NASA's Heliophysics Summer School - August 16, 2024 - Robert Ergun

Uh, I don't know about that. I, I completely, I'm gonna be completely off topic. You don't know about particles, or you? I don't know that they're going to learn all about particles. Um, one, we were having lunch yesterday. Yeah. Um, we were discussing this sort of like different, different ways to focus your career, right? And I would, I would, if you could talk a little bit about like, uh, so we were saying that, well, there's some people are, I do physics, so, you know, I don't care which planet I'm on. I don't even know which planet I'm on half the time, but that's me. Um, but, but I like the physical processes. So if magnetic reconnection is happening at the Sun or Jupiter or Mars, I'm happy. That's in my talk. You got ahead.

Well, good morning, everybody. Um, as, uh, he said, my name is Bob Uran. I'm here at the University of Colorado. You're getting a lot of us, I think. Uh, we're saving on the travel budget, is that it? So we have a, we have, we, we, we, we would like to think that we're pretty good here. And, um, I, um, am going to talk on two parts. I've got, you got me all morning, sorry. But, um, I'm gonna talk in two parts. One, I'm going to talk a little bit of introductory, and I would like to sort of motivate the physics part of heliophysics and why we would do heliophysics as physicists. Um, that's where my background is. Um, as he was saying, I have a colleague, Fran, who's going to be talking later. Fran Bagol. And, and she's Miss Jupiter, you know, she doesn't, you know, you say the word Mars, she walks away. Um, she does, she not only that, gets mad again. Um, but in any case, that's interesting. That is really, really cool. I really respect that. But I have a whole different view. I want to, when you say magnetic reconnection, I'm happy. I don't care where you are. You could be in a supernova shell, you could be in, in the Sun, you could be anywhere. So that's the phenomenon. You know, mine is more physics phenomenology, and I want to show you this point of view, okay? Because a lot of us are solar physicists or Mars experts or Jupiter experts. I'm just a physicist. All right. So let me go on.

So I'm going to start with motivation and ask, why heliophysics? Why would anybody do heliophysics? Anybody in their right mind actually want to do this? Okay? Where is the discovery? Where is, why is this valuable to society? We've all heard about space weather. We've all heard about other, you know, knowing or quest for knowledge on planets and things. But I will also say that the physics part is extremely interesting to me. Okay? And I, I want to start with some motivation on why we could do this. Many of you may not know, but heliophysics has been around for hundreds of years. It started with, I think, one of the earliest. I'm not sure this was the earliest. I'm not a historian, but with the Aurora. People saw the Aurora. Men, men and women saw the Aurora for hundreds of, not thousands of years, and wondered what the heck that was, particularly the Northerners, right? I mean, you have a lot of the people in Sweden and Norway wondering what this is. Ultimately, this led to the discovery of three acceleration mechanisms, three particle acceleration mechanisms, the idea that they're parallel electric fields. Okay? So this, this really is, you know, heliophysics. This is not known. And in fact, I will say in my career, I was told that parallel electric fields didn't exist. That was the mantra in the '60s and '70s. And now we know there's everywhere. Okay? So heliophysics measurements broke that myth. So you could see how science can go wrong and how this was a valuable contribution to science.

Back in the, I think it was 1915, somebody sent up a balloon and got a cosmic ray track. Let me see if I could get this right. And that's how you did it back in the day. Um, and this, this actually was heliophysics, but it started the entire, um, the entire research on particle physics. This was it. This was the beginning of energetic particle physics. Physics. This was a major mystery. Why are, why do we see these extremely high energy particles that have this, this tail on the distribution? Why is it a Gaussian? What happened to the central limit theorem? Okay? Wow. How do we get these particles that are all the way up to a Joule? Okay? You're talking about 10 to the 21 EV or 10 to the 20 EV. So this was a major mystery that heliophysics really is. And the work that we do is critical in in this understanding.

Um, one of the early mysteries was during eclipses. Um, some, back in the day, people didn't have sunglasses, so they looked up. Okay? I don't know how many of them are blind, but, but, um, the whole point is, it was very clearly noticed. This is one of the first pictures, an early picture of the corona, the solar corona, and the solar wind. It was very clear then that there was something happening at the Sun. This was another mystery hundreds of years ago. So this is not all brand new stuff. And people were wondering, where does this come from? Where, what's going on with this Parker start? That's where, you know, Parker, Eugene Parker's work was highly based on was trying to understand this picture.

Um, later on, we made discoveries of the solar wind, their properties. And to tell the truth, we're still doing that. Very, this ongoing work. And Parker Solar Probe is giving us our biggest next step right now. You probably heard a lot of, I mean, Marco was up here, right? Probably mentioned the Solar Probe, Parker Solar Probe, word 100 times by now, but that's fine. This is an incredibly wonderful mission that is going to a place we've never been before and really opening our eyes up to how solar winds and stellar winds are accelerated. This will be rewriting the textbooks.

Um, another early mystery. This was a picture, image taken a long time ago, but people noticed these bright flashes. Now, this is more recent. This is about a hundred years ago when people, when cameras existed and other things existed, you know, we, we had a way of recording this. But what are these all about? This discovery led to the idea of magnetic reconnection, which I will show you later. And I'm going to talk about a lot on this, you know, in over this morning, which is probably one of the most central processes in all of plasma astrophysics and in any plasma, even in laboratory plasmas. So this all started with the Sun, somebody noticing the solar flare and trying to explain it.

Um, ongoing physics. There's a lot of ongoing, um, heliophysics work on this magnetic reconnection with the MMS mission, which is active now. And since I'm up here, you're going to hear MMS about how many times? Har? About a hundred times? Yeah, yeah, yeah. About right. Um, so you're going to hear the MMS word quite a bit. Magnetospheric Multiscale. And the, the, the MMS satellite has really led to, this is a great combination. The solar physicists first hypothesized it, and now the magnetospheric physicists are going in and telling us all the details of exactly how it works because we can. All right.

Shocks. This is a major discovery. Collisionless shocks. Again, when I was a student, collisionless shocks could happen. The particles would just go right through each other, okay? That's exactly what people thought. But oh, all of a sudden, you start taking a look at this. Think, look at that. How did these things happen? These are collisionless plasmas. And this is a picture. It's, it's sometimes easier to see. This is actually what our helio, um, um, heliospheric shock would be. That this is the termination shock of another star, okay, inside of a huge stellar wind. We can't see us because we're inside. Sometimes it's better to get in an airplane and look at your backyard to see the whole thing, right? But this is essentially what we're seeing here is a shock. Well, we now, with a number of our missions in heliophysics, can tell you exactly what these things look like inside. And they are messy. They are turbulent. They are much more complex than first meet the eye. So a lot of the cosmic ray, I'm going to come all the way back to cosmic ray acceleration theories are based on shocks and really need this information to fully understand how we get accelerated particles. That is a non-thermal tail on a particle distribution.

Um, well, I'm not going to talk much about this, but I will say that radio emissions were detected from Jupiter early in the, um, 19, uh, well, after Marone, sometime we started picking up radio emissions from all these galactic sources. We didn't know that Earth was a radio, radio emitter because the Earth's radiation act, or, or, or a moral kilometric radiation with the Earth emits, can't get through our ionosphere. But Jupiter's can. So we saw Jupiter's emissions before we saw the Earth's emissions. Okay? Back in the days. And this is like, these are extremely intense, very fine frequency. They have all sorts of things. This is a bunch of dancing streaks. What is going on? Well, it wasn't until we actually got into the auroral kilometric regions, source region, we had a source region passing, which really ultimately did. I just go backwards? I don't know what I did. Hang on a second. Okay, backwards. Uh, okay, that's right. I had it right. So this is the, uh, a source region crossing, which showed exactly that these things were coming at the electron cyclotron frequency. And we were able to just measure the particle distributions and and unravel this whole mechanism called the electron cyclotron Maser. It's a fantastic mechanism. For those of you that don't know about this, it depends on a small relativistic effect where the electron mass of the higher energy electrons, the 5-10 kilovolt electrons, is one or 2% higher than the other electrons. And without that shift in mass, you couldn't get this emission. Okay? So it's a really cool theory. Um, if anybody wants to deal with it, it's great. But be prepared. Roll up your sleeves. Learn your relativity. Learn your plasma physics, um, functions, and all that other stuff. This is one of the most complex, um, mechanism. But the, the, the cyclotron, electron cyclotron masers now believe to create Jupiter's emission, Saturn's emission, so, um, solar flare binary systems, um, a lot of the emissions, it is evoked in blazar jets now. So we see these radio emissions coming from blazar jets from deep from other galaxies, and we believe this is electron cyclotron maser. It is one of the fundamental mechanisms, and this was entirely discovered by heliospheric missions. So heliosphere, spheric missions have been contributing to fundamental physics for a long time. And this is the motivation I want to give you. Okay?

Now, some of you might say, well, okay, but I want to do Mars. That's fine. I like that. Okay? I know you, you want to do Mars, so that's all right. You're Martian. Um, we have a lot of Martians. We have a lot of Jovians, Saturnites, or whatever they're called. And so, but remember, there's a huge amount of fundamental physics in here. The other type of, um, um, physics that you're going to hear about later today will be turbulence, I think, right? Now, plasma turbulence is poorly understood, and it's going to be heliophysics again that leads our way to the understanding of plasma turbulence. It will be our missions. In fact, the next NASA mission will be targeting at at turbulence. Um, so we see turbulence in the Sun, Sun's surface, but we also see very, very strong turbulence all through our magnetosphere. Now, you want to recognize turbulence by eye? This is a very bad way of doing it. So all the turbulence people are going to yell at me, but take a look. Look at these magnetic field signals and electric field signals. To me, when they start rattling up and down like that, very strong possibility that it's turbulence. Okay? But if you look at this, at the same time, you get the turbulence. We're getting accelerated electrons and accelerated ions. And this, at the same time, you may not be able to read this, but there's a flow reversal indicating a magnetic reconnection event in the center of it. So here I am going to all these fundamental things: shocks, magnetic reconnection, turbulence, and particle acceleration. And they are all interrelated. This is our next challenge to understand, not just the shock in isolation in our nice, happy version of it, but understand with all its turbulence and how it accelerates particles. This is our challenge that is coming up. All right.

So that, I hope, will motivate you to be a physicist. Maybe I don't know. It's okay. I, I really have. I was also talking with Nick and and having a discussion that it's really nice that we have graduate students from all departments, all five different departments. We have them from geology, we have physics, we have astrophysics and astronomy, and, and atmospheric, I don't know what else I miss. Aerospace engineering. I'm sorry, Tanya. We're already having aerospace engineering. Actually, they're becoming the leaders in in a lot of this. And that's great because we have these people from different backgrounds mixing together and talking to each other. And that's important to respect and and talk to each other because not one background is going to solve this problem. So this is a cool thing, I think. All right.

So I'm going to talk a little bit about my view of plasma physics. And and this is all sort of introductory stuff. I will get into the details and and make, you know, make you dizzy on the second talk, hopefully not on this one. Okay? I am famous for being able to overload people. Um, so be prepared. But this is basically my view in plasma physics that I'd like to go at. And this is it. That's it. It's really bone simple. I always see it as a bunch of electrons, they're green, and a bunch of ions, they're red, all moving around and banging into each other. That's it. That's what a plasma is. This is bone simple, right? Just got a bunch of particles going all over the place. So what's the problem here? Okay? Not much of a, a, a, uh, you might say, oh, there's not much new physics in this, is there? Well, there is a heck of a lot of new physics. Now, plasma physicists, when I step into that arena, um, you're dealing with space plasmas, solar plasmas, laboratory plasmas, and fusion people, etc. This is fine. We all have a lot of the same ideas. But there are three major approaches to solving problems in in plasma physics. And I want to make sure that this is understood. There's kinetic. Now, kinetic is actually the simplest way of thinking about it, but the most difficult way of doing it. Okay? If you think about it, why can't we just use L's equation and follow all these particles? Right? We could calculate E and B from all, you know, we could because we know all the currents and and charges from all the particles. You sum them all up and then, see, take a time step and move all the particles, and then stop, and then recalculate all the fields. You could do this on a computer simulation if your computer could swallow 10 to the 20 particles. Guess what? It can't. Okay? Not yet. But we're getting very much better at it. And this is the, the, the, uh, basis of many what we call PIC simulations, or particle-in-cell simulations. This is a very, very accurate method. This will give you very good answers, but it's highly intractable. It's very unwieldy. It cannot do large-scale problems very well because we just don't have the resources. You have to cheat and do dirty tricks like change your electron mass ratio and ion mass ratio to 25 or 100 and things like that, and then try to hope you didn't change all the rules of physics. So, or change the speed of light. A lot of people change the speed of light, you know. So this is actually, you know, but I will say this is a growing field. Large-scale PIC simulations are around the corner. They're coming soon because computers are getting that large. Um, um, the other part is this multifluid. Now, most of you have taken, how many of you know Chen, you know, book by chance, Introduction to Plasma? That's multifluid. That's two-fluid, right? You have ions, you have electrons. You calculate the, now you, you're going to reduce them to velocities and and flows and and everything for each species, and then you'll adapt, um, um, Maxwell's equations or something to calculate the electric fields and and so on and so on. This is the second most accurate, and it's just kind of in between. Now, the most useful, and you heard this on yesterday, is Magnetohydrodynamics. What Magnetohydrodynamics does is, oops, is combines these two into a single fluid, just with plasma density, plasma velocity, and pressure, and it calculates E and B self-consistently with the MHD equations. This is, is the least accurate because there are a number of assumptions one has to make, okay, particularly on small scales. I will say it is amazingly accurate for given the given the assumptions you've made. It's almost frustratingly accurate. You say, oh, that won't work on this problem, and it does. Okay? So, um, it is, it, the way you do, one does research is that this becomes the most useful of all the, um, um, this is probably the most useful way to, and the way you would start any plasma problem. When I start a plasma problem, I always go to the MHD and take a look at the big picture solutions. Then you go to two-fluid or kinetic if you have to understand something that's really not in the MHD realm. Okay? So the, you, one, it used to be that MHD people, you know, and and kinetic people used to sort of like be off in their own corners, and I mean, they wouldn't even talk to each other. Heck, their computers wouldn't even talk to each other. And and the, the, the, uh, the, the, uh, PIC people used to say, or the kinetic people used to say to the MHD people, you're wrong. They were typically in physics departments because it was a cardinal sin in a physics department to be wrong. But being useless was not okay. It was fine. Um, on the other hand, in the astro, astro astronomy departments, they used MHD because, heck, if they're wrong, nobody will figure it out anyway, and they didn't want to be useless. So they just called the, the, the kinetic people useless. So in my day, you had a choice of being wrong or useless. Okay? Or both. Um, but it really didn't matter. So we don't have a unified approach other than the, that I say, use them all. Don't be in this camp like, I need to use MHD, or I use PIC simulations. Both of them are extremely accurate, accurate, and multifluid can be very, very useful to solve a problem. Pick the right tool. You have a toolbox. If you need a small hammer, pick the small hammer. If you need a big hammer, pick the big hammer. Get the right tool to do the work. So these, this means that you have to take three courses, right? And this is, there's no other way around it. I'm sorry to tell you. All right.

So again, kinetic is very, very basic. You just simply, if you really want to do kinetic calculations, you could just on a computer. It's very simple, okay? It's not that complicated. If you, it gets complicated because it gets massive, okay, and you have to do a lot of, you know, computer tricks. But really, all you're doing is you're taking Lorentz equation, and I should have had dp/dt because it would be relativistic. But then, then you take Maxwell's equations, and you, you would step the particles forward. Then once you step them forward, you'd stop and, you know, from every particle location, calculate E and B, and then pump the particles forward. That's not so hard, is it? I could write that program in, in, you know, you could write the program in half an hour. Most of you make it a little Python program, it would never do anything because you couldn't put enough particles in it. Okay? So that's an easy approach. Um, generally speaking, it's a lot easier if we reduce it into distribution functions, which you've all been told about now. And basically, distribution functions are generally just the number of particles per unit, not just per unit volume, but per unit volume in, um, um, velocity space. And therefore, you have these very, very strange units of of of seconds to the cubed meter to the sixth or something like that. But it's per unit volume per unit, um, velocity volume. These get complicated. This is a very, very powerful way of doing kinetic fit plasmas without having to go through, uh, and do your computer.

Um, the next, um, the next part. Now, now when you reduce distribution functions, nominally, the next thing that we do is then reduce these distribution functions. And when we reduce them, we lose information. When you calculate the density and the velocity and the temperature, pressure, you're basically bundling up all of these particles, and you're losing a tremendous amount of information when you do this. But maybe we're keeping the best part of the information we've learned over the years. This is sometimes enough to do the problem. All right.

So once you've done that, you can go into multifluid. And that means that you could start treating it with Navier-Stokes equation. This is my version of it. I do not have the collision terms in it, but you've seen this before. It's a, you've seen various versions. By the way, in my writing, when I use a v, that's for an individual velocity of an independent particle. When you see a u, it's for the fluid velocity. So I distinguish them that way. That's my style. I think some other people use that too, but, um, it might be old or something, I don't know. Um, and so you could, you could reduce this to a set of equations, and you still use Maxwell's equations to combine all the species. So you have to treat every species, and there could be source terms and loss terms. This can get complicated as well.

Um, then the basic idea is to go into ideal MHD, or this is ideal MHD, but there's other types, there's resistive MHD, etc., which I think was explained very well in yesterday's lecture. I'm not going to go into it. Um, but the basic idea is that now we've combined these two fluids by by making these definitions of of density, velocity, and pressure, and current, and we can get a series. Actually, you could reduce this to four equations if you want, just by getting rid of of E and and J and and U. One can solve these equations, you know, either by hand analytically or by computer simulation. But there are a number of assumptions that we had to make when we went to this one, of which is, of course, the principle of quasi-neutrality. You have to force the density of electrons into density ions to be the same, which is great for large scales. I mean, there's just nothing wrong with that assumption. Only on the tiniest smallest scales will that that that difference be meaningful. Okay? So that is not a bad assumption. The frozen-in is the problem, and we'll talk about that because all the happy things, all the fun, exciting discoveries are when the plasma is not frozen in. And MHD basically assumes resistive or some sort of method of unfreezing the plasma. Frozen in, and we'll talk about it, is when a particle's stuck to a field line. I mean, it's, it must be, um, it stays on its tagged field line. So, well, this would be the basis of ideal MHD. So these are the basic points. And again, to solve problems, what I like to do is start with MHD. Okay? Get the big picture. Look to see if there's any problems with it. Is there something happening on a small scale that MHD couldn't possibly describe? Right? Then zoom in on that small scale and start using your PIC because the PIC can't handle the whole darn thing, or using your your your kinetic simulations. So this is really a, a physics approach method. Don't be afraid to use all the tools in your tool chest. Don't say, oh, I don't use MHD, I don't use, you know, PIC. Use them all because they're all very, very useful and neat. All right.

I want to make a discussion. I'm going to talk about collisionless plasmas versus collisional. I am going to apologize to all ionospheric and interior star people because that's very collisional. It makes a huge difference, um, in a plasma on whether collisions are actively happening. Um, I'm going to tell you a lot of stories about collisions and and not collisions a little later. But the interior of the Sun, planetary ionospheres, um, um, these have high densities and they could be very highly collisional. When you have collisions, momentum and energy exchange between species happens via these collisions. Could be dominated by that rather than the electric fields in the plasmas. And the force equation has to include a viscosity term, which is often tricky to calculate, and how momentum is being exchanged between that the electron and neutrals, ions and neutrals, ions and electrons, etc. They often, however, lead to very nice Gaussian distributions due to the central limit theory. If you have enough collisions, your your plasma, your like the air here, has it's all collisional. You'll find it's very, very Gaussian. The central limit theorem is very powerful because it's dominating. Okay? Yes, the central limit theorem is basically, oh, come on. I, you want me to really state it mathematically? It's basically if you take a, um, random sample of something, even if your randomness is not Gaussian, if you keep doing a random event, it'll eventually lead to a Gaussian. Okay? That's like the random walk. If you take a step one way and then randomly take a step right or left, and you do this a number over and over again, N times, take 20 steps, or you'll end up with a Gaussian. Okay? And that's a very powerful theorem, and that's been proven. Okay? It doesn't matter whether it's, you know, um, you know, this is a discrete part, um, um, whether you're, you're, I mean, your action is Gaussian, you will always end up with a Gaussian. So the collisions end up being that action that happens in times where N is an extremely large number. So if you have collisions, you often will end up with a Gaussian distribution.

Now, on the other hand, the collisionless plasmas are interesting to me. That's what I deal with because they're actually the trickiest ones. The solar corona, solar wind, Earth's magnetosphere, and many astrophysical plasmas do not have collisions as the dominant mechanism for determining momentum exchange. It's going to be through waves and and particle interactions, and it's dominated by the electric and magnetic fields, not by a collision. Due to the, either have low damping, so they tend to be very turbulent. They tend not to settle down very fast. There's no damping. You start mixing them up, they, they keep mixing around for a while, and finally, they don't often end up with Gaussian distributions. So guess if we're going to try to explain cosmic rays, this pretty much has to be collisionless. There's no way that we're going to get cosmic rays in a highly collisional environment. Okay? So this means that you don't have Gaussian distributions. You have to accept the fact that, you know, you just walk away from that Gaussian, which we all know and love, which makes it trickier. All right.

Um, I was asked to do a quick review of particle motion and adiabatic invariance, or view of it. But I noticed it was also reviewed earlier, so I am going to do a lightning review just in the sake of of time. Is there a clock in this room anywhere? No? Okay. Um, I gotta figure out what time it is so I can keep track of myself. Oh, okay. So I want to do a quick review of particle motion, very, very rapidly. That's how you do quick reviews, by the way. Um, and I just want to point out that the first thing you'll always learn, and you should understand this very, very well, is that you can is single particle motion. Now, this is not self-consistent. What we're going to do is half, we do half of the, the, the, um, plasma physics. We calculate how the particles move given an electric and magnetic field. We're not going to recalculate the electric and magnetic fields after the particles move, which which is wrong. But this is still very, very instructive to understand how a particle behaves in an electric and magnetic field. And the first thing one does is that you, you take a force equation and you break it up into its two components. And, uh, the easiest part is is is, um, taking the electric field equal to zero, and you could, um, um, instantly get this harmonic oscillator, and you could calculate the orbits, and you find that the particle just simply gyrates about the magnetic field line, which opens up two ideas. One, it's stuck on its own magnetic field line. The particle cannot be separated from a field line, but I have to define what a field line is more carefully, but I will do so. Um, but it is free. You'll find very free to travel along the field line. This breaks the symmetry. It's no longer like a three-dimensional symmetric problem anymore. This, this magnetized plasma, you know, causes preferred directions, right? So that is definitely in there.

If you add an electric field, um, you'll find that the particle will move at a constant speed. Now, this is the trickiest part that a lot of students don't understand. That particular speed, which the particle drifts at, if we define that speed, the E cross B, the E cross B drift, to be the frame of the magnetic field, that will be the magnetic field line's frame. So we're going to define that if you were to move, so right here I have an electric field pointing this way, and the particle's drifting, say, this way. Okay? If you were to walk with that particle exactly at the same speed, what is the electric field in your frame? Now, remember, electric fields are not frame independent. What is the electric field, Tanya? You have to be able to answer this question because you took my class, so you're on the spot. Zero in that frame. The electric field is zero. Do you understand that? Does that make sense to you? In other words, in that frame, if you're walking along with this thing as it's gyrating and drifting at the same time, all you're seeing is the gyration. To me, you guys see this as gyrating and drifting. I just see it as gyrating. Do you see that? So the plasma frame, the rest frame of the magnetic field, in the rest frame is where the electric field is zero. Okay? So this is a beautiful phenomenon. You have to get a little relativistic here, okay, but that's fine. You can handle it. You all learned that. So think of it that way. I love to think of it that way because then you don't have to worry about why it's gyrating and drifting. These drifts start making all sorts of sense. Now, the plasma just loves, and that is now our definition of a magnetic field line. We could take that field line, a point, we could trace it by, you know, following the magnetic field, but we could also trace it in time with the E cross B drift. Okay? Okay. Not in all cases. If B goes to zero, or there's an anomaly or something like that, we're going to have a little bit more trouble. Okay? But for the base level, we can do that. It's not as simple as I'm making it. Okay. All right.

So one can go on, and this is why I'm saying lightning quick, is that, you know, we, we know about this electric field drift, but this is actually really, in my opinion, not much of a drift. It's just a frame change. But you do have, you can have a force such as gravity, and this is a general, um, drift equation. F over Q replaces E, and, um, the, the other part, there's other two other really interesting drifts. One is when B is changing, and I don't have a blackboard. I always draw these ones on a blackboard, and I didn't have time last night at 12 o'clock when I was finishing this thing up to make a, make a picture of a, of a, um, gravity gradient B per drift, or a curvature drift. That's a little easier understanding. If you have an electron going on a curved magnetic field, it actually feels a centripetal force, so it drifts normal to that line. So these are important drifts. But I want to warn you that they're not the best way of thinking about it because the plasma has to be self-consistent. But they really are useful, for example, in radiation belts and other places where you could have trapped electrons. The fusion people love this stuff, etc., etc. So it's a good way of of of of approaching a problem. Okay? But what I want to drill into you is this concept of the adiabatic invariant. All right.

So you have a particle, you have a magnetic field line, you have this particle going around the circles, right? It's stuck on that field line. It's just, can you, we love in physics to find a conserved quantity. Energy is conserved. Now, you're going to note that I use W's for energy. Do you see the W there? That's because E is an electric field, and I'm an electric field guy, so E doesn't change from it. It is first and foremost an electric field. Second is energy, if you only if you don't have any electric fields. But I use W for energy just to stop the confusion. Um, so we're going to define the, um, uh, this is, this thing sometimes gets tricky. We're going to define the perpendicular and parallel energy, and you know, the sum total of the energy, which I'll call W, has got to be constant. This means that when you learn these conservation principles, they're important because they can actually make problems that are otherwise extremely tricky, very easy. Right? Just conserve energy if you can. You could solve a problem very quickly. But there's a new type of adiabatic invariant in a plasma, and one of the things that we will find is that that this, this is basically called a mirror force or a, a, the force along a changing magnetic field line. But what I want to point out is that we define this quantity of W perpendicular over B as mu. Okay? The first adiabatic invariant. We're, I'm going to show you that is very strongly conserved. In other words, the perpendicular energy of a particle gyrating around B divided by the magnetic field is a conserved quantity. The only way to change that that energy is to change B, or the other way to do it is to violate its frozen-in condition. Okay? Okay. In other words, you have to have an action that happens faster than it could gyrate. If I could, if it gyrates many times and I have an action, nothing's going to happen to its energy. If I could kick it really fast, really hard, then I could change its energy. But this is a very important. We're going to be talking about particle acceleration, right? So to actually energize something perpendicularly, we need to be able to change that adiabatic invariant. And we'll talk about that quite a bit.

Now, I'm going to, um, I don't want to go through this proof, and I'm going to leave it on my, um, um, my slides and show you that there is a proof for this. Um, there are many, many proofs on this. They're, they're all over in every plasma textbook. But, but you start by just taking the fact that the energy has to be conserved. Where am I here? There it is. That the energy has to be conserved. Serve. So that means the total of the parallel and perpendicular energy. And we write this, rewrite this perpendicular energy as mu B. With a lot of fancy manipulation, you could show that you could manipulate that equation that I showed you, that d/dt and take the derivatives, and you end up with this thing, B dot dB/dt must be equal to zero. Okay? After a lot of manipulation, I, I, I think everybody should know this idea. Okay? And and go through this. I don't think this is a good setting. I, I always find it awkward without a chalkboard trying to teach this. So I'm going to let you read the notes. But basically, in order to change this, this, this mu is conserved, but I want to tell you this is a strong conservation. You really have to have something, a, a force imposed on that particle that is faster than the time the particle takes to gyrate once in order to change its energy. And that actually is, you know, um, it works both ways, though. How would you change the energy under this? What if I changed B? I could change B. I could change the energy of the particle. Okay? So the perpendicular energy of the particles is highly, um, basically tagged or glued to the strength of the magnetic field it's on. Okay? This is a concept, sort of like quasi-neutrality. Ion density, electron density, almost in all circumstances equal. You know, you get a huge electric field if they're off by one part in 10 to the billion. So for all practical purposes, that they're saying, yes, well, you could throw it away if B is not zero. The adiabatic invariant is not conserved when B is zero. That's the way it's usually written. Don't, don't blame me. But you're, you're absolutely right. You could throw the B away if it's not zero. Okay? You could say that. But then you have to add for non-zero B. Okay? So this, this, this is a very powerful, um, and I'm going to use this quite a bit and talk about this a little bit later when we go on. So remember this one. It's defined as W. Now, there are two other adiabatic invariants. Um, one is called this bounce, and the other is a drift. They are much easier, more easily broken because their frequencies are so low. It's easy to create. They could easily find themselves in a situation that breaks it. This is the one that is the most difficult to break. So we now, in plasma physics, this is a beautiful one. We have the idea of gyration, quasi-neutrality, frozen-in, ex-drifting, and this adiabatic invariant. Those are the things to get into your head so that you can envision what, how plasma actually works. You could fall back on these sometimes to understand what's going on in the problem. Now, I'm not going to go into mirroring at all. Yes. Well, well, adiabatic means that you're not exchanging energy with the rest of the world, right? So this means that you have a magnetic field and, and, and a particle without exchanging energy with the rest of the world. And that's basically what it means. I, I didn't make that up, okay? Um, I find the use of adiabatic and isothermal kind of a little bit nebulous. They're not as precise as they should be, but I think it's generally agreed on that this is a good definition for this type of invariant is because it's not exchanging energy with the rest of the world. If somehow we're exchanging energy, if I were to actually put an electric field, it had a curl to it, for example, right? A curl V, um, then you need a dB/dt though there. So B's not constant and steady state, then that particle could wind up or wind down, right? So that means that we're time stationary, not exchanging energy with the rest of the world. When you do an adiabatic experiment, you're often, you know, you're often insulated from the rest of you have an insulator around it. Every time they draw one in your fluids class, right? They put an insulator right and say, okay, we're not exchanging energy with anything. What happens to this gas or this fluid or anything like that? So that is, I don't mind the use. I think it's actually a proper use, personally, but I've never really thought of it. So good question. You, you can always stump me easily. You'll find. All right.

So, so, um, let's move on to the next part. And now we're going to get down and dirty a little bit. So with those basics, I want to talk about shocks and magnetic reconnection because these are the basis of a lot of transport problems. And shocks are extremely important. Um, and shocks were actually discovered by helio, collisional shocks were discovered by heliophysics missions, um, a long time ago, basically in the '70s and '80s. The first satellites we put up were really, it was a real eye opener to see all these collision, um, collisionless shocks. So what is a shock? Um, I, I'm showing you this here. Um, most of you know that if you travel at high Mach on an airplane or something, or that you can develop a, a what is known as a shock in front of, in front of you in a, a fluid. And, and, um, the, again, the idea is, what happens when you're, when you have a collisionless plasma? How does the magnetic field may take the role of the collisions? And same with the electric field. Um, I'm not going to go into all the details on shocks. I'd just like to show you where they can be. There are massive amounts of shocks in supernova shells. You could, it's not only turbulent, but, um, um, all, each and every one of these lit up regions is a shock front. Okay? Remember, this is huge. I mean, this is, you know, 10,000 parsecs or something like that. So the, you know, Earth's bow shock is only a little teeny bit on that. Um, so you can get these types of shocks everywhere in plasmas, in, in, at the Earth's bow shock, in the Sun. They're, they're, they're not an uncommon feature.

So to understand shocks, um, you have to understand the force equation a bit from MHD. Now, without going into details, we're going to go to quasi-steady state, so you could just cross out the, um, um, um, any time derivatives. Okay? And what we want to do is discuss the concept of magnetic pressure. Most of you have seen this, that the J cross B force, um, can be broken up into two parts. One is this what is called magnetic pressure term, and the other, it represents really the curvature of the magnetic field. So to make this problem really simple, a start simple, let's, let's pretend our magnetic field isn't curved, okay? Because if we curve it, life gets harder. And, you know, if any of you taken my classes, and Tanya will attest to this, I will do the simple problem and then give you the hard problem as a homework set. Um, so the idea then is, let's try to understand it. If you look at this ma, this this term here, which is this is our force equation, we're going to keep this term, which is going to be called the ram. This is the actual particle pressure, and we're going to talk about magnetic pressure. We're going to throw away curvature, gravity, and acceleration. Okay? We're going to go to steady state, so we're only going to end up with three terms. But this term, the, this term, this grad B squared over two mu naught, already looks like a pressure term. Do you see that? It looks like pressure. So we're going to call B squared over two mu naught plasma pressure, magnetic pressure. And if you don't have, uh, uh, any ram speed, which is, we're going to put it back, take my word for it, then you could write this equation as this, that zero equals grad particle pressure minus grad magnetic pressure, which means that the particle, plus the magnetic pressure, must be a constant. How many of you know this already? Anyway, I mean, half of you, right? So some of you haven't heard this before. Oh, Harry, you know this, put up your hand. Um, so, so the idea then is that that the magnetic field itself is an interesting concept. It could deliver perpendicular pressure, but not parallel pressure. Okay? So it's kind of like a gas in itself. It's like a zero mass gas that is delivering pressure, and that is really how it acts. All right.

So if we have a situation, um, one of the solutions to this problem would be to have a strong magnetic field on one side and high particle pressure here. And you'll see that as long as the, the, the sum total of P and and B squared over two mu naught, particle pressure and magnetic pressure, is constant, then this will be an equilibrium solution. So that's allowed in a plasma, okay? You can't have a strong magnetic field here and no magnetic field over here and have the same density and pressure on the plasma. It just won't work. That will be non-equilibrium. The plasma will adjust this. Okay? So that's the first thing you.

have to the first part to understand when we go into shocks. The second thing is Ram pressure. Now, Ram pressure, I, I don't know why I didn't write it here. I'll go back. Is really coming from this term here. Now, Ram pressure is pretty easy to say. If you have, if I took a garden hose, you want to feel Ram pressure. If I got a garden hose and squirt it at you, that's Ram pressure. Okay, there's not part of there. You, I'm just, that is, is the idea that there's momentum and it has to stop an incoming, uh, fluid. So wind causes Ram pressure. You stand out in a high wind, you could feel the wind's Ram pressure. All right, so that's, that's an easy, um, concept. It may be a little bit more difficult in, in, in understanding.

So the problem I have is is engineering school versus physics, um, and a lot of you probably know or don't know this part. Um, Ram pressure comes from this row .ra operating on a grad on you. Now, if you have an incompressible, um, problem, then row is constant, and you could, you will, you could solve this and you will get that this becomes 1/2 gradient row U squared, which is Bernoulli's equation and is valid for water and incompressible fluids. If you could see, we don't do water, okay, in this class. So we can't use Bernoulli's equation, Bernoulli's approach.

The other is if you're compressible in 1D and you want to be a little bit less exact, then this is not an exact solution. You, you now could say that row U is a constant, which means that it's a compressible fluid and we're conserving. That's, that's our, uh, from the conservation equation. Row and U have to be constant unless there's a change in time. And basically, you could say this is the divergence of row U squared, which looks awfully same as this with that factor of one half in there, out of there at this point in time. Okay, so a lot of people get confused because you'll see an engineering text say 1/2 and you'll see a, you know, a plasma text say not 1/2. So that's where that comes from. Okay, it's incompressible.

Now, Bernoulli's equation is very, very powerful. And so don't, don't, don't, don't poo-poo it. It's just simply, it's made for incompressible fluids. Um, all right, well, this means that we add a third pressure to our little cartoon here, in which we could have Ram pressure coming in and, um, on one side, we could have magnetic pressure on the other side, and we could have maybe plasma pressure. This isn't done right. Oh my goodness, this should be lower, lower, um, plasma pressure. Oh well, ignore the diagram. And, um, um, you can see that you can have a balance now of all three of these pressures. You could have the magnetic pressure, the particle pressure, and the Ram pressure that have to be balanced.

So again, I want to mention, what are the, for this equation to be exact or be useful, what are the assumptions we made? Time independence. Is that what you said? Straight, straight field lines. Is that what you, no bending of the magnetic field lines? Time has to be very, very, um, uh, time independent, and you have to be a quasi-1D problem. Okay, don't try this otherwise. Okay, a lot of people will start putting this up, and in fact, this magnetic pressure term is abused to no end in, in, in many, many scientific talks. So, so be careful about that, not to be the, the one that abuses it.

So let, what, oh, thank you, thank you, thank you. I got to get going. So I'm going to talk really fast. Earth bow shock. So if I don't finish it, this section, I'll finish it next. That's the idea of having two sections. So the Earth's bow shock is, is, is a great example. So what you can have here with a shock is you can have change of these, not of the total pressure, but you have a change on which one of these dominates. For example, in front of the Earth, you have the solar wind, which is dominated by Ram pressure. It's moving at high Mach, meaning that it's, Ram pressure is higher. Mach, basically, is the ratio of the Ram pressure to the particle pressure. And if you're at high Mach, that means your Ram pressure dominates. It shocks, it creates higher magnetic fields, uh, and higher pressure, and it, it loses its Ram pressure. And then there's another boundary on this, which is where the diversion occurs, where we ultimately end up with almost all magnetic field pressure on, that is dominated by Earth. There's a little bit of particle pressure as well, but there's no Ram pressure inside of the Earth's magnetosphere. So you got to think of it these three ways that shocks actually translate these terms between each other. They, they allow the, the Ram pressure to go into particle pressure and magnetic field pressure.

Um, I'm not going to go through this. You could read this if you want. You could calculate via MHD some conditions, conservation conditions on this side versus this side without actually calculating what happens in the shock. MHD can actually calculate conservation. The same number of particles going in the shock has to be the same number of particles going out. The same momentum coming in has to be the same momentum going out. The same energy coming in has to be the same energy going out. Okay. Once you've done that, and then there's, you know, um, some Maxwell's equations, you can get four conditions, which are these called the Rankine-Hugoniot jump conditions. And these are the bases for solving shocks analytically. So we, we know how to solve them on the MHD basis. But I want to tell you, the MHD solution only tells us what the final jump conditions are. They're not really telling us exactly how you change the Ram pressure into particle pressure and magnetic and generate magnetic field. That requires kinetic or two-fluid. Okay. So be careful, you know, this is a great case where MHD is telling us the big picture and setting up for a two-fluid or, or, or a kinetic analysis.

All right, so I want to show you a shock. And this is one of the first ones. Okay, this is early and old. Um, but this is the, this was a, a 1977. Okay, so this is 50 years ago, almost, almost. The, um, ISEE satellites went busted through the Earth shock, and they see the density jump by a factor of about 3.5. They see that the velocity dropped by about a factor of 3.5. This can often be somewhere between one, two, and, and one could be as low as one, I guess, one point something, and as high as four. And you'll find that four is the limit for an adiabatic shock. So this is a pretty high Mach shock. And they also see the magnetic field decrease. So the magnetic field increases, that's magnetic pressure increases. The density increases, the temperature increases, that's a pressure increase. And the velocity decreases. So you're no longer at high Mach. Okay. If I go back to those jump conditions, you could see exactly what they, that that means. This is basically meaning the same number of particles come in. Meaning if the density increases, the velocity's got to decrease. Same amount of magnetic field has to transfer through. If the, velocity it decreases, the magnetic field increases. So you have decrease in, decrease density, a density increase, a magnetic field increase, a pressure increase. The only thing that decreases is the velocity. So you're taking Ram energy and changing it into magnetic energy and pressure and, and particle pressure. That's a shock.

Why is shock so, oh, sorry, why is shock so important? This is, this is one of the first measurements that showed that collisionless shocks are, are fine. There's all sorts of little things you could talk about. The upstream, we call it the upstream and the downstream. There's an overshoot, there's a foot, there's a ramp. There's all sorts of little indications on shocks. Um, this is what we know about shocks now. Okay, this is all that action that's happening inside that little teeny box that I drew that we jumped over. The MHD equations go from here all the way over to here. So if you look in between, it's a turbulent mess. We really understand what's going on. This is where the rubber is meeting the road. This is where the kinetic physics is going on. This is where the particles, individual particles, are changing their orbits, and the electrons are being, um, sucked into the shock. The ions are being partly reflected. There's all sorts of, of, of interesting phenomena going on. This is more to excite you than to explain to you exactly what's going on, but this is an active area of research. It's, it's pretty, um, there have been a lot of work on this. So if you get into this field, you got to have to read a lot of papers first. Okay.

Yes, the jump in, what? Okay, yeah, you could see, well, you, you got to talk about frames. I mean, basically, Rankine-Hugoniot jump conditions are satisfied for most cases, but that's actually a moving shock. So you got to go into the shock frame to actually see the velocity decrease properly. And there's also this idea that you have to be in a shock normal, which is called it the Hoffman-Teller frame. I, this goes on and on and on. I'm only scratching the surface here. Okay, I'm making the simple picture of it. If you want to look at these things, they're fascinating. There's a huge amount of physics that goes on in this thing. All right, so this is showing, in fact, that it's a complex reflection of the ions from the shock and mixing process that, that, that ultimately results in a slowing down in that layer of this, of the solar wind. But that's usually due to mixing, and there's massive amount of turbulence, and you're going to keep seeing turbulence pop up inside this shock. Okay, so this is somewhere we have to understand shocks, turbulence, and all sorts of kinetic plasma physics. The MHD gives you the basis on how to do this. It's very valuable. The kinetic part is also very valuable if you really want to know how the rubber meets the road. Okay.

Um, in this particular shock, there's a huge cloud of reflected ions, which is just a fascinating way of saying, this is highly kinetic. This is no longer a Gaussian or happy distribution anymore, and this is going to have to relax itself through turbulence as you go downstream or upstream. Yeah, yeah, that's an observation. That's, that's from the previous one. This is from this, this particular, this isn't Goodrich at all. Um, so, I mean, I always love that picture because it shows you a double, actually a double reflection. These are the first reflected ions, and this is the second shell. So it shows you these various shells of ions bouncing off the shock, gyrating, and increasing in their energies, just like Schwarz et al. and other people have predicted. It's a beautiful thing, but I'm way past, way over everybody's head at this point. Okay.

Um, so finally, magnetic reconnection. And tell me when to stop. Okay, back there. Um, this is one of my favorite, favorite, favorite topics. So I could go on forever. So what is magnetic reconnection? Um, this is the idea. Okay, I'm gonna go back, um, and then push this again. So it does, it, you could see the idea is that you are annihilating magnetic field in opposite directions. You put them together, you annihilate them. But magnetic field carries energy and carries pressure and carries, and plasma is frozen in on it. Okay. So my point is, what's so big about annihilating magnetic field? Field. Every time you close your refrigerator door, you cause magnetic reconnection. Okay. So, so literally. So what's the big deal? The big deal is the plasma. Okay. When you have a strong enough plasma, uh, that magnetic field, sufficiently, magnetic reconnection is no longer as simple as closing your refrigerator door. Okay. In the vastness, in the middle of space, this is an important concept. And the idea that, um, um, plasma, magnetic field can annihilate, and the leftover energy goes into the plasma, and it has these flows, really comes from this whole idea that you could have inflow, and then you could see the outflow jets going on in that region. That's the structure of magnetic reconnection in a nutshell. The, um, main question in magnetic reconnection was always this area, which we call the diffusion region, right here, where these magnetic field lines meet each other, they break, and they form a different field line that goes out the side. So the plasma now has a way of staying on a magnetic field line. You can't just eliminate the magnetic field without eliminating the plasma somehow. But this is a way of allowing the plasma to exist while we annihilate the, the magnetic field. That's the way, one way of thinking about it. There's all sorts of ways of thinking about it, not just mine. So this violation here in the diffusion region is where we understand that the frozen-in condition cannot be taking place. We need to violate that frozen-in condition. That is on MHD in there. That's why it's exciting. It's being violated.

Okay. So the next idea, and let me just tell you a little history, because this is a very fascinating history of magnetic reconnection. Really started. Now, I'm probably giving you all the wrong version. Everybody, you forgot about this and that and this, but that's okay. Here's my short version of history. Is that back in the 50s, people noticed these solar flares. Once the solar flares were noticed, they, they erupted in one minute. So first thing people thought of is maybe right here in this area, we got magnetic reconnection, the top of this loop letting this thing go and creating a huge dumping, a whole lot of magnetic energy into the plasma. That's how you get your gamma rays or your X-rays or your, your, your ultraviolet, all your emissions, and and all the accelerated particles that come out of that is from this. But solar flares are a one-minute phenomenon. Okay, not 100-second phenomena. They could last maybe longer, maybe a thousand seconds, but they're not really that. But they onset in about a minute. Okay, even faster sometimes, but that's the rough order of magnitude timescale. So the first thing people did was, was scientists did was say, okay, there's got to be some sort of violation of the frozen-in condition. Let's take a look at this resistive term, this, this resistive due to collisions, times J, and and and calculate the, the time it will take to diffuse the across this field line. If you do that, you're going to get some ridiculous number. Okay, I think I put up here 10 to the 16. That's a high number. Some people got it as low as 10 to the 12. Okay. If you're an astrophysicist, being off by 10 orders of magnitude, well, heck, even an astrophysicist likes being off by 10 orders of magnitude, let alone an engineer. An engineer is off by a factor of like 1.1 or 95%, they're upset. I mean, this thing's off by 10 orders of magnitude. Okay, this really was a conundrum. This was a conundrum at the age that led to this idea of magnetic reconnection, perhaps we could transport the plasma in and have all this action happen in a much smaller region, much, much faster. And that was Parker's sweet Parker's idea that came up early on.

The next, the next phase of history was shortly after Dungey realized that maybe the Earth's getting its aurora from magnetic reconnection. It's opening up the Earth's magnetosphere. But this even created a bigger conundrum, because it's collisionless at the Earth. You can maybe make up some collisions at the Sun, you know, you can hypothesize and scratch your chin and say, maybe there's something going on, anomalous resistivity, or something. But this, this is very, very hard to do at the Earth. So this meant that was even a bigger mystery. And, and the problem was, it controversy raged on this at the time. People were really yelling and screaming in controversy. Rubbish, rubbish, right? And, and, and no, no, it was, it was true. I, I was at one of them where one person said, this is rubbish. And, um, it was polite yelling. So, so the, the basic idea then is, how is this happening? At the same time, people were saying fusion, which there's a new constant in the world. I always joke, 20 years, that's when fusion is going to break even, no matter when you are. Um, you will have break-even in fusion in 20 years. They said that back in the 60s. They were like, no problem, we got a tokamak, we're going to put it together, we're going to get fusion, right. But they had these disruptions called sawtooth crashes. And this was noticed in the early 70s. Okay, these sawtooth crashes, basically, it would get it all pumped up, they would start pumping in the magnetic, they would get the pressure up to the point where it could start to fuse, and then boom, all their magnetic field, the whole confinement just exploded, blew to pieces. And they call these sawtooth crashes. Guess what? Magnetic reconnection. So we love reconnection. If you're a solar flare person, I like it. If you're an Earth person, they hate it. Okay. Believe it or not, I would say magnetic reconnection, to a large part, is why we're still here with fusion, 20 years off, to a large part. Not, I mean, there's a whole lot of other problems, but it is a contributor, and not an insignificant contributor to this problem. All right. So I would like to say nowadays, it's evoked in the magneto-rotational instability around accretion disks. Yes. Oh, gosh, maybe I, I, I knew at one point in my life, but all I can only venture a guess, and I don't want all, yeah, crashes, yeah, yeah, it's a good, yeah, good question. But again, it's, it's an interesting. I will like to say that mag, it happens in gamma-ray bursters, pulsar nebulae. I'm not going to go, I'm going to go quick because I think I'm almost out of time. Um, five minutes here. So you could see magnetic reconnection event. Jack Gosling found them in the solar wind. Now we're finding more. I think, um, Parker Solar Probe finding them in the solar wind. So it is really a universal process that is really at the root of lab plasmas, solar plasmas, magnetospheric plasmas, accretion disks, gamma-ray bursters, almost all of astrophysics. It is ubiquitous. I don't like using that word. It's universal. Okay.

So the major question came down, and a lot of work started with solar physics on this, but how do we break this, this happen, this make fast reconnection happen? How do we take care of that 10 order of magnitude problem we have in the Sun? And it, by the way, it's like a 50 order of magnitude problem at the Earth. So really, you know, we really have a problem here. The first breakthrough really came on, well, we ended up, I'm sorry, I got ahead of myself. But the main thing you have to do is you cannot just sit here and sit on the resistive term. That's the first thing we thought. People tried and tried making anomalous resistivity. And every, we've got to start using all the terms in the generalized Ohm's law, which is the resistive term, the Hall term, the electron pressure term, and the electron inertia term. And each and every one of these are going to be examined over the next 50 years, over the last 50 years, to no end. The first thing it was found out is Hall reconnection can speed up reconnection dramatically. If we can include the Hall term, meaning we need some sort of small scale effect on the current. But it can't answer all the questions like it. If we use the Hall term, which is J cross B, and you dot it into J, E dot J is zero, so you can't release energy through the Hall term and so can't explain energy transport, um, very, very well. But it did speed it up quite a lot. PIC simulations then came in. PIC simulations are limited, though. They were mostly in two dimensions. Three dimensions were almost completely impossible to do. Um, so PIC simulations showed that that one thing I failed to mention here is that the, the Hall, um, simulation showed, well, we now understand what's happening on the larger scale, but there's this small scale region. So now have instead of one diffusion region, we have two. The larger scale one is the ion diffusion region, and the smaller one is going to be called the electron diffusion region, IDR and EDR. Okay. So the next thing that happens is that, um, PIC simulations start looking at the EDR. This went on and on and on. Um, we then had lab experiments, and I will say the Princeton lab experiments, the Milwaukee on, or the Wisconsin ones, and UCLA ones were extremely valuable in in helping us get to the point of understanding how this reconnection went so fast. By the way, Hall reconnection changed our solar problem from 10 to the 2 to 10 to the 4 or 10 to the 5. So instead of being 10 orders of magnitude off, we only three or four orders of magnitude. Wasn't the answer. Well, for astrophysicists, that was the answer. I mean, a couple of orders of magnitude was the problem, but for physicists, that was, that was an issue. So, um, it really wasn't until we got space flight and we got satellites into these electron diffusion regions that we actually understood that there was an off-diagonal electron pressure. I'm not going to be able to explain that very quickly, but pressure is not a number, it's a tensor. It's a 3x3 tensor, and it's the terms that are not on the diagonal that you're not used to seeing. This means that a lot of the pressure that was building up in this, in the, in the region where the diffusion region was, was being laterally thrown out sideways. It's like throwing on a moving object. You have a moving object, you want to get rid of this momentum, you throw it sideways without really getting rid of the momentum and let somebody else take care of it. That's essentially what that off-diagonal term was doing. But it wasn't, and these crescent distributions were, were found, and a lot of this was predicted, um, uh, earlier, but there were a hundred other predictions that were wrong at that point in time. So this ended up being a very, very, um, big breakthrough in magnetic reconnection. It's still ongoing. Do we understand everything? No, but I think we've gotten a huge breakthrough in trying to understand how we go forward with magnetic reconnection. A beautiful example of how heliophysics from the Sun to the interplanetary medium to the magnetospheres of planets all mixed together to solve a huge problem. And we also worked with lab. I must, I must say that lab, uh, experiments were large, large contributors. Okay.

I did it. Am I on time? Okay, I'm a little over. Okay, so take a, take a longer break. I could go shorter on the next one. So I don't want everybody to lose their break. Okay. All right, I'll take questions, um, um, after the break. Oh, it's a, a Q&A after the next talk. Okay, we'll do that. I, I pity you guys if you think this was hard to follow. Wait, I'm gonna turn on the speed. Okay, I'm gonna take you from sort of a tutorial to current research now and try to understand what's going on. All right. Hey, thank you guys for being such great listeners. And you could ask questions all the time. Just don't be afraid. All right, go take a break. Okay. Um, um, Nick asked me to start, um, since you didn't have many much chance to ask questions on the last, on the last section, if there are any questions, um, that you have on the last talk. It's a little bit, here's the problem, Nick, is that I don't have a last talk up, but maybe, maybe we could answer him. Well, I can wave my hands a lot. So there are questions. Are there any general questions here?

Yes, I have a few questions, but I, I'll just ask one. Okay, so first question I had was regarding the reflected ions, and I had read some papers that also talked about backstreaming ions from the shocks, but it feels like that is falling out of favor, and it's just the ions that are seen in the upstream are basically the reflected ions, and there is nothing that's backstreaming out of the shock. So could you please comment on that a bit?

Well, I'm, I'm trying to understand the difference between reflected and backstreaming. The backstreaming would go inside towards into the shock and then reflect, come back out of the shock. Well, I'm not sure that a measurement of reflected ions or backstreaming ions would be any different from the upstream point of view. Um, what I understand is, um, I, I really Gosling and and Schwarz and others have done a lot of work on this, and from their work, as I understand it, these reflected ions are critical to the energization. So some, um, hard to imagine, but as this is your shock, the ions are coming in and they get shocked, right? But they, they, um, they go through this, the, the magnetic field a lot faster than the electrons. So there develops an electric field that actually acts against the ions, and a part of these ions will actually bounce off the shock if they're not coming in at the right angle and the right energy. So a small percentage of maybe five, 10% of them will bounce off. But in that bounce off, they actually gyrate half a gyro period, okay, and they gain energy from dropping down the electric field. And the next time they enter, they can come back in. And so, oh, here's the part, one talk, not sure how to go fast forward on this, but, um, so the, some of the most of those then will, will actually blow through the shock, go right through the shock because they have enough energy. But that's part of the energization process in itself, as far as I understand. Um, here we go again. Where was that? Where was that picture of the clouds? There. So this is hard to understand. This is the solar wind core right here, as you can see, um, um, in this distribution, this a 2D distribution, and this is the velocity in the X direction. And so these are hitting and being gyrating as they come off. And this first cloud is the first reflection, okay? Since this is a log scale, it looks pretty robust, but in a linear scale, it would be pretty small. Some of those actually will, of the reflected ones, even though they've gained this energy, will hit again and reflect again and then go back down the shock with even more energy. And that is the second cloud here, okay, this, this one right here. Then there's a third cloud, triple reflected ion. That's what I understand. This, this model is just, I guess, from Schwarz and Gosling. Excuse me. They're, they're, when you get down to the detailed, um, physics, kinetic physics, these are very, very part and parcel to the energization. This is how the ions actually get energized. A lot of people, in fact, I did it once, thought it was just a squeezing of the magnetic field, the adiabatic moment conservation, but that is not enough. Okay.

So now backstreaming. I, I, honestly, I don't know the backstreaming theories. I can't imagine that there's there's I can imagine there's turbulence in the on the downstream side of a shock, and that that might send some ions back upstream. I am, I, I can very much believe that. I do know that in Earth shocks, which I have looked at data at, there's very little of that. We, um, if you go back in this, you'll see, um, these reflected ions, which are right here, these are the reflected ones. You see that right there? They really stop. I don't see them going on, um, um, much forever, right? Um, and that's a lot of gyro radius of the most energetic ion. So they, you know, you get fewer and fewer because this is gyro radius depending. I mean, they have to, they only go one gyro radius upstream of the shock and then come right back in. So that's a very good question. Um, I just don't understand what, I, I haven't read very much literature on backstreaming ions, so I'm just not an expert on that.

Could I ask a follow-up regarding reflected ions? So do you think that these could also favor the Petchek reconnection theory rather than Sweet-Parker, because we have shocks and they will get reflected and energized?

So, I, I think Petchek had a lot of great ideas, but we've never ever seen a real shock on the, you know, um, I, I don't want to poo-poo it just because there's no shock. The whole idea though of flaring was extremely powerful. He thought it was by be a shock. Um, it could be later on, but I don't, we don't see that on MMS in the near reconnection side. So, but it is Petchek, like in a lot of other ways. So it's just like physics. Some people, I mean, Sweet Parker is not correct either. They were using diffusion region, I mean, but still, it was an incredible step forward. Okay, and then we fix it up and fix it up and fix it up. We keep fixing these models. Very good questions.

Oh, we got two people over here. Oh, my goodness. Hello. Uh, so, uh, yeah, more about shocks. Um, so the MHD jump conditions don't, uh, tell us anything about what happens in the black box that is the actual shock itself, and the data here show how complicated it is. Um, but I was just wondering if you have a simple answer, zero-order, or kind of intuitive answer to the question of why don't the particles in a collisionless shock just fly right through each other? What is happening?

Well, there's two types of shocks. One are called quasi-perpendicular, which means that they're entering perpendicular to the magnetic field. Now, that becomes more obvious because they have to drift and gyrate. Okay, so that's pretty much why they don't intermix terribly well. Uh, and quasi-parallel shocks, basically, it's a terrible instability that occurs, okay, mainly on an acoustic driven, because the, the, this plasma is entering a slower plasma. And yes, they're mixing of waves and turbulence, and it's the waves and turbulence that that do this. There's a very good recent paper by, um, um, Trudinger et al. that shows how the magnetic fields bending and bending. So in part, what happens in a quasi-parallel, that's when the magnetic field is just going right into the shock. So it should be no mag, the magnetic field doesn't count anymore, right? Is, is the thought. Say, a demagnetized shock. The, the, the magnetic fields bent and curved, so that you actually get reflection, just like in a quasi-perpendicular shock, only it's nasty. Okay, it's very turbulent. Um, and, and I would say quasi-parallel shocks are very poorly understood at this point in time. Okay, if you like really, you know, dizzying problems, that's a good one. Okay.

Okay, because you, because you asked me that question, I'm gonna ask you questions now. Peter, then it gets even more fun when the IMF is radial everywhere, FY parallel. So I have a bit of a slightly more obnoxious question in terms of the implementation on your turbulence plot, you had broken up the B, magnetic field, and it was wibbly-wobbling everywhere, but you had segmented it into an average BZ of like positive and a BZ average of negative. And this is a really just random implementation question, how do you draw that line to be able to make that identification?

That's simply a, a, a, uh, um, an averaging routine on the data. We just simply take a smoothing routine and smooth the data. Let me, let me see if I could get everybody. Oh boy, what happened to that picture? Was all the way in turbulence. Oh, was all the way in the turbulent section. I'm going to actually going to talk about that. Okay, so why don't I answer that question, um, on my next talk? Okay, I think we ought to probably move on unless there's another burning question that, okay, I need, I can't hear very well. Okay, so, uh, just a quick question. If you're going to talk a bit about how all of this connects to heating?

Oh, I'm going to talk about how shocks, reconnection, turbulence, and particle acceleration all mix together in the next talk. Okay, but what did you, was that your, uh, question? I was curious about if you're talking, you're going to talk a bit about heating. Uh, oh, yeah, heating, that's acceleration, energization. Okay, um, I will be talking about that. All right. If you thought you were drinking from a fire hose on the first talk, we are now going to turn the fire hose fully up. Okay, so get ready. Um, I'm going to start by talking about the one thing I haven't talked about yet, which is particle acceleration basics. So this is a little bit of a, a quick review of what to look for in particle acceleration, of giving you some hints with adiabatic invariance and other types of things like that. So we'll just dive right in.

The really, a lot of particle acceleration started a long time ago, about over a hundred years ago, with the discovery of cosmic rays and, um, how these particles get accelerated to begin with. We, the first step was, of course, understanding this whole shower through our atmosphere, which is very, very complex. But in the end, when we go to space and we extract how many cosmic rays are, uh, what is the flux impinging on us, you could see that there is a very strong power law. The power law has this galactic, um, um, um, part of it, and then it has a little ankle. And these are considered to be extragalactic, um, or, um, extragalactic part of the cosmic rays because their gyro radii are so large that they could actually get out of our galaxy. Okay. So, um, below around 10 to the 12th or 10 to the 10th, um, this is where ions start becoming relativistic. And as you can see, this is both, both relativistic and, um, takes a lot of, of, and I mean, these are extremely highly energetic. So the question really comes, why aren't they Gaining? This was the first question. What is going on? In fact, this ended up starting all the research on a lot of the research on particle physics. We end up with accelerators and etc., etc., etc. So it branched off into another different, uh, whole field.

Before I, um, let me come back to this. This is maybe, um, um, um, something I want to talk about is collisions and collisional and collisional. So a lot, this is, I'm going to go back a long time and talk about what Fermi talked about. Fermi was the first one of the first people to really start seriously addressing the cosmic ray spectrum in this acceleration process. And you'll hear Fermi acceleration all the time. Okay, and it has five different meanings, but I'll explain that one to you. The basic idea that Fermi had is, let's just take a, a flux distribution, which is this, this flux versus energy, and I'm going to break up these, this flux versus energy into N, into a large number of bins, right? And go start from very basics. F would be simply the number of particles in that bin for the time being, and we won't even use flux, we're going to use number density in a region, integrated number density in a region, or number of particles. So if you take a look at any arbitrary bin in this distribution function, say bin N, you could see that it's going to gain its energy if there's energization going on from particles in in bin N minus one. So the particles in bin N minus one have slightly lower energy, and if there's energization occurring, they might end up jumping into being categories, you know, into bad. That's how it gets particles. Um, very, very basic, simple idea. The second thing is, there's two ways of losing particles. One is they could escape. Are we have to draw a volume that's bounded, and they could escape our volume bounded area, and we lose it. And it happens from all the bins, not just bin N, but and we're just concentrating on bin N. Or these particles can get heated and or energized, and they could jump into the next bin. Okay. So we're going to take a time step that's small enough that we're not jumping 10 bins or something like that, and and try to track this. So he basically just, you know, wrote down a very simple formula that the number of particles you gain is really proportional to the number of particles in the previous bin, in the bin lower, times the heating rate, divided by your bin size, times delta T. It's a very, very basic idea. Just do the, just do a, a dimensional analysis, and you can see that this is pretty clear. Then the loss will be the same. It's going to be the particles going, you know, that jump to the next bin, but then it has this, this loss function, uh, uh, escape function also involved in it. Okay, and that's the particles that escape. So you have to have the probability of escape. That's what P of E is. Okay. So you have to take into account the probability it will escape. And so this, if you say gain equals loss in a steady state, you get an equation that that that looks pretty much like this. It's just the gain equals the loss. Hold a second. Okay.

So here's that, that same equation, and, and, uh, what you can do is manipulate this. You see these delta Ws? You could try to put them all on the one side. And if you look at this, this looks, you know, and we do this in calculus. This is freshman calculus, right? You then take the limit when delta W goes to zero, and the limit when, and delta T goes out of there. And so you get this derivative of the, the distribution times W dot, which is the energy, uh, um, energization rate, DW time, energy must equal the escape rate times this, this, um, distribution F. This is a, a, a simple function. Now, there's a lot of solutions to this. But Fermi de, I looked at it and said that, you know, if the energization is directly proportional, the energization rate is proportional to the energy, which isn't the normal thing in the world. Okay. This means that the energetic particles are more strongly energized than the non-energetic particles. So that's rule one. You got to have an unfair energization process, meaning that, you know, I like to say the rich get richer. So we, we, I jokingly say this is capitalistic. You mean the rich people get a lot richer. They don't pay as many taxes, and they get a lot richer on that. If you have that, so it's got to be directly proportional. And then you have an escape rate that is actually even, it's the same for any given particle. Okay. Now, this is what he came up with. It's not the answer, but this said that if we have that, you have a solution that looks like a power law, which is what the cosmic ray spectrum looked like. And there's a power law index, and it has something to do with the, the one plus the, this, the, the acceleration versus time versus the escape time. And this was, this became, um, a controversy because in it, in its own, the acceleration time and escape time, um, of course, you could pick two numbers that would match the cosmic ray spectrum, but that was very unsatisfying. And Fermi himself wrote, this is not very satisfying, but it is a solution. Um, later Blandford and, and others, um, got much, much better, more detailed on these solutions.

So now I want to talk about the role of of ions a little bit. Um, um, oh, well, let me just talk about the, um, all right, I, I think I got it a little out of order. I don't know why this is. This was the latest at night. So what I'm going to do, I'm jammed. Is there a way of getting this to move? This thing's not working. Oh, there it goes. All right. So what I want to talk a little bit about are collisions. This cannot happen in a collisional plasma, say, say collisional gas or anything. Say we have an energetic particle that comes into this room, okay, that's an atmospheric particle. So we got, you know, we got some sort of oxygen or nitrogen into atom that's just going really fast, and it's way out in the end of the, all the distribution. What that's going to do is collide with something, and every time it collides, it gets taxed. It gives up a little bit of its energy. Okay, and that giving up of energy, it will bounce, and particle will bounce, it will collide again and again and again and again. And by the time it gets through colliding all this time, it's just one of the, one of the folks. You don't get any rich people this way. I call this socialism. I don't know. This, I'm just, I don't want to make it, I'm tenured, so I don't have to worry about all this stuff. But, but, but, um, um, the whole point I'm making is that is a distribution of energy. Gain is really a fair distribution of energy. Any particle could have anything. But if you have a collisionless plasma, it's, it's even worse because you're depending on Coulomb collisions. Coulomb collisions actually reduce with your speed. It's one over V to the fourth is the cross-section. So the faster particles don't have even less collisions than the slower particles, so they get taxed less. Okay. So if this were a collisionless Coulomb area, the fast particles just go zipping through and they don't pay any taxes. Jeff Bezos, Elon Musk, you know, they, they, they just don't pay taxes, and so they keep their energy. And this is an important part to cosmic ray acceleration. You wouldn't get that tail if there were taxes, if there were collisions in this. And that's because of Coulomb collisions. Once they get relativistic and get these high speeds, the Coulomb cross-section is just so small that they're not giving up their energy anymore. Okay. So that's the important part of all this is that Coulomb collision cross-section is really vital on all this.

Um, all right, so the next, um, um, so we can get this power law. And I want to point out, I want to say that there's two re, two things that we need. We need collisionless, no taxes, but we also need an energization mechanism that favors energetic particles. That means when there's some money available, the rich people get more of it. Okay, geez, doesn't this sound like people? And if, if it were a collisional system, everybody would get a random amount, but equal probability of an equal share. So this is basically how we get our power law tails on this. And this is the root of acceleration. If you had high collisions, you get a Gaussian central limit theorem actually works in that case, very, very well. Okay.

So, um, I want to talk a little bit about diffusive shock acceleration, which was the next step in all of this. The idea was, how, so Fermi thought, and a lot of people thought back in the day, and a lot of this, I think, came from Blandford, and there's another person, Axford, etc., that thought, how would we do this? How do we get an energization mechanism that favors that not only favors, but is slightly proportional to, um, um, the energy a particle already has? And the whole idea came from the shocks. If you take a look at a shock, you can map it this way, where there's an upstream particles ram in and go to a downstream. But let's go to a moving shock frame. If I move this frame, you know, rapidly this way, you could see that we have what appears to be converging, um, flows, but actually the shock is moving. So the particles are just building up in the high density area behind the shock. So don't worry about it, there is conservation, it's a moving, but in this frame, let's think about what happens. And this is what Fermi and Blandford and all the, and, and, and Axford all said, let's think about this, um, in this frame, when a particle, um, um, oh, I think this thing may be out of batteries. Uh, oh, oh, remove it to the, ah, you're right, you told me that. All right. So if a particle goes running this way and bounces off of this, it's like a, a ball bouncing on bouncing off a ping pong paddle or a baseball bat. The particle will come in with a velocity of, of say, U particle, and when it goes out, it has a velocity of minus U plus twice this incoming speed, okay, because it's bouncing off the bat. It's just, you swing a bat, the ball comes in, it goes out with its velocity, but twice the velocity of the bat speed. Okay, try it. You know, if you throw a ball in the air, it comes in with zero velocity, and it just goes off twice the.

velocity that you swinging on a bat, um, on the other. So then it, it will bounce back and end up on this side. And when it goes on this side, it will, uh, you know, gyrate. But because this, these magnetic field lines are moving, it will end up going with its initial velocity, but twice the velocity of the incoming of that speed. Each time it crosses the shock, it gains energy. It's always an energy gain.

This is beautiful because I don't know, have you ever, how many of you played ping pong and ever did this with a ball? You know, you can really accelerate it that way. And, and it's just basically like you're squeezing something, and it's just going faster and faster and faster. And this is called diffusive shock acceleration. It's a, uh, own simple explanation of it. People that made the theory are going to shoot me because there's a whole lot of other stuff to it. You have a question, Becca? Yeah, yeah. I should had ping pong balls or something like that.

So this is a, basically known as diffusive shock acceleration. It's been widely accepted as the, the way that we can get the cosmic rays. Not only that, but the more energetic particles are going to cross the shock more. And since it's a velocity gain, if you go to relativity, it ends up being that the higher energy particles, if you give them the same velocity kick, they get more energy. Okay, so now you have a part, an energization mechanism that favors high energy, already high energy particles. So this, this is just perfect. It works in almost all senses. Called diffusive shock acceleration going on with that.

Then the, um, the whole idea, I got to go backwards now. F-I-E-R-O-E acceleration ends up being, in my opinion, very confusing to most people. There are several different meanings of F-I-E-R-O-E acceleration, but it really is the idea of this ping pong ball underlying it all. But if you talk to other people, so this is energization that often involves a reflection of two objects moving together, or an object from an object. So you gain twice the velocity of that object. You can actually lose energy if the object's moving in the same direction as you. But, but that doesn't happen as often. Because when it's moving in your same direction, you just don't collide very well. When it's moving against you, you have the highest chance of colliding.

A common use, however, has turned out to be this acceleration in a reconnection zone where it actually goes through a curvature drift and, and, and bounces out of a reconnection, um, zone. I, I, it's been adapted. I stomp up and down in meetings, but I'm, I lost. Um, it has been adapted as, people just say F-I-E-R-O-E acceleration. And, um, then they say first order and second order. First order is what F-I-E-R-O-E acceleration is to begin with. Um, but in reality, involves multiple, multiple acceleration bounces. And you, you'll feast here now, hear me say, if you're looking at interplanetary shock or the Earth's bow shock or the reconnection in the Earth's tail, you don't get that many bounces. So it's very, very hard to prove that's happening in our environment. Okay. But if you go to a, a, a, a supernova shell, you'll get a lot. In fact, once you get out of one shock, you'll get into another. There's just no end to, to the acceleration. Okay.

So, um, multiple reflections can happen. However, the best use of it I've seen is in the article by Drake and Shay, where, where they show a collapsing magnetic island. Okay. Magnetic island can actually cause an electron to go back, boop, just really, and it will do it multiple times. All right. So that's the, the word I want to put in. What do we need? We need a collisionless media, and we need an acceleration mechanism that favors high energy electron. If it's just, if it, if it's heating, so I'm going to talk about this. Heating is just heating the core, putting something on you. You are going to gain, you just get warmer. That's fine. Um, energization is an overall term. It captures everything. Acceleration means that you're favoring something. Now, acceleration can also mean bulk acceleration and other things like that. So it's often, it's got dual meanings as well. So be careful when you use those, those terms. Um, all right.

Another way of accelerating or energizing, I should just call this beta-tri energization, is basically what they use in labs. You, you use your adiabatic environment. Use it, don't, don't fight it. Okay. If I were to take a plasma, I really wanted to heat it, and I put it in a chamber, crank up B. Okay. If I could crank up B by a factor of a thousand, its energy will draw perpendicularly by a factor of a thousand. That's all from an external energy source. Okay. So how does that happen in nature? Well, in nature, we have a factor of a thousand energy difference between outside in our magnetosphere and inside in our magnetosphere. So particles that are sort of forced in from the outside to the radiation belts gain energy because this is conserved. Now, the radiation belt people are going to shoot me because there's whistler waves and ten other ways that energization occurs. But this is a primary aspect of particle energization. It's called betatron. And that's called betatron. It's just simply magnetic pumping. If you pump the magnetic field up, you energize. One of the problems with having that is in a turbulent region is when you pump back down, it de-energizes. Okay. So one, the only way you could do it is to either pump it up and permanently keep your magnetic field high, or pump it up, allow them to escape, then pump it down, allow them to refill, pump it up. You can imagine that that's called magnetic pumping. But you have to give time for the particles, the hot particles, to get out after you pump them up, and then so they empty and then have time for the, you know, particles to refill when you, after you pump back down. And so it's not as simple a process as just that. But it is quite a bit of heating. And you could see this vast pumping. You can get almost a factor of a thousand in many cases as you move in towards the Earth's radiation belt. So that's, but again, those particles are going from a low magnetic field to a high magnetic field and not leaving it permanently there after that. All right. So that's a very important process.

Now, auroral particle acceleration involves two types, several types, three main types. We have the upward current region, the downward current region, and the alfenic regions. And I'm just going to go through this briefly. Um, this is an area I, I really, um, spent a lot of my early career working on. Um, but as we went through the aurora, we learned that these electrons that are causing the aurora, that are being accelerated down into Earth and lighting up our, our sky with the exciting oxygen, which emits a green light. So these are in high energetic electrons, are basically about a kilovolt that strike the oxygen, excite it, it emits a green light, 5577 angstroms, and that's why it looks green. Um, that acceleration process is by completely dominant in the, uh, in the upward current region, which is where electrons come down. It's by a parallel electric field called a double layer, which don't exist, by the way, according to people that, some of the people that I, I mean, I literally, I was one of the first people to support this, and I had tomatoes thrown at me all the time. But now it's kind of accepted, which is a good thing. Um, so parallel electric fields can form and accelerate particles. This is a very powerful mechanism that could cause a lot of interesting plasma interactions. Among it, I talk about it very much. However, um, the other thing can happen in the opposite direction. You could accelerate electrons anti-earthward and ions downward by having what we call the downward current region. The other thing that has been really interestingly found is that Alfven waves or plasma waves can strongly accelerate particles by resonance. It's like surfing. If you could pick up and catch a wave and you're out on the ocean, you, you know, drop in, okay? And that wave actually speeds up, it'll really get you some acceleration. It's like dropping down a wave and accelerating. Very powerful mechanism, um, in the aurora. So these are three more, two more really, upward and downward current region are the two regions of the aurora. But the acceleration mechanisms are both parallel electric fields. This pretty much the same. So there's the parallel electric fields and the wave acceleration. Now, Alfven waves aren't the only waves. There can be whistler waves, and there can be cyclotron resonances and other waves. But so we'll just say wave acceleration, and I'll wave my hands. All right.

Um, I want to talk about stochastic energization, though, because it's usually left out, and because it's called a second order process, and, and I think this is, um, way underestimated in the magnetosphere and in solar physics. Um, um, so I'm going to give you a little bit of bottom baseline on stochastic acceleration. This process involves random impulses on particles. Okay. So if I have a room full, imagine that our air here is ping pong balls bouncing all over the place, and I have a paddle, and I just swing it back and forth, right? And, and it was conservative, would those ping pong balls gain energy? Come on, swinging us back and forth. There's resistance. When I swing it, I go boom, boom, boom, boop, boop, sweeping ping pong balls. Some lose, some gain. I'm going to claim more of them gain energy than lose energy, and eventually the room will heat up. It's got to. I swing a bat in this room, just in this room with the air. If I swing it back and forth, I'm heating it up. I mean, you might think I'm cool with pan, but it's actually heating. That's called stochastic. In the re, what happens in stochastic acceleration is that you're going to, we're going to imagine this mathematically, that we get these impulses, delta B, that are just from a small correlation time, E times the correlation time, how long that electric field lasts. So if I take an electron or ion and I just give it a boop with an electric field, it'll gain some momentum, which is or or velocity. Now, I'm going to pretend it takes a random walk in V. Gets as many going forward as backwards and and sideways and everything. You can then calculate each time during this, what the energy change is. And the energy change is going to be one half M V plus delta V squared minus one half M V squared, where V naught was its initial energy or or velocity, and delta and V, V naught plus delta V is its final after you swung the bat, right? After got the impulse. Well, this ends up having two terms: one half M V times delta V dot, the dot product there, plus one half M delta V squared. Okay. One half M V squared drops out. That's initial energy. Drops out of this. That's the extra added energy. All right.

Well, there's two things. If it's first order, this term, that means it's not random. If V dot delta V averaged over a lot of swings, kind of like F-I-E-R-O-E acceleration, is not zero, we'll call that first order. But if we're completely random, like we are in this problem, that's a zero term. You get nothing on that because on average V dot, you know, if delta V is is completely random from V naught, you're not going to end up gaining anything on that term. But that second term doesn't go away. There's always a small energy gain. Okay. And this is the favoritism that happens, but it's second order. Okay. It's just if delta V is small, you could see it could be a smaller energy gain. All right. So when you average this over time and you want to get your energy rate, you you just take N bounces and then you divide that by period to get N times its correlation time. So you've got N waxes, and you can get this W dot, which is equal to the amplitude of the electric field impulses squared. And that's the second order. Okay. And that's considered small. Okay. But nonetheless, if you keep rattling something back and forth and back and forth and back and forth, you will end up getting energization. This is called stochastic energization. Everybody get that? Because this is important. All right.

So this, um, um, those are the basics. And I, I'm going to apologize to anybody whose favorite energization mechanism I left off, left out. I mean, like boiling water and stuff like that. But there are a number of ways of energizing particles. Okay. But where, where, where's the part where I talked about the, um, breaking of the? Oh, I think I did. I must have skipped the slide here or lost the slide. Oh, here it is. Um, I want to point out that in this slide, there's an important factor that if you want to energize something perpendicularly, it doesn't work stochastically or otherwise unless these impulses, um, these electric field or the correlation time is much less than the gyro period of the particle. Do you see that? So it's hard to energize electrons because they're driving, they're going around like this really fast, and you have to give them an impulse that's faster than that. If the impulse is slower, that first adiabatic invariance conserves. If it's faster, you could break it in and accelerate things perpendicularly. So this is an important concept. All right.

So, um, the next thing I would like to talk about then is, I want to give you just a quick, simple picture of magnetotail reconnection. I'm still staying simple here. Um, I think, um, this is what the Earth looks like, very quickly. You have reconnection on the subsolar side, and, um, you have reconnection in the tail. And, um, I, I, there's a lot of interesting physics here, and I've done a lot of work on that. But I also more recently working on the tail. So, um, it was a lot quicker for me to do some tail stuff. This all applies anyway. But we found some exciting results with reconnection. So let me tell you what the big picture on magnetotail reconnection. The Earth's magnetosphere is kind of like a, a spoiled child. Okay. The front side reconnects, and that magnetic field then, by the Dungey cycle, remember France dance goes to the tail, and it should reconnect in the tail because you can't to conserve the magnetic field. But the tail says, no, I am not going to reconnect. Okay. So that's your spoiled child. Okay. So what do you, you know? And the reconnection keeps happening and happening and happening, and the tail keeps saying no, no. Okay. Then it gets so much pressure, right? Parent, and that it explodes. It's, it's explosive, and it goes off all at once in five or ten minutes, and then it restores to a quiet tail. Okay. So you got to understand that it's not steady state, it's very impulsive. And what happens is as that magnetic pressure builds up, you'll start to get a collapse point right here in in the tail. I'm going to put MMS right back here or some satellite, right? And you can see you got this anti-parallel magnetic fields now being jammed together. You're setting up for magnetic reconnection in this, in this area. Boom, the reconnection starts to go off. There's your diffusion region right here. Okay. You get your ion jets coming out. And if it's inside earthward of a satellite, you'll actually see the ion flow going tailward. And this, this is now the reconnection occurring. It's exploding in there. The next thing that happens, though, is a reconnection region doesn't like staying. This is an important point. It doesn't like where it is because there's a stronger magnetic field on the Earth's side than on the tail side. Maybe that's a good reason. That's kind of BS reason. But it, the, the, the reconnection region retreats tailward. That's just an observed fact. It goes tailward almost every time. And it will pass over this, our satellite. This is a good thing. Everybody knew that. So if you could set a satellite back there, I'll go forward, you could set a satellite right here, you can actually capture the reconnection region waiting for it to pass over by you. Now, unfortunately, it could pass to the north of you, to the south, to you, but sometimes it'll pass right through you. And that's a good thing. Okay. So that's how we see this tail reconnection. So when you want to look at data, you have to be very, very careful about how you, you view it. Yes, I would like to say that they're not very symmetrical because the things is retreating. So you'll find the, you would think the tail jets should be stronger, but they're not. The earthward jets are the higher velocity one. Don't know why. All right.

So keep this picture in mind when we talk now, because I'm going to talk about electron acceleration in the tail. So this is the culmination of adding turbulence, reconnection, and acceleration. So now we're going on to taking those three things I talked about, reconnection, turbulence, and acceleration, and putting them all together because they're inseparable. Okay. Reconnection begets turbulence, which then causes small scale reconnection, which causes more turbulence, and it's a vicious circle until, and that's how the plasma chooses to release its ex, its free energy. So I want to talk about electron acceleration first. So I'm going to talk because there are two different processes here, and I want to talk about a very interesting event that occurred actually near in a recon, not in the reconnection site, but in this reconnection jet that's going earthward. So we're going to start by, um, uh, talking about this reconnection jet going earthward and slimming into the Earth. It actually will stop and divert. It has to, once it gets towards the stronger magnetic field, and we see that going on. So I want to show you what a reconnection jet slamming into the Earth looks like, and I'm going to show you some data now. So let's go through this slowly. Um, this is a multi-panel plot. How many panels do we have here? Is ten? Okay. Um, this is measured by the MMS satellite. The top panel is the magnetic field. Now, you, you can't really see it, but, um, the fact that we're in, we have a BL, the blue line, which is the X-directed field, which is the sun-directed field, okay, is negative. That means that we're in, uh, oh, dear. Sorry, pushing operator here. That means that we are in the southern lobe. Okay. That means we're south. If we weren't south, we'd see X positive. Okay. So that's how one, one of your first things you're going to learn to interpret the data. It's pretty strong. We're pretty close to Earth. We're only about six R-E from Earth in this case. We're really where this reconnection jet is coming in. Now, this is the detrended magnetic field. In other words, this is just delta B. So you could see it, it's gone turbulent. You can't see it in the original signal very well because it's so large, but you can see strong fluctuations in the magnetic field right here. Um, yes, we, um, you do the opposite. You put a high pass filter on it. You just take the data, you know, high pass and low pass filters. We could do that to data. You're throwing away the DC. We call it detrending. It gets rid of the baseline and just looks at the fluctuation. Time scale is ten seconds, if you really want to know. Okay. So I also want to point out, along with this strong plasma turbulence, right between these lines, you're seeing the electric field light up. Remember I say when you see all these squiggles, I don't want to go, you're going to have a turbulence talk later on, so I'm not going to go into all that. But squiggles mean possible turbulence like that. So these are very, it just lights up in between those lines, just everything lights up. Um, you also can see that magnetic field turbulence. What happened here? Ion acceleration and electron acceleration. Where is the? Yeah, okay. Well, I skipped a few slides, but here goes. You also see at the same time, huge amount of ion acceleration, a huge amount of. So you see how these, these particles are going to, are, are really starting to heat up here. Look at the temperatures, which are over in this region. The ions and electrons are both heating up rapidly. Now, interestingly, they're going to cool a little bit, but we immediately enter here on the right into the radiation belt. So those particles are not being accelerated. They're already accelerated. We just, we just fell into them. But these particles here, um, where we're right between this, are being locally accelerated. This is all occurring locally. All right.

So if you're a turbulence person, all turbulence people do is they take spectra, they take an FFT, and then they have a com, they have a Kolmogorov slope, which is five thirds, and this is right here. This is five thirds. And then they have a spectral break where it goes into the dissipation region. This is called the inertial region, and you're going to learn all about that. So you go, ah, turbulence. Okay. So I'm going to go, ah, turbulence. But there's also a very strong, the electric field doesn't obey the standard turbulence. It actually has a shoulder on it where you have a huge amount of electrostatic activity going on in this region. All right.

So what happens with these, this, um, um, electrostatic region? If you look carefully at the electric field power spectral density, this is the power with respect to the frequency. And you go to the electron cyclotron frequency, which is right here. A little bit of power down there, but that is nothing. How are you going to heat electrons? All the power in this spectrum is below, well below the gyro period of an electron. So if you know about adiabatic invariance, you'll say, can't heat electrons. The electric field has to do it. Magnetic fields because V cross B is is perpendicular, always. It can't energize. So how you going to heat these electrons? Anybody know? What's the idea? We see the electrons getting heated. So how is this happening? There's no energy at the electron cyclotron frequency or above. We're going to go and use our friend Doppler. The electrons move very fast. So the first thing we understand about turbulence is turbulence cascades things down to small scales where dissipation could happen. So we're going to measure the scale size now of these electric field impulses. Okay. This means that if you have a very small scale impulse right here, just sitting here, and the electric is whizzing, you know, it's just really fast past it, boom. If it sees that in its frame as faster than the cyclotron frequency, it can gain energy. So maybe if these things are small scale enough, they can energize. And that's essentially what's going on. The turbulence naturally does that. And right here, if you, so we would immediately take all the power here, here, and try to cross-correlate it between, we have four spacecraft, and try to find the correlation length between these measurements. And we can't. They're completely decorrelated. Okay. And so it's a null result. But that means that the correlation length has to be, can't, it can't be 15 kilometers because that would be out of range. It could be ten, maybe five, or anything below ten kilometers. In this case, electric, how fast can an electron travel ten kilometers faster than its cyclotron frequency? That's all we need. Okay. So you have a bunch of electrons traveling so fast that they are getting batted back and forth as they travel through different correlation zones. So the electric fields this way here, it's this way here, it's this way here. Right? Imagine an electron pair traveling along the field lines, just get to get whap, whap, whap. These are the impulses of stochastic energization. Okay. The interesting thing about this that you're going to like, you know, these are two diagrams. This one's a little harder to understand. But let's just think about a gyro period. If you have a very low energy electron, its gyro radius is not very large. So it basically sees the same electric field all the time. It does not get energized. The high energy ones, though, the faster they move, the faster their gyro radius. Now this one's getting whacked this way, then this way, then this way, then this way. It's getting energized stochastically because it has high energy. Now, remember what I said about F-I-E-R-O-E acceleration and creating a power law? What do you need? You need an energization process that is favors energetic particles. Wow. So turbulence not only creates the environment of the small scales, it is capitalistic. Okay. It creates the environment where the rich get richer. And that is essentially going to form a tail. You could take a look at the distribution functions before and after of the electrons in this event, and you'll see, see that before you see a core of about 1.7 kilovolts. After the core is 1.7 kilovolts. It didn't change. That's what we expected. The only, the fast moving ones. And now look what happens. This whole tail gets ripped out. Look how big that tail gets. It's all the energetic electrons being, being energized more. We're seeing this. So turbulence turns out to be a natural energization, um, um, way for electrons. Now, we put this into a test particle simulation, and sure enough, we get a very similar result on that. So the lesson learned here is that turbulence and stochastic energization can be very powerful. The reason being is those electric field amplitudes, huge. The mistake most people made early on in just ignoring this was they thought delta was going to be on the MHD equations. But the actual electric fields that we see, these wave spikes and all this stuff, are either one to two, a factor of ten to a hundred higher than the MHD would predict. If you're a factor of a hundred higher, heating rate squared, it's a factor of ten thousand faster. So now stochastic energization, which used to be very low and doesn't count, is dominating. Amazing. So turbulence can be a very, very powerful energization mechanism. So that's the one thing we want to talk about. By its very nature, turbulence cascades electric field power to smaller and smaller scales. That's what this shoulder is. Uh, we're not moving very fast. So in our frame, that's all below the cyclotron frequency. But in the electron frame, they see impulses, particularly the fast-going electrons. They'll see a lot of impulses faster than they gyrate, and therefore they get tremendously energized. This explains that energization we're seeing in the electrons. All right.

What about ions? Okay. So ions have a whole different story. They actually are, mu is not a big problem on the ions. The ions, they're like rhinos, and electrons are like the flies around the rhino, right? The electrons are going, ions are 2,000 times heavier. They're basically going boom, boom, boom, boom, slowly around this magnetic field. And impulses above their free gyro frequency are not uncommon. So we don't have a problem. They should just be energized to no end. Um, so you would think that. But here goes again. Now I'm going to talk to you about this event. Um, the top panel are the ions, um, um, and this is the energetic ions, and this is the thermal ions. First off, the thermal ions just disappear during this event and go all into the energetic. This is hundreds of K. This, we call this local acceleration again. The electron, you could see, or, oh, they're about a kilovolt, and then boom, they get very hot, and then they come back and cool. I like that. There's, there's an encore event here. Here's your magnetic field again, wiggling and waggling away. It's turbulent. Electric field at the same time is turbulent. And the density drops out in this case because we're very, very near a reconnection site. All right.

Now I'm going to show you how you see a recon, how do I see the reconnection site in this data? Well, I'm going to talk about that. You look at this flow here. Remember this diagram where the reconnection starts earthward, passes over MMS, and then goes tailward? So we should see an ion VX negative on the ions. We should see the, the, the, um, um, ion velocity going tailward. Well, look, there's the ion velocity being negative, negative, right in the beginning of the event, right when it crosses zero. We call that a flow reversal. This is right here. We hit the reconnection site, and then the ion velocity goes positive right here. So in the beginning of the event, just as expected, the reconnection event is just sliding tailward. We see magnetic rec, we see that earth, the, tailward jet, the reconnection site, the ion jet. So all this is related with reconnection. You could also do this with the BZ component, but I don't want to get into that. That's very tricky. So, um, the idea here is that we have a magnetic reconnection event, and it's evacuating all the density but superheating the ions and super energizing the electrons. So there's tremendous amount. I'm going to claim this is stochastic energization by turbulence again. All this F-I-E-R-O-E acceleration just isn't occurring here in this particular event. Um, so I'm showing the energized particles and the flow reversal, and we talked about the turbulence. So the way we go about understanding this was is it's very difficult to simulate. We would love to get a PIC simulation, but, but just for a lot of reasons, it's almost impossible to have this vast scale size and the vast number of scales we're dealing with. We're dealing with from 16 Earth radii scale all the way down to a kilometer. That's many, many orders of magnitude. So we're going to use a test particle simulation domain when we attempt to answer this one. Um, in doing that, we, we just make a box which encompasses this, uh, reconnection site. And we, what, what we're going to do on this is we're not going to make it self-consistent. We're going to do more like particle trajectories, but we're not going to be that simple. We are going to take the measured electric and magnetic fields and we're going to reproduce those things in the simulation domain as a function of time, everything correctly. If we don't do that, so we're going to try to make a realistic environment. So we're going to make the whole thing shaking and kind of random and all these waves in there in this box. And those are imposed. They're not, they're, they're drawn from the data, recreated because there's a lot of things we have to do and a lot of explanations. So it's not perfect, and this is not self-consistent. Okay. So the reaction of the ions from these is not necessarily feeding back into the, don't me. So that's the downside of the test particle simulation is lack of self-consistency. Um, this is a tool in our toolbox. We'd love to be self-consistent, but we, you know, this, the simulations actually have two bigger problems to do this. What for one, they can't get the proper mass ratios, um, and domain sizes, and they can't have fully open boundaries to do heating escape. You've also learned is, is part of the formula for how particles heat, just importantly, how they enter and escape. So the ions have to be freely, freely entering and escaping this domain in order to have this work. All right.

So we started by making this box, and we were having a big problem when we started this. We didn't know how long the X-line of reconnection was, and no clue. When we were like, okay, is it ten R-E? Is it one R-E? What is it? We can measure everything else. We can measure the size in, in the X direction and the Z direction, which is north-south, because we know all these numbers, we've measured them, had those nailed. But we had no clue on the width. So what we did was we turn, made that a knob. We just kept turning that knob. And lo and behold, when we turn that knob to an X-line length of about two or three radii, we could take the measured particle distributions, which are the points here in purple and red, and the simulation particle distributions, which are these circles going like that, and match them quantitatively, which was amazing to us. Okay. So this match was forced by turning that knob. Okay. I wish we could have just said, oh, we knew it's two Earth radii, and this proves everything. But we couldn't. So we're going to throw Spritz, the ions in, let it run, get distribution functions out, and then keep turning that knob till we get the right place. Not only did we get that, but you could see in that, once we, we turn the simulation on, the particles get really hot. This is stochastic heating. We take all of our data after the particles have been already, you know, everything settled down. But you could also see in space, we get that density depletion, which was, if you look carefully, is clear in that data. Here's the, here's the density depletion occurring right there. We get the same density depletion. So this is beautiful. We can really, gives us a lot of confidence that we have done something right. Okay. That's all I could say. I mean, we haven't answered any questions, but we can else look in and see how those waves are heating the particles. And this is in a paper by Seod, all, who was a grad student here at Colorado. I think he's not here anymore. I think he's gone to Arizona somewhere. But the idea is that the other thing we could do with test particle simulations is we could turn on and off the turbulence. We could say, okay, no turbulence. Hit a switch, it's off. What happens? Well, everything's pretty well behaved when we do that. The particles come in and they gyrate. You can see their orbits. These are ions. And some of them actually F-I-E-R-O-E reflect and gain energy from the reconnection. So we're looking at the F-I-E-R-O-E acceleration from, um, um, the reconnection. It's almost zero, by the way. It's just, just almost negligible. There's another type of energization I don't want to talk about too much, but ions can be demagnetized right at the current sheet, and they can actually travel along the reconnection electric field, and that's called spitzer acceleration. I wish I had a lot of time. It's a wonderful process that started that, lo and behold, was very strong. Okay. And that was the first thing we learned is that spitzer acceleration, something I haven't even talked about, was dominated, not the F-I-E-R-O-E. The other thing is that when we start turning on the turbulence, oh, went back and forth here. Um, when we started turning on the turbulence, you can see there was a dramatic difference in the trajectories of the ions, particularly when they came near the current sheet. They all started winding up and getting energized a lot more. So that process became clear that it was not only the stochastic acceleration, but something was going on at the current sheet where the magnetic field reversed. I don't know if you know this, but magnet, you have a reversing magnetic field. Think of an ion that will gyrate one way here and the other way there, and they can make these figure eight orbits. They're called spitzer orbits. Okay. And they're very, very complex and chaotic. But this turns out to be where the energization was taking place with the ions. And so a clever way of putting this together was to say, if we have no turbulence, and we want to look at the amount of energy gain, which is here as a function of actual displacement of a particle, beginning to end along Y, and we plot every particle, these are actually dots of every particle. With no turbulence, the black line, of course, it's conservative. The only way to gain energy is to travel along the reconnection electric field. So it's conservative as a straight line. That works. Then when you turn a turbulence on, everything happens. But here, look, there's energization. All right. But you don't get a tail, nothing over 50 or 60 Kev. When you turn turbulence on, you get those 100 Kev electrons that we saw. So it's almost dominated the energetic tail. The acceleration process is dominated by the stochastic turbulence. The, um, another way of looking at this is to slowly turn up the turbulence amplitude, just crank that knob slowly, and see what happens. With nothing, you get a little bit of energization, which is right here, which is from that spitzer energization. And then you get very little, um, energization above 80 kilovolts. In this case, we just, it's an arbitrary number, but it's, it's picked. And then as you turn the knob up, this just shoots. It just goes way up. Okay. So as we increase and increase the turbulence, and not only that, it's quadratic right here. You see this quadratic fit. That's the way it should be. It should be E squared. For some reason, when we overcrank it, it, it goes flat. But that has a lot to do with the escape process. Okay. Once we turn it too high, these things just escape very, very rapidly. Okay. So this is forefront research. This isn't common. This isn't the most, um, um, um, you know, this may or may not be, um, incredibly important. But I just want to point out this is all due to a mixture of reconnection, turbulence, and acceleration processes going on. We can't separate them. Do you see that? We can't separate them. And we're only now starting to scratch that surface. So all these processes are very nice. I, I laid them out to you. A shock, but a shock can't be separated from turbulence. Reconnection can't be separated from turbulence. Um, uh, shocks and reconnection, I mean, you see reconnection downstream of the shocks. So all this is a whole system. And that is the challenge. I think this is the next big challenge is trying to make a big step in physics and really understand what the role of turbulence is, what the, you know, how reconnection and turbulence, um, energize particles. And I think this may play a huge role in cosmic ray acceleration. Now, we've just learned a bunch of lessons. Old lessons that that F-I-E-R-O-E said, you know, 80 years ago. F-I-E-R-O-E said, you need an energization process that favors energetic particles. We found that turbulence supplies that. Okay. You need, um, a collisionless plasma, Coulomb plasma, so that the particles aren't taxed after they're energized. We found that that's what's going on. Those are the two main roles. This, but I also want to point out because I see a lot of papers with published spectral indices and make a big deal of them. They are not only an energization, but they're an escape process dominated. And so I think a lot of misinterpretation. So be careful when you publish a spectral index and remember it is influenced equally by the escape process as it is by the energization process. That's P-E-T, P3. This is what we're going to go. Where we're going next. All right. That's it for me. I actually finished on time, two minutes. So why don't we take a, a, a, a break, um, so I could get my voice back, and, um, then I'll answer questions, um, at your leisure. All right. So why don't we come back in ten minutes? Perfect. Huh? Okay. Can everybody hear me? Yes. All right. By the way, I get to sit down, don't I? Oh, sure. Right. I, I don't have to. I like, you could do whatever you want. If you need to sit down, sit down. All right. You can either ask a lot of questions or have an early lunch. Your choice. Peter, so, oh, yeah. For the, uh, electron, um, energization, the stochastic interaction, you're talking about how that relied on Doppler shifting. I was just curious, uh, specifically if you were referring to the, the parallel velocity of electrons. It could either be the parallel or the per. It doesn't, um, you need one or the other. Um, there's this second diagram, the one on the right, is more complicated. If you're traveling parallel to the field line and you have a high parallel velocity, you'll go into different correlation zones, and you have a correlation, parallel correlation length, of course, but you're going into different perpendicular energy and parallel energy correlation, you know, V parallel, the res, and so, yeah, the whole idea is that the, the electric field turbulence has gone to small scale, not necessarily high frequency, but small scales. So if I chop the electric field up again, it's pointing this way here, this way here, this way here, and an electron goes zip through it, it will go, it'll feel boom, boom, you know, I'm going this way, then this way, then that way. It's like a bumpy road. Okay. If you're driving a car down a bumpy road and you go very slowly, the bumps are at low frequency. If you go really fast, high frequency. Okay. So it's, think of a bumpy road. Now, the parallel one's a little trickier, that's the diagram on the right. Um, but in either case, the faster you travel, the more energy you get. And if you, get either Usov and Urgan or Urgan and Usov, we explain that process B parallel, per, and they turn out to be about the same. Um, the perpendicular one's a little easier to understand because of the gyro radius, and we could do a 2D diagram. The parallel one takes a 3D diagram, which makes it extremely difficult. Okay. Yeah. Maria Th made all these pictures best she could. I think they're pretty good. Good question. Yeah. Uh, in initial MMS, uh, period, there, there was some observation in a magnetotail region of some phenomena called as current sheet flapping. And there are also some signatures of acceleration of electrons and ions with that current sheet flapping. So what type of mechanism was there for acceleration of electrons in the vicinity of current sheet flapping? And another question is about, uh, there are some flux ropes, some flux tubes, magnetic islands or plasmoids there in the vicinity of reconnection regions. So how do particles affect that magnetic islands and fluxes and all? Yeah. Um, I carefully said, don't yell at me if I missed your favorite mechanism, um, because there are about 50 of them. Um, as far as the flapping is concerned in the tail, um, that's hard to tell the difference between just turbulence and flapping, because isn't flapping sort of the beginning of turbulence? So that would be, we, we have words. There's waves, and then there's turbulence. Turbulence basically is when the nonlinear terms start to dominate. And if that flapping starts to have nonlinear terms, you will get electric fields going, and you will get the stochastic acceleration, particularly of the ions. Um, so I, it's a, it's a cousin. It's certainly a cousin of what I was talking about. The other thing I want to mention is that these regions are very small. Okay. So if I go to that data, which I just showed here, of that, um, energization, this is a very tiny region where everything lights up. Um, I want to point out something. There is a very subtle point in this that some of you may have caught or not caught. You see these, these electrons before the event and after the event. Now, are they being locally accelerated? Are they just there because they were accelerated somewhere else? The way you could tell is by how choppy this is. During local acceleration events, there's tremendous amount of structure in difference in the electron distributions because they're being actively accelerated. These are cloudy looking. You see how they're cloudy? Just sort of the same. These are being accelerated somewhere else. The problem then is, do you'll see accelerated electrons and ions all over the place? Sometimes you'll see accelerated electrons and ions like, like right here. There's nothing going on. Nothing. Okay. That's because they're leaking. They don't go away. I mean, they, they exist. These regions are small, but they create electron smoke all over the room. So let's just think of it as the fire. Say the fireplace is this, this electron here. Think of smoke all over the room. But you'll see the most intense smoke right by that. You'll see a little difference, a lot more action in the smoke, whereas in the rest of the room, it'll be more evenly distributed. So think of the electrons as smoke, and the turbulence is the fire. Does that make a lot of sense? So you'll see a lot of correlation studies kind of getting off kilter on this. Um, it's really hard, hard thing to nail down. A lot of work left to do. B on this, on this, um, uh, uh, stack plot here. I just wanted to check on the time scale. The time scales are, that's, that's hours and minutes. Um, yes, so that, that's, that, that is, um, uh, one hour total time scale. And this event here is about 16 minutes. Yeah. Do you know 16 times 60 times 400 kilometers per second to get a L scale from from? Yeah, yeah, you could get a scale size along with. Right. Actually, I guess in the tail, I don't know whether what we, we estimated 16 Earth radii extend of the region. Yeah, pretty long. We're way down tail. So and it, it probably is expanding as we're, you know, as time's going on. We get a little oncore performance of the jet, the earthward jet later, somehow went off of us and then came back on us, which is kind of nice too. I love the encore on that. I, I was wondering for F-I-E-R-O-E acceleration if you

Have two moving shocks moving towards each other and a particle bouncing that continuously bounces back and forth between them. Is there a way for that particle to escape through the shock or does it?

Well, yeah, escape is even bland. I mean, as I was trying to tell something, FM's original papers, oh, he, he was very dissatisfied. He even wrote that in his paper, very dissatisfied by his acceleration mechanism, even though it fit the cosmic ray and everybody was celebrating it. Won a Nobel Prize, but not on that, on other things. Um, the, the, this is a very messy process. It's, it's just not clean. The particle goes back and forth, it jumps from shock to shock. There's turbulent shocks all over the place here. If you ever looked at a supernova shell, um, somebody asked me to prove that this was turbulence and I almost, oh, going the wrong way, going wrong way. If you ever look at a supernova shell, I mean, it's j.

And so the reason that this FM acceleration is hard to see in heliosphere, so this is one thing that we don't see very well in heliosphere is FM acceleration. Um, this is something like 10,000 parsecs. It's very old and there are probably 10 to the 10th shocks in that small little shocks. So the particle bounces back and forth in one shock and then squirts out to another shock. So escape is actually what FM would do or Blandford did would say, let's just take the whole darn thing and and not worry about things. So yes, the escape process is extremely important. How does that particle escape? Well, if the shock's like this and it's bouncing along the shock, maybe the shock ends and it's gone. Maybe it simply goes, the magnetic field changes and it travels along the magnetic field right out of the region. Um, again, this is highly stochastic and it's highly variable. Um, but the only way one can do it properly is with simulations. I defy you to simulate that. Um, that would be extremely difficult. So there's a lot of work left to do on this.

Um, my point is, I think diffusive shock acceleration is very well accepted because there are shocks. Um, supernova shells have the energy to create that cosmic ray spectrum. Is an energy source, the supernova explosion. Um, there's big differences between early stage and late stage. I should say there's two shocks on a supernova, forward and the reverse, but my opinion is is that there's just one. There's just a million massive shock, small shocks. So your your question is very good. I mean, this could happen temporarily and then the particle can go and get trapped in another shock doing it again. Um, some can lose energy, some can gain energy, but in the end, you get this cosmic ray spectrum that is not just from one shock or supernova shell, but from the pretty much, I think 100,000 or maybe no, no, 10 million supernovas that have expected to occur in our galaxy over the history of the universe. There's a lot of supernovas, okay? Um, you you don't think so, but there are a lot of stars and a lot of supernovas. Um, particularly early on. So this is actually a very robust theory that that, um, I think is very well accepted.

There is a a problem with it. It's called a supply problem. Um, and that's where I think turbulent acceleration may may take a a very large role. Um, the supply problem is is that this whole diffusion of shock kind of falls apart unless the ions are already up to about 10 to the 12 EV. They have to be relativistic and already accelerated. So then the problem is, how do you get the ions up to 12, you know, from the our our temperature, 10 to the four EV to 10 to the 12? And that may be where the turbulence plays a huge role in my opinion, but that's very speculative and you'll get shot if you repeat that by some other scientist, I'm sure. Does that answer your question or or or yeah, yeah, thank you. Okay, at least we talked about the energization processes, but I was wondering, so I do not understand uh, the energy dissipation processes very well. So in the sense that what is fundamentally different between wave energy dissipation and something like magnetic reconnection turbulence? What, what is fundamentally different about?

You're you're when you're going to hear a turbulence talk and and they have different language. Um, then, um, um, in some senses and turbulence, so the word dissipation is a loaded word, okay? Um, in in U fluid, if you take statistical physics or fluid dynamics, right? Dissipation is the act of changing free energy, like flow energy of a particle or magnetic energy or some other energy source into thermal energy. And thermal energy means there's an increase in entropy, okay? Um, the point at which entropy increases in a collisionless plasma is kind of questionable, but let's, let's just accept the the concept of this, okay, which is a very powerful concept. Um, so dissipation is just the, is like energization. It's you're energizing, you're taking what was collective energy, you know, like a ram, a a particles flowing into a shock, that's collective energy, that's one half, that's kinetic energy, and that ultimately ends up being rendered and increased. Um, thermal energy, temperature goes up, for example, and that's classical fluid dynamics. When you get into the particle aspect of it, which is creating this the kinetic aspect, which is creating this accelerated tail, the accelerated tail and the heating of the core are both dissipation in a way, right? Because you're taking free energy, magnetic energy is the free energy source in reconnection, the ram energy is the free energy source and shocks, and you're creating a hotter plasma, and that's dissipation. So turbulence doesn't sort of distinguish that. They like to talk acceleration versus heating. They just love to talk about the dissipation, which is just really the energization of the, you know, random energization, the increase in entropy. And, um, um, that there, one and the same. When you get into acceleration, which is what I'm talking about, we want to understand that energetic tail. We want to understand why it's not Gan, which is a whole different, a little bit of a different animal than than what general turbulence goes at. That's why I'm emphasizing that the turbulent people, people seem to skip over that part that they actually are a very good accelerator, not just Energizer or dissipator, but accelerator, which is different as the formation of the tail. That helped.

Thank you very much. Might have said, but, um, do we know why the the reconnection region in the tail moves anti-sunward? Uh, why it moves tailward? Okay, so you asked the question, why does the reconnection move tailward? I've heard a kind of a, I hate to say it, but BS answer that that it's because the magnetic field's so strong at the Earth that there's, you know, going to be a force going backwards on it. I really never seen the reason for that. Um, I'd hate to speculate why. I don't really understand that. But I do know for that observationally, we've had Cluster, Geotail, Poe, I mean, a number of missions now go out the tail, themus, and now MMS, and we almost always see this tailward motion. And it probably has to do with some imbalance of the magnetic field being stronger at Earth and weaker in the tail, but I, I really couldn't have something to do with that, but I can't give you a push-pull explanation. Um, on that at all. And a lot of people just say momentum conservation. I, I'm to to me, it's, it's, it's a very interesting fact. It would be really nice to understand why. What push-pull turbulence? I mean, the reconnection regions don't have to move. I mean, they don't have to. There's no reason for it. In Jupiter, they probably don't move. So it's a bad question for France because she's going to go, Earth, who cares? Jupiter, they don't move. Why do you get? France, she's great. I mean, we're really good friends. So, you know, I, I could, I could tease her.

All right, I think it should be our last because I don't want to hold up lunch, otherwise I become very unpopular. Do we have another question? Yeah, I had a question. Hopefully it's, um, you talked about like sort of two different energization mechanisms, either like stochastic or resonant, particle acceleration or heating, and primarily about like, the the tail getting accelerated. But I was wondering if you had thoughts on whether those could sort of occur simultaneously? Like one mechanism energizing the core, a different one? Or do you expect? Oh, yeah. The same mechanism throughout the distribution function? Yeah. I hope I, I understood this that when I said the stochastic is dominating in these events that we've seen, and that's the new result. Um, there's also SP energization, which I really haven't talked. I should have talked more about it. Um, there's Fermi acceleration going on, but as I said, it was surprisingly weak, but it's contributing. Um, there's a little betatron pumping. There's actually a some betatron pumping going on, but again, it's kind of weak. Um, I think there's just about everything you could think of going. There's wave energization, wave surfing. Um, there's Alfven waves all over the place there. So the answer is, they're all going on. The real question is, what's dominating? And, um, um, you know, just, I'm, we're just trying to find the answer. And, and I was surprised to see personally that Fermi was so weak, but but, um, SP turned out to be so strong. And that's, you know, something I should have talked about. But it turns out to be a very, very, it's, it's when an ion could travel along a current sheet in in along an electric field in a current sheet, just becomes demagnetized, goes. And a lot of people thought that was just a small amount, but it was, it was really showing up. So we were surprised to see that. So there are more than one acting. Is that what your question was? There are a lot of energy mechanisms acting at the same time? Yes, energization mechanisms. Yeah, I guess I was more curious if you expected the dominant mechanism to differ depending on where in like velocity space in the distribution function you are? Like if the core is heated primarily by different mechanisms and like the tail? Yeah, different parts of. Is that you are you saying different parts of the distribution function are affected by different mechanisms? That's what I was asking. Yeah, yeah, that's true. You get core heating in these. The core heating is probably from SP, Fermi, and other things. The tail is very much largely dominated by the stochastic part. That's what what we were trying to say. So that forms the tail on that. The turbulence seems to give a tail in the distribution, which is really exciting in in one way because, you know, there, there's dissipation is just heating. I mean, heating is, I mean, heating is dissipation and acceleration is dissipation. Tail formation or core heating, we we differentiate that because we're human beings and we love to pigeonhole. But believe it or not, there's everything. Think all shades of gray, absolutely. You know, 100 shades of gray in there. And everything I'm saying is for a specific region. I can imagine the solar physicists are going to have their own ideas of this.

All right, statement about like models in general, right? We have we have all these models because we like because that's what we each each model is something that we can manage and and, and right. But then the, you know, all the models are could be happening all at the same time, right? I, I mean, that that there's this is often the problem with plasma physics is there's more than one thing going on at the same time. You can't get away from wave-wave acceleration and wave heating and wave all this when you have turbulence because it's just there's a lot of waves in there. So so it's really hard to, you know, sometimes pigeonhole things. And this is the point of my talk is that we're saying, oh, reconnection heats. Well, it does, but the turbulence in the reconnection actually is doing more than the reconnection itself in some cases. Uh, and maybe the waves are doing something, maybe something else. That's the challenge of of really trying to sort all this out. What you're trying to do in this case is take a look at the bottom of a waterfall and explain why it's like it is. Really not that easy.

All right, anybody have anything pressing that they want to delay lunch for? Yeah, you want to delay lunch now and be very unpopular? Ask another question. Boy, you're joining us for lunch. Is that what you're? You'll you'll stay with us for lunch, right? Yes, I will. Okay, great. So you can all right, pit your hold Bob at lunch. So thanks, Bob. All right, well, thank you guys. Thank you for it's a great audience and good questions and I hope I hope I didn't overwhelm you.