted harmonics for $n>1$ are shifted roughly near half harmonics, i.e. $\left(n+1/2\right){\mathrm{\Omega }}_{\mathit{cO}}.$ It has been shown that the relative amplitude of the individual spectral lines can be linked to the proximity of ${\omega }_0$ to $2{\mathrm{\Omega }}_{\mathit{ce}}$ with the lower harmonics having a larger amplitude for ${\omega }_0$ very close to ${n\mathrm{\Omega }}_{\mathit{ce}}$ in general [16] as observed in Figure 4.

Figure 4.

HAARP observations of NSEE spectral lines shifted from ${\mathrm{\omega }}_O$ by the $O^{+}$ gyrofrequency, ${\mathrm{\Omega }}_{\mathit{cO}}\approx 50$ Hz, for ${\mathrm{\omega }}_O\approx$$2{\mathrm{\Omega }}_{\mathit{ce}}\approx 2.8$MHz (left). A typical continuous broader band spectrum (right) resulting from higher pump power and/or pump electric field vector more off perpendicular to $B_0$ relative to pump parameters that produce the spectrum on the left. Oblique ion acoustic decay waves propagating near the upper hybrid layer are believed to be associated with this broader band spectral line. Adapted from [16].

It is observed that with increasing pump amplitude or a pump electric field vector more oblique to $B_0$, possibly indicating an interaction altitude further above the upper hybrid layer and closer to the reflection altitude, the line spectrum shown on the left of Figure 4 transitions to a broadband continuous spectrum similar to the right of Figure 4. This transition can be replicated with theory as discussed in Section 3.2. The low frequency decay wave mode in this case is an oblique ion acoustic wave propagating 10° or so off perpendicular to $B_0$ near the upper hybrid layer. Such an oblique ion acoustic wave mode has linkage to the dispersion characteristics of IB wave modes and this provides insight into the nature of this transition. Also, this broad continuous spectrum can be observed on occasion with absorption lines ordered by ${\mathrm{\Omega }}_{\mathit{cO}}$. It can be shown that such a broad continuous spectral line indicates development of strong turbulence and electron acceleration along the magnetic field at the upper hybrid layer as will be discussed in Section 4.2.

2.2.2 Hydrogen spectral lines

Atomic hydrogen ions $H^{+}$, or protons, are expected to be a minor ion species, with density typically less than 1%, at the interaction altitude during ionospheric heating experiments. However, during geomagnetic activity there are possibilities of proton precipitation [20, 21]. In line with the possibly of utilizing the ion gyroharmonic spectral lines as a mass spectrometer, observations of NSEE spectral lines ordered by the proton gyrofrequency will be discussed. Figure 5 (left) shows a frequency spectrum observation taken during disturbed geomagnetic conditions as described in [20]. Spectral lines both above and below ${\omega }_0=2.9\mathrm{MHz}\approx 2{\mathrm{\Omega }}_{\mathit{ce}}$ordered by the proton gyrofrequency, ${\mathrm{\Omega }}_{\mathit{cH}}\approx 800$ Hz, are observed. The first downshifted spectral line shift below ${\omega }_0$ has a shift that is less than ${\mathrm{\Omega }}_{\mathit{cH}}$. It should be noted that the frequency shifts are greater than ${\mathrm{\Omega }}_{\mathit{cH}}$ for the higher harmonics $n>1$. The $n=1$ harmonic will be considered in detail to consider its diagnostic possibilities in Section 3.2. Figure 5 (center) shows an expanded frequency view near the $n=1$ spectral line. It can be seen that the shift is roughly 100 Hz less than ${\mathrm{\Omega }}_{\mathit{cH}}$, i.e., $∆\omega \approx$ 700 Hz. Also, the oblique ion acoustic spectral lines as observed in Figure 4 (right) are also observed near 300 Hz shifts. It was proposed in [20, 21] that due to the low proton density, the low frequency decay wave mode associated with this spectral line is the $H^{+}-O^{+}$ hybrid wave which has a frequency shift slightly less than ${\mathrm{\Omega }}_{\mathit{cH}}$, for low proton density, as will be discussed in Section 3.2. The proximity of this spectral line to ${\mathrm{\Omega }}_{\mathit{cH}}$ can be used to determine the proton density. Information on the relative $H^{+}$ and $O^{+}$ temperature could possibly be obtained as well. The low frequency decay modes associated with the $n>1$ proton spectral lines are proposed to be hydrogen ion Bernstein waves with frequency shift slightly larger than ${\mathrm{\Omega }}_{\mathit{cH}}$. These are similar to the oxygen gyroharmonic spectral lines shifted above ${\mathrm{\Omega }}_{\mathit{cO}}$ as discussed in Section 2.2a. These proton gyroharmonic spectral lines may also provide diagnostic information. It should be noted that on occasion, however, the $n=1$ proton spectral line shift has been observed to be larger than ${\mathrm{\Omega }}_{\mathit{cH}}$ as shown in Figure 5 (right). The low frequency decay mode in this case is proposed to be a hydrogen EIC wave. It is interesting to note that the SBS oxygen EIC spectral line is observed along with this proton EIC line in Figure 5 (right). The theory for these wave modes and possibilities for diagnostics will be discussed in more detail in Section 3.2.

Figure 5.

NSEE spectral lines with shifts below and above the pump frequency (${\omega }_0$ = 2.9 MHz) ordered by the proton gyrofrequency ${\mathrm{\Omega }}_{\mathit{cH}}\approx$ 800 Hz (left). An expanded frequency view showing the $n=1$ harmonic which has a shift below ${\omega }_0$ that is less than ${\mathrm{\Omega }}_{\mathit{cH}}$. This shift is proposed to be a diagnostic for determining the density of the minority species protons in the heated region near the upper hybrid layer (center). Another expanded view showing a spectral line shifted above ${\mathrm{\Omega }}_{\mathit{cH}}$ believed to depend on electron and proton temperature (right). Adapted from [21].

2.2.3 Heavy metallic ion spectral lines

The previous section considered detection of light ion species, that is, protons, using NSEE spectra that exhibit spectral line shifts ordered by the ion gyrofrequency near ${\omega }_0$. This section will consider the alternative of heavy metallic ions that can possibly be detected with this mass spectrometry capability. These observations were made during ionosonde detection of a sporadic E layer between 100 and 130 km during a HAARP heating campaign detailed in [22]. Although these observations are for SBS EIC lines as described in Section 2.1, there are advantages to comparing this mass spectrometry capability for heavy (relative to $O^{+}$) ions alongside that of the light ion detection in the previous section. Figure 6 (left) shows a time-frequency spectrogram during heating where ${\omega }_0$ is swept near $3{\mathrm{\Omega }}_{\mathit{ce}}$. The frequencies shown are 4.15, 4.16, 4.17, 4.19, 4.22, 4.24, 4.29, and 4.34 MHz. There is a 30 second heating cycle shown for each of these eight frequencies.

Figure 6.

Spectrogram showing SBS EIC spectral line behavior upon stepping ${\omega }_0$ near $3{\mathrm{\Omega }}_{\mathit{ce}}\approx$ 4.2 MHz (left). The corresponding power spectrum for the case when ${\omega }_0$ = 4.17 MHz which reveals an EIC spectral line shifted below ${\omega }_0$ by 36 Hz is shown on the right. This spectral line has been interpreted as detection of sodium ions ($N_a^{+})$ inside a sporadic E layer near 120 km altitude. Adapted from [22].

At the altitude of 120 km, which is near the center of the observed sporadic E layer, metallic ion species expected to exist along with their gyrofrequencies are sodium ($N_a^{+})$, ${\mathrm{\Omega }}_{c{N}_a}\approx 37$ Hz, magnesium ($M_g^{+})$, ${\mathrm{\Omega }}_{c{M}_g}\approx 34$ Hz, calcium ($C_a^{+})$, ${\mathrm{\Omega }}_{c{C}_a}\approx 20$Hz, and iron ($F_e^{+})$, ${\mathrm{\Omega }}_{c{F}_e}\approx 14$Hz. Again, this compares to the $O^{+}$ gyrofrequency at this altitude ${\mathrm{\Omega }}_{\mathit{cO}}\approx 49$ Hz. The observations show several important effects of stepping ${\omega }_0$ near $3{\mathrm{\Omega }}_{\mathit{ce}}$. First there is a weakening of the $O^{+}$ SBS EIC spectral line when ${\omega }_0\to 3{\mathrm{\Omega }}_{\mathit{ce}}\approx$ 4.2 MHz for the frequencies shown in the range 4.17 MHz $<{\omega }_0<$ 4.22 MHz. As noted earlier, similar behavior has been observed by Fu et al. [19]. As the dominant $O^{+}$ EIC line becomes weakened, this allows another spectral line to be observed shifted below ${\omega }_0$ by approximately 36 Hz as pointed out in the spectrogram. Figure 6 (right) shows a spectrum when ${\omega }_0$ = 4.17 MHz. The NSEE spectral line can again be observed more clearly downshifted by approximately 36 Hz and this has been identified as a $N_a^{+}$EIC line and of course provides a detection of sodium ions in the sporadic E layer. It was proposed by [22] that the $N_a^{+}$ EIC line was of course generated by the interaction of the pump wave with the sporadic E layer near 120 km while the $O^{+}$ EIC line was produced near the reflection altitude interaction which was predicted by ray tracing calculations to be near 270 km. Although these observations show promise for the NSEE ion gyrofrequency lines to be used for detection of metallic ion species, further experiments and modeling are required. Also, the NSEE from the reflection altitude (IA and EIC spectral lines) can possibly obscure the metallic ion associated spectral lines at lower altitudes as can be seen from Figure 6. As was shown by the observations, stepping the pump frequency close to the ${n\mathrm{\Omega }}_{\mathit{ce}}$ weakens the $O^{+}$ EIC line revealing the heavier metallic ion spectral lines which may be developed into a useful diagnostic. Behavior of the SHG spectral lines as ${\omega }_0$ is stepped through $n{\mathrm{\Omega }}_{\mathit{ce}}$ will be discussed in more detail in Section 2.3.

2.3 Pump second harmonic emission lines

As noted earlier, there has been recent interest in second harmonic generation (SHG) during ionospheric heating given the potential of obtaining ionospheric plasma diagnostics, for example, hydrodynamic evolution, density scale lengths, determination of interaction regions etc., as has been done in LPI, and the facility it offers to study SHG in magnetized plasmas in general. Although SHG observations had been reported in the early days of SEE research at EISCAT [3]. There were early EISCAT reports of NSEEs ordered by ${\mathrm{\Omega }}_{\mathit{cO}}$ above and below $2{\omega }_0$. However, the important advantage of the SHG observations presented in this chapter is the systematic investigation of the effects of the pump wave conditioning, for example, frequency (${\omega }_0$), power, offset from $n{\mathrm{\Omega }}_{\mathit{ce}}$ and offset of the transmit antenna beam from the magnetic zenith which is essential in investigating magnetic field effects. Also the SHG observations here are juxtaposed with NSEE within a narrowband of ${\omega }_0$, that is, PW-NSEEs. This juxtaposition is important in order to properly gain insight into the wave-mixing processes underlying SHG and possibly the regions in the ionospheric plasma where the dominant interactions initiating SHG emanate from. Results from three experiments conducted at HAARP to investigate SHG are presented in this section.

The intent of the first series of experiments was to determine the power threshold for generation of SH-NSEE by varying pump power. The pump beam was pointed at a zenith angle (ZA) = 14^o i.e., in the direction of the local geomagnetic field at HAARP, and an azimuth angle (AZ) of 198°. Inference from the ionogram yielded a reflection altitude of 190 km and using the International Geomagnetic Reference Field (IGRF) model yielded $3{\mathrm{\Omega }}_{\mathit{ce}}\approx 4.324\mathrm{MHz}$. ${\omega }_0$ was stepped near $3{\mathrm{\Omega }}_{\mathit{ce}}$ from 4.20 to 4.36 MHz, and at each ${\omega }_0$ the power was ramped from a corresponding ERP$\approx$28 MW to ERP$\approx$783 MW over a 45 s ON cycle. Figure 7 shows PW-NSEEs (top row) and SH-NSEEs (bottom row) for progressive (left to right) sections of the pumping cycle. An SH-NSEE, labeled SH decay line, downshifted from $2{\omega }_0$ by $\sim 2∆\omega$ is seen (bottom row) where $∆\omega$ is the downshift of its corresponding SBS PW-NSEE line from ${\omega }_0$. The PW-NSEE and SH-NSEE are observed above the noise level roughly at the same time (implying similar power thresholds) and grow progressively as the ERP increases. As previously noted in the observations of Section 2.1 and the theory that will be discussed in Section 3, $\mathrm{\Delta }\omega$ is expected to be associated with the growth of ion acoustic waves.

Figure 7.

SHG results showing similar power thresholds for the SH decay SH-NSEE line (lower row) to its corresponding SBS PW-NSEE line (upper row) when the pump antenna beam is along magnetic zenith. Pump ERP is ramped left to right. Adapted from [6].

The second set of experiments were designed to consider the impact of stepping ${\omega }_0$ through $n{\mathrm{\Omega }}_{\mathit{ce}}$ on SHG. Prior to providing the details of the observations, it is important to briefly note an important physical process that occurs in general as ${\omega }_0\to {n\mathrm{\Omega }}_{\mathit{ce}}$ which impacts the SEE spectrum in general. The formation of Artificial Field Aligned Irregularities (AFAIs), which are regions of deficit plasma density aligned along the geomagnetic field in the UH layer, produced during ionospheric heating is known to lead to a greatly attenuated pump wave or even possibly pump wave cut-off at the reflection altitude [3]. This diminishes the possibility of occurrence of SEEs in general. This was expected to likely be true for SHG proposed to be generated near the reflection altitude and was the motivation for the experiments. Therefore, the second set of experiments compared the characteristics of SH-NSEEs vis-à-vis same of PW-NSEEs for a linear power ramp from ERP ≈ 28 MW to maximum of ERP ≈ 783 MW for a 45 s pumping cycle, and for a constant maximum of ERP ≈ 783 for a similar duration pumping cycle. As usual, the WSEE was monitored as a proxy for AFAIs [6]. Although experimentation was done for ${\omega }_0$ in the $2{\mathrm{\Omega }}_{\mathit{ce}}$and $3{\mathrm{\Omega }}_{\mathit{ce}}$regimes, the trends for the different regimes are similar and hence only results for the latter frequency regime are shown. Figure 8 shows the suppression of the SH line and SH decay line as well as the SBS decay line upon frequency sweeping through $3{\mathrm{\Omega }}_{\mathit{ce}}\approx 4.3$ MHz with ${\omega }_0=$ 4.26, 4.28, and 4.32 MHz shown. This is in line with the suppression of the SBS $O^{+}$ EIC line by frequency sweeping through $3{\mathrm{\Omega }}_{\mathit{ce}}$ in Figure 6. Although not shown here, the SH-NSEE is frequency is broadened as is its corresponding PW-NSEE line for a constant high ERP pumping as shown in Figure 3.

Figure 8.

SHG results showing simultaneous suppression SH decay SH-NSEE line (lower row) to its corresponding SBS PW-NSEE line (upper row) for ${\mathrm{\omega }}_0\approx 3{\mathrm{\Omega }}_{\mathrm{ce}}\approx 4.324\mathrm{MHz}$ (rightmost column). Adapted from [6].

The final set of observations are from an experiment that was conducted to more directly investigate the impact of the geomagnetic field, $B_0$, on SHG. The assessment of the impact during experimentation involved varying the pump antenna beam tilt direction relative the $B_0$ direction, that is, magnetic zenith (MZ), that is, MZ = ZA = 14^o, and stepping the pump wave frequency ${\omega }_0$ in the neighborhood of an electron gyrofrequency harmonic, specifically $2{\mathrm{\Omega }}_{\mathit{ce}}\approx 2.803\mathrm{MHz}$. The results in Figure 9 show ${\mathrm{\Omega }}_{\mathit{cO}}$ ordered SH-NSEEs coincident with ${\mathrm{\Omega }}_{\mathit{cO}}$ ordered PW-NSEEs similar to those in Section 2.2a for ${\omega }_0=2.803\mathrm{MHz}\approx 2{\mathrm{\Omega }}_{\mathit{ce}}$ or for ${\omega }_0\ne 2{\mathrm{\Omega }}_{\mathit{ce}}$only when pump beam is titled away from MZ, but not beyond a certain relative pump beam tilt angle [23]. In summary, these experiments indicate that proximity of ${\omega }_0$ to $n{\mathrm{\Omega }}_{\mathit{ce}}$ and antenna beam angle are two critical parameters determining the magnetic field impact on both the SH-NSEE spectrum as well as the PW-NSEE spectrum. These results also further underscore the connection of the SH-NSEE and PW-NSEE spectra that will motive and guide a qualitative theory in the next section.

Figure 9.

SHG results showing ${\Omega }_{\mathit{cO}}$ ordered SH-NSEEs (lower row) coincident with similarly ordered PW-NSEEs (upper row) for ${\omega }_0$ variation near $2{\Omega }_{\mathit{ce}}\approx 2.80$MHz and varying pump beam tilt (ZA). Adapted from [23].

3. Theory

This section will consider some basic results from plasma parametric decay instability theory to provide guidance for interpreting the observations in the previous section. This theory can provide important information on the physical processes that produce the spectral lines that are observed. Also the frequency shifts can be related to physical parameters in the ionosphere such as which species are present, density, temperature, plasma flow speed, etc. Key results such as the spectral line frequency shifts and parametric instability growth rates will be primarily summarized here with references to the details of the treatments provided. In the following discussion, it will be assumed that the frequency of the low frequency decay mode can be written as ${\omega }_2=\mathrm{\Delta }\omega +\mathit{i\gamma }$ where the real part of the frequency $\mathrm{\Delta }\omega$ is equal to the frequency shift from ${\omega }_0$ and $\gamma$ is the growth rate of the sidebands.

3.1 Stimulated Brillouin scatter

For ionospheric Stimulated Brillouin Scatter SBS, it is assumed the pump electromagnetic wave decays into a scattered electromagnetic wave and either an ion acoustic (IA) or electrostatic ion cyclotron (EIC) wave [7]. The frequency shift of the SBS IA sideband below ${\omega }_0$, as shown in Figure 2, can be determined by using a ray tracing model and considering the frequency and wavenumber matching conditions at the upper hybrid ${\omega }_0\approx {\omega }_{\mathit{uh}}$ and resonance ${\omega }_0\approx {\omega }_{\mathit{pe}}$ altitude layers for ion acoustic waves [9, 10, 13, 19]. The ion acoustic wave frequency is the frequency shift below ${\omega }_0$ and depends on the angle $\theta$ (off-perpendicular to $B_0$) and the ion acoustic wavenumber $k_{\mathit{IA}}$ determined from frequency and wave number matching on the ray path. Therefore, the shift of the IA sideband is given by

$${\mathrm{\Delta }\omega }_{\mathit{IA}}^2\approx \frac{k_{\mathit{IA}}^2{c}_{\mathit{ia}}^2{\mathit{cos}}^2\theta }{\left(1+\frac{k_{\mathit{IA}}^2{c}_{\mathit{ia}}^2}{{\mathrm{\Omega }}_{\mathit{cO}}^2}\right)}$$E3

where $c_{\mathit{ia}}=\sqrt{({\gamma }_e{T}_e+{\gamma }_i{T}_{i)}/m_i}$ is the ion acoustic (or sound) speed where $T_e$ and $T_i$ are respectively the electron and ion temperatures and ${\gamma }_e=1$ and ${\gamma }_i=3$. From the matching conditions $k_{\mathit{IA}}\approx 2k_0$, where $k_0$ is the pump wavenumber, and $\theta$ can be determined from the ray path. Since $\theta$ at the upper hybrid layer is relatively close to 0, the SBS ion acoustic associated sidebands generated nearer the upper hybrid layer have larger frequency shifts which is in line with interpretations of the experimental observations. Frequency shifts for the sideband generated just below the resonance altitude can be calculated from this method to be of the order of 10 Hz which is what is typically measured during experiments. The frequency shift of the EIC sideband, which is slightly above the $O^{+}$ gyrofrequency ${\mathrm{\Omega }}_{\mathit{cO}}\approx$ 50 Hz is given by

$${\mathrm{\Delta }\omega }_{\mathit{EIC}}^2\approx {\mathrm{\Omega }}_{\mathit{cO}}^2+\frac{k_{\mathit{IA}}^2{c}_{\mathit{ia}}^2{\mathit{cos}}^2\theta }{\left(1+\frac{k_{\mathit{IA}}^2{c}_{\mathit{ia}}^2}{{\mathrm{\Omega }}_{\mathit{cO}}^2}\right)}$$E4

Note the second term in Eq. (4) is assumed very small in comparison to ${\mathrm{\Omega }}_{\mathit{cO}}$.

It can be observed from Figure 2 that the SBS IA spectral line has a much larger amplitude than the SBS EIC spectral line. Also the growth threshold of the SBS IA spectral line is much lower than the EIC spectral line. These characteristics can be understood at least to some degree by first considering their growth rates. Approximate analytical expressions have been provided by Shukla and Stenflo [24] and are given by

$${\gamma }_{\mathit{IA}}\approx \frac{k_{\parallel }{v}_{\mathit{osc}}{\omega }_{\mathit{pO}}}{2\left(1+b_O\right)\sqrt{{\omega }_0{\mathrm{\Delta }\omega }_{\mathit{IA}}}}$$E5

$${\gamma }_{\mathit{EIC}}\approx \frac{k_{\perp }{v}_{\mathit{osc}}{\omega }_{\mathit{pO}}}{\sqrt{{\omega }_0{\mathrm{\Omega }}_{\mathit{cO}}}}{\left[1+\frac{b_O{k}_{\parallel }^2}{k_{\perp }^2\left(1+b_O\right)}\right]}^{1/2}$$E6

where $b_O=k^2{c}_{\mathit{ia}}^2/{\mathrm{\Omega }}_{\mathit{cO}}^2$ and ${\omega }_{\mathit{pO}}$ is the $O^{+}$ plasma frequency. $v_{\mathit{osc}}=e{E}_0/m_e{\omega }_0$ is the electron oscillation velocity in the pump field where $E_0$, $m_e$, $e$ are the pump electric field strength, electron mass and unit charge. Finally, $k_{\parallel }$, $k_{\perp }$, $k$ are the parallel and perpendicular components and the magnitude of the wavevector. Bernhardt et al. [10] provided a useful simplified expression for the ratio of these two growth rates ${\gamma }_{\mathit{EIC}}/{\gamma }_{\mathit{IA}}\approx \sqrt{{\mathrm{\Delta }\omega }_{\mathit{IA}}/{\mathrm{\Omega }}_{\mathit{cO}}}tan\theta$ (note $\mathit{\text{cosθ}}=k_{\parallel }/k$). This expression implies that the IA sideband should be dominant when the pump wavevector is along magnetic zenith (i.e., along the magnetic field). However, the EIC SBS line requires that the pump wave vector be off magnetic zenith as has been observed in experiments described in Section 2.1.

Another important approach to interpreting the lower threshold of the IA sideband relative to the EIC sideband is calculation of the threshold pump electric field $E_0$. At this time, there has been relatively little theoretical work in this area. However, a simplified approach was presented by Mahmoudian et al. [13] which follows the concepts in [25]. The threshold field $E_0$ may be roughly estimated from the expression

$${\gamma }_{\mathit{IA},\mathit{EIC}}\approx \sqrt{{\gamma }_C{\gamma }_L}$$E7

where for the IA sideband ${\gamma }_C\approx {\nu }_{\mathit{en}}{\omega }_{\mathit{pe}}^2/2{\omega }_0^2$ and ${\gamma }_L\approx$$\mathrm{\Delta }{\omega }_{\mathit{IA}}\sqrt{\pi /8}\sqrt{m_e/m_i}$ are the collisional and ion Landau damping rates, respectively, which are the two primary dissipative mechanisms prohibiting sideband growth. Note ${\nu }_{\mathit{en}}$ is the electron neutral collision frequency. Since the sideband growth rates are directly proportional to $E_0$, this threshold field can in principle be determined from Eq. (7). Mahmoudian et al. [13] considered a computation of Eq. (7) and determined a threshold field of order 1 V/m for the experiments under consideration, however, estimating the actual HAARP field amplitude in the interaction region for growth was of order 10 V/m. At this time, there are limited comparisons between observation and theory for calculation of the threshold field so this is an important future area of investigation.

The dispersion relation and growth rate expressions for IA and EIC NSEE sidebands just described in this section are valid under the cold plasma assumption. The following Section 3.2 will require plasma kinetic theory corrections to consider the dispersive characteristics of the IA and IB low frequency decay wave modes. This is necessitated by close proximity of ${\omega }_0$ to ${n\mathrm{\Omega }}_{\mathit{ce}}$ which enhances kinetic effects for interaction near the upper hybrid layer.

3.2 Ion gyroharmonic spectral lines

From Section 2.2, NSEE ion gyroharmonic spectral lines have been observed shifted from ${\omega }_0$ near multiples of the $O^{+}$, $H^{+}$ and heavy metallic ion gyrofrequencies. Therefore, the parametric instability model used here is a general electrostatic model used for a multi-ion component plasma [26, 27]. The model considers a dipole (long-wavelength $k_0=0$) pump approximation to represent the pump electromagnetic wave. This three-wave decay model considers decay of the pump into high frequency upper hybrid/electron Bernstein modes and low frequency decay modes which are primarily ion Bernstein modes in this case. Since the model is electrostatic, the assumption is that the high frequency decay sideband modes mix with ion density fluctuations (i.e., AFAIs) to produce beat currents that ultimately result in the electromagnetic radiation observed on the ground shifted below the pump by multiples of the ion gyrofrequency [16]. Upshifted sidebands may also be produced by this mixing process.

As before, the frequency and wavenumber matching conditions are described as ${\omega }_0={\omega }_1+{\omega }_2$; $k_0=0=k_1+k_2$ where the subscripts ‘0’,‘1’, and ‘2’ denote the pump, high frequency decay mode, and low frequency ion decay mode, respectively. The parametric decay instability model of Ono et al. [27] can be stated as follows:

$$ϵ\left({\omega }_2\right)+\frac{{\beta }_e^2}{4}{\chi }_{\sigma }\left({\omega }_2\right)\left\{\frac{{ϵ}_e\left({\omega }_2\right)}{{ϵ}_e\left(-{\omega }_1^{\ast }\right)}-2\right\}=0$$E8

where $\left({\omega }_2\right)=1+{\chi }_e\left({\omega }_2\right)+{\chi }_{\sigma }\left({\omega }_2\right)=1+$${\chi }_e\left({\omega }_2\right)+\sum _i{\chi }_i\left({\omega }_2\right)$, ${ϵ}_e\left({\omega }_2\right)=1+{\chi }_e\left({\omega }_2\right)$ and ${ϵ}_e\left(-{\omega }_1^{\ast }\right)=1+{\chi }_e\left(-{\omega }_1^{\ast }\right)$ with * denoting complex conjugate. Note the summation is over all the plasma ion species to provide the contribution ${\chi }_{\sigma }\left({\omega }_s\right)$. The general plasma susceptibility for species $j$ is given by

$${\chi }_j\left(\omega \right)=\frac{1}{k^2{\lambda }_{\mathit{Dj}}^2}\left\{\frac{1+{\varsigma }_{j0}{\sum }_{n=-\infty }^{n=\infty }{\mathrm{\Gamma }}_n\left(b_j\right)Z\left({\varsigma }_{\mathit{jn}}\right)}{1+\frac{i{\nu }_j}{k_{\parallel }{v}_{\mathit{tj}}}{\sum }_{n=-\infty }^{n=\infty }{\mathrm{\Gamma }}_n\left(b_j\right)Z\left({\varsigma }_{\mathit{jn}}\right)}\right\}$$E9

where ${\mathrm{\Gamma }}_n\left(b_j\right)={\mathrm{I}}_n\left(b_j\right)exp\left(-b_j\right)$, ${\varsigma }_{\mathit{jn}}=\left(\omega -n{\mathrm{\Omega }}_j\right)$, $b_j=k_{\perp }^2{v}_{\mathit{tj}}^2/{\mathrm{\Omega }}_j^2$, ${\mathrm{I}}_n\left(b_j\right)$ is the modified Bessel function of first order and $Z\left({\varsigma }_{\mathit{jn}}\right)$ is the Fried Conte function. Also, $k,k_{\perp },k_{\parallel }$ is the magnitude, perpendicular and parallel component of the wavenumber, respectively, ${\mathrm{\Omega }}_j$, $v_{\mathit{tj}}$, ${\nu }_j$, and ${\lambda }_{\mathit{Dj}}$ are the gyrofrequency, thermal velocity, collision frequency, and Debye length of plasma species $j$, respectively. The coupling coefficient proportional to the pump field $E_0$ is

$${\beta }_e^2=\frac{e^2}{m_e^2}\left\{{\left(\frac{E_{0\parallel }{k}_{\parallel }}{{\omega }_0^2}+\frac{E_{0\perp }\bullet k_{\perp }}{{\omega }_0^2-{\mathrm{\Omega }}_e^2}\right)}^2+\frac{{\left(E_{0x}{k}_y-E_{0y}{k}_x\right)}^2{\mathrm{\Omega }}_e^2}{{\omega }_0^2{\left({\omega }_0^2-{\mathrm{\Omega }}_e^2\right)}^2}\right\}$$E10

where $e$, $m_e$, are the unit charge and electron mass, $E_{0\parallel }$, $E_{0\perp }$, $E_{0x}$, $E_{0y}$, $k_x$, $k_y$ are the parallel, perpendicular, $x$ and $y$, components of the pump electric field vector and wavenumber, respectively. Note the magnetic field $E_0$ is assumed in the $z$ direction. Due to the complexity of the ion Bernstein mode structure, a Newton Raphson technique must be used to solve Eq. (8) numerically. The solution provides the real and imaginary parts of the frequency ${\omega }_2$ which are equal to the frequency shift $∆\omega$ of the high frequency decay mode below the pump frequency ${\omega }_0$ and the growth rate of this mode $\gamma$, respectively. However, an approximate analytical expression can be derived from Eq. (8) for the neutralized $O^{+}$ Bernstein harmonic wave frequency [16].

$$\mathrm{\Delta }{\omega }_{\mathit{nIB}}\approx {n\mathrm{\Omega }}_{\mathit{cO}}\left[1+\frac{T_e}{T_O}{\mathrm{\Gamma }}_n\left(b_O\right)\right]$$E11

Note the $n=1$ case describes the classic cold plasma EIC wave in Eq. (4) in the long wavelength limit $b\to 0$. Also, Eq. (11) assumes propagation very close to perpendicular to $B_0$ ($k_{\parallel }/k\lesssim$ 0.1). An rough expression for the wavenumber of the $n^{\mathit{th}}$ mode is $k_{\perp }{\rho }_0\sim n$ where ${\rho }_O$ is the $O^{+}$ gyroradius

Figure 10 (center and right) shows calculations using Eq. (8) to characterize the transition from the discrete $O^{+}$ gyroharmonic spectral lines into a broadband oblique ion acoustic associated spectral line for increasing angle of the pump electric field vector off perpendicular to the magnetic field [16]. Again, this change in pump electric field vector orientation may be attributed to the interaction altitude being further above the upper hybrid layer and closer to the reflection altitude. The frequency shift is similar to Eq. (3) assuming the long wavelength limit and propagation near perpendicular to $B_0$ (i.e. $\theta \to$0) which implies $\mathrm{\Delta }{\omega }_{\mathit{IA}}\approx k_{\mathit{IA}}{c}_{\mathit{ia}}$. The growth rate $\gamma$ of the sidebands is shown versus frequency shift $\mathrm{\Delta }\omega$. The pump frequency is assumed to be near the second harmonic of the electron gyrofrequency, that is, ${\omega }_0\approx 2{\mathrm{\Omega }}_e$, as in the experiments of Section 2.2. The theoretical spectral line structure is in relatively good agreement with past observations as shown in Figure 4. The threshold electric field calculation using Eq. (8) is not shown here but has been estimated by Samimi et al. [16] to be in the range between 1 and 10 V/m. As will be noted in the following section, the broader bandwidth oblique ion acoustic spectral line can be associated with strong turbulence processes in the ionospheric upper hybrid layer including intense electron acceleration and density caviton collapse by using nonlinear plasma simulations. Therefore, observance of this NSEE spectral line may provide a very useful diagnostic for characterizing the turbulent state of the ionospheric plasma [17].

Figure 10.

Growth rate calculations using Eq. (8) for $O^{+}$ gyroharmonic spectral lines similar to those observed in Figure 4 (left). Note transition of the discrete line spectrum into a continuous broadband spectrum as the pump electric field vector moves further off perpendicular to the magnetic field (center and right). The continuous spectrum is in line with Figure 4 (right). Adapted from [16].

Figure 11 (left) shows the calculations using Eq. (8) to characterize $H^{+}$ (proton) gyroharmonic spectral lines produced during ionospheric heating under the circumstances of geomagnetic activity in which proton precipitation was expected to exist [20, 21]. As noted by [20, 21] the low frequency ion decay mode in this case is the $H^{+}-O^{+}$ hybrid wave mode that exists in the frequency band between the $H^{+}$ and $O^{+}$ gyrofrequencies. The frequency approaches the $H^{+}$ gyrofrequency as the $H^{+}$ density decreases. An approximate analytical expression (derivable from Eq. (8)) for the frequency shift of this sideband is

Figure 11.

Growth rate calculations for NSEE $H^{+}$ spectral lines such as those shown in Figure 5 (left). Note the shift less than ${\mathrm{\Omega }}_{\mathit{cH}}$ can be used to estimate the $H^{+}$ density from Eq. (12). Growth of $H^{+}$ spectral lines with shift larger than ${\mathrm{\Omega }}_{\mathit{cH}}$ are also possible (right). These may provide information on $H^{+}$ temperature. Adapted from [21].

$$\mathrm{\Delta }{\omega }_{H-O}={\mathrm{\Omega }}_{\mathit{cH}}\left(1-∆\right);∆\approx \left(\frac{{\omega }_{\mathit{pH}}^2}{{\sum }_i{\omega }_{\mathit{pi}}^2}\right){\mathrm{\Gamma }}_1\left(b_H\right)/b_H$$E12

Assuming long wavelengths ($b_H$ <<1) and only two ion species, namely $H^{+}$ and $O^{+}$, then $∆\approx 0.5{\omega }_{\mathit{pH}}^2/{\omega }_{\mathit{pO}}^2=0.5\left(n_H{m}_O\right)/\left(n_O{m}_H\right)$. Therefore, the shift $∆$ below ${\mathrm{\Omega }}_{\mathit{cH}}$ as observed in Figure 5, is directly proportional to $n_H$ and therefore this spectral line can be used as a diagnostic for $n_H$. Typically, the concentration of protons is expected to be considerably less than 1% at the heating interaction altitude, however, enhancements in proton density could be detected using the frequency shift of the relatively strong $H^{+}$ NSEE spectral line shift below ${\mathrm{\Omega }}_{\mathit{cH}}$, i.e. $∆\approx 0.5\left(n_H{m}_O\right)/\left(n_O{m}_H\right)$$\approx$ 100 Hz [20]. Therefore, this NSEE spectral line may provide diagnostics of a minority light ion species, namely $H^{+}$ as well as an appraisal of geomagnetic activity. In the case of the observations during this experiment, the shift of the NSEE spectral line predicts a percentage of $H^{+}$ to be 10% or so. The $H^{+}$ density is also observed to be very transient (bursty) and only exists for periods of 10’s of seconds at a time during the heating cycle [20, 21].

It should be noted again that $H^{+}$ spectral lines have also been observed to have frequency shifts from ${\omega }_0$slightly larger than ${\mathrm{\Omega }}_{\mathit{cH}}$ as shown in Figure 5 (right) [21]. This positive shift can also be described by Eq. (8) [21]. The low frequency ion decay wave is the neutralized $H^{+}$ Bernstein wave, which has a dispersive characteristic similar to Eq. (11), that has the approximate shift

$$\mathrm{\Delta }{\omega }_{\mathit{nIB}}\approx {n\mathrm{\Omega }}_{\mathit{cH}}\left[1+\frac{T_e}{T_H}{\mathrm{\Gamma }}_n\left(b_H\right)\right]$$E13

Also, for $n=1$, in the long wavelength and oblique propagation regime this mode becomes a hydrogen EIC wave and implies a shift of the form similar to Eq. (4) with the substitutions ${\mathrm{\Omega }}_{\mathit{cO}}\to {\mathrm{\Omega }}_{\mathit{cH}}$ and $T_O\to T_H$. This wave mode is easier to drive unstable when the pump electric field vector is further off perpendicular to the magnetic field relative to the $H^{+}-O^{+}$ hybrid wave mode responsible for spectral lines shifted less than ${\mathrm{\Omega }}_{\mathit{cH}}$. An example growth rate calculation for shifts larger than ${\mathrm{\Omega }}_{\mathit{cH}}$ is shown in Figure 11 (right). The growth rate threshold has been estimated by [21] to be between 1 V/m and 10 V/m. When there is no $H^{+}$, then only $O^{+}$ gyroharmonic associated NSEE spectral lines should be observed as in Figure 10 (left). A small percentage of $H^{+}$, 5% in the case of the calculation, introduces $H^{+}$ gyroharmonic lines (aka hydrogen EIC for $n=1$) with shifts larger than ${\mathrm{\Omega }}_{\mathit{cH}}$ and amplitudes larger than the $O^{+}$ gyroharmonic spectral lines. This is consistent with observations reported by [21]. From Eq. (13), it can be seen that the shift is related to the relative $H^{+}$ temperature. Therefore, there are diagnostic possibilities for characterizing the $H^{+}$ temperature using the upshifted lines. As a final note, Eq. (8) can also be used for growth rate and threshold calculations involving the heavy ion spectral lines described in Section 2.2c. This has not been done currently and there is opportunity for future investigations.

3.3 Pump second harmonic emissions

Second harmonic generation (SHG) has been an active area of research in the Laser Plasma Interaction (LPI) community since the early 1970’s [28]. Significant theoretical understanding in this community has led to the development of SHG into a useful diagnostic of the heated plasma. Using concepts from [29], the Second Harmonic (SH) line shown in Figure 7 is taken to be generated by coalescence of the pump wave with a Langmuir wave (LW) produced by direct conversion of the pump. The mixing of these two waves of frequency ${\omega }_0$ produces the observed line at $2{\omega }_0$. Diagnostic information can be obtained from observations of very small frequency shifts of this line from $2{\omega }_0$. For instance, the SH line may be used to determine the relative plasma density to the critical density ratio $n_s/n_{\mathit{cr}}$ and also the bulk plasma flow speed $u$ in the interaction region by using the small shift $\mathrm{\Delta }{\omega }_{\mathit{SH}}$ of the SH line from $2{\omega }_0$, Approximate analytical expressions for this shift are given by Basov et al. [29].

$$\mathrm{\Delta }{\omega }_{\mathit{SH}}\approx 4\frac{{\omega }_{0}u}{c};\mathrm{\Delta }{\omega }_{\mathit{SH}}\approx 1-\frac{n_s}{{\mathrm{n}}_{\mathit{cr}}}$$E14

where $c$ is the speed of light. Yellu et al. [14] used these expressions to estimate $u$ and $n_s$ in recent HAARP experiments.

SHG concepts from LPI can also be leveraged to interpret the observations shown in Section 2.3 for the Second Harmonic Decay lines (SHD). Observations were shown in Figure 7 simultaneously for NSEE near ${\omega }_0$ and NSEE near $2{\omega }_0$, SH-NSEE. An important observation is the SBS IA decay line which implies narrowband ion acoustic waves are present in the ionospheric plasma. An explanation of the SHD line observations can be made in line with LPI SHG, assuming for the moment that the magnetic field effects can be neglected when the pump wave antenna beam angle is along $B_0$ (i.e. along the magnetic zenith direction) and ${\omega }_0$ is not too close to $n{\mathrm{\Omega }}_{\mathit{ce}}$. In this case, the SHD line may be produced by a process in which the pump field decays into a LW and an IA wave. This results in a LW with frequency ${\omega }_0-{\mathrm{\Delta }\omega }_{\mathit{IA}}$. The coalescence of two of these LWs produces a sideband shifted below $2{\omega }_0$ by $2\mathrm{\Delta }{\omega }_{\mathit{IA}}$ as observed in Figure 7. It should be noted the possibility exists for coalescence of the downshifted LW with the original pump wave which would result in a SHD line with frequency ${\omega }_0-{\mathrm{\Delta }\omega }_{\mathit{IA}}$. Basov et al. [29] shows that this is possible but much less likely. This appears to be consistent with HAARP observations since the shift ${\mathrm{\Delta }\omega }_{\mathit{IA}}$ is only observed during a small minority of experiments and these cases are under investigation. In summary, the SHD line shift can be written as

$$\mathrm{\Delta }{\omega }_{\mathit{SHD}}\approx 2\mathrm{\Delta }{\omega }_{\mathit{IA}}\text{or}\mathrm{\Delta }{\omega }_{\mathit{SHD}}\approx {\mathrm{\Delta }\omega }_{\mathit{IA}}$$E15

with the former being the more likely to be observed.

Figure 9 also shows $O^{+}$ gyroharmic spectral lines may be produced near $2{\omega }_0$. It was shown for the antenna beam angle off magnetic zenith (MZ) that these lines begin to appear just as they do around the ${\omega }_0$. Also, when the ${\omega }_0$ is in close proximity to $n{\mathrm{\Omega }}_{\mathit{ce}}$ these spectral lines also appear as well. An explanation of these lines near $2{\omega }_0$ can possibly be interpreted by leveraging the work of Tyagi et al. [30] for LPI. It is known that the $O^{+}$ Bernstein modes are produced by the three-wave parametric instability such as shown in Figure 9. That is, the pump wave decays into the EB/UH waves and IB waves. From [30], the pump wave with frequency and wavenumber (${\omega }_0$, $k_0)$exerts a nonlinear ponderomotive force of frequency and wavenumber ($2{\omega }_0,2k_0$) which in turn causes the electrons to oscillate at velocity $v$ with frequency and wavenumber ($2{\omega }_0,2k_0$). From Eq. (11), the density fluctuations of the IB modes are described with approximate frequency and wavenumber (${\mathrm{\Delta \omega }}_{\mathit{nIB}},n/{\rho }_O$). These density fluctuations beat with this velocity to produce current density $J$ with frequencies characterized by $2{\omega }_0\pm {\mathrm{\Delta }\omega }_{\mathit{nIB}}$ which produce the observed radiation on the ground. Therefore, in summary, frequency shifts for these SHD lines as observed in Figure 9 are

$$\mathrm{\Delta }{\omega }_{\mathit{SHD}}\approx \pm {\mathrm{\Delta }\omega }_{\mathit{nIB}}$$E16

It should be noted that the theory presented here is very qualitative but builds on past work in LPI. Again, the magnetic field obviously plays a critical role in the SH-NSEE. There has been limited theoretical work on SHG for the ionosphere so there is much room for future investigations in theory, modeling, and also observations.

4. Modeling

Ionospheric heating with high power radio waves is an inherently nonlinear plasma process, therefore nonlinear plasma simulations are a powerful tool to interpret many of the important physical processes. The NSEE spectral lines are often observed to be highly transient during the heating cycle and exhibit increase or decrease in spectral amplitude and broadening in frequency bandwidth due to nonlinear processes. The spectral lines may also be directly related to evolution of specific nonlinear processes. The previous section considered small wave amplitude parametric decay instability theory which can be used to initially interpret observations. However, the steady state NSEE spectra will be more accurately described by nonlinear plasma simulations after saturation has occurred. The plasma simulation models discussed in this section use both the electrostatic and electromagnetic Particle-in-Cell methods with Monte Carlo collisions. These models allow the full kinetic plasma description of the nonlinear evolution of the parametric decay instabilities just discussed. Such simulation tools have long been used to investigate interaction of high power electromagnetic waves with plasmas. They will be used here to provide insight into basic nonlinear processes associated with the NSEE spectral lines.

4.1 Simulation studies of stimulated Brillouin scatter

A recent advance has been the use of computer modeling, specifically Particle-In-Cell (PIC) simulations, to investigate PW-NSEEs observed during ionospheric heating experiments. In PIC simulations, the plasma ions and electrons are modeled as simulation particles and are subject to the electric and magnetic field forces. The plasma particles, which exist within a spatially gridded domain, are moved using the field forces and weighted onto grid points. Similarly, the electromagnetic (EM) and electrostatic (ES) fields are computed using Maxwell’s equations and projected to grid point values and evolve with time.

The goal of these initial simulation studies is to investigate the differences in characteristics of PW-NSEEs produced during two pump power regimes as noted in the observations described in Section 3.1. A simplified PIC simulation which approximates the essential physics for the HAARP experiments in which the observations, that is, broadband and narrowband SBS PW-NSEEs, respectively, for high and low pump power regimes, was adopted. The PIC [31] simulation model is a one space and three velocity (1D3V) dimension electromagnetic PIC simulation with Monte Carlo collisions as described in Birdsall et al. [32]. The model has plasma of uniform density in a single spatial extent in the x-direction, and is 3-dimensional for particle velocities, wave electric field and magnetic field vectors. The model is shown in Figure 12. Although this simulation model does not include a background magnetic field to simulate the effects of the geomagnetic field, the current model aligns with O-mode experiments at HAARP where the pump field is injected into a ZA = MZ = 14°. In this case, the nonlinear interactions that initiate PW-NSEE generation occur near the plasma resonance altitude as with the HAARP SBS PW-NSEEs observations discussed in Section 3.1. The PIC simulation model includes vacuum (moat) regions separating the plasma region from the edges of the simulation space to reduce boundary effects. The EM pump (incident) wave $\left(E_i,B_i,k_i\right)$ polarized in the y-direction in the adopted coordinate system is injected into the moat on the left from the left boundary. A reflected EM pump wave $\left(E_r{B}_r{k}_r\right)$ propagates back into the left moat region where its frequency spectrum is calculated and assessed for sidebands shifted from the pump frequency ${\omega }_0\lesssim {\omega }_{\mathit{pe}}$. Since the simulation space as shown has aperiodic boundaries (drop-off from plasma region to plasma deficit moat regions), that is, particles that propagate outside the plasma region are not injected back, the charge densities at the boundaries are set to 0 in order to enforce periodicity and thus be able to exploit Fourier methods to compute the electrostatic (ES) field ($E_x\parallel k_x$), which exists only in the plasma.

Figure 12.

PIC simulation model with a 1-D spatial extent $\left(L\right)$ of 8192 grid cells, a plasma domain $\left(L_p\right)$ of 4096 grid cells and left and right moat (vacuum) regions 2048 grid cells used for investigating NSEE stimulated Brillouin scatter (SBS) near the reflection altitude. $\left(E_i,B_i,k_i\right)$ and $\left(E_r,B_r,k_r\right)$ are the pump and reflected ELECTROMAGNETIC (EM) waves, respectively. $\left(E_x\parallel k_x\right)$ represents the ELECTROSTATIC (ES) low frequency ion decay waves in the plasma. Adapted from [31].

The pump electric field amplitude$\mid E_i\mid$was chosen so that the ratio of the electron oscillatory velocity in the pump electric field to the electron thermal velocity, that is, ${\stackrel{\sim }{v}}_{\mathit{osc}}=e\left|E_i\right|/\left(m_e{\omega }_0{v}_{\mathit{te}}\right)$, is reasonably consistent with a 1100 K electron temperature in the interaction region. An artifice, that is, reduced ion-electron mass ratio, commonly adopted in PIC simulations was used for the simulations to increase computational efficiency, increase resolution, but appropriately delineate the timescales of the ions and electrons involved in the wave interaction processes that produce the PW-NSEEs. Figure 13 shows results for the low pump power case in the top two panels and the high pump power case in the bottom two panels. The ratio of the low power to high power pump electric field was taken to be 0.125. The total EM field $\left(E_i+E_r\right)$ time series is captured and averaged over a small region in the left moat. The frequency spectrum of this time series is used to be representative of the PW-NSEE observed during experiments and assess the sideband frequencies relative to the pump field. These spectra are shown in the top left and bottom left panels of Figure 13. The ES field time series is captured and averaged over a small region in the plasma. The spectrum of this time series is used to assess characteristics of the low frequency ion decay mode. These spectra are shown in the top right and bottom right panels of Figure 13.

Figure 13.

PIC simulation results showing the EM field spectra (left column) and ES field spectra (right column) for low pump power (upper row) and high pump power (lower row). Frequency is normalized to ${\omega }_0$. The high power case shows broadening of the spectra which is in line with the power stepping observations shown in Figure 3. The ES waves are presupposed to be ion acoustic. Adapted from [31].

The PIC simulation results in Figure 11 show that as with the observations from actual ionospheric heating experiments shown in Figure 3, the SBS PW-NSEE for the low power case (Figure 13a) is a distinct, narrow bandwidth spectral line whilst for high power (Figure 13c), it is relatively broadband. An essence of PIC simulations is the ability to probe directly the ES waves in the plasma which allows a direct means of determining the ES low frequency decay waves and therefore the specific parametric decay processes. This probe reveals corresponding narrow (Figure 13b) and wider bandwidth ES waves (Figure 13d) herein noted by virtue of proposed SBS decay causation as ion acoustic (IA) waves for the low and high-power pump regimes, respectively. The IA waves for the high-power case have a semblance of a cascade process in which initial EM waves produced in the initial parametric decay of the pump wave act as pumps to initiate subsequent parametric decays.

To investigate further the causation for the difference in PW-NSEEs spectral characteristics for the two power regimes, the ES wave $\left(E_x\right)$ and the EM wave $\left(E_y\right)$ in the plasma region, the ion density $\left(n_i\right)$ and electron temperature $\left(T_e\right)$ as determined for the high-power simulation are presented in Figure 14. The power in the waves, and the ion density are normalized, respectively, by the pump wave amplitude $\left(E_0\right)$ and the ion density $\left(n_0\right)$ at the start of the simulation. The results show that for higher power, unlike the low-power case, cavities develop in $n_i$ in which $T_e$ and $E_y$ are significantly increased, whereas for the ES field $E_x$, there is not a significant correlated increase in all the cavities. Regions of particularly substantial enhancement are noted with dashed boxes in the Figure 14. The ES waves in the cavities are proposed to lose energy via Landau damping to heat up the plasma, thus are short-lived. The long-lived, high-power EM waves in the cavities are proposed to be indicative of strong plasma turbulence which is the causation of the broadband SBS PW-NSEEs structuring observed for high-power ionospheric heating experiments [31]. These strong EM fields trapped in the cavities imply high reflectivity and result in the amplitude of the scattered sideband having comparable or even larger amplitude to the pump as observed in heating experiments.

Figure 14.

ES wave (a), EM wave (b), electron temperature (c) and ion density (d) for high-power PIC simulations showing development of cavities in ion density containing high temperature electrons and enhanced EM wave amplitudes suggestive of strong ion acoustic turbulence. Adapted from [31].

4.2 Simulation studies of oxygen Gyroharmonic spectral lines

Figure 15 shows the configuration of an electrostatic two-dimensional PIC model (2D3V) using Monte Carlo collisions to investigate nonlinear processes associated with NSEE $O^{+}$ gyroharmonic spectral lines near the upper hybrid layer as discussed in Section 2.2a [17]. In this case ${\omega }_0\approx 2{\mathrm{\Omega }}_{\mathit{ce}}={\omega }_{\mathit{uh}}$. The model uses a dipole pump approximation (i.e., $k_0\approx 0$, as does the theory in Section 3.2). Therefore, the pump electric field is applied as a uniform driver across the entire simulation domain and is of the time-varying form $E=E_{0}cos\left({\omega }_{0}t\right)$. The constant background magnetic field $B_0$ is applied in the $\widehat{z}$ direction as shown. The electric field vector is varied at an angle that is off perpendicular to the magnetic field ${\theta }_E$. Within this electrostatic model framework, the current density in the simulation domain would be assumed to produce the SEE observed on the ground. The first set of simulations to be discussed investigated the $O^{+}$ gyroharmonic spectral lines. Therefore, the neutralized $O^{+}$ Bernstein waves are the low frequency ion decay mode. In this case ${\theta }_E\gtrsim \sqrt{m_e/m_O}$. The destabilized waves propagate near the direction of the pump electric field vector. All the simulations are run to nonlinear saturation in which the field and plasma particle thermal energies have reached a nonlinear saturated state which occurs on the order of 10 growth periods.

Figure 15.

Schematic diagram of 2-dimensional electrostatic PIC simulation model used to investigate generation of parametric decay instabilities that produce NSEE near the upper hybrid layer. Adapted from [17].

Figure 16 (top right) shows the temporal growth of the electric field energy in the $y$ direction, which is nearly perpendicular to $B_0$, for the parametric instability involving low frequency neutralized $O^{+}$ Bernstein decay waves. It can be seen that early in the simulation, the electric field energy grows linearly which is in line with small amplitude growth predicted by Eq. 8. After linear growth, the field energy eventually reaches saturation. Figure 16 (top left) shows a frequency power spectrum of the electric field time series after the simulation reaches a saturated state. It can be seen that there are roughly 10 $O^{+}$ gyroharmonic spectral lines shifted below the pump frequency which is similar to the observation spectrum shown in Figure 4. The results in Figure 16 (top left) are also in line with the theoretical predictions of Eq. (8) in Figure 10. A closer examination of the dispersive properties of these waves is provided in Figure 14 (bottom left) by using a $k_y-k_z$ wavenumber spectrum. This wavenumber spectrum indicates the expected characteristic wavenumber $k_y{\rho }_{\mathit{ci}}\sim n$, $n$ the harmonic number, which validates the production of neutralized ion Bernstein waves. It is observed in Figure 16 (bottom right) that significant bulk heating of the electrons across the magnetic field occurs. The electron kinetic energy across the magnetic field is shown and it can be seen that this electron kinetic energy grows eventually reaching nonlinear saturation near time ${\mathrm{\Omega }}_{\mathit{cO}}t\approx 7$ as does the electric field energy. It was observed that the number of harmonic lines observed in the simulations is related to the degree of electron heating across the field [17]. The number of harmonics, of course, increases with increasing pump power.

Figure 16.

Power spectrum of simulation waves showing existence of spectral lines shifted below ${\omega }_0$, ordered by ${n\mathrm{\Omega }}_{\mathit{cO}},$ after nonlinear saturation (top left) similar to Figure 4 (left). Wavenumber spectrum showing characteristic neutralized ion Bernstein modes (bottom left). Growth of electric field energy associated with the parametric instability involving neutralized ion Bernstein waves (top right). Electron kinetic energy showing bulk heating of electrons across the magnetic field associated with $O^{+}$ gyroharmonic spectral lines (bottom right). Adapted from [17].

The second set of simulations performed with this model consider the generation of the broadband continuous NSEE spectral lines associated with the ion acoustic waves near the upper hybrid layer as shown in Figure 4. Again, rather than IB low frequency decay wave modes as in the previous simulations, the low frequency decay modes in this case are IA. This implies that the pump electric field vector must be further off perpendicular to $B_0$ so that ${\theta }_E\gg \sqrt{m_e/m_O}$. This range of ${\theta }_E$ allows coupling into the IA waves which propagate at a more oblique angle off perpendicular to $B_0$ than the IB waves that result in a discrete line spectrum. Figure 17 shows results from simulations to consider the NSEE line shown in Figure 4 (right) and theoretically predicted in Figure 10 (right). Figure 17 (top left) shows an electric field power spectrum in the simulation after nonlinear saturation. A spectral line can be seen that is downshifted from the pump frequency. The spectral line has a broad bandwidth relative to the $O^{+}$ gyroharmonic lines observed in the simulations of Figure 14. A sideband upshifted by approximately the same frequency can be seen as well that has a smaller amplitude. This is in line with the observations of Figure 4. Figure 15 (top right) shows the evolution of the electron velocity distribution along $B_0$ during the simulation. Strong tail heating of the electron velocity distribution occurs. Figure 17 bottom shows the electric field on the spatial grid during the simulation. The red areas show intense electric fields that are associated with cavities in the density similar to Figure 12. These intense electric fields in the cavities are responsible for the acceleration of the electrons along the magnetic field. The density structures (not shown) show caviton collapse behavior in which the cavities (and electric fields within the cavities) intensify and then collapse, transferring energy to the electrons through acceleration along the magnetic field. This is similar to elevation of the electron temperature in the cavities shown in Figure 14. Therefore the observation of this NSEE spectral line is a diagnostic for intense acceleration of the electrons along $B_0$ and development of cavities containing intense electric fields in the upper hybrid layer.

Figure 17.

Power spectrum of simulation waves showing development of a spectral line associated with ion acoustic decay waves at the upper hybrid layer (top left). This spectrum is in line with observations in Figure 4. Electron acceleration and development of intense electric fields inside density cavities associated with the spectral line (top right and bottom). Adapted from [17].

5. Conclusions

Significant progress has been made during the past decade in beginning to develop pump wave NSEE (PW-NSEE) into a useful diagnostic for the ionosphere during heating experiments. Of particular note is the possibility for investigating various plasma species during the heating experiments in terms of species mass, density, and temperature although further work must be done for development into a more robust technique in comparison to other diagnostics such as Incoherent Scatter Radar (ISR), e.g. [11]. Even with the current state of knowledge that has been surveyed here, PW-NSEE is clearly an important diagnostic that should be utilized with other mainstay diagnostics during heating experiments. At this time, investigation of heavy ions at lower altitudes, that is, Section 2.2.3, is a particularly attractive possibility due to the difficulty of making such measurements, however, considerably more observations are necessary. Also, at this time, little if any theoretical and modeling development has been performed to quantify the parametric instabilities that are at play for heavy ions, however, the framework discussed in Sections 3.1 and 3.2 could be leveraged as a starting point. Possible assessment of geomagnetic activity with PW-NSEE as noted in Section 2.2.2 requires further observational investigation as well, however, a useful theoretical framework has been provided in Section 3.1 and 3.2 that imply a useful diagnostic technique.

Although there has not been elaboration on AFAIs given the scope of this chapter, AFAIs play an important role in the generation, evolution and possibly the quenching or attenuation of PW-NSEEs and SH-NSEEs. Past experimental observations have shown enhancement of AFAIs for ${\omega }_0\approx 2{\mathrm{\Omega }}_e$ heating and suppression of AFAIs for ${\omega }_0\approx {\mathrm{n\Omega }}_e$, for n > 2, e.g. [33]. For PW-NSEEs which are proposed to originate from a parametric decay in which the high frequency decay mode is electrostatic or for SHG processes proposed to be due to the mixing of initially generated electrostatic modes, the mode or “mixed” mode must scatter from gradients in AFAIs into an EM wave in order to be observable on the ground as PW-NSEEs or SH-NSEEs, respectively. AFAIs are known to be formed near the UH altitude, and thus may inhibit SEEs proposed to be generated at the reflection altitude. The foregoing can thus be used to design heating experiments, for example, pumping${\omega }_0\approx {\mathrm{n\Omega }}_e$ in different gyroharmonic regimes with high resolution frequency stepping, and observing the development and evolution of the SEE spectral lines and AFAIs. This may enable the distinction of generation altitudes and, also possibly yield confirmation of wave decay modes involved in the underlying nonlinear interaction processes.

Use of PW-NSEE as a diagnostic for nonlinear evolution and strong turbulence during heating experiments has been greatly aided by utilization of plasma simulation models, however, considerable work remains in this area as well. Spectral line characteristics and temporal evolution have been shown to be linked to specific strongly nonlinear signatures such as density cavity development, density cavity collapse, electron heating, electron velocity distribution tail acceleration, and trapping of both EM and ES waves in density cavities. These phenomena all provide insight into the heating process and nature of the interaction between the high power radiowave and ionospheric plasma. Although progress has been made, future modeling investigations are necessary. Of particular importance is the extension of the model described in Section 4.1 to include magnetic field effects which would enable more careful study of the SBS EIC spectral line. This line has been shown through observations to be particularly important as a mass spectrometer, however, observations also show important temporal evolution that are likely of great importance, e.g. [17]. At this time specific nonlinear physics associated with this spectral line are not well known so there are significant opportunities for contributions in this area. Finally, the change in PW-NSEE spectral characteristics and associated physics upon stepping ${\omega }_0$ through $n{\mathrm{\Omega }}_{\mathit{ce}}$ have been studied through observations, for example, Sections 2.2.3, 2.3, but more careful modeling work is required.

The last critical area that would benefit from considerable more investigation, observations, theory, and modeling, is Second Harmonic Generation SHG during ionospheric heating experiments, described in this chapter as Second Harmonic NSEE (SH-NSEE). Although a number of successful experiments producing useful observations have been performed over the past 5 years or so, little work has been done on theory and modeling. It is clear from the LPI community that SHG is capable of providing important diagnostic information and the same should be true for ionospheric heating. Only a qualitative theoretical model has been provided in this chapter that is based on concepts from LPIs. An extension of the model of Section 4.1 would be a plausible starting point.

In summary, the outlook for continued development of NSEE into a useful ionospheric heating diagnostic is promising. A coordinated approach of observations, theory, and modeling is critical to exploit the full potential of this interesting new area of investigation in ionospheric research.

Acronyms and abbreviations

SEEs

Stimulated Electromagnetic Emissions

NSEEs

Narrowband Stimulated Electromagnetic Emissions

PW-NSEEs

Pump Wave NSEEs

SH-NSEEs

Second Harmonic NSEEs

SHG

Second Harmonic Generation

HAARP

High Frequency Active Auroral Research Program

EISCAT

European Incoherent Scatter Radar

SBS

Stimulated Brillouin Scatter

MSBS

Magnetized Stimulated Brillouin Scatter

IA

Ion Acoustic

EIC

Electrostatic Ion Cyclotron

ES

Electrostatic

LH

Lower Hybrid

UH

Upper Hybrid

LW

Langmuir Wave

IB

Ion Bernstein

EB

Electron Bernstein