Solar Wind Driven ULF Waves and MeV Electron Radial Diffusion in the Magnetosphere: Requirements for the Development of a ULF Index

We present the results from a statistical analysis of the relationship between ground-based ULF wave power spectra and upstream solar wind parameters. We find that solar wind speed is universally the best correlated with Pc5 ULF wave power in the magnetosphere, both on the ground and in space, and both of these are correlated with MeV electron flux. However, we show that a narrow band ULF index is essentially uncorrelated with MeV electron enhancements. The ground-based data show clear evidence of a spectral peak indicative of the local fundamental field line resonance (FLR), this peak being a strong function of latitude, as expected. Interestingly, the geosynchronous satellite data show no evidence of the FLR spectral peak, and demonstrate power levels orders of magnitude less than observed on the ground, consist with the Pc5 power being dominated by disturbances with fundamental field aligned harmonic mode structure. Importantly, this shows that geosynchronous magnetic field data alone is of little use for monitoring ULF wave power in the magnetosphere, and that it cannot be used as the basis for the development of a ULF wave index. Field aligned Alfven eigenmode calculations show that whilst ionospheric E-field is a strong function of ionospheric Pedersen conductivity, the corresponding ground-based B is almost independent of conductivity, so long as the waves are not critically damped. Significantly, however, the ratio between wave ground-based B and equatorial E is a strong function of magnetospheric density, increasing with the higher density expected both during geomagnetically active times and within the plasmasphere. This means specific ground-based ULF power levels map to lower equatorial E, and slower diffusion, both during storms as well as inside the plasmasphere. For observed ground-based ULF power levels, the diffusion inside the plasmasphere may be very slow, perhaps explaining the link between the position of the plasmapause and the peak in radiation belt flux. Hence for the development of a ULF index, a measure of the density in the magnetosphere is important in addition to ground-based ULF power. Finally, we estimate MeV electron diffusion times expected for the observed ULF power as a function of solar wind speed, L-shell, and magnetospheric density.