2011 THEMIS SCIENCE NUGGETS

Observations and Modeling of Forward and Reflected Chorus Waves Captured by THEMIS

by Oleksiy Agapitov

Introduction

Discrete ELF/VLF chorus emissions are the most intense electromagnetic plasma waves observed in the radiation belts of the Earth's magnetosphere. Chorus emissions, whistler-mode wave packets propagating roughly along magnetic field lines from a well-localized source in the vicinity of the magnetic equator to polar regions, can be reflected at low altitudes. After reflection, wave packets can return to the equatorial plane region. Understanding of whistler wave propagation and reflection is critical to correctly describe wave-particle interaction in the radiation belts. We focus on properties of reflected chorus emissions observed by the THEMIS (Time History of Events and Macroscale Interactions During Substorms) spacecraft Search Coil Magnetometer (SCM) and Electric Field Instrument (EFI) at ELF/VLF frequencies up to 4 kHz at L ≥ 8. We determined the direction of the Poynting flux and wave vector distribution for forward and reflected chorus waves. The data set chosen for this study was recorded by the THA THEMIS spacecraft on 26 July 2008 near 14:00 UT in the outer magnetosphere. The data made it possible to compare the properties of forward and reflected chorus waves generated by the same source. Although both types of chorus waves were detected near the magnetic equator and have similar discrete structure and rising tones, reflected waves are attenuated by a factor of 10-30 and have 10% higher frequency than concurrently-observed forward waves. Propagation of whistler wave packets was also simulated in the framework of ray-tracing with realistic magnetospheric plasma particle density and magnetic field distributions. Modeling of wave propagation and reflection using geometrical optics ray-tracing allowed us to determine the chorus source region location and explain observed propagation characteristics. We found that reflected wave attenuation at a certain spatial region is caused by divergence of the ray paths of these non-ducted emissions, and that the frequency shift is caused by generation of the reflected waves at lower L-shells where the local equatorial gyrofrequency is larger.

Data Analysis

THEMIS consists of five identically-instrumented spacecraft (THA, THB, THC, THD, and THE), launched on 17 February 2007. The main goal of this mission wais to conduct multi-point investigations of substorm phenomena in the tail of the terrestrial magnetosphere. For the current study, Search Coil Magnetometer (SCM) observations and plasma measurements of the Electric Field Instrument (EFI) were analyzed. The three search coil antennas cover the same bandwidth, from 0.1 Hz to 4 kHz, in the ULF/ELF frequency range. The electric field components are measured directly in the same frequency range. Three components of magnetic field waveform and three components of electric field waveform captured in the wave burst mode (on-board trigger) with 8192 samples per second were used.

In this study the Means (1972) method is used to determine the wave normal vector k. The Means method involves computation of a spectral matrix that consists of power and cross-power spectra from the three magnetic components. Although this method has an inherent 180° ambiguity in the wave normal direction, this ambiguity can be removed if the Poynting vector S is known. Since the wave normal vector must have a component in the direction of the energy flow, a scalar product (S·k) should be positive. The Poynting vector is calculated directly: S(f)=1/2 Re(E(f) x B*(f)), where * represents the complex conjugate, Re stands for the real part, and E(f) and B(f) are the Fourier transforms of the electric and magnetic field waveforms, respectively.

Figure 1 presents detailed time-frequency diagrams of magnetic field and electric field perturbations and the Poynting flux vector recorded aboard THA on 26 July 2008 when it was close to local magnetic noon and to the geomagnetic equator plane, RSM = [8.4, 0.15, 0.42], MLat = 2.8° - 2.9°, Kp=0, Dst= -8 nT. The local electron gyrofrequency is fce = 1750 Hz. Discrete chorus emissions are clearly seen in the two frequency diapasons (0.15 - 0.45 fce and 0.5 - 0.6 fce) typical for chorus waves generated in the vicinity of the magnetic equator. The projection of the Poynting vector on the local magnetic field is shown in the lower panel of Fig.1. The Poynting flux direction along the local magnetic field (poleward) is marked with red color gamma and the opposite direction (equatorward) is marked with blue. High-amplitude discrete chorus elements are followed by lower amplitude elements with a frequency range from 0.2 fce to 0.5 fce and different frequency rise speed. These elements can be clearly seen in the Poynting vector flux panel as elements with the Poynting vector directed equatorward.

Figure 1. Detailed time-frequency power spectrograms of magnetic
(top) and electric (middle) field fluctuations near the source region
recorded by the SCM (a) and EFI (b) instruments aboard THA on
26 July 2008. Frequency-time dependence of the Poynting vector
direction of forward and reflected chorus observed by the SCM/SCW
(c) The field aligned waves elements are marked with red color and
the elements propagated in opposite direction are marked with blue
color. Spectral power is in logarithmic scale. The reflected chorus
elements are marked with white arrows.
Click here to enlarge the image.

The frequency shift with respect to chorus propagating from the magnetic equator observed by THA shows that the reflected chorus packets were generated closer to the Earth in the vicinity of the geomagnetic equator. The direct chorus elements propagate roughly along the local magnetic field which is usual for the generation region. The Poynting vector direction of the reflected chorus elements is close to the local magnetic field, but the k-vector is inclined nearly 35° with respect to magnetic field but in the opposite direction. The amplitude ratio for forward and reflected waves varies from 10 to 30 for the magnetic field perturbation and from 10 to 30 for the electric field. Estimation of the Poynting flux ratio gives a value from 100 to 400 (Figure 2). Assuming that the initial amplitude of the reflected chorus was of the same order with the observed direct waves, the decrease in the amplitude of the reflected signal could be due to geometrical effects of chorus wave propagation and spreading of the pulse by dispersion. Chorus waves can be generated in the extended radiation source in a similar frequency range relative to the local electron gyrofrequency. In this case, the observed wave amplitudes on similar frequency ranges relative to gyrofrequency are close.

Figure 2. Magnetic and electric field fluctuation spectra (THA
SCW and EFI measurements). Red and blue correspond to times
when forward and reflected chorus elements were registered.
The estimation of reflected chorus energy gave it nearly 0.01 of
the forward chorus energy.
Click here to enlarge the image.

To test this hypothesis, we modeled chorus wave propagation and reflection using a ray-tracing technique. As we see below, this technique allows us to reconstruct the chorus source region and explain its observed frequency shifts and propagation characteristics (see Agapitov et al., 2011 for details).

Figure 3. Whistler ray trajectories for three different wave
frequencies. The angle between the magnetic field and whistler's
k-vector is varied in the range 0°-11°. Rays propagate in the
meridional plane.
Click here to enlarge the image.

From Figure 3 it is evident that the chorus of whistler waves with frequencies in the range (0.32 to 0.38)fce generated in the vicinity of the magnetic equator at L = 8.0 will return to the equatorial region after the first low-latitude reflection with L ≈ 8.4, where THA registered forward and reflected chorus emissions. From Fig.3a and Fig.3b it is also evident that the low-frequency chorus sub-band returns to the regions with L > 8.4 after reflection. Thus, at the point of registration, the reflected whistler chorus spectrum will be truncated from the low-frequency side, which is in excellent agreement with observational data. Qualitative estimations of the spatial energy density of whistler waves after reflection show that the divergence of ray trajectories results in geometrical spreading, and the power of the reflected signal was found to be 20-40 times smaller than the power of the primary signal. After polar reflection, the whistler rays return back to the plane of magnetic equator forming there some pattern with reflected rays distributed non-uniformly within it. Attenuation ratio range was estimated as maximum (or average) value of the specific power of the reflected signal divided by the specific power of the initial signal.

Conclusions

Electric and magnetic field fluctuations detected aboard THEMIS satellites by SCM and by EFI detectors in the burst mode were used to study magnetospherically-reflected chorus emissions in the outer magnetosphere (L-shell >7). Chorus waves, which propagate from a well-localized source in the vicinity of the geomagnetic equator to polar regions, can be reflected at lower altitudes. After reflection, wave packets can return to the equator region. Using waveforms of the electric and magnetic field fluctuations, we determined the direction of the Poynting flux and wave vector distribution for forward and reflected waves. We showed that the reflected chorus emissions observed in the vicinity of the magnetic equator also have a discrete structure roughly similar to that of the chorus emissions propagating poleward; the magnetic and electric field perturbation amplitude of the reflected signal is significantly (20-30 times) smaller, however. Geometrical optics ray-tracing simulations of chorus propagation in the magnetosphere with the realistic model of the geomagnetic field (Olson-Phitzer model) and plasma density distribution (GCPM) were used to explain experimental results. Numerical estimates of the spatial energy density for reflected whistler waves show that because the divergence of ray trajectories results in geometrical spreading, the power of the reflected signal should be 20-40 times smaller than the power of the primary signal. It is worth nothing that observations of ducted whistlers show energy conservation for primary and reflected signal with some temporal power spreading due to wave dispersion. Such effects are mostly observed at low L-shells (L = 2-3); magnetospheric reflection is typically observed for L>5. Reflected emissions observed by particular spacecraft have a frequency shift with respect to the primary chorus that propagates from the magnetic equator. Ray tracing confirms that reflected waves were generated near the geomagnetic equator closer to the Earth where the magnetic field magnitude is larger (L-shell is smaller). They have similar frequency diapason relative to the local value fce in the generation region.

Source

Agapitov, O., Krasnoselskikh, V., Zaliznyak, Yu., Angelopoulos, V., Le Contel, O., and Rolland, G.: Observations and modeling of forward and reflected chorus waves captured by THEMIS, Ann. Geophys., 29, 541-550, doi:10.5194/angeo-29-541-2011

Biographical Note

Agapitov Oleksiy is an associate professor in the National Taras Shevchenko University of Kyiv. His sphere of interest is ULF MHD waves and whistler waves in the magnetosphere.

Vladimir Krasnoselskikh, Directeur de Recherche with LPC2E/CNRS-University of Orleans (Orleans, France).

Yurii Zaliznyak is a senior researcher in the Institute for Nuclear Research, Kyiv, Ukraine.


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