Estimation of wave frequency and azimuthal wavenumber of high-m ULF waves by ST-5 satellite observations at low altitudes

With short azimuthal scale lengths and high azimuthal wavenumbers (m), the high-m ultra-low-frequency (ULF) waves in the magnetosphere occur due to drift and drift bounce resonances of energetic particles. Measuring the azimuthal wavenumber (m) of high-m ULF waves can be challenging in many types of observations. It requires multiple satellites that meet stringent separation requirements to confirm the short azimuthal wavelengths. The vast number of ground-based magnetometers cannot detect high-m waves because the variations in short horizontal scales are screened by the ionosphere. In our recent study [Le et al., JGR, 116, A08203, 2011], we discovered many events of high-m ULF waves in the ST-5 observations at altitudes ranging from several hundred km to over 1000 km. The wave frequencies observed by ST-5 are at the order of 0.1 Hz (in the Pc 2-3 band), but they are considerably Doppler shifted due to the rapid satellite motion at low altitudes. In this previous study we infer from ground-based observations of field line resonance that the frequency of high-m waves in the Earth frame should be less than 10 mHz. In this study, we make use of the pearl-on-a-string configuration of the three ST-5 satellites to estimate the wave frequency in the Earth´s frame by using satellite data exclusively. The frequency, amplitude, and phase at each location can be calculated by the observations from the three ST-5 satellites. We find that the inferred wave frequencies in the Earth frame are indeed only several mHz. Consequently, the azimuthal wavenumber is determined essentially by the angular velocity of the spacecraft. We find that that azimuthal wavenumbers of the high-m waves observed by ST-5 range from 40 to 250. We also emulate the expected magnetic field oscillations along the ST-5 trajectories with a heuristic model of high-m waves, and the results suggest that the L-value of wave activity alone can explain why only one wave packet was observed in some events whereas t- o wave packets were observed in other events. These results suggest a new opportunity for many low-altitude satellites, such as the recently launched Swarm mission, to monitor the occurrence of the high-m waves and infer the state of energetic ions in the magnetosphere.