When Science is Simple:
The Role of Localized Compressional Ultra-low Frequency Waves in Energetic Electron Precipitation
I am a scientist. Every day I wake up a scientist. I eat breakfast (maybe just coffee) and then do science. Then, I come home and talk about science with my scientific partner. I live in a bubble of science. But even given this, I still think of science as a complex entity filled with mind-numbing equations, jargon, and systems. But I know that this is not all true! Yes, we often study complex systems or ideas, but science can be simple. You can ask simple questions and use simple approaches and get the answer.
Science can be intimidating, to say the least. It shouldn't be. Not all science is the three-page long equation that takes months to solve and simplify to something akin to E = mc^2. This paper I'm writing about today is really quite simple and beautiful and makes you think.
The Role of Localized Compressional Ultra-low Frequency Waves in Energetic Electron Precipitation by Jonny Rae et al. takes a simple idea and shows how it can have a significant impact. It follows from some previous work I wrote about back in 2016. One of the big questions in inner magnetospheric physics is what drives particle dynamics. Why are the radiation belts sometimes full of particles and sometimes not? Another question stems from this: when particles are lost from the magnetosphere, how much ends up in the ionosphere and upper atmosphere? Now that's a very magnetospheric-centric way to put it. Suppose you are more interested in the atmosphere and ionosphere. In that case, you may rephrase it to say, what drives ionization or particle loss from the magnetosphere? This is a very subtle difference, but we'll talk about that a bit later.
So what did Jonny and us all look at? Well, Jonny is interested in ultra-low frequency or ULF waves. These are very long waves with a period of more than 1 second and often something closer to minutes long. Below are two metronomes, one with one beat per second (60 beats per minute - the upper end of the ULF waves) and another with one beat per minute ( still not that long of a ULF wave).
Many of the waves we look at in the magnetosphere are slow but also big. They are often ten times bigger than my favorite EMIC waves. I like to think of them as Great Danes or Bullmastiffs - massive dogs compared to the chihuahua-like chorus waves. These waves are so large that they interact and affect the particles differently than the EMIC or chorus waves. So let's take a closer look at this.
Let's start by reminding ourselves about how particles move in the magnetosphere. If you want to play a few games instead of reading a quick summary, I suggest Magnetospheric Mini Golf or Magneto Bowling. Charged particles, when in the presence of a magnetic field, will move in a circle around it; this is called gyromotion.
When all things are quiet, particles in the magnetosphere bounce from one pole to the other (North to South to North to South ....). Because the magnetosphere is curved, the particles will also drift around the Earth, the ions in one direction and the electrons in the other due to their different charge signs.
You can check out more of the physics that goes into determining how a particle moves in the magnetosphere at the NASA science visualization studio. Search Plasma Zoo to see things like particle drift in a magnetic gradient.
Some particles might get lost in the ionosphere and upper atmosphere when they bounce. They will "hit" or interact with neutral particles and no longer be able to bounce back into the magnetosphere. Why would this happen? Well, something has to happen to change their typical motion. For example, the particles move into a region where the magnetic field is at the surface of the Earth. In this case, the particles would move further along the magnetic field and thus into the ionosphere and upper atmosphere. Earth's magnetic field isn't wholly symmetric and has a region where the magnetic field is weaker. This region is called the South Atlantic Anomaly (SAA).
Okay, but that's something the particles see every time they go around the Earth. Waves can also change the particle's path, which we've discussed in this blog previously. But unlike the cyclotron, surfing waves discussed in the other post, these ULF waves effectively create a giant sinkhole for the particles. The ULF waves move the particles onto a path that will push them further down the field line and are more likely to interact with the atmosphere and ionosphere. Suppose you are a plasma physics or space physics student. In that case, you can see the effect by conserving the first and second adiabatic invariants.
So a bit more information before we look at how big of an effect this is and why one may or may not care. First, we should look at how we measure this. A particle will have a pitch angle. This is the angle between the velocity vector of the particle and the magnetic field.
Above, you can see the equatorial mirroring particle will have a pitch angle of 90 degrees. In a quiet magnetosphere, particles with 90 degrees are trapped (okay, a bit more complicated, but we're keeping it simple today). A particle that will be lost entirely (because even if the atmosphere and ionosphere weren't there, it would run into the Earth) will have a pitch angle of 0 degrees. Most particles have something in between.
As the particle moves down the field line, it moves towards a stronger magnetic field. This stronger magnetic field changes the velocity vector of the magnetic field, pushing it toward 90 degrees.
If the particle has a pitch angle of 90 degrees above the atmosphere or a location where it may start colliding with other particles in the ionosphere, it will bounce back. As it moves toward the magnetic equator, the pitch angle will decrease. Once it passes the magnetic equator and starts going down to the other pole, the pitch angle will increase until it either reaches 90 degrees and starts the process all over again or is lost.
If the particle reaches a 90-degree pitch angle in the atmosphere or ionosphere where it may collide with other particles (and what height it is lost at depends on energy, density, etc.), it will become lost.
At this point, the particle has been removed from the magnetosphere and is no longer trapped.
Thus there is a set of pitch angles at the magnetic equator where we know those particles will be lost entirely from the magnetosphere. They have no hope of being trapped. These sets of pitch angles are defined as the loss cone. They are dependent on the height that the particle will be lost (and thus the energy of the particle). It is also dependent on where you are starting in the magnetosphere. A particle at L=3 will hit the atmosphere at a higher altitude than a particle at an L of 8. L is the number of Earth radii from the center of the Earth at the magnetic equator- so L of 1 is the surface of the Earth, L=8 is 8 Earth radii or four total Earths away from the center.
Now let's look at some data from the magnetic equator. Below is particle data from the Van Allen Probes mission. The particle flux is plotted in colors, the Y(vertical) axis is the pitch angle, and the X(horizontal) axis is time. On the left, I've tried to draw a cartoon of the pitch angles that the satellite sees and the loss cone. As you can see, the loss cone at the magnetic equator is relatively tiny. This makes looking at what particles may be lost easier if you sit in the magnetic equator.
So what does this mean with the ULF wave? How does the ULF wave change the loss cone that a particle sees? Well, the ULF wave breaks the third adiabatic invariant. That means that a particle's bounce and cyclotron motion won't be affected if the changes to the magnetic field are slower than those motions. The drift of radiation belt particles around the Earth is on the order of 1 - 10s minutes... okay, so that was a lot of jargon and spatial visualization with things not everyone is familiar with.
This means that the ULF wave will push and pull on the particles. At times it will move the particle closer to the Earth (into a region with a larger loss cone) or pull them away from the Earth (into a region with a smaller loss cone). Thus some of the particles will see a larger loss cone and be lost from the magnetosphere.
So how big is this sinkhole? Well, not that big. It may affect ~1% of all pitch angle space. And this is where it gets interesting. This process is only somewhat important when looking at radiation belt dynamics. If you remember from above, it's only sometimes observed by our satellites in the radiation belts! But! If you are interested in what ionizes the atmosphere, can cause changes in the ionosphere, or even affects radiation at aviation altitudes. What's not much loss from the magnetosphere can be vast amounts of radiation into the ionosphere and atmosphere!
It's all about perspective.
Okay, now you know what the paper was about, the key takeaway, and why perspective matters... Why am I saying this was simple? There are many figures and ideas and more jargon than is probably helpful in all of the above text.
When we start learning about plasma physics and magnetospheric physics, we first learn about the three adiabatic invariants. Then, we learn how they control how the particles move through the magnetosphere. Finally, we often look at times when all three are broken; the more that break, the more complicated the math, the interactions, and the impacts. Usually, when two or all three adiabatic invariants are broken, many different phenomena occur simultaneously, so it takes time to determine precisely what is causing what effect.
When we started looking at this study, we found it was beautifully simple - it was clear what different phenomena were happening. This straightforward mechanism could explain the observations. It's something that most first-year graduate students could solve, and the math was some simple algebra. No more complicated tools or theories were needed to explain the observations. You don't always get a chance to work on a paper like this. So it's nice when it does happen.
So why would you care?
Well, suppose you study magnetospheric radiation belts or precipitation of radiation into the ionosphere or atmosphere. In that case, you may care because it helps explain different dynamics. It's also interesting because ULF waves frequently occur, like almost always. So while mechanisms that perhaps affect a more comprehensive range of energies happen less frequently, this happens much more often.
Why do you care if you aren't a magnetospheric, ionospheric, or atmospheric person? We're progressing toward a better understanding of the environment in which we live (if you spend a lot of time in a plane, maybe) and work (where all the satellites live). With this mechanism, we better understand why we have days with drizzle, you know, when you can't quite tell if you need a radiation umbrella. Leave the umbrella at home if you spend only a few minutes in it. If you spend a whole day in it, you may want to bring a rain jacket.