Electron and ion Bernstein waves excited in the ionosphere by high power EM waves at the second harmonic of the electron cyclotron frequency



[1] The transmission of a high power electromagnetic (EM) waves from the HAARP facility in Alaska can excite stimulated electromagnetic emissions offset from the transmitter frequency near harmonics of ion cyclotron frequency. Stimulated ion Bernstein (SIB) occurs when the pump frequency is tuned to an electron Bernstein (EB) frequency near twice the electron gyro frequency. The SIB process is thought to involve mode conversion from EM to EB waves followed by parametric decay of the EB wave to multiple EB and IB waves. The production of SIB waves may be an indicator of strong cyclotron acceleration of electrons by the EB waves that lead to artificial aurora and impact ionization of neutrals.

1. Introduction

[2] Stimulated electromagnetic emissions (SEE) provide a window on the ionosphere when excited by high power radio waves [Leyser, 2001]. SEE can been employed to measure electron temperatures with ion acoustic waves [Bernhardt et al., 2009], ion composition with electrostatic ion cyclotron waves [Bernhardt et al., 2010], and possible conditions for acceleration of electrons [Leyser, 2001]. Resonant acceleration of electrons requires electrostatic (ES) modes such as electron plasma, upper hybrid and electron Bernstein waves that couple more efficiently than EM waves. High power radio waves transmitted from the ground can enter the ionosphere and become transformed into electrostatic waves by mode coupling or parametric decay. The decay products may be electromagnetic (EM) waves that propagate to the ground and are detected by ground receivers. The decay products may also be electrostatic waves that are mode converted to EM waves for propagation to ground receivers. The EM signals have frequency offsets from the EM pump wave corresponding to the low frequency waves in the plasma.

[3] The production of SEE requires five factors for excitation. First, the EM pump wave must have sufficient amplitude in the ionosphere to excite the parametric decay process. Second, the EM pump wave must propagate to a region where it can couple into a resonant mode of the plasma. Third, the large amplitude EM or ES resonant mode (ω0, k0) drives a parametric decay instability to generate two other resonant modes (ω1, k1 and ω2, k2) in the plasma. Fourth, at least one resonant mode in the plasma should be weakly damped. Fifth, the high frequency daughter wave of the parametric decay process may need to be converted into an electromagnetic wave to be received on the ground.

[4] With these factors in mind, the HAARP HF facility in Alaska was used to produce harmonic sidebands near multiples of the ion cyclotron frequency. These sidebands are called stimulated ion Bernstein (SIB) emissions. A description of the observations is followed by a theoretical explanation of their source. Finally, the observation is made that the presence of ion Bernstein waves indicates the parametric decay of electron Bernstein (EB) waves that can resonantly interact with electrons for cyclotron acceleration to high energies. These energetic electrons may be contribute to the production of artificial optical emissions and enhanced ionization of neutrals.

2. Observations of Stimulated Ion Bernstein Waves

[5] A large dynamic range HF receiver was set up by NRL at HAARP to record stimulated electromagnetic emissions. The digital receiving system sampled the HF signals from a 30-m folded-dipole antenna at a rate of 250 kHz. This system has been previously used at HAARP to study the excitation of slow MHD and electrostatic ion cyclotron waves with HF transmission frequencies away from electron gyro harmonics [Bernhardt et al., 2009, 2010]. The sampled data are decimated, windowed, and processed with the Fast Fourier Transform to yield low frequency spectra. With this processing, the dynamic range of the instrument is estimated to be better than 90 dB.

[6] Observations of the Stimulated Ion Bernstein (SIB) Scatter were obtained with HAARP by tuning the transmitter to 2.85 MHz at the second harmonic of the electron cyclotron frequency. The O-Mode HF beam was pointed to the magnetic zenith with an azimuth of 202 degrees and a zenith angle of 14 degrees. The transmitter was operated with 4 minute on and 4 minute off cycles at full power with 3.6 MW into the antenna. The estimated effective radiated power was 280 MW at 2.85 MHz. The radio beam is about 100 km diameter in the ionosphere. The digital ionosonde at HAARP was used to determine that the reflection height was near 221 km altitude where electron cyclotron frequency over HAARP is estimated at 1.429 MHz using the IGRF model. The optical, radar, and GPS receivers operated at HAARP are described by Kendall et al. [2010].

[7] When the transmitter was turned on at 02:34 UT on 28 October 2008, the spectra immediately showed downshifted and upshifted emissions at harmonic frequencies of the ion gyro frequency (Figure 1). The intensity of the ion-harmonic emission lines did not show significant fluctuations over the 4 minute transmission period. The downshift (Stokes) emissions were paired with weaker upshifted (anti-Stokes) emission lines. The stimulated electromagnetic emission spectral only showed the pump frequency at 2.85 MHz, the ion-gyro-harmonic offsets from the pump, and weak emissions at harmonics of 120 Hz introduced into the transmitter by the full-wave rectified AC supply operated on 60 Hz power. The emission lines from the ionosphere are attributed to the stimulated ion Bernstein (SIB) process described in the previous section.

Figure 1.

Spectrograph of stimulated emissions near harmonics of the ion cyclotron frequencies.

[8] The measured SEE spectrum shows ion Bernstein lines with maximum intensity at n = 4 (Figure 2). Strong lines are observed between n = 3 and n = 6 with significant harmonic lines extending to n = 16 where the frequency offset is 781 Hz. The strong downshifted (Stokes) lines have corresponding upshifted (anti-Stokes) lines that are about 11 dB weaker. The HAARP transmitter has weak power supply modulations that are 80 dB or more below the transmitter carrier. The locations of these interfering emissions are indicated by red dots in Figure 1. No other lines out to ±125 kHz from the pump frequency were seen in the SEE spectra at the time of the observations in Figure 1. The power supply harmonics are narrower than the SIB lines.

Figure 2.

Stimulated Ion Bernstein Scatter observed at HAARP with the transmitter tuned to precisely twice the electron cyclotron frequency. No other SEE emissions are observed within 80 kHz of the pump frequency. The red dots show the location of power supply harmonic interference at multiples of 120 Hz.

3. Stimulated Bernstein Waves at the Second Gyro Harmonic

[9] The production of stimulated ion Bernstein (SIB) emissions is considered for an electromagnetic pump wave tuned to the second harmonic of the electron cyclotron frequency. For maximum pump amplitude, the plasma frequency should be nearly equal to the pump frequency. This double resonance occurs if the EM pump frequency is tuned to match the frequency at the altitude where the plasma frequency in the plasma layer is equal to twice the electron gyro frequency. The double resonance of ω0 = ωpe = 2 Ωe insures that a large amplitude wave is formed at the point where the pump electric field can couple into the electron Bernstein resonance at twice the electron cyclotron frequency.

[10] The electron and ion Bernstein modes along with upper hybrid and lower hybrid modes are of interest to ionospheric modification experiments because they can propagate perpendicular to the magnetic field without Landau damping. The general formalism for parametric processes driven by an electromagnetic wave has been given for unmagnetized plasma [Drake et al., 1974] and for magnetized plasmas [Porkolab, 1978; Liu and Tripathi, 1986]. The simple dispersion relation from Porkolab [1978] is given as

equation image

where μe is the normalized pump electric field that displaces the electrons, subscripts e and i denote electrons and ions, χe and χi are the linear susceptibilities at the low frequency ω2 and wavenumber k, the + and − signs represent the sidebands (ω2 ± ω0) with electromagnetic pump ω0. Equation (1) was derived assuming that that μe ≪ 1. The linear dielectric function is ɛ(ω, k) = 1 + χi(ω, k) + χe(ω, k) and, for a hot plasma with a Maxwellian distribution, the linear susceptibilities are

equation image

where ςne,i = equation image, Ωe,i = equation image, vt2 = equation image, be,i = equation image and Z(ζ) is the Fried-Conte plasma dispersion function [Swanson, 1989]. The plasma drift induced by the pump electric field is represented by

equation image

Without an electromagnetic pump field (μe = 0), (1) reduces to equation image. Substitution of the susceptibilities into the dispersion equation provides the normal modes of the plasma including ion and electron Bernstein waves, lower and upper hybrid waves, etc. This standard plasma dispersion relation for electrostatic waves in a magnetic field is also given as equation 4.68 of Ichimaru [1973] or equations 11-85 and 11-87 of Stix [1992].

4. Plasma Modes Excited at the Second Electron Gyro Frequency

[11] The plasma resonances are computed for conditions over HAARP. The ionospheric parameters for the HF experiments with transmissions near the 2nd electron gyro frequency are given with B0 = 5.1 10−5 T, ne = 1.01 1011 m−3, Te = 2500 K, Ti = 800 K, VA = 8.75 105 m/s, ρe = 0.022 m, ρi = 3.64 m, Ωe = (2π) 1.43 106 Rad/s, ωpe = 2 Ωe = (2π) 2.86 106 Rad/s, ωUH = (2π) 3.2 106 Rad/s, ωLH = (2π) 7560 Rad/s, Ωi = (2π) 48.7 Rad/s. The plasma response can be investigated by normalizing the transmission frequency ωH and the plasma frequency ωpe by the electron cyclotron frequency Ωe. The characteristics of high frequency plasma waves near the second electron gyro harmonic have been computed for k = 0 and shown in Figure 3. When ω0 ≈ 2 Ωeωpe, the upper hybrid cannot be excited and only an electron Bernstein wave will be generated as either a mode conversion or a parametric decay product.

Figure 3.

High frequency (ωH) electrostatic modes near the second harmonic of the electron cyclotron frequency (Ωe). The constant electron density curves are labeled with the plasma frequency normalized by Ωe.

[12] With either an EM wave or an electrostatic (ES) electron Bernstein wave as a pump, the parametric decay products can be simultaneously produced electron Bernstein (EB) and Ion Bernstein (IB) waves. Simultaneous satisfaction of the frequency and wave-number matching conditions (ω0 = ω1 + ω2, k0 = k1 + k2) and the electrostatic dispersion equations for the modes is illustrated in Figure 4 for representative ionospheric parameters. Simultaneous parametric decay will generate multiple high-frequency electron Bernstein waves with staggered frequency offsets associated with second and higher harmonics of the ion cyclotron frequency Ωi. The initial pump wave, represented by the red dot in Figure 4, is an ES-EB wave with a small perpendicular wave vector but it could also be a low wave number EM wave with an initial k0 that can be taken to be zero using the dipole approximation.

Figure 4.

Multiply matched modes for stimulated scatter into ion Bernstein (IB) and electron Bernstein (EB) modes labeled by ion gyro frequency harmonic number.

[13] The growth rates of the parametric decay instability into EB and IB waves must be large enough to overcome collisionless and collisional damping. Threshold conditions for pump electric fields may be calculated by balancing the parametric decay instability with the damping processes. For resonant decay into a normal mode near the high frequency ω1 = ω0ω2 the resonance condition is given by ɛ(ω1) = 0 and the linear grow rate, g, is given by

equation image

where R denotes the real part and Γ1,2 are the linear damping rates of each high frequency (ω1) and low frequency (ω2) modes, respectively [Porkolab, 1978].

[14] The simultaneous decay of an electron Bernstein wave at 2 Ωe into multiple electron Bernstein waves and ion Bernstein waves is investigated using (4). The 11 resonant frequencies and wave numbers illustrated in Figure 4 are substituted into the growth rate expression for resonant decay into low and high frequency sidebands. The damping rates are set to zero to yield the fastest growth rates. The computed mode number dependence on the stimulated ion/electron Bernstein (SEIB) decay instability has been presented in Figure 5 where the grown rate is normalized by the electric field amplitude (E0) of the pump wave. The growth rate values are labeled with the ion Bernstein mode harmonic of the ion gyro frequency. This theory indicates that the third and forth ion-cyclotron harmonics will be the most strongly excited.

Figure 5.

Computed growth rate for parametric decay of pump electric field into ion and electron Bernstein waves. Theoretically, the third ion gyro harmonic mode should grow the fastest.

[15] The threshold for a parametric instability is found by solving γ2(E0) ≡ νiνe for E0. Using typical ion neutral collision frequencies (νi = 3 Hz) and electron-collisions with ions and neutrals (νe = 400 Hz) the threshold electric field for the fastest growing SEIB mode is 250 V/m. This is a large field considering that the free space electric field from HAARP is less than 1 V/m in the ionosphere. Near the F-layer reflection altitude, the EM wave can swell to a much larger value. A numerical, full-wave model of electric fields near the reflection altitude used by Bernhardt et al. [2009] to give values over 600 V/m. The computed standing wave at 2.86 MHz shows this field is readily exceeded just below the reflection altitude using the HAARP transmitter operating with a full 3.6 MWatt power feeding the HAARP antenna array with a gain 19 dB. To exceed this large SEIB threshold, interactions must occur just below the reflection altitude of the O-mode pump wave.

5. Discussion

[16] The low frequency SEE measurements at HAARP when the transmitter is tuned to the 2nd electron gyro frequency have shown the generation of ion Bernstein modes. This has been attributed to the simultaneous parametric decay of electron Bernstein waves into multiple electron Bernstein and ion Bernstein waves. Previous SEE measurements using extraordinary (X-mode) transmissions near the 2nd harmonic of the electron cyclotron frequency showed upshifted spectral emissions close to multiples of the ion gyro frequency near 45 to 50 Hz according to Thide et al. [1983]. These authors of this work could not “exclude instrumental effects” for these observations. This spectra was attributed to ion-Bernstein waves (IBW) resulting from a parametric decay of the X-mode into UH and IBW [Sharma et al., 1993]. The SIB spectra shown in Figures 1 and 2 provide the clearest, unambiguous observations of ion-Bernstein wave excitation by high power EM waves in the ionosphere.

[17] These SIB observations may enhance our understanding of both electron acceleration and generation of artificial field aligned irregularities. Second harmonic transmissions using the HAARP transmitters produce not only SIB but also optical rings, enhanced artificial aurora and ionization layers [Pedersen et al., 2009, 2010]. Future studies will review the observational data at HAARP to determine the coincidence of ion Bernstein waves in stimulated electromagnetic emissions with artificial aurora and man-made layer production.

[18] SEE can be a proxy for field aligned irregularities (FAI). The downshifted maximum (DM) feature of SEE is well known to be an indicator of field aligned irregularities near the upper hybrid resonance altitude [Bernhardt et al., 1994; Leyser, 2001]. Electrostatic ion cyclotron (EIC) [Keskinen et al., 1995] and ion Bernstein (IB) [Kuo et al., 1998] waves may be responsible for density irregularities in the ten-meter scale range. SEE with EIC or IB frequency offsets from the pump may be a valuable indicator of these irregularities. Two rocket experiments have been used to measure the in situ wave spectra for 5.1 MHz waves launched by the Arecibo facility. Bernhardt et al. [1995] provide evidence of simultaneous electron density cavitons, low-frequency ion-acousitic waves and high frequency Langmuir waves with the rocket pass through the critical layer. The second rocket flight occurred when the Arecibo HF facility operating near the 5th gyro harmonic generated both O- and X- modes because the antenna phasing units were on fire. During this experiment, FAI was generated above and below the reflection altitude with a few tens of seconds heating of turbulent operation [Gelinas et al., 2003]. The structures were attributed to electron Bernstein modes produced by parametric decay of a Z-mode converted from the O-mode component of the pump. The present observations are produced with the much more powerful facility at HAARP with continuous operations of the transmitter antenna beaming 2nd harmonic (not 5th) waves to a high latitude ionosphere. It would have been useful to record the SEE from the Arecibo operations for either of these experiments.

[19] Future experiments should consider SEIB generation at other harmonics of the HF pump frequency. These experiments will be conducted at HAARP in conjunction with theoretic research for precise determination of the frequencies in the SEIB SEE spectrum.


[20] This work was sponsored by the Naval Research Laboratory Base Program. The experiments at the HAARP facility were funded by the Air Force Research Laboratory.

[21] The Editor thanks K. Papadopoulos and an anonymous reviewer for their assistance in evaluating this paper.