Predicting the effect of the solar wind on the ultra-low frequency plasma waves driving Earth’s radiation belts

Earth’s radiation belts represent a hazardous environment for spacecraft. Ultra-low frequency (ULF, 1-20 mHz) plasma waves in Earth’s magnetosphere are responsible for the bulk transport and energisation of energetic electrons via radial diffusion. These large-scale waves are strongly driven by the solar wind and need better characterisation in order to improve radial diffusion coefficients in radiation belt diffusion models; current parameterisations of radial diffusion coefficients vary by orders of magnitude. However, selecting solar wind properties on which to base an empirical model of ULF occurrence is difficult due to the complicated interparameter relationships between solar wind properties which mask their relationship to ULF wave power. Using fifteen years of solar wind and ground-based magnetometer measurements, we identify three non-derived solar wind properties that are causally correlated to dayside ULF wave power at a single representative frequency and station. Solar wind speed vsw, southward interplanetary magnetic field Bz < 0 and summed perturbations in proton number density δN p are all found to contribute significantly to ULF wave power. The corresponding driving mechanisms - magnetopause deformation processes - are discussed and it is concluded that they are highly interrelated. With these three parameters, an empirical model for ground-based ULF wave power is developed and tested across a range of frequencies, magnetic latitudes and azimuthal angles throughout the magnetosphere. Model output is a probability distribution instead of a single deterministic value; this probabilistic approach will allow the uncertainty in radial diffusion coefficients to be quantified. This model can be used in two ways to reproduce wave power; by sampling from conditional probability distribution functions or by using the mean (expectation) values. A method is derived to test the quality of the parameterisation and the ability of the model to reproduce ULF wave power time series. Sampling is a better method for reproducing power over an extended time period as it retains the same overall distribution, while mean values predict the power in a time series better than the assumption that power persists from the preceding hour. Other sources of uncertainty in radial diffusion coefficients are reviewed. Although this wave model is designed principally for the goal of improved radial diffusion coefficients to include in outer radiation belt diffusion based modelling, we give examples to illustrate how it may be used to investigate the occurrence of ULF waves throughout the magnetosphere and hence the physics of ULF wave generation and propagation