Geomagnetic activity and local time dependence of the distribution of ultra low-frequency wave power in azimuthal wavenumbers, <i>m</i>

Abstract

Abstract. The azimuthal wavenumber m of ultra lowfrequency (ULF) waves in the magnetosphere is a required parameter in the calculations of the diffusion rates of energetic electrons and protons in the magnetosphere, as electrons and protons of drift frequency ω d have been shown to radially diffuse due to resonant interaction with ULF waves of frequency ω = mω d . However, there are difficulties in estimating m, due to lack of multipoint measurements. In this paper we use magnetic field measurements at geosynchronous orbit to calculate the cross-spectrogram power and phase differences between time series from magnetometer pairs. Subsequently, assuming that ULF waves of a certain frequency and m would be observed with a certain phase difference between two azimuthally aligned magnetometers, the fraction of the total power in each phase difference range is calculated. As part of the analysis, both quiet-time and storm-time distributions of power per m number are calculated, and it is shown that during active times, a smaller fraction of total power is confined to lower m than during quiet times. It is also shown that in the dayside region, power is distributed mostly to the lowest azimuthal wavenumbers m = 1 and 2, whereas on the nightside it is more equally distributed to all m that can be resolved by the azimuthal separation between two spacecraft.

Estimating the Azimuthal Mode Structure of ULF Waves Based on Multiple GOES Satellite Observations

“…For example, through ionospheric radar observations, Fenrich et al () found that m > 17 ULF waves are concentrated in the midnight and local afternoon, while m < 17 waves are concentrated near the flank regions. Similarly, Sarris and Li () found that the mode number values of Pc5 ULF waves are generally higher at the nightside than the dayside. Therefore, assuming a uniform mode structure around the Earth in radial diffusion calculations, rather than using a realistic local time distribution of the mode number, can lead to significant uncertainty in D LL estimation where the local time dependent mode structure needs to be properly drift averaged.…”

“…Despite its crucial importance, physical quantification of the azimuthal mode number of ULF waves is difficult and has been a missing part in the calculation of the radial diffusion coefficients (e.g., Tu et al, ; Sarris, ; Sarris & Li, ). In principle, to determine the mode structure of a simple harmonic wave at a given frequency up to mode number m max , we need at least 2 m max equally spaced azimuthal coherent field measurements.…”

“…Even though significant progress has been made in quantifying the mode number of ULF waves, when applying the mode number results to calculations of radial diffusion coefficients, two aspects of the mode structure are usually oversimplified. First, some of the methods mentioned above using the cross‐phase techniques (e.g., Sarris & Li, ) or global MHD simulations (e.g., Tu et al, ) assumed only positive m values for the ULF waves, whereas in reality the mode number can be either positive or negative corresponding to the waves propagating in either eastward or westward direction (e.g., Chisham & Mann, ; Murphy et al, ; Yeoman et al, ). This assumption will lead to uncertainty in D LL quantification since only positive‐mode ULF waves would resonate with radiation belt electrons, which drift eastward.…”

Global‐Scale ULF Waves Associated With SSC Accelerate Magnetospheric Ultrarelativistic Electrons

“…Our results indicate that ULF waves with a global scale are highly efficient at accelerating ultrarelativistic electrons in the outer belt. ULF waves (essentially the compressional mode or compressional poloidal mode) with an azimuthal wave number of 1 have also been found to be the dominant component by both multispacecraft observations (Sarris & Li, ) and magnetohydrodynamic simulation studies (Tu et al, ). Within the time scale of an hour, flux enhancement of an order of magnitude can be achieved with the presence of such waves at SSC.…”

Capturing Uncertainty in Magnetospheric Ultralow Frequency Wave Models

“…However, in practice, this is often simplified by assuming m = 1. Sarris and Li () found that the amplitude of power is indeed concentrated in low m numbers for the dayside and for less geomagnetically active time periods but less so for the nightside and geomagnetically active periods. Murphy et al () found that the m number during a moderate storm is typically low but the distribution of positive or negative values depends on radial location; this initial study gives some idea how the direction of propagation (i.e., m < vs. >0) is distributed among ULF waves but due to challenges in measuring m much more work is required.…”