Which solar wind properties drive large-scale plasma waves in Earth’s magnetosphere?

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.

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Figure 1: Earth’s radiation belts contain particles (mostly electrons and protons) that are trapped by the Earth’s magnetic field. These need to be understood in order to protect satellites, many of which orbit in the heart of this environment. Missions such as the Van Allen probes (depicted here) provide a way to measure the particle population and the plasma waves which allow for particle acceleration, loss and transport.  Credit: JHU/APL, NASA

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)

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Figure 2: Perturbations at the magnetopause can drive waves that propagate inwards. As the wave travels through the magnetosphere, these oscillations disturb Earth’s magnetic field. We can use the fact that these magnetic disturbances travel along dipole magnetic field lines to measure ULF waves at Earth’s surface.

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.

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Figure 3: Establishing causal relationships is particularly difficult when looking at the solar wind as many properties are highly interdependent. If a quantity D correlates with B and C, is that because they both affect D? Here, only C affects D. But B will still correlate with D because B and C are interdependent. We want to identify only causally correlated parameters.

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.

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Figure 4: As fast solar wind catches up with slow solar wind, this creates a compression region ahead and a rarefaction region behind. This is one example of many solar wind interactions that make it difficult to separate the effect of different solar wind properties on the magnetosphere.

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.

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Figure 5: A two-parameter plot taken from Bentley et al., 2018. We bin the ULF power observed at one station (roughly corresponding to geostationary orbit) at one frequency (2.5mHz) and observe whether it increases with increases in solar wind speed vsw and/or the component Bz of the interplanetary magnetic field. Cut-throughs at constant speed and Bz are shown in (b) and (c).

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.

References:

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.

 

How does plasma from the solar wind enter Earth’s magnetosphere?

Earth’s radiation belts are a hazardous environment for the satellites underpinning our everyday life. The behaviour of these high-energy particles, trapped by Earth’s magnetic field, is partly determined by the existence of plasma waves. These waves provide the mechanisms by which energy and momentum are transferred and particle populations physically moved around, and it’s some of these waves that I study in my PhD.

However, I’ve noticed that whenever I talk about my work, I rarely talk about where this plasma comes from. In schools it’s often taught that space is a vacuum, and while it is closer to a vacuum than anything we can make on Earth, there are enough particles to make it a dangerous environment. A significant amount of particles do escape from Earth’s ionosphere into the magnetosphere but in this post I’ll focus on material entering from the solar wind. This constant outflow of hot particles from the Sun is a plasma, a fluid where enough of the particles are ionised that the behaviour of the fluid is then dominated by electric and magnetic fields. Since the charged particles in a plasma interact with each other, with external electric and magnetic fields, and also generate more fields by moving and interacting, this makes for some weird and wonderful behaviour.

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Figure 1: The area of space dominated by Earth’s magnetic field (the magnetosphere) is shaped by the constant flow of the solar wind (a plasma predominantly composed of protons, electrons and alpha particles). Plasma inside the magnetosphere collects in specific areas; the radiation belts are particularly of interest as particles there pose a danger to satellites. Credit: NASA/Goddard/Aaron Kaas

When explaining my work to family or friends, I often describe Earth’s magnetic field as a shield to the solar wind. Because the solar wind is well ionised, it is highly conductive, and this means that approximately, the magnetic field is “frozen in” to the plasma. If the magnetic field changes, the plasma follows this change. Similarly, if the plasma flows somewhere, the magnetic field is dragged along with it. (This is known as Alfvén’s frozen in theorem – the amount of plasma in a volume parallel to the magnetic field line remains constant). And this is why the magnetosphere acts as shield to all this energy streaming out of the Sun – while the magnetic field embedded in the solar wind is topologically distinct from the magnetic field of the Earth, there is no plasma transfer across magnetic field lines, and it streams past our planet (although this dynamic pressure still compresses the plasma of the magnetosphere, giving it that typical asymmetric shape in Figure 1).

Of course, the question still remains of how the solar wind plasma enters the Earth’s magnetic field if such a shielding effect exists. You may have noticed in Figure 1 that there are gaps in the shield that the Earth’s dipole magnetic field presents to the solar wind; these are called the cusps, and at these locations the magnetic field connects to the solar wind. Here, plasma can travel along magnetic field lines and impact us on Earth.

But there’s also a more interesting phenomenon occurring – on a small enough scale (i.e. the very thin boundaries between two magnetic domains) the assumptions behind the frozen-in theorem break down, and then we start to see one of the processes that make the magnetosphere such a complex, fascinating and dynamic system to study. Say we have two regions of plasma with opposing orientation of the magnetic field. Then in a middle area these opposing field lines will suddenly snap to a new configuration, allowing them to peel off and away from this tightly packed central region. Figure 2 illustrates this process – you can see that after pushing red and blue field lines together, they suddenly jump to a new configuration. As well as changing the topology of the magnetic field, the plasma at the centre is energised and accelerated, shooting off along the magnetic field lines. Of course even this is a simplification; the whole process is somewhat more messy in reality and I for one don’t really understand how the field can suddenly “snap” to a new configuration.

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Figure 2: Magnetic reconnection. Two magnetic domains of opposing orientation can undergo a process where the field line configuration suddenly resets. Instead of two distinct magnetic domains, some field lines are suddenly connected to both, and shoot outwards and away, as does the energised plasma.

In the Earth’s magnetosphere there are two main regions where this process is important (Figure 3). Firstly, at the nose of the magnetosphere. The dynamic pressure of the solar wind is compressing the solar wind plasma against the magnetospheric plasma, and when the interplanetary magnetic field is orientated downwards (i.e. opposite to the Earth’s dipole – about half the time) this reconnection can happen. At this point field lines that were solely connected to the Earth or in the solar wind are now connected to both, and plasma can flow along them.

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Figure 3: There are two main areas where reconnection happens in Earth’s magnetosphere. Opposing field lines can reconnect, allowing a continual dynamic cycle (the Dungey cycle) of field lines around the magnetosphere. Plasma can travel along these magnetic field lines freely. Credits: NASA/MMS (image) and NASA/Goddard Space Flight Center- Conceptual Image Lab (video)

Then, as the solar wind continues to rush outwards from the Sun, it drags these field lines along with it, past the Earth and into the tail of the magnetosphere. Eventually the build-up of these field lines reaches a critical point in the tail, and boom! Reconnection happens once more. You get a blast of energised plasma shooting along the magnetic field (this gives us the aurora) and the topology has rearranged to separate the magnetic fields of the Earth and solar wind; once more, they are distinct. These dipole field lines move around to the front of the Earth again, to begin this dramatic cycle once more.

Working out when and how these kind of processes take place is still an active area of research, let alone understanding exactly what we expect this new plasma to do when it arrives. If it doesn’t give us a beautiful show of the aurora, will it bounce around the radiation belts, trapped in the stronger magnetic fields near the Earth? Or if it’s not so high energy as that, will it settle in the cooler plasmasphere, to rotate with the Earth and be shaped as the magnetic field is distorted by solar wind variations? Right now I look out my window at a peaceful sunny day and find it incredible that such complicated and dynamic processes are continually happening so (relatively) nearby. It certainly makes space physics an interesting area of research.