The Generation of Magnetospheric Chorus Emissions

What is Chorus?

Whistler-mode chorus waves are one of the most common and most intense natural plasma waves occurring in the Earth's outer magnetosphere (Helliwell, 1969; Allcock, 1957; Helliwell, 1965; Storey, 1953). Usually observed in the region outside of the plasmapause, chorus waves are discrete emissions often containing rising and falling tones, as well as short impulsive bursts (Burton and Holzer, 1974; Dunckel and Helliwell, 1969; LeDocq et al., 1998; Lauben et al., 2002; Sazhin and Hayakawa, 1992; Burtis and Helliwell, 1969). Chorus occurs over a broad frequency range, from hundreds of Hz up to about 10 kHz (Gurnett and O'Brien, 1964). Within this range, chorus waves typically occur in two distinct frequency bands, a lower band with frequencies 0.1 $f_{ce-eq}\leq f <$ 0.5 $f_{ce-eq}$ and an upper band with frequencies 0.5 $f_{ce-eq}\leq f \leq$ 0.65 $f_{ce-eq}$ , where $f_{ce-eq}$ denotes the equatorial gyrofrequency. There is typically a gap between these two bands at 0.5 $f_{ce-eq}$ , where the wave power is at a minimum (Tsurutani and Smith, 1974; Burtis and Helliwell, 1976; Burtis and Helliwell, 1969). An example of this configuration, known as banded chorus, can be seen in Figure 1.

**Figure 1:** An example of banded chorus. The white line represents half the equatorial gyrofrequency, above which is upper band chorus and below which is lower band chorus.

Resonance Condition

Recent studies show chorus waves play a role in both the acceleration and precipitation of relativistic electrons through resonant scattering. This pitch angle scattering and energy diffusion can occur when the resonance condition, $\omega - k_{\parallel}v_{\parallel} = {m\omega_{ce}\over{\gamma}}$ , 0, $\pm1$ , $\pm2$ , $\pm3$ ,..., is satisfied. In this expression, $\omega$ is the frequency of the wave, $k_{\parallel}$ and $v_{\parallel}$ are the components of the wave vector and particle velocity parallel to the ambient magnetic field, respectively, m is the resonance harmonic number, $\omega_{ce}$ is the local gyrofrequency, and $\gamma = \left(1-{v^{2}\over{c^{2}}}\right)^{-\frac{1}{2}}$ is the relativistic correction factor, where v is the particle velocity and c is the speed of light (Kennel and Petschek, 1966). The wave vector is typically specified with respect to the direction of the local magnetic field, $B_{o}$ , with the polar wave normal angle, $\theta$ , defined as the angle between $B_{o}$ and the wave vector (from 0 $^\circ$ to 180 $^\circ$ ) and the azimuthal wave normal angle, $\phi$ , measured about the direction of $B_{o}$ (from 180 $^\circ$ to 180 $^\circ$ ). This coordinate system is illustrated in Figure 2, with the direction of $B_{o}$ assumed to be in the z direction. The polar wave normal angle is needed to evaluate the resonance condition, while both $\theta$ and $\phi$ are needed to predict how the wave will propagate in the magnetosphere from its current location.

**Figure 2:** Coordinate system depicting polar wave normal angle, $\theta$ , azimuthal wave normal angle, $\phi$ , and wave vector, k. The direction of the local magnetic field, $B_{o}$ , is assumed to be in the z direction in this system.

Observations on the Polar Spacecraft

Wave normal analysis was done using observations of magnetospheric banded chorus on the Polar spacecraft. Launched on 2241996, the Polar spacecraft has a highly elliptical, 86 $^\circ$ inclination orbit with a period of approximately 17.5 hours, perigee of 1.8 $R_{\rm E}$ , and apogee of 9 $R_{\rm E}$ . The Plasma Wave Instrument (PWI), onboard the Polar spacecraft, provides high-resolution plasma wave data within the chorus band. The PWI detects magnetic fields through the use of a triaxial magnetic search coil antenna (70 $\mu$ VnT-Hz sensitivity) and detects electric fields using three orthogonal electric dipole antennas, two in the spacecraft spin plane (100 and 130 m, 6 s period), and one aligned along the spin axis (14 m). Images of the Polar spacecraft and its orbit are shown in Figures 3 and 4, respectively.

**Figure 3:** Image of the Polar spacecraft, with 3 electric antennas and a triaxial magnetic search coil antenna.

**Figure 4:** Orbit of the Polar spacecraft over time.

The signals from these antennas are processed by several receiver systems, one of which is the High Frequency Waveform Receiver (HFWR). Coincident sampling from 20 Hz to 25 kHz of 3 orthogonal components of the electric and magnetic wave fields is provided by the HFWR. In the high-telemetry rate mode, 0.45 second waveform snapshots are recorded from each antenna at intervals spaced 9.2 seconds apart (Gurnett et al., 1995). Figure 5 illustrates lower band chorus in one of these snapshots.

**Figure 5:** 0.45 second spectrogram, using Polar PWI wave power density data, showing lower band chorus.

Further Analysis of Banded Chorus

The results of the wave normal analysis using observations of banded chorus from the Polar spacecraft can be found in Haque et al. (2010). Using this data set from Polar, along with observations of chorus from other satellite systems, a theory of the source region of banded chorus is currently being tested. An overview of this theory is given in Bell et al. (2009).

Bibliography

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