The Field Guide to Particle Physics

To explain the origin of cosmic rays, we discuss how out-of-equilibrium plasma physics can boost ions to extremely high velocities.

Show Notes

The Field Guide to Particle Physics
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The definitive resource for all data in particle physics is the Particle Data Group:

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The Particle Data Group's write up on cosmic rays. See Figure 29.8 for a representation of the "ankle" feature in the spectrum.

Another representation of the power laws can be found in Professor Peter Gorham's Coursework on Ultra High Energy Cosmic Rays:

Natalie Wolchover has written two great articles in Quanta on Cosmic Rays, both which talk about what might accelerate these particles.
The Particle That Broke a Cosmic Speed Limit and Cosmic Map of Ultrahigh-Energy Particles Points to Long-Hidden Treasures

Cosmic Rays
Part 2 - Plasma Physics

What might you say is the most insightful law in theoretical physics? E = mc2? The general theory of relativity? The quantum nature of the atom? The debates could rage for days. Looking back on my own education, I’d isolate two really important ones.

The first is Newton’s FIRST LAW of motion:

A body at rest will stay at rest or a body moving in a straight line with a constant speed will not change in its motion unless acted upon by a force.

The second is probably Dalton’s Law of Multiple Proportions, otherwise interpreted as the modern theory of atoms. You know, that everything in nature is made of up individual molecules and those molecules are made up of atoms.

These ideas run counter to much of our direct, daily experience. At least that kind of experience we’ve had in common with our ancestors for thousands of years.

So please don’t ask me to pick between the two. Both Newton and Dalton’s laws are crucial.

Putting those ideas together - which involves a lot of mathematical work - physicists arrived at the modern, kinetic theory of gases.

There are LOTS of details and lots of implications, but one way to understand it goes like this:

Gases - like the air we breathe - is made up of molecules and those molecules move at different speeds. Their average speed tells us the temperature. The higher the temperature, the higher the average speed. But also - and importantly - the higher the temperature the wider the spread on molecular velocities.

In other words, all around you there are gazillions of tiny molecules. At room temperature, they’re moving at 1000 miles per hour, on average. Of course, some are moving really very slowly, and some are moving quite fast. A  tiny fraction of those molecules are moving, really, really quickly, more than twice as fast as average.

But we can’t see any of it because they’re just too small.

When gases get really hot, the individual atoms inside the gas begin to break down. Their collisions have too much energy. The impacts are too powerful. The electrons and nuclei split apart and form separate components of the gas. Perhaps not surprisingly, this often - but not always - coincides with a very low density of atoms.

When a gas has its charged particles ripped apart, we call that gas a plasma. Plasma’s are kind of a BIG DEAL in astrophysics.

If you’ve stood around a bonfire, you’ve seen a plasma. Those tongues of fire are little pockets of air whose atoms have been ripped apart by the intense heat. The intense speeds of electrically charged particles zipping past each other is what causes those tongues of fire to give off electromagnetic radiation - otherwise known as light.

We discussed another sort of plasma in our last mini-series on the ALPHA particle, where we discussed the solar wind and the Earth’s magnetosphere. Of course, the outer bits of the sun itself are in a plasma, hence all the glowing we see every day. And that giant plasma ball we call our sun spits a constant stream of charged particles our way - the solar wind. The magnetic field generated by our Earth’s spinning core captures much of those charged particles well before they hit the Earth’s atmosphere. Thereby protecting both it and us.

Those particles are confined so the so-called Van Allen belts which hold the plasma - a very low density plasma compared to what you’d see in a bonfire - thousands of miles above the Earth’s surface.

Magnetic fields contain that solar wind by bending the trajectories of the individual particles - it curves their motion. That’s just what magnetic fields do. The strength of the magnetic field means that those particles can - at best - move in circles. The faster the particle, the bigger the circle. Approximately anyway.

Like any gas of particles, the van Allen belt plasma has particles moving at very low speeds and very high speeds. Very small circles and very large circles. The average speed - in part - determines the approximate size of those van Allen radiation belts.

Particles moving stupidly fast through a magnetic field - like cosmic rays from space - will also bend, but not enough to get trapped. Instead they fly through the magnetosphere and into the upper atmosphere. Breaking apart by spreading their energy around, leaving us to content with that debris of particles.

Plasmas in Space
You might wonder where those high energy particles from space - those cosmic rays - come from.

Well, there’s a lot of stars in space and subsequently a lot of plasmas. Stellar winds blow off particles all the time. But that’s not really enough energy to generate cosmic rays. But sometimes, when stars explode as supernovae, even more charged particles get ejected into space.

Those astrophysical gases - plasmas - often give us beautiful photographs to look at here on Earth. But don’t be fooled. The density of those gorgeous gas clouds - even in star forming reasons like the Horsehead Nebula - aren’t really that visible to the naked eye. Even if you were right up on it, you’d probably have to leave the camera shutter open for a bit to capture all that light.

That is to say, that astrophysical plasmas are pretty sparse. By comparison our atmosphere feels like a thick, pea soup. The particles inside those astrophysical plasmas don’t really smash into each other like they do down here on Earth. Rather, the particles interact via the longer range, electromagnetic force.

Astrophysicts will sometimes call them Colisionless plasmas to emphasize that fact.  The gas behaves less like a game of billiards and more like…  traffic… or a flock of birds.

Fermi Acceleration
In a diffuse, astrophysical plasma there are really three components to worry about. The electrons with negative charge, the ions with positive charge and the magnetic field itself.

The importance of the magnetic field can be felt even here in our solar system. Like the Earth, the sun has a magnetic field. A bit one. Unlike the Earth, the sun is constantly producing a large stream of energetic particles, so things are a little… hectic. Every once in a while, the sun’s magnetic field gets so twisted up that a little bit pinches off.

That’s right. The magnetic field pinches off. It heads outward into space. Sometimes towards us. And a large chunk of the sun’s outer plasma sometimes goes with it.

These are called coronal mass ejections, and they’re a big deal. VERY out of equilibrium, they say. Like a tsunami of plasma, a coronal mass ejection can wreck havoc on our satellites and other electronics.

On earth, these kinds of events are experienced as a shockwave in the solar wind. And - so far as we can tell anyway - shockwaves, even bigger shockwaves, like you’d find in a supernovae - are the things responsible for accelerating cosmic rays out of astrophysical plasmas.

Sources for Magnetic Shockwaves

So what causes these shockwaves to pass through interstellar clouds of electrically charged particles?

Well supernovae for sure. Those exploding stars can be brighter than entire galaxies, so it’s probably no surprise they’re sending out a lot of sudden shocks during their expansion.

There are a few other candidates.

Neutron stars - city size nuclei left over from one of those supernovae - are really extreme objects. They’re just on the cusp of becoming black holes, and the only thing keeping them from collapsing is the strong nuclear force: you know, gluons and pions and that kind of subnuclear goo.

So they’re very dense. So dense that the force of gravity on their surface is a couple of hundred billion times stronger than on earth. The gravity is so strong that we would be immediately crushed into thin layer of nothing but neutrons. Pretty extreme.

Just like neutrons themselves have a tiny magnetic field, a neutron star - composed of a gazillion such neutrons - can have a really big magnetic field. A massive one, as it turns out, that spins as the neutron star does, sweeping our a huge wave of electromagnetic energy.

That wild, sweeping motion together with those ginormous magnetic fields surely has a massive impact on any nearby plasmas.

Fermi Acceleration
Shockwaves accelerate particles in a plasma into cosmic rays, but not all in one go. It’s not like a baseball bat. It’s more convoluted than that.

The moral of the story is that some particles pass through the shockwave, back and forth, picking up an an enormous amount of energy as they go. That’s the standard explanation - filed under technical phrases like diffuse shock acceleration or a first order Fermi acceleration.

It’s a funny thing to think about. Initiatively, its feels like a surfer passing through a wave, going faster each time. Which makes NO SENSE. Of course, that picture is wrong.

The thing to keep in mind is that the gas of charged particles - the plasma - is VERY far from the normal, equilibrium thermodynamics we experience down here on Earth. The shockwave is by definition moving faster than the speed of sound in a gas. A shockwave will also very likely be spread out broadly with multiple fronts. Some a little ahead, some a little behind. This texture in the electromagnetic field can give electrically charged particles of the plasma a lot of shock fronts to bounce off of, picking up energy each time. Eventually they can get boosted to such a high energy that they shoot off into space - and eventually - towards us.

Next Time
When those high energy cosmic rays smash through our magnetosphere and collide with molecules in the upper atmosphere. A cascade of particle debris is formed. But almost all of it decays before it hits the Earth.

Indeed, down here, on Earth, the vast majority of those debris particles that we can see are muons.

Those muons are moving really fast. Very close to the speed of light. Which makes sense given the outrageous energy the original cosmic ray had. But muons are something a curiosity. 

We don’t normally see muons hanging around in other contexts, like chemistry. That’ because they only live for an average of 2.2. microseconds. While extremely long lived by particle standards, the muon’s life really isn’t that long.

Those muons are born way up at altitudes of nearly 30 miles above sea level, which is good because that’s far above where human normally live - or even where we fly. If we were out there, being bombarded by cosmic ray and pions and who knows what else, we would probably get TOTALLY FRIED. 

But this also presents a puzzle. LIGHT can only travel about half a mile or so in 2.2 microseconds. So how it these muons can travel well over 10 times that distance without decaying? 

What is The Field Guide to Particle Physics?

This is your informal guide to the subatomic ecosystem we’re all immersed in. In this series, we explore the taxa of particle species and how they interact with one another. Our aim is give us all a better foundation for understanding our place in the universe.

The guide starts with a host of different particle species. We’ll talk about their masses, charges and interactions with other particles. We’ll talk about how they are created, how they decay, and what other particles they might be made of.