We examine possible correlations between occurrences of nighttime E-region plasma line (PL) enhancements over Arecibo and 40.75 kHz NAU emissions. On the night of January 1–2, 2006, the experiments were conducted from 22:00 to 6:00 local time (LT). NAU transmitter was initially turned off until 01:45 LT, when continuous operations resumed for the remainder of the experiments. Enhanced PL events lasting <10 s had central frequencies and bandwidths of about 2.5 and 1.5 MHz, respectively, indicating that Arecibo radar detected 2.3 to 8.5 eV suprathermal electrons streaming along geomagnetic fields. The rate of PL event detections increased by a factor of 2.8 after NAU turn-on. We suggest that 40.75 kHz radiation sporadically leaked though local ionosphere, probably abetted by field-aligned irregularities. The radiation propagated in whistler mode into the L = 1.35 inner radiation belt where gyroresonant interactions with trapped 390 keV electrons increased the precipitation rate.
 A 100 kW and 40.75 kHz transmitter code-named NAU is operated by the United States Navy at Aguada, Puerto Rico, about 52 km to the west of the Arecibo Observatory. As illustrated in Figure 1 most of NAU's emitted power propagates in the Earth-ionosphere waveguide (Ray 1). However, in the presence of ionospheric plasma irregularities some fraction of the NAU carrier signal scatters into the ionosphere and magnetosphere where it propagates along magnetic field lines in the whistler mode (Ray 2). Although the NAU transmitter operates exclusively for naval communications, its proximity to the Arecibo Observatory offers occasional opportunities to observe geophysical effects of whistler-wave coupling. Arecibo is located at ∼30°N magnetic latitude where it is magnetically conjugate to the inner radiation belt at L = 1.35.
Lee et al.  reported results of 1997 Arecibo experiments in which the HF ionospheric heater at Arecibo created large, sheet-like ionospheric density irregularities that aligned parallel to the magnetic meridional plane. These induced irregularities extended to great heights above the heated volume and acted as “ionospheric ducts” or parallel-plate waveguides for whistler-mode wave propagation experiments. As part of the experiments identical VLF-receiver antennas were set up at Arecibo and Trelew. The local receiver monitored detailed characteristics of the emitted carrier waves for comparison to those detected at Trelew. Starks and Lee  and Starks et al.  used different time delays to distinguish between signals confined to the Earth-ionosphere waveguide and those guided by “heater-induced ionospheric ducts” to propagate along the L = 1.35 magnetic field lines. Ducted NAU-generated 28.5 kHz whistler mode was recorded in Trelew, Argentina near the magnetic conjugate point of Arecibo [Starks et al., 2001]. Ray tracing work by Starks  suggests that significant quantities of radiation from NAU should enter the magnetosphere. However, the occurrence probability of magnetospheric ducts decreases with L-shell and they had never been observed to occur naturally below L = 1.7, according to Cerisier . Hence, further Arecibo experiments were needed to better understand how low-frequency radiation penetrates the inner magnetosphere and propagate through the inner radiation belt. Unfortunately, in 1998 as Hurricane George crossed Puerto Rico the ionospheric heater at Arecibo was severely damaged and later dismantled. While the loss of the ionospheric heater renders the controlled creation of ionospheric ducts for whistler-mode wave propagation experiments impossible, intermittent observations of large, natural irregularities above Arecibo [Labno et al., 2007] raises the possibility of detecting local effects of NAU-generated whistler-mode waves.
 It is reasonable to expect that NAU-generated whistler-mode waves also scatter off and are guided by natural irregularities to propagate into the conjugate magnetosphere. During propagation from Puerto Rico these whistler waves could affect the pitch angle distributions of energetic electrons trapped in the inner radiation belt. Electrons that see NAU signals Doppler shifted to the local gyro-frequency should interact strongly with them to cause changes in pitch angles [Kennel and Petschek, 1966]. Phase-space density gradients near the edge of the loss cone require that most resonant electrons scatter to lower pitch-angles. Some may even stay in resonance long enough to scatter into the loss cone and precipitate into the lower ionosphere over Arecibo.
 Effects of strong wave-particle interactions were directly observed during the stimulated emission of energetic particles (SEEP) experiments, conducted with the S-81 satellite. Imhof et al.  reported on the controlled precipitation of energetic electrons from the outer radiation belt in response to modulated bursts of 17.8 kHz radiation from the NAA transmitter in Cutler, Maine. Sensors on the S-81 satellite also detected fluxes of precipitating electrons with E > 45 keV caused by VLF bursts from the Siple-Station antenna in Antarctica [Imhof et al., 1989] and lightning discharges in the troposphere [Inan et al., 1989].
 During December-January of the past two years we conducted a series of experiments using the Arecibo 430 MHz incoherent scatter radar (ISR) to identify large plasma irregularities and monitor possible ionospheric plasma disturbances induced by NAU transmissions. Section 2 summarizes ISR detections of sporadic enhanced plasma-line backscatter from the E layer above Arecibo. When compared with NAU's OFF/ON history, the distribution of prominent E-layer events suggests that nearby transmitter was their probable cause. Section 3 develops a plausible scenario to explain how NAU-generated whistler-mode waves pitch-angle scatter electrons trapped in the inner radiation belt, causing them to precipitate into the lower ionosphere above Arecibo where sporadically enhanced plasma-line effects were detected by the ISR.
2. Arecibo Experiments
 This report focuses on experiments in which the ISR and a local ionosonde monitored properties of local ionosphere on the night of January 1–2, 2006. Spread F signatures appeared in ionosonde measurements and lasted for several hours during the experiments. Photoelectron contamination from both the local and conjugate hemispheres are minimal during nighttime experiments. The 430-MHz radar emits in a highly focused, 1.6° wide beam and operates in two modes that we refer to as backscatter-power (BP) and plasma-line (PL) measurements. Throughout experiments reported here the radar transmitted vertically from a stationary linefeed. During BP operations the receiver was tuned to 430 MHz to determine height profiles of plasma densities from the time histories and intensities of reflected signals. PL operations used a coded-long pulse technique to sample altitudes between 90 and 495 km with a height resolution of 150 m. Here the receiver observed the time history of reflected waves at frequencies within the 430 ± 7 MHz band. Altered frequencies result from the Doppler-shifting of signals that have coherently scattered off plasma modes with wavelengths near 0.35 m, propagating toward/away from the radar. At ionospheric altitudes the plasma modes are excited by electron beams that match the phase speed of the waves.
 We also fielded a VLF/LF receiver to monitor the status of NAU operations. The NAU transmitter was turned off when ISR experiments began at 22:00 local time (LT) on January 1. It remained off until 01:45 on January 2 when operations resumed and continued uninterrupted through 06:00 when our observation period ended. During the entire 8 hour period the ISR looked to local zenith, operating in repeated sequences of 20-minutes BP and 10-minutes PL operations.
 The geometry of the experiments is schematically illustrated in Figure 1. Signals transmitted from NAU mostly propagate at subionospheric altitudes (Ray 1) within the Earth-ionosphere waveguide. In addition, when 40.75 kHz waves reach the interface between the neutral atmosphere and the ionosphere, some fraction of the transmitted power penetrates the ionosphere (Ray 2) via refraction and mode conversion. Using a simplified slab model of ionospheric plasmas, we can compute the transmission coefficient and, subsequently, estimate that ∼15% of the incident NAU power can couple into the ionosphere at the altitude of the nighttime F region. As indicated in our earlier experiments [Labno et al., 2007], coupling between NAU transmissions and the ionosphere was enhanced when spread F irregularities were present, while E region irregularities were absent in our nighttime experiments. Gradients at the edges of large field-aligned irregularities can act as waveguides that direct linearly polarized NAU signals along the Earth's magnetic field. Following the physics (optics) convention, the left (right)-hand circularly polarized component of guided NAU signals converts into a whistler mode. Therefore, the overall coupled power in whistler-mode wave is ∼7.5% of the incident NAU power.
Figure 2 shows a typical set of PL measurements in the form of three frequency-altitude-intensity (FAI) spectra. From left to right the FAI plots indicate results of PL sequences that began at 05:01:07, 05:01:17, and 05:01:27 LT on January 2, 2006. The middle plot shows an E-layer PL enhancement characterized by spiky bursts that last for a short period of time. The intensities of PL signals are marked by vertical lines with lengths linearly proportional to backscattered power, given in arbitrary units. Each PL spectrum was acquired over a 10 s integration time. The enhanced PL events have a signal-to-noise ratio (SNR) of 4 to 5 and appeared at altitudes near 120 ± 20 km. Near this time neither the ISR backscatter power profile nor the ionograms showed the presence of significant E-layer or sporadic E plasmas. The enhanced plasma line spectrum has center frequency of ∼2.5 MHz with a ∼1.5 MHz bandwidth. Figure 2 also shows no PL enhancements in samples acquired before or after the event recorded between 05:01:07 and 05:01:17 LT. These data suggest that E-layer PL enhancements above Arecibo are episodic phenomena of <10 s duration.
Figure 3 shows the timeline for ISR experiments conducted on the night of January 1–2, 2006. Heavy red dashed lines mark PL mode operations. NAU ON/OFF periods are indicated below the local-time axis. Fourteen PL mode operations (840 ten-second samples) occurred with/without NAU transmissions. We assigned PL enhancement levels as relative powers according to SNR, quantized as multiples of 0.5. For example, cases with SNR = 4 and 2 have power levels of 1and 0.5, respectively. The bar chart display in Figure 3 clearly shows that the occurrence rate of PL enhancements at E-layer altitudes increased significantly after NAU turned on at 01:45 LT. The average occurrence rate increased from 0.2 event per minute when NAU was OFF to 0.75 event per minute when NAU was ON. We recorded 16 (1.9%) PL enhancement events while NAU signals were absent and 45 (5.35%) after transmissions resumed. This factor of 2.8 increase in PL enhancement rates between NAU on/off periods strongly suggests a causative relationship between them.
 Although PL enhancements in the E layer often appeared in Arecibo measurements, prior to January 1–2, 2006 experiments, it was impossible to demonstrate an unambiguous correlation between their occurrence and NAU transmissions. As an operational Navy communications device, NAU activity is beyond our control. By happenstance on the night of January 1 our VLF/LF receiver detected no NAU signals from 22:00 to 01:45 on January 2, indicating that the transmitter was turned off. From 01:45 through the end of our experiments at 06:00 our VLF/LF receiver showed that the NAU transmitter had returned to continuous operations. This unexpected sequence provided an opportunity to test for correlations between PL enhancements and 40.75 kHz NAU emissions.
 Returning to Figure 1, the schematic shows some Ray 2 signals from NAU scattering off spread F irregularities along field-aligned, ionospheric ducts into the magnetosphere. In the magnetosphere Ray 2 signals may propagate in either the ducted or unducted whistler-modes. Ducted whistler signals can reach the conjugate locations near Trelew, Argentina in the southern hemisphere. Unducted whistler waves reflect back toward the equatorial plane of the magnetosphere at altitudes where their frequencies match that of the local lower-hybrid resonance [Kimura, 1966]. However, for 40.75 kHz whistler-mode waves, there is no LHR surface available to reflect the unducted waves in the magnetosphere. Thus, they should only experience one hop with a possible specular reflection at the ionosphere in the conjugate hemisphere. Energetic electrons that see these waves Doppler shifted to their local gyrofrequency scatter in pitch angle. If the scattering is sufficiently strong some electrons trapped in the inner radiation belts precipitate into the atmosphere to create new free electrons at E-layer altitudes. Field-aligned beams of secondary electrons and radiation-belt primaries with residual energies < impact ionization energies ∼13 eV [e.g., Brown, 1967] were detected by Arecibo radar.
 The PL frequency distribution centered at ∼2.5 MHz with a bandwidth (Doppler spreading) of ∼1.5 MHz indicate that the phase speeds of streaming suprathermal electron-induced waves off which the radar scattered were in the range 6.2 × 105 to 1.2 × 106 m/s. The corresponding energies of resonant streaming electrons fall in the range 2.3–8.5 eV [Carlson et al., 1982]. The unperturbed densities and temperatures of plasma in the nighttime E layer at mid latitudes are very low, and support no electrons in this energy range. We conclude that the ISR detected effects of suprathermal electrons, introduced by an external agent. In the E layer the mean free path (a few kilometers) of electrons with energies of a few eV is small. Thus, they had to be created locally. The magnetic conjugacy of NAU through the inner radiation belt leads us to look there for the source.
 The equatorial region 1.2 < L < 2.5 constitutes the domain of the inner radiation belt in which energetic electrons and ions are magnetically trapped and follow gradient-curvature-drift orbits around the Earth. Measurements taken near the equatorial plane during the Combined Release Radiation Effects Satellite (CRRES) mission show that the spectrum of trapped electrons is described by an exponential relation j(E) = j0 exp [−(E/E0)], where E0 = 0.18 MeV and j0 ≈ 4 × 107 (cm2 s sr MeV)−1 (D. H. Brautigam, personal communication, 2004). The inner radiation belt is collocated with the inner portions of the geo-corona and plasmasphere, respectively, that are populated with gravitationally bound neutrals and cold plasma of ionospheric origin. The region is also characterized by broadband low-frequency electromagnetic waves that propagate in the unducted whistler mode. Trapped electrons escape magnetic confinement via either gyroresonant wave-particle interactions or Coulomb collisions with the nuclei of geo-coronal neutrals and/or plasmaspheric ions.
Kennel and Petschek  showed that whistler-mode radiation pitch-angle scatter energetic electrons that meet the gyro-resonance condition
k∥ is determined from the whistler wave dispersion relation:
where ω0 and (k∥) k0 denote, respectively, the frequency and (parallel) wave number of the 40.75 kHz whistler-mode wave; ωce and ωpe represent the angular cyclotron and plasma frequencies of cold plasmaspheric electrons. The symbols v∥ and v⊥ represent the velocity components field of collocated radiation belt electrons parallel and perpendicular to the magnetic field; c is the speed of light in a vacuum. Note that the calculation of this electron energy employs a relativistic correction to the gyro-resonance condition given by Kennel and Petschek .
 For simplicity we assume that NAU-generated whistler-mode waves propagate along Earth's magnetic field, i.e., k∥ = k0. We also approximate the equatorial plasma frequency (ωpe/2π) = 0.57 MHz (corresponding to a plasmaspheric electron density of 4,000 cm−3), the electron cyclotron frequency (ωce/2π) = 0.32 MHz. At the magnetic longitude of interest the loss cone angle is 33° wide over Arecibo. Combining equations (1) and (2) we calculate that 40.75 kHz whistler-mode waves interact resonantly with electrons with energies near 390 keV. CRRES spectral measurements cited above indicate that the inner radiation belt contains an ample supply of electrons at this energy.
 Arecibo is situated at the foot of the L = 1.35 magnetic flux tube, near the westward edge of the South Atlantic Anomaly (SAA). Eastward drifting, inner-belt electrons undergo maximum precipitation in this longitude sector at the southern end of flux tubes where the magnetic field is weak and consequently the atmospheric loss cone is large [Luhmann and Vampola, 1977]. The angular widths of the equatorial loss cone for electrons reaching the ionosphere above Trelew and Arecibo are 47° and 33°, respectively. The loss cone is ∼14° wider in the southern than the northern hemisphere. This magnetic asymmetry renders electron precipitation far more likely to occur in the southern than northern hemisphere. This is demonstrated daily in the hemispheric asymmetry of DMPS sensor contamination by energetic particles above Trelew but not Arecibo.
 The large difference between the widths of the loss cone makes it seem unlikely that NAU-generated whistler-mode waves would scatter many energetic electrons by 14°. In fact the sporadic PL enhancements reported above confirm this conjecture. Pitch-angle scattering is a diffusion process based on wave-particle interactions that are essentially stochastic. NAU generated whistler-mode waves, whether ducted or unducted, should pitch-angle scatter energetic electrons in the inner radiation belt, but very few by 14° or more. After mirroring in the northern hemisphere most pitch-angle scattered electrons should precipitate at the southern end of the field line. The very few electrons scattered by 14° mirror to E-layer altitudes where they would collide with ambient neutrals to create new ion-electron pairs. Newly created secondary electrons would then move upward and downward along the magnetic field away from the collision sites. As the secondary electrons and precipitated primaries with residual energies streamed along the Earth's magnetic field, ISR waves coherently backscattered from them. The Doppler-shifted backscattered waves were consequently detected as PL enhancements.
 During the On-Off operation of NAU transmitter on January 1–2, 2006, a total of 16 natural electron precipitation events were recorded, when NAU transmitter was off from 22:00 to 01:45 LT the next day (Figure 3). Since no thunderstorm activity occurred nearby, we attribute these 16 electron precipitation events to Coulomb scattering encounters with geo-coronal neutrals or plasmaspheric ions. Induced precipitation events resulted from the stochastic pitch-angle scattering of marginally trapped electrons by 40.75 kHz whistler-mode waves that entered the inner radiation belt through naturally occurring ionospheric ducts. This expectation is indeed consistent with the increased rate of 45 PL enhancement events observed after the NAU transmitter was turned on. We note that event rates nearly doubled around 04:00 LT. Perhaps it was just an instance of a general increase in the natural event rate unrelated to the turning on the transmitter. Finally, we also note about an hour difference between NAU turn-on (∼2:00 LT) and a detectably increased rate of plasma line enhancements (∼3:00 LT). This discrepancy probably resulted from the absence of ionospheric ducts when spread F irregularities were rather weak during this one-hour period.
 This work is supported by the Air Force Office of Scientific Research and National Science Foundation. A portion of this paper was presented at Arecibo-Argentina Magnetic Conjugate (AMC) Workshop held at Arecibo Observatory, April 17–19, 2006.