Earth’s radiation belts are a hazardous environment to satellites, which are at risk from the charged particles trapped in near-Earth space. The behaviour of these particles is strongly determined by a spectrum of plasma waves. Ultra-low frequency (“ULF”) plasma waves are large-scale waves with periods on the order of minutes (frequency 1-15 mHz). While these are a fascinating component of near-Earth space, they’re particularly of interest to radiation belt modelling because of their role in the energisation and transportation of radiation belt electrons, so we want to know when and where to expect these waves.
These plasma waves are predominantly driven by perturbations of the magnetopause – the boundary between the solar wind and the area dominated by Earth’s magnetic field. A simple example would be a constant tapping on the magnetopause by solar wind pulses – each tap causes a small compression and a magnetic field oscillation (they’re coupled together) which can propagate into the magnetosphere. (Figure 2)
But can we predict when and where these waves are likely to occur? Since the solar wind is the main driver of ULF waves, we want to be able to predict their effect on electrons from observations of the oncoming solar wind, while most existing models are based on the global geomagnetic activity index, Kp. There are many reasons why this is a poor parameter to base predictions on, the two most relevant being that firstly, it’s a 3-hr averaged index, so we don’t know the value of Kp at the current time (not great for either forecasting or nowcasting) and secondly, it’s so highly derived that it is not really suitable for any kind of statistical description of ULF waves (Murphy et al., 2016).
Previous studies have used a variety of methods to parameterise ULF wave power using solar wind properties (See review in Bentley et al., 2018). It turns out that a difficult part of this question is the solar wind itself. For starters, there is a lot more data describing some conditions than others, e.g. we have far more observations of the solar wind with a speed of 400 km s-1 than 600 km s-1 , and we must account for this if we don’t want our results to be skewed towards the situations where we have more data. But a more difficult problem is the tangled nature of the solar wind properties, which are highly interdependent. (Figure 3) This is partly due to the fact that the solar wind can come from different solar sources, and each one is likely to have a consistent set of properties which then occur at the same time. But also important are the multitude of interactions within the solar wind before it reaches Earth.
For example, fast solar wind is generally less dense than the slow solar wind, so speed vsw will anticorrelate with proton number density, Np. But when a region of fast solar wind catches up with some slow solar wind, we will end up with a compression region (Figure 4), so the onset of high speed solar wind will also be related to sudden dense regions and corresponding oscillations of the interplanetary magnetic field (as it folds up due to the compression). If on average we see increased ULF wave power in the magnetosphere when we see high solar wind speeds, is that then due to the speed or due to properties of density or the magnetic field that happen to occur at the same time? Other examples of interdependencies include turbulence, wave interactions and the composition in certain types of solar wind. Many solar wind properties correlate with the speed, because it’s quite a good proxy for all the different types of solar wind.
Unfortunately most of the existing techniques we might use to construct a parameterisation of ULF wave power on these solar wind properties aren’t appropriate – either they require unphysical assumptions about these interdependencies or they will be difficult to use to investigate the physics behind ULF wave occurrence.
Instead we opted for something simpler – systematically examine all solar wind parameters to find out which ones are causally correlated with ULF wave power. An example of this is shown in Figure 5: take two solar wind parameters to make a grid, and in each bin show the median observed ULF wave power. This allows us to see whether power increases with one parameter when a second is held constant, across different values. This accounts for the interdependence between a pair of parameters and so by systematically comparing many of these plots, we can identify which parameters are causally correlated to power, rather than just correlated to other parameters that affect the wave power. In the example here we can see that when the interplanetary magnetic field Bz component is above zero, ULF wave power increases only with increasing solar wind speed. However, when it’s below zero, ULF power increases with both speed and with more strongly negative Bz.
While this method is very simple, it turns out to be surprisingly powerful – there’s clearly a threshold at Bz=0 that would be averaged over by other techniques, and it also turns out to be the change in proton number density δNp rather than the number density Np that’s causally correlated with power. We can speculate on what physical processes driving the ULF waves are represented by these parameters (see Bentley et al., 2018). It’s likely that the Bz threshold is due to different physical processes that occur when Bz <0, i.e. magnetic reconnection, which I briefly described in a previous blog post.
So by using a simple and systematic method to identify the properties of the solar wind that drive magnetospheric ULF waves, we can resolve three parameters: speed vsw, magnetic field component Bz and proton number density perturbations δNp. Having identified these three parameters opens up new opportunities to model magnetospheric ULF wave power and explore the physics – just when, where and how do we see these waves? And can we quantify how much these parameters contribute – does this change in different regions of the magnetosphere?
Like much of scientific research, answering this one question has opened many more avenues of study to understand these large-scale plasma waves and their role in the dynamics of Earth’s magnetosphere.
Murphy, K. R., I. R. Mann, I. J. Rae, D. G. Sibeck, and C. E. J. Watt (2016), Accurately characterizing the importance of wave‐particle interactions in radiation belt dynamics: The pitfalls of statistical wave representations, J. Geophys. Res. Space Physics, 121, 7895–7899, doi:10.1002/2016JA022618.
Pizzo, V. (1978), A three‐dimensional model of corotating streams in the solar wind, 1. Theoretical foundations, J. Geophys. Res., 83(A12), 5563–5572, doi:10.1029/JA083iA12p05563.
Bentley S.N., C.E.J. Watt, M.J Owens, and I.J. Rae (2018), ULF wave activity in the magnetosphere: resolving solar wind interdependencies to identify driving mechanisms, Journal of Geophysical Research, 123, doi:10.1002/2017JA024740.