NASA's Heliophysics Summer School - August 21, 2024 - Robert Marshall

All right, um, so thanks everyone. My name is Bob Marshall. Uh, I'm a professor in aerospace engineering. So, I'll, I'll give you this. I made a slide that apparently has animations that I keep forgetting are there. Happens all the time. Um, and there's a reason that I put this here, but so this is my background. My background is actually electrical engineering, uh, as an undergrad at USC and then as a grad student at Stanford. Um, I should say Stanford at the time had this group called the VF group, and in the electrical engineering department, Bob Hellwell was the heritage of that group, and then my advisor, Iman Enan. So, even though it was in electrical engineering, it was really a space physics group, very focused on VF. It's kind of funny to have a research group that's focused on a technique as opposed to a science topic, but that's the way it was. It was radio science and processing of radio signals. So that's what got me into space physics. I was an engineer doing circuit design for years, and then suddenly got into space physics.

Um, after I graduated, went to JHU. I worked at the center for space physics where Nick, uh, sits. Um, decided Boston winters weren't for me, came back to Stanford for a few years. And at Stanford, I got, uh, kind of pigeonholed into becoming the project manager for a CubeSat development. And I knew nothing about how to build CubeSats, but I said yes. If you get asked to do something weird like that and you don't think you can do it, say yes anyway, uh, because that's led to where I am now, which is the PI of three CubeSat missions, um, contributing instruments to other missions, working on big mission proposals, all sorts of stuff that's really, really fun. And it probably would have never happened if I hadn't said yes to being the project manager for something I didn't know how to do.

Um, okay, so anyway, now I'm at CU. I got a faculty job there nine years ago. Um, got tenured recently. Spent a year in France, no, spent six months in France with my, my little people hanging out at the Eiffel Tower. Um, and then recently started, uh, job as the associate chair for Graduate Studies. So I oversee our graduate program. This morning I did orientation for our new grad students. Uh, so there's the story of me.

Um, I have a research group that includes, um, a decent number of people: six or seven PhD students, couple postdocs, engineers. When we're building a lot of hardware, we have to have a lot of engineering talent involved as well. Um, so there's just a little bit about my group.

Um, do like making acronyms and logos. As don't, don't we all? Space physics, we love our acronyms. So the Lair, and anybody get the reference of Basil by any chance? You guys are way too young. You have to look at the sign and then pronounce it as "basil" instead of "Basil." Anybody in the back? Faulty Towers? Yes, Leica knows it's Faulty Towers. Go, go watch Faulty Towers.

Um, my research group, this is a little bit of explanation that leads into the lecturing here. Uh, right now, I focus a lot on the radiation belts and radiation belt interactions with the atmosphere and ionosphere, uh, through energetic particle precipitation. So a lot of our CubeSats here, there you go, there you are, are looking at precipitation of energetic electrons into the atmosphere, how they modify the lowest part of the ionosphere, the D region. Um, but also measuring magnetic fields, measuring VF waves, etc. And we do modeling, we do instrumentation development, ground-based instruments, space-based instruments, data analysis, you name it.

Um, I used to do a lot more ionosphere, actually. I did D region research when I was a postdoc and grad student. I was doing some F region heating with the HAARP facility, airglow studies, etc., but have kind of shifted as our, you know, our careers tend to always bounce around between different areas. So I have a little bit less ionosphere stuff today. Um, but I know enough to at least explain the basics to you.

Okay, so today's, uh, discussion, um, about the ionosphere. Uh, here's kind of the goals of what I want to convey to you. We'll do basic physics of the ionosphere. Many of you may have seen this before. Uh, origin, the composition, the how the different layers arise. There's a little bit of chemistry involved, a little bit of physics involved. Um, and then we'll look at the variability: the diurnal variability, seasonal, solar cycle, um, and some other cool anomalies that you, you've probably heard about. I'll, I'll, if I get time, we'll talk a little bit about effects.

So, like I said, I'm in a department, I didn't do that. Okay. I'm in a department that is aerospace engineering sciences, and so we, I really try to emphasize both the science as well as the engineering applications of that. Um, if you're, if you're a scientist, let me just say, in an engineering department, if you explain what you're doing to somebody and it's very science-related, they always ask the question, "Why do we care about that?" Or if they don't ask you directly, you know that they're thinking it. Um, and so the, you know, the engineering applications are where we convey a lot of that information. With the atmosphere, largely it comes down a lot to radio communications, GPS impacts, etc. There's much more than that, of course. Um, but that's kind of the main sort of technological societal effect that I'll touch on today. And then I will definitely, if I have to, I'll skip ahead so we can get to the Jupiter and Mars stuff, which is fun.

Okay. Um, oh, and by the way, uh, please interrupt me with questions. Just, uh, raise your hand. Um, I don't want to just be constantly talking and not have any interruptions. Get tired. Okay.

So, very beginning here. I've crammed all of this into one slide. The picture on the right actually comes from Dolores Knipp's textbook, which is great. Um, origin of the ionosphere. I like to think of this as sort of the, the, the, the product of two things: the sun, of course, which is the source of the energy, and then our own atmosphere. Any, uh, body that has a star and has an atmosphere will probably have an ionosphere, unless it's 290 Kelvin sun. But, um, you have the sun putting out radiation. Um, you can see on the picture in the top left, the spectrum is showing you, you know, the sun's black body spectrum, which is mostly visible light, but the stuff that extends to the left that I'll show you more of in a second, uh, into the ultraviolet, that is the source of ionization. Um, we'll get to that in just a second.

So on the top, you've got the, you know, the, the source from the sun. On the lower left, you've got the atmosphere. So these are just profiles of the neutral constituents of the atmosphere: N2, O2, oxygen, atomic oxygen, helium, argon, etc. Um, and then they, the, the radiation, of course, impacts the atmosphere, produces ionization. Um, so in this picture, it's showing you the, first of all, there's the temperature profile, and it's divided up by regions of the atmosphere: from the troposphere, stratosphere, mesosphere, thermosphere. And the different sources and sinks of energy. In the troposphere, the primary source of energy is the visible light from the sun, which heats the surface, reradiates in the infrared. The infrared gets absorbed by the troposphere. That's why you have the decaying temperature with altitude away from the Earth's surface. Actually, the infrared leaving the surface that heats the atmosphere. Um, in the stratosphere, mesosphere, thermosphere, now you're starting to get, uh, more ultraviolet absorption and therefore ionization. The ultraviolet in the stratosphere is absorbed by ozone, produces the ozone layer, um, produces some ionization down there in the D region down here. Um, in the mesosphere, you're getting some UV absorption, but not nearly as much. And then the thermosphere, of course, where, which is largely the overlap with the ionosphere, is where most of that UV and extreme ultraviolet is getting absorbed.

So I won't touch, I won't get into too much detail on all the S's and everything, but, um, I like this diagram because it kind of talks about how energy comes in and out of each of these regions. Let's see.

So the really basic physics of this. How many people have seen this before? This is Beer's Law. You haven't seen Beer's Law? At least one person. Time has seen it. Um, the basic principle here is how, how do you calculate the amount of energy that's being absorbed in the, in, in a section of the atmosphere? You have some intensity from the sun, I. By the way, when I, when I lecture for this in my class, I'm working this out on the board, so I'm going to go through it much faster because it's already written down. Um, you've got some intensity at the top of the atmosphere, I, or I of infinity. Um, can we click away the, the bar at the top? Cool. Thank you. Um, so that's some energy flux, right? Watts per square centimeter or Joules per per square centimeter per second. Um, and you look at the amount sort of passing through a region DH. So you have a DI in that, in that region DH. And we say that the amount of energy absorbed, DI, is proportional to the intensity and the step size in altitude. The proportionality constant, then, Sigma times N. Sigma is some constant, which we're going to call a cross-section, and then N is the number density of absorbing molecules. So there's your very basic equation for the loss of energy as a function of altitude. And you integrate this out, and you can get now a profile of I of H, which is I infinity e to the minus tau. And that looks like the red curve here on this, on this plot. It depends on N in blue, where N is the neutral density profile. Um, and so that N is buried in, in either the minus tau. And it ultimately leads to this sort of red absorption profile. So most of that absorption is going to happen at a high altitude, but only when you start to get appreciable absorbers, right? Um, so you have maximum intensity at the top, minimum intensity at the bottom, where the N of H curve is flipped compared to that. It's lowest density, high altitude, high density at the bottom. And the product of those two things leads to an ionization peak. So this is in green, the electron density, sort of why you end up with a peak at some altitude that's not the ground, right? Making sense? Cool.

Okay, so how does the heating occur and lead to actually ionization? Um, like I said, the visible light of the sun is actually not ionizing. I'll get to that in one second. Um, most of the ionization is from wavelengths below about 300 nanometers, or even actually significantly less than that. Um, oh, excuse me, 300 nanometers is the source of most of the heating, of direct heating of the atmosphere. Everything above that is reaching the ground. Um, so you have various processes that can occur here where this laser pointer is really throwing me off. I know how to do it, but where are you? There we are. Nope, there we are. Um, these are the processes that can occur when some photon interacts with some neutral molecule, right? Uh, could be visible, UV, infrared, etc. You get, so this is showing N2 plus some photon, which we write as gamma or as h-nu. Uh, you get excitation, which means, um, the molecule, an electron is getting kicked up to a higher energy level, but the electron is still, um, uh, still attached. You can get dissociation, so N2 can get split into two neutral N's, or you can get ionization. And ionization is just the process where there's enough energy to absorb that the electron gets freed. It's not just going to an excited state, but it's actually going much higher. Um, in excitation, of course, you also get situation. You know, energy gets absorbed, you get to a higher state, then it ultimately relaxes back down to some other state. It could relax back down to the ground state or to a different state, and each of those relaxations emits a photon. And because it's a very well-known discrete energy level, you get a photon of a discrete wavelength. So these are showing you the various wavelengths that get, um, that get emitted by the atmosphere, uh, through the excitation and relaxation process.

Okay, so ultimately for the ionosphere, what we really care about is ionization here at the bottom. So we're going to spend most time thinking about that. So every molecule has kind of a threshold. There has to be a minimum amount of energy for the photon absorbed to reach that high energy level where the electron is freed. Um, and each molecule has its own threshold. So here's a table of ionization thresholds for typical atmospheric molecules. Hydrogen, being just a proton and electron, has the lowest threshold. And as molecules get larger and heavier, the thresholds tend to get higher, although then the molecules get bigger and the electrons farther from the nucleus. So all those things play into it. But for our atmospheric molecules, they're all kind of in this 13-15 EV range. That energy then corresponds to a photon with this wavelength, uh, so 100 nanometers or less. This is, this is well into the ultraviolet. Um, as far as the minimum photon energy necessary for ionization.

So here's that solar spectrum again on a log scale in solar flux units, watts per cubic, watts per meter squared per meter of wavelength, um, and as a function of wavelength and Angstroms. So here is about a 100, this is 1000 Angstroms, so that's about 100 nanometers. You know, here's the visible spectrum, orders of magnitude higher intensity compared to the ultraviolet, etc. But all of this stuff down here, here, this is what is ionizing the atmosphere. And all of this stuff down here, the visible and infrared spectrum of the sun, is pretty constant, um, over the day, over the solar cycle. As the sun rotates, you name it, changes by a fraction of a percent. But the ultraviolet changes much more significantly. This is responsible for ionization. It's also has a huge variation, hence the changes in the ionosphere.

Um, I like this plot as well because this now highlights a couple of other interesting features. First of all, the red curve is my ionization cross-section. You can think of it as ionization probability in units of centimeters squared. The solid black line is the dissociation cross-section. So it takes less energy, as you can see, to dissociate N2 in this case. Um, but it's got a similar shape. And then the, uh, the dashed curve is actually a crude approximation of the excitation cross-section. All the different types of excitations are buried in that. So the realistic curve has a lot more ups and downs. Um, but that gives you the basic idea. The key thing to take away from this plot is that even though I told you there's a minimum ionization energy, there's still a probability that is a function of energy. And the maximum ionization occurs at a significantly lower, higher energy, lower wavelength. Um, so you actually need this entire, you need the spectrum of the sun, and you need this cross-section to really understand how much ionization you're going to get.

Okay. Okay. So getting into the ionosphere. So here's a very cartoony, but actually reasonably accurate picture of what all this looks like. Um, here's the sun putting out X-rays, EUV, FUV, MUV, NUV, and then visible and infrared. And it's actually showing you where each of those different wavelength, um, bands stop, where they get absorbed in the atmosphere. I have a much more quantitative picture for you in a little bit. Um, so all of that absorption there is leading to this heating in the thermosphere, um, which extends up to all the way to the exosphere in terms of the temperature. And leads to, these are neutral profiles as well as electron density profiles, showing you where most of this ionization is occurring, right in that altitude range where all this stuff is getting absorbed.

So, uh, semi-quantitative picture of what's going on. Um, here's the, uh, sort of more quantitative picture of an ionospheric profile. You guys have seen this this morning already a little bit in what you've been doing. Um, but, uh, it's just highlighting the layers. So way down at the bottom, 80 kilometers or so, is the D region. E region from 100 to 130-ish. A minimum. And then the F, F region, which is sometimes split into F1 and F2. I might, might spend time explaining that. Um, and then at the same time, you can kind of see the significant variation between solar minimum and solar maximum. And of course, between day and night. Between day and night is should be pretty obvious. At night time, your source is gone, uh, for the most part. There's still ionization source from galactic cosmic rays, for example, galactic x-rays. Um, and then between solar min and solar max, as I said, there's huge variation in the sun's EUV and x-ray output, changes the ionization significantly.

Okay. All right. Uh, here is my, so I, I made this plot back when I knew how to plot things in MATLAB. Um, this is a plot showing you everything there is in the atmosphere. And this comes from an IRI and an MSIS simulation. MSIS run. You guys use IRI today? Yes. Can I get a hand? Hi, sir. But what about just producing a profile? IRI? No, it's, it's built in there, isn't it? Or it's got its own. Okay. So anybody familiar with IRI? A few people. It's the IRI is the International Reference Ionosphere. T-I-C-M is a much bigger model, three-dimensional model. IRI is a nice, simple model. You can pick a time and date and location and get a single altitude profile of all the constituents, um, etc. Understood. Understood. So, um, as I said, this is from IRI. So you're seeing the neutral profiles here. The black is, of course, the total neutral density. The N2, the O2, the atomic oxygen. And then the, the dashed lines are the corresponding ionization, ion ions. That's the word I was looking for. So for example, where N2 is in solid blue, you will see N2+. I think it's this one. It's not labeled in the dashed blue. Um, and where there is atomic oxygen here is dashed and red, O+ is this slightly more dashed and red line that matches to this guy. So the, the black curve here is the electron density. Um, and then all these guys sort of to, to its left are the constituent ions. All the positive ions add up effectively to the electron density, right? Um, so you'll notice O+. This red line is not the major fraction initially, but above about 250 kilometers, uh, it's almost all O+. The O+ density pretty much matches the electron density.

Um, so I'm going to get into the composition in a second here and talk a little bit more about this. Um, see what else did I want to highlight here? So, uh, major ions. You see O. Okay. So one of the key things I wanted to point out with this plot, the reason I plot them on the same plot is to highlight the massive discrepancy in densities. So even at ionospheric altitudes, let's pick 300 kilometers, the neutral density is 10 to the 15. The electron density is 10 to the 12. We're still an extremely weakly ionized plasma, uh, even all the way up to the top here at 600 kilometers. There's still a well more than an order of magnitude difference, neutral and ion densities. Um, so there's the electron density profile. We'll get into the layers, of course. I already highlighted that the O+ is kind of the main ion for most of the ionosphere. Um, down at the bottom in the E region, O2+ and NO+ are the dominant ions. And if I could show it on this plot, way down at the bottom in the D region that I'll talk about, um, we get some other weird ions. Um, and I'll explain where they come from a little bit. At higher altitudes, you do start to see things like H+ and He+, and I'll say a little more about that in a second as well. Correct. It does. And there are, you're right, thanks Tom. There are doubly ionized molecules, but in Earth's atmosphere, they're extremely, extremely, uh, low density. Yeah, there's not much. Okay, what else have we got?

Um, I talked about this a little bit already. So this is getting into the calculation. What I was, what I wanted to do here, I don't want to spend too much time though, is a calculation of how you get like an electron density peak. You get something that obviously has, you know, decreasing density at higher altitudes and decreasing density at lower altitudes, and there's a peak somewhere in the middle. So we went through, I went through this earlier. Um, you've got your absorption of solar, um, incident radiation. I got to this equation, and then I said this was I e to the minus tau, right? So this is tau. So now I can go back and I can plug in a neutral density profile. And if we can assume the Earth's atmosphere is exponential, which is a very good approximation for the very bottom of the atmosphere below 100 kilometers, um, you plug that in, and now you've got this equation for the intensity as a function of altitude. Kai here is what's called the solar zenith angle. And so the direction, the incident angle of the sun, actually plays a very large role. Um, I changes this profile significantly, as we'll see. H in here is the atmospheric scale height. It's coming from this neutral density profile, which depends on the atmosphere temperature, mass density, etc. Um, so in the end, you have an intensity profile that's a function of altitude, but is also a function of, um, wavelength lambda and solar zenith angle Kai. And it's this big ugly mess. And once again, that is simply e to the minus tau. This is effectively an optical depth problem, right? So we'll take that, and I think on the next slide, yes.

So, uh, now we've got this intensity, and the intensity as a function of all these variables is producing ionization at a rate P. So P is production rate. And the production rate depends on that intensity as a function of altitude, etc., the density of absorbers, right, cross-section. And this is a sort of an absorption cross-section. And I'm varying that now with an ionization efficiency, which is to say that Sigma is all the absorption. Eta is what, what's the probability that that absorption leads to ionization as opposed to excitation and dissociation, which I don't really care about. Um, so that's my production rate. And I can plug everything in and get this new equation that has all this ugly stuff. And it's got an exponential within another exponential. It's a big ugly equation. Um, but if we plot it, it looks more interesting. So here are, here's that intensity profile, um, as a function of different solar zenith angles from 0 to 90. As you get to 90, the intensity goes up in altitude because you've got a more grazing solar angle. Um, and it's normalized. The intensity decreases significantly, but I've normalized them to one for now. And if I plug that intensity into the equation for P, and I plot P, now I've got a production rate that exponential of an exponential, which has a peak. And a peak is somewhere here at this altitude, using again using an MSIS atmosphere profile. Um, and again, as a function of solar zenith angle. And a couple of the interesting takeaways, of course, are that at the, at the zero solar zenith angle, so the sun's directly overhead, you get the maximum production, no surprise, at the lowest altitude. As you go to higher solar zenith angle, closer to the horizon, not only does the ionization rate get lower, but the altitude actually increases a little bit. Um, as I said, it's sort of grazing the atmosphere a little bit more. It doesn't get as deep into the atmosphere. So this is on a linear scale. And then this plot on the right is just the same thing on a log scale, showing you that that altitude variation a little bit more obviously.

All right. So this is, uh, this, um, derivation that I've shown you, assuming an exponential profile, assuming a single ionization, um, molecule, element, single, single ion, is what's called a Chapman layer. So it's a very simple ionosphere. Gives you the basic picture and the dependencies. And of course, we'll see that our actual atmosphere, actual ionosphere, is much more complicated. But the Chapman layer is actually a very good approximation, as you'll see, for a lot of the ionosphere.

Okay. So, um, if I back up a quick, a second. This is the production rate. This is the source of ionization. It is not the electron density. What we actually measure and observe is the density. We don't measure the production rate directly. So to get to an electron density, we need the balance between production and loss. And so where loss comes in is where things are going to get interesting. Um, so the ionosphere is in equilibrium when production and loss are balanced, which is to say DN/DT = P - L = 0. So P = L. Um, I, if I assume again, if I assume a single, uh, a single source atmosphere like atomic oxygen, then this is my production equation, where the photon is ultraviolet. And then the loss, I can simplify this initially just to say my loss is just recombination. So O+ encounters an electron, they recombine, they release a photon and the infrared when they recombine. And that's the loss mechanism. And that, this is the chemistry equations. This is where our chemistry comes in. Um, has some reaction rate alpha, um, which in this case is the recombination rate. So loss, then the, the loss rate of pairs per cubic meter per second, um, is simply the, the, um, recombination rate times the O+ density times the electron density. It's those, those three things multiplied together, effectively. So if, if I assume again, if this is a single source ionosphere, then N+ is equal to NE, and that's equal to the loss is equal to NE squared, proportional to NE squared. All right. So if production is equal to loss, that means to get this balance, I have P is equal to alpha times NE squared. And now I can solve for NE. So this is my equation for the analytical equation for the electron density profile, given a production rate and given a recombination rate. This very simple ionosphere.

Okay. So now I can go back to what I had before. Um, and I've got the same plots as before: the incident radiation, the production rate. And now I actually put in and solve for the electron density from that equation. And here's the result. And similar to the production rate, obviously, you get the maximum electron density at the lowest solar zenith angle, sun directly overhead. And it relaxes to higher altitudes and lower density as the sun sets. Not super complicated. I skipped over a couple of things. Um, uh, a couple of slides ago, but in the production rate equation, we could actually solve for the maximum production rate, which is the peak of this curve. And you can solve for the maximum altitude, which is the altitude of this curve, altitude of that peak. And so you can actually write the equation for NE in a relatively simple way as a function of P max and Z max, where we've taken an extra simplification of writing this as Z1. And you can think of Z1 here as the Z1 is is altitude minus the peak scaled by the scale height. So it's how many scale heights are we away from that peak ionization altitude. And so there's your equation, pretty basic. This is the Chapman layer. And no questions? Okay.

So, um, of course, in the real ionosphere, the real atmosphere, we have a variety of wavelengths absorbed at different altitudes. We have a bunch of different species. So things are going to get more complicated. As the plot, I'm repeating this plot down here. The intensity depends on the absorption for each species, and that species is wavelength dependent. Sorry, that absorption is wavelength dependent. The production rate depends on the ionization cross-section, which is also wavelength dependent. This plot on the right is what I, I really like. This is a quantitative plot of where different wavelengths are getting absorbed at different altitudes. So down on the left here, this is really, we're getting into the x-ray, all the way down below 50 nanometers, um, extreme ultraviolet, ultraviolet, etc. And then visible is off the plot to the right. Um, so what you can see, x-rays are primarily absorbed actually in the thermosphere, as well as all this EUV. As we get sort of into the more mid-UV, now you're seeing stuff get down to the mesosphere, get down into the stratosphere, etc. And this curve would continue then down to the ground as you go further to the right. And there's three, three lines that are kind of showing you the one over e to the minus five, e to the minus one, e to the minus 1.5. So not only is it showing you the altitude where they get absorbed, but also the altitude range. Some wavelengths get absorbed in a very tight, narrow altitude range, and others are spread out over a large range of altitudes.

All right. And so at those different altitudes, of course, they're going to encounter different molecules in the atmosphere and be absorbed depending on that wavelength-dependent absorption cross-section, etc. Um, let's see. What am I showing here? Um, same kind of story here. We're just showing how the different layers, um, um, the, the, the layers depend on the composition and the solar spectrum. And so now we're sort of getting into where you start, start to see structure from absorption due to different molecules. So, uh, this is going to lead me into discussion of the D and F regions, dominated by different ions. In the E region, the atmosphere is still mostly N2 and O2. And so you're getting ionization of O2 leading to O2+, you're getting ionization of N2, N2 leading to N2+, and then through some ion chemistry, you're actually producing NO+. So ultimately, it's the N2 and O2 in that region that lead to those ions. In the F region, the, uh, atmosphere is dominated by atomic oxygen. And so the ionization is also largely dominated by atomic oxygen. As you go to higher altitudes, uh, the atmosphere is more helium or more hydrogen. And so you start to see more ionization. The higher altitudes get simpler. It's just ionization of atoms, pretty straightforward, not much chemistry going on up there.

Okay. Um, okay. So let's talk about the, the loss channels a little. All the different production and the loss channels. Um, so this is showing you all the chemistry that can possibly happen. Okay. This is showing you most of the chemistry that does happen in, in the ionosphere. There's lots of other stuff. Um, so I talked about the primary ionization. So we're looking at ionization of atomic oxygen, O2, and N2. Those are all the same equation for these things. Again, at higher altitudes off this plot, you have the same thing: ionization of helium and hydrogen, leading to protons, as well as H+. Now, once we produce a lot of these ions, they can have charge transfer reactions. So O2 charge transfers with O+ to make O2+ and neutral atomic oxygen. N2+ transfers with O+ etc. And here N2+. So N2+ gets ionized directly by the sun, but it relatively quickly, very quickly reacts with atomic oxygen. This reaction constant K, that I, as I say, is fast. And that's what leads to NO+. So N2 gets ionized very easily, relatively easily, but very quickly turns into NO+. And that's why the E region is dominated by NO+ and O2+, and not N2+. And that also leads to your atomic nitrogen. So this is a, you know, you could think of this as a production mechanism of N+. It's also a loss mechanism of N2+. And then at the bottom, there's all the recombination reactions for our main constituents. O2+ reacts with, recombines with an electron and creates two O. So that's what we would call dissociative recombination. There's lots of great chemistry terms that are very, uh, descriptive. NO+ same thing, creating NO, dissociative recombination. O+ would recombine with an electron, and it'll create, it'll create atomic oxygen, but it'll be atomic oxygen in an excited state, O*, metastable atomic oxygen. And that atomic oxygen, when it ultimately relaxes back down to the ground state and emits a photon, we get photons of very particular wavelengths from atomic oxygen. And the most common in the ionosphere are 630 nanometers and 577.010. Everybody? Yes. Is anybody not familiar with this? Okay. Yes. Honest. Thank you. There, 630 is the red line, uh, aurora and airglow. This would be airglow. Um, and 577.010. In May? Yeah. Okay. That's a great question. I don't actually know any, any particular wavelengths in orange. My guess is they're yellow and red. It's mixing sodium, maybe? Yeah. But which colors, right? My my immediate thought when you said it was sodium. Sodium has a very yellow emission, that's a natural emission. But I don't know if sodium would be excited during this. Anyway, yeah. Yep. I, I should, I should spend more time talking about the colors and the wavelengths of the aurora, but I tend to skip over it in the airglow. But yeah, you know, I've pointed out here, these are, these are the main wavelengths of atomic oxygen, among others. But nitrogen, N2, has its own emission lines. N2+ has its own emission lines. O2+, O2, etc. The diatomics have like huge spectrum of lines because they're, uh, rotational and vibrational band systems as well. The, the atoms are much easier to understand. So yeah, you're probably getting, you get like red and purple and stuff from N2 and N2+. Then you get the red and green from atomic oxygen, and they're going to, they're going to mix, and people are going to see different things. Personally, my eyesight's terrible, everything's black and white. Tanya? Yep. So in the E region, yes. And E region and below. And there's two reasons for that. Number one, your N2 density is sufficient. As you go to higher altitudes, there's just not as much N2, therefore there's less N2+. And then there's less of charge transfer happening. But also, there has to be just enough density for these reactions to take place, right? Of of both constituents. Yeah, the probabilities of these things happening go with the densities, right? Okay. Question over here. What causes Steve? I think you have to ask, uh, Professor Cel about about Steve. I don't know Steve very well at all. That's the question you're asking. Okay. So the, the wavelengths are all, are the same. All of these, when you look at the aurora, you're seeing electrons actually. This is a slightly different process. Electrons colliding with neutrals and exciting those neutrals, and then they relax and emit photons. The, the wavelengths are the same because their excitation of the same molecules in our atmosphere. So the question you're asking about what causes Steve, that gets down in then now gets into like magnetospheric processes, and I don't really know Steve very well. Okay.

[Music] Yeah, when you say it's broadband, you know, again, ultimately everything is emission lines from the neutral atoms in the atmosphere. So broadband could just mean there's a lot of wavelengths, like the full N2 and O2 bands, for example. So it looks white, but it's still got discreet emission lines. Okay. Okay. Separate discussion, maybe we can take that up later. Okay. Uh, let me go forward.

Okay. So what I, what I was going to do now is I, you know, I've given you the sort of the full list of things here, and then we can kind of break it down by, uh, different regions. So, um, in the E region, again, the E region is mostly below about 150 kilometers. The, um, what we'll see is we actually get a very good fit to a Chapman model most of the time. The, in the E region, O2, this is, this is the symbol for concentration, same as density. O2 density is much greater than the atomic oxygen density. So what I can do is pick and choose the reactions from the previous slide that dominate. So we have ionization of O2 as the dominant ionization channel, and then recombination as the dominant loss mechanism. So my loss rate then becomes alpha, the, the reaction rate, right, times the O2+ density times the electron density. And if these two are about the same, then that's alpha times NE squared. And I've got back the same equation for NE. Um, and then I'm pointing out we do also have ionization of N2, and then charge exchange to make N+, and then NO+ dissociative recombination as the loss mechanism. But the, the reactions here at the top with O2+ largely define the electron density profile. Um, yeah, I guess that's all I was going to say there.

In the F region, you can look at the F1 layer. So on this plot, you know, we can kind of separate F1 and F2 layers and look at them separately. In the F region, in the F1 region, the dominant neutral is atomic oxygen. So ionization of atomic oxygen is the main production mechanism. The recombination of O+ is very slow, like I said, so that's not the dominant loss mechanism. Instead, you get the charge exchange with O2. Um, you get charge, this, this reaction, which I don't know the name of. It's a charge exchange plus plus dissociative exchange, ion exchange, um, giving you more NO+. Um, and then ultimately the dissociative recombination of the O2+ here as the main way of losing electrons. So this becomes the dominant loss mechanism. Uh, there's also the NO+ recombination. This guy, I added that in later, sorry for the mess. And so the loss mechanism is again, uh, some recombination coefficient times N2+ times NE from this equation, and a second term, a recombination rate of NO+ with electrons, and another recombination coefficient. Both of those are ultimately approximately proportional to NE squared. And so we get the same equation of P is, or, uh, uh, NE is equal to the square root of P over alpha. And we have a pretty good Chapman layer in the F region as well, in the F1 region.

Okay. In the F2 region, things are a little bit different. We still have ionization of O. Um, now we have charge exchange between O+ and O2, leading to O2+. And same thing with N2 as before. Um, but the loss channel is now the, uh, this reaction. The primary loss mechanism is this one, which is the proportional to the O2+ density, the O2 density, and that reaction rate. So this is not proportional to NE squared. And so F2 region is not as good of a layer fit to the Chapman layer. On the diagram here, I've actually drawn in, here's a Chapman layer in the E region, here's a Chapman layer in the F region, F1, and here's what would be a Chapman layer in the F2 region. And it's starting to deviate pretty significantly. Um, at the top of the F region. Um, so anyway, the, the one thing I want to highlight at the bottom here, all the stuff I've shown you is basically a chemistry-dominated ionosphere. But there are other factors we haven't included, like the dynamics, vertical transport, diffusion, electrostatic forces, the magnetic field, and ion drifts, and all that other stuff are going to control the electron and ion densities as well. And so those haven't been included here yet.

Okay. Okay. Finally, the D region. This is my favorite, of course. Um, the D region has extremely low densities, orders of magnitude lower density compared to EMF region. Um, and in addition to our basic, uh, directly ionized ions, N2+, O2+, and NO+, it also has a lot of other weird ions. Um, and so I mentioned at the top here, light and heavy positive and negative ions. And the, the, uh, the presence of those ions leads to really weird chemistry. So here's our production. We have quite a bit of NO. So the ionization of NO is important. You get attachment processes leading to a lot of negative ions. So O2, an electron, and another O2. The electron will attach to one of those O2s, creating O2-. Um, or it can happen directly this way with a photon emission. Um, and then you get detachment mechanisms as well, where these negative ions collide with something or absorb a photon and then free that electron. So there's this constant exchange of electrons attaching to neutrals and then detaching, etc. Um, so things get very, very interesting. The plot over here on the right is just showing you some examples of the positive and negative ion densities. And so here's an electron density profile, um, coming down like so. And then the positive and negative, excuse me, the electron density profile is, this is the thick one going this way. And then there's a negative ion density profile. And as you can imagine, the electron and negative ion density profiles add up to the positive ion density profile. So things are a little bit more weird there. The A here, by the way, is, uh, absorption of radio waves, which I'll talk more about later.

So I mentioned chemistry. The chemistry in the D region is fun. Um, there's water in the atmosphere. And so we get these weird ions, which are N is, is some number, some integer number of water molecules, which create a cluster, and then they get an H+ attached to them, and they're called water cluster ions. Um, and there's a lot of them. In these plots, a lot. So the chemistry I showed you before for F and F region, right? We had production, loss. You can see the pieces of that in these equations. This is a simple five-species model that was created actually by the group that I did my PhD in at Stanford to kind of try to model this D region chemistry. It's really, really hard to measure anything happening in this region. How do you go up there and measure reaction rates, right? Um, so a lot of this is is taken from laboratory experiments or best estimates. There's, there's a here's a DN/DT equal to in this equation. Q is production, so that's P. And then way over here, you can see an alpha times positive ion density times an electron density. So that's, that's the loss rate term for N+ and NX+. So that looks like what we had in the, in the E region and F region. Um, but this five-species model has our simple positive ions, our heavy positive ions, um, some simple negative ions, N-, and some heavy negative ions, X-, and we've just kind of grouped them together into these four ion species to try to simplify what's going on. So what that means is with five species, you have five equations, and you have reactions between every possible pair of equations. And all the A's and B's and gammas and alphas here are charge exchange coefficients or, uh, recombination coefficients, etc. All the coefficients that define all the reactions that will change these densities. Okay. So it's actually a very simple five equations, you know, first-order differential equations. We have a, we have a model of this that runs in seconds, and you can solve for an electron density profile, uh, if you know all those coefficients. So you get out an electron density in the D region. Here's kind of what it nominally would look like. The dashed line, this plot is actually comparing these two models for an electron precipitation event. We got a huge increase in electron density, and I was comparing the two models to see if they agree. They're within 50%. It's not bad. Um, so the other model, this one called the Sodankin ion-neutral chemistry model, has been around. The group in Sodankin has been building and maintaining this model for a couple of decades now. And as you can see, it's much more complicated. So where this one is five species, this one has hundreds of species, all the different water cluster ions, all the different weird negative ions. They're not grouped together into classes, they're individually categorized. And all the little lines connecting them are effectively one of these reactions. Each of those has a reaction rate. So ultimately, you would have a set of equations that looks like this, but is, you know, hundreds of reactions long. And then they do the same thing. They solve the set of differential equations and get out density profiles. Um, and they're constantly trying to update and maintain coefficients, etc. The SED, as a little bit of history, of the Sodankin ion-neutral chemistry model, was integrated into WACCM in around 2009 as a sort of a first attempt. They created a simplified version of it. They didn't want to put everything. So the, I believe it's the green stuff is the, the WACCM D version. So it's a, it's a reduced SED model integrated into WACCM. Um, and they used it. Essentially, now we run a three-dimensional D region ionosphere. Um, and that's actually now a part of WACCM. It's built in, and it's, it's automatically there. I think you can turn it on and off. But so the D region chemistry is now in WACCM.

All right. E region.

Okay, really quickly, the part that I haven't talked about is the top side. So, as we get above the F region, um, above the F region, the densities are low. So, as I said, chemistry becomes less important. Um, have you guys all done a little bit of atmosphere stuff and learned about diffusive equilibrium? The, the way the atmosphere, the atmosphere separates into layers by diffusive equilibrium of the different species, okay?

In the 30-second tutorial, the atmosphere at the bottom side, below 100 kilometers, is N2 and O2. It's, it's, well, it's a well-mixed atmosphere. So, N2, O2, and argon densities follow the same profile with altitude. Uh, above that, the atmosphere becomes heterogeneous. It's called the heterosphere, and you start to separate by, uh, ion mass, very simply. So, you transition from an N2O2 atmosphere to an atomic oxygen atmosphere is the next heaviest molecule, and, uh, and then above that, you have, uh, uh, helium. Well, O+ and N+ above that, you have helium. Above that, you have hydrogen. Essentially, you're getting a separation in the atmosphere just by mass. The lighter elements go to higher altitude. It's why helium rises through the atmosphere, right? So, the same is true of the ionosphere. Just because that's where those molecules are, as you get up into the F region, we're mostly O+, a little bit of N+. As we go to higher altitudes, ultimately, eventually helium plus will become the main ion because it's the main atmospheric species. I take that back, H+ is a little bit lower because if you remember all the way back at the beginning when I showed the ionization thresholds, uh, helium has a very high ionization threshold. So, it's harder to ionize, needs more energy. Um, but we do start to see its profile. You also start to see the, the proton density profile, and then you're essentially are transitioning now from the ionosphere into the plasmasphere. And the plasmasphere is mostly H+. It's protons, protons, and electrons. The ion, the I, um, the ion density profiles now follow what looks like an atmosphere profile. It's e to the minus C over H, where H is the scale height for that species. And the lighter the molecule, the more shallow that scale height. They get less and less sloped. Okay, make sense? Upside? Okay, here's a quick summary. I can skip over this, but, uh, you'll have the slides. Um, this is a nice chart from Dolores Kips' book. It kind of summarizes the different layers, their constituents, and some key characteristics, but I'll just skip over that for now.

Okay, um, I've talked about density. These, really quickly, on temperatures. The other thing you'll have, uh, each, the atmosphere has a temperature. The atmosphere has a temperature. They are sometimes the same and sometimes not. Below about 100 kilometers, again, where the atmosphere is well-mixed, you do have some low ion and electron densities here, and they're basically the same as the atmosphere temperature because everything is pretty well-mixed. Not really magnetized. Electron and ion densities are the same as the neutral densities, neutral temperatures, not densities, temperatures. As you get above 100 kilometers, when you're into the thermosphere and the ionosphere, you start to see a deviation from the neutral temperature. In black here's the thermosphere, and the electron and ion temperatures. Uh, and this is again from the MSIS model. So, this is just a crude estimate of the temperatures. Don't worry about the shape. I'm just using this to show that they're different. Um, so the electrons and ions have their own temperatures. Um, you know, this just means that you've got velocity energy distributions of those ions that are different from the velocity distributions of the neutrals. Um, you also get eventually, as you get into the magnetized part of the upper atmosphere, you get different temperatures along the magnetic field and perpendicular to the magnetic field, but we won't worry about that right now.

Okay, okay. Where, how are we doing on time? We're doing great. Question at this point before I move into other stuff? Okay, so I'll move into variability. This is going to be a little bit, there's, there's less of the chemistry and physics, and it's more fun pictures. Okay, so there's a variety of processes in that. So, transport is one of the key mechanisms of variability, of course. And there's a variety of things that move the ionosphere around. Uh, we'll talk a little bit about winds. Um, there are neutral winds in the upper atmosphere, and neutral winds drag on ions with them where there's sufficient collisions between ions and neutrals. Say a little bit about that. Um, we get various drifts. I know earlier in the week, you learned about single particle motion in magnetic fields. Did you learn about drifts as well? You cross B drifts, gradient drifts? Good. Talk about drifts. Um, and so these things help drive the complexity of the ionosphere, both spatially and temporally. And I'm going to touch on some of the key things here. Um, this is just a snapshot. Now, in your, in the work you did this morning, I think you've probably produced pictures like this. This is just a picture of, uh, electron density as a function of geographic region over the map. Um, and on two slides, I've just got two different snapshots. And the key as I flip back and forth is just showing you the significant variation. You know, there's, in this picture, where I've marked the X, that's the subsolar point. So, to nobody's surprise, you have the largest density below the sun. We actually slightly east of that. In the other, whoops, wrong way, in the other plot, there's a subsolar point right here, but there's a lot of other interesting structure. Um, these are just a couple of random pictures that I took. Um, and there are, there's a lot more structure and more pictures I'll show you in a second. In this plot, when you're trying to produce a two-dimensional map of the atmosphere, which is a three-dimensional object, um, what we're doing is collapsing it in altitude. And so the units of this are no longer electron density, but they are sort of electron column density. If you think of, I've got electrons per cubic meter and I integrate an altitude, now I have electrons per square meter, right? I've lost one unit of altitude. Um, 10 to the 16 electrons per square meter has been defined as one TEC unit, one total electron content unit. And we'll get to this later, but TEC is what is typically measured, um, by GPS or GNSS systems that study the ionosphere. And they measure it in these units. Um, so you're looking at the sort of column-integrated electron density, um, in a unit that is just, just like so, um, in a unit that we'll see a lot with, with GPS measurements.

Okay, so there's two pictures of the, the ionosphere. Um, if we look more locally, if you look at an individual altitude profile, as we've been doing before, we can actually characterize the ionosphere by a couple of parameters rather than a full electron density profile. If I want to look at the variation at one location as a function of time, I'm not necessarily just going to plot a whole bunch of profiles. I want to take some parameters. So, the two parameters commonly used are foF2. F2 is essentially the peak density, um, and hmF2, which is the altitude of that peak density in the F2 region. All right, the reason for foF2, which is a frequency in megahertz, has to do with this equation and has to do with how we measure the atmosphere using radio waves. And I'll come back to that later. But ultimately, the, the, the frequency F, the plasma frequency is directly related to the electron density, or the square root of the electron density, like so. And so, it's actually a very good approximation that the, uh, this F2 frequency, f, is about N times the square root of the electron density in cubic centimeters. Um, so this plot that is in megahertz, if you divide that by nine, then you're getting essentially the square root of the electron density.

Okay, so here's just a couple of examples of this. So, here's on this plot, you can see here's foF2 and hmF2 from the profile. This is showing you how the ionosphere varies just diurnally, right? Um, I've got an foF2 and an hmF2 from a site here in Grahamstown and another one in Hermanus, two sites in South Africa from 2015. And just over five days, you can see the variation in the, uh, the peak density. So, at night, it's down here at about 3 megahertz, and then in the daytime, it peaks up to 8, and then sometimes much higher, and 11 megahertz. Seeing the same thing at Hermanus, and the altitude as well, you can start to see what I showed you before, which is that at nighttime, here's the altitude around 300 kilometers. The sun comes up, ionizes it, and pushes it down to a lower altitude. And then as you get through the afternoon and into the night again, the, the ionosphere sort of relaxes back to higher altitude. Um, the plot on the top is just looking at the, uh, percent change. Okay, so foF2 and hmF2 are parameters you see very often reported in ionosphere stuff. So, that's a diurnal variation. There's also a huge solar cycle variation, uh, which we'll see in just a second here. Um, it's at solar maximum. I showed you this plot earlier. You get order of magnitude higher density from solar minimum to solar maximum. So, it's going from the two dashed lines to the two solid lines. And that's largely, as I said, due to the higher EUV and X-ray fluxes from the sun at solar maximum. So, the plot on the right has, um, here's the solar flux. The solar radio flux F10.7, as I'm sure you've heard of, is, you know, sort of a proxy of solar activity. You can also look at sunspot number, and you're seeing how that increases and decreases over six solar cycles. And foF2, again, at one particular location, has the very similar variation with about a factor of two difference. So, that factor of two difference in foF2 is like a factor of four difference in electron density. The bottom plot I include just for fun because this is the Ap index, which I hope you've all heard of as well, as a measure of sort of geomagnetic activity, substorm activity. And the key here is that you don't see the solar cycle dependence with Ap index. It's much more geomagnetic activity related. So, that's not what's driving the ionosphere variation. There's not a good correlation between this and this. Okay, some of this is latitude location dependent. This is probably like a mid-latitude site. There are different drivers at high latitudes, which I'll touch on partly as well.

Okay, I'm, I'm going to, so, so I look in at, you know, a global picture of the ionosphere, showing you that there's a lot of structure, diurnal variation, solar cycle variation. I'm going to spend a little bit of time just showing some cool features of the ionosphere. And this one is my favorite. Uh, it's a, and fortunately, you've had a little bit of magnetosphere already, so this will, that'll help. So, this is a picture of the equatorial electrojet. And the color plot is current. Um, and the current, sorry, current density in amps per meter, varying from about plus or minus two. If you integrate over the size of this feature, this current feature, you get on the order of 100 kiloamps of current flowing around the Earth. Um, so this is a current that arises due to the Earth's magnetic field. Drives this current, which flows eastward in the dayside ionosphere, primarily. This current, by the way, leads to a change in the Earth. It, this current actually drives a change in the Earth's magnetic field on the order of 50 nanotesla, which is a significant difference. Um, and so here's kind of the picture. This is looking at the, the side view, north to south. Here's the Earth's magnetic field lines. So, you've got this current sort of flowing into the page, perpendicular to the Earth's magnetic field, around the Earth. And that current also therefore leads to an electric field through the conductivity of the ionosphere. So, not only is there this current flowing in the dayside, there's also an electric field that's produced, um, across the entire dayside ionosphere, which closes with some charge centers on the terminators. Okay, it's, as you can see from the picture, it's pretty narrow in latitude. It's really an equatorial feature. It's following the Earth's, um, magnetic equator pretty closely, uh, due to the horizontal nature of the magnetic field there. And it's also pretty narrow in altitude, right in the E region, between 110 and 130 kilometers. This, it's a pretty narrow ribbon of current.

Question? You know, that's a great question. The question was, how is it supported in the collisional atmosphere at this altitude? Um, I, some of these guys might know much better than I do. I actually don't know too much about how this current arises and is supported. I'm looking back at you two. No, they don't know either. Okay, great question. We'll come back. We'll, we'll, we'll come back to that. That's my standard answer. Try to come back to that.

Okay, so, um, so this current and this electric field now lead to this other really, really cool feature. You've got, uh, this picture is a bit of a mess. I apologize. I didn't make it. Apologies for it, anyway. Here's those magnetic field lines. So, this picture that I drew up at the top, turn that on its side this way, and here it is again. And so now north is to the left. Up, up means like towards the sun. And then east geographically. And so the J and the E are into the page in this picture. And there's this electric field into the page. So, now what happens? The, the current is leading to the electric field. There's an electric field here everywhere. And the Earth's magnetic field is horizontal in this picture. So, I have an electric field into the page and a magnetic field horizontally. Um, from this stuff that you learned earlier, there is a drift. With any given force, you end up with this drift velocity. The force is Q times E. So, we end up with a drift velocity that's E cross B over B squared. So, E cross B direction. E cross B leads to a drift velocity that is up, away from the Earth. So, these electrons that are moving, you know, the current is moving, moving into the page, electrons are actually lifted away from the ionosphere up to a higher altitude through this E cross B drift. At some point, they reach an altitude where the electric field is diminished. They leave that region of the electrojet current. Um, and now they're no longer supported by that electric field. The drift kind of stops. They get to some altitude. Now they're actually, you know, they're, they're still within the Earth's magnetic field. They're trapped by magnetic field lines, and they move very easily along magnetic field lines. So, these electrons that have now been lifted to a higher altitude fall back down the magnetic field lines back into the E region, um, equatorward of the equator, both north and south of the equator. That leads to a higher electron density in the ionosphere here and here in the E region. So, this whole process that raises electrons and then they fall back down the field lines is called the fountain effect, and it leads to this thing we call the equatorial anomaly. And here's just the picture showing you the magnetic field. I don't know if I need to go into details here. Skip over this.

So, here's that equatorial anomaly. This is from a model. This is not data. But what you're seeing, the middle of this stripe is the magnetic equator. And here is enhanced electron density both north and south of the equator. And there's nice. This is actually a nice animation produced, um, by the ICON team or for the ICON mission team, showing you the equatorial anomaly. And as the, so, so of course, where it's brightest is where the sun is above it, because this is largely a dayside effect. As we get to night side, it mostly disappears. Here comes the sun again. Um, and you're seeing this anomaly just regularly, constantly. So, that is a really key and important structure of the ionosphere, which I think is really cool because it involves the magnetic field. You guys think it's cool? Then, are you, are you voting for cool, or you have a question? Yes? No? Why is it an anomaly? Well, it, it was originally called the Appleton anomaly, as you pointed out, right? And so, at the time of Appleton, it was probably not well understood. And so that's what they named it. We understand it reasonably well now. You can think of it as an anomaly because it's anomalous relative to normal background density one would expect without this effect, right? Without physics? Yes. Well, from everything that I pointed, that I discussed before, direct ionization, you've got a baseline ionosphere. The anomaly is sort of a second-level perturbation. I don't know. Don't ask me these things. Fine. Yeah, there's definitely Joule heating. Yeah, anytime you got J and E, there's Joule heating, right? So, yeah, there's definitely Joule heating happening in the electrojet as well. That's a good question. I don't know the answer to that. If there's a big temperature anomaly as well? That's a great question. Do you know the currents in the polar electrojet? Yeah. Yep. So, it's going to depend on the current density, of course, and the electric field intensity. So, great question. Let's, you can, can you write these things down and send me all your good questions that I don't know how to answer? Um, yeah, the potentially you have, because you have a higher density, you're going to have higher absorption of, of GNSS signals or rotation of GNSS signals. So, you could lead to higher position errors for sure. Yep. And the ionosphere is known to be, at this point, the largest source of error for GNSS. Um, largely, though, it comes down to how well we know it, right? Like, we know there's this anomaly. If we can predict how intense the anomaly is, then we can use that information. So, how constant is it? How variable is it? And that's actually largely, I think, one of the science goals of the ICON mission. I don't know if they've answered that question yet, but I have a slide later that shows a little bit about ICON.

Okay, uh, some other cool things that I just like to show. Um, in the F region, you also get a lot of plasma instabilities occurring that lead to all sorts of interesting structures. So, there's a phenomenon called spread F, where the plasma moves along magnetic field lines and spreads to higher altitudes. It's largely in these sort of mid-latitude regions where, uh, shear forces can sort of push the plasma up the magnetic field lines. So, the F region can get up to much higher altitudes in those regions. Um, you also get a lot of structure in here. There's structure that shows up with these different spatial scales and time scales.

I'm going to skip over this stuff pretty quickly. This is a fun one, the equatorial plasma bubbles. You know, when you have a, um, plasma in the F region, that's got a certain electron density, and the magnetic field here is important as well. And it's essentially, you've got a fluid sitting on top of a different fluid. And if any of you were have any, um, sort of fluids backgrounds, you know that if you have a heavier fluid on top of a lighter fluid, you get the Rayleigh-Taylor instability arising, like so. So, we see that in the F region, um, frequently as well. And on top of the Rayleigh-Taylor instability, you get all the little structures along those channels that are Kelvin-Helmholtz instabilities. So, the F region gets really interesting. This type of structure is what is thought to lead to scintillation effects on GNSS signals. So, understanding how and when they arise helps us understand when to expect scintillation, if not to correct for it. In the E region, at mid-latitudes, there, it's got its own cool phenomenon, which, uh, I, I worked on spatial, a long, long time ago, very brief, when it was not super well understood. I think it's better understood now, um, where the basic principle is that in these regions, first of all, you see a massive increase in density in the E region of a couple orders of magnitude. And, um, that can knock out HF communications, which typically go through the E region to the F region and back down again. But the large increase in E region density can absorb that HF communication. There haven't been a lot of good measurements directly of it, so spatial scales of these patches are not well known. What's happening, though, is that you have shear winds. This picture is trying to show you. So, here's a dashed line, which is some nominal altitude in the E region. There are winds below it blowing to the right, and winds above it blowing to the left. And as the winds move, they push ions along with them. But the ions also kind of want to follow the magnetic field lines. So, they end up sort of converging in this narrow altitude range between those shear winds, enhancing the density at that altitude. So, you get a narrow layer with a significant increase in density.

I'm just giving you some highlights here. Um, at high latitudes, there's polar cap absorption. So, this will lead to massive increases in electron density in the polar region. There's a lot more we could say about polar atmosphere, but I'm not going to today, um, due to, uh, the solar energetic protons and other things sort of entering the Earth's magnetosphere and getting absorbed in the polar region. So, here's the picture of the sort of connection between the sun and the solar wind in the polar region. And this picture on the right is, um, actually looking at observations of solar energetic protons by low-altitude satellites. So, you, you very dramatically go from basically zero at low and mid-latitudes up to many, many thousands of counts per second. So, those protons lead to more ionization, lead to enhanced density in the, in the atmosphere. Okay, those energetic protons, by the way, um, largely get down to the D region. And I'll, if I get to it, we'll talk a little bit about how the D region affects radio wave absorption as well.

All right, um, I threw in a couple of other things because we were looking at this this morning. The Mother's Day storm, Ganon storm from earlier this year. Did you guys run, ran simulations of this thing? Well, these guys ran simulations of this thing, reviewed simulations. Well, these are the outputs of, uh, May 10th and May 11th of this year from TYCM. Again, units of total electron content in TEC units, ECU. Um, so there's the pre-storm ionosphere. And exactly 24 hours later, this feature here, I just showed you, this is the equatorial anomaly feature. And it hasn't really changed much from pre-storm to during the storm. The, the, the color bar changed, so it looks like it's weaker, but I think it's actually about the same. But what did change was a significant increase in densities here at higher latitudes. And this line here is pretty much the auroral altitudes. So, all of that, uh, input from the solar wind from the storm, which perturbs the magnetosphere, ultimately gets dumped into the atmosphere at auroral latitudes, creating these ribbons of enhanced density like so. All right, so that's what happened earlier this year. So, this is, I mean, look at this from, from pre-storm, there is a feature there, but it's pretty weak. And then post-storm, there's a dramatic increase. Um, again, the ionosphere profiles themselves. These are from the same model simulation at a latitude of 40 degrees, which is equivalent to Boulder. Boulder is right about 40. In fact, Baseline Road is 40 degrees. Longitude of minus 175, which is what, somewhere in the Pacific Ocean? Yeah, pretty close to the, pretty close to the G line. Um, so this is very much a mid-latitude observation. Keep that in mind. So, if I go back to the previous plot, somewhere over here, so pre-storm and post-storm, should I expect to see anything significantly different between those? Doesn't look like it. So, here's the atmosphere profiles that come out of this. You've got, uh, I had, I, I had trouble, and still have trouble reading this, but electron density, O+, and O2+. I think one of these is, this one's going to be O+, and electron density. This will be O2+. Um, but from pre-storm to post-storm, you don't see a huge change. This is 600,000. So, this is, uh, 700,000 here, and there's 700,000 there. And the altitude is about 380, and it's maybe a little bit lower. So, really depends on the spot that we pick for these plots. We picked somewhere in the Pacific Ocean where the change wasn't very interesting. All right, but the model did capture a lot of interesting stuff. Certainly captured the high-latitude features. Um, it's probably, it's only been a couple of months, so the time to actually do detailed quantitative comparisons with data is still ongoing.

Okay, there's a lot more to this. I'm not going to get into the features. This is a fantastic plot that was created 20 years ago or so by someone in our community. Um, and I like to show this kind of at the end of this discussion of all the stuff because I, you know, I touched on a lot of these things. I touched on the, um, didn't touch on that, the fountain effect, equatorial anomaly, irregularities, etc. Touched on some of these features, but you can see how there's many, many more things happening in the ionosphere that we, you know, understand to different degrees. And it's all a complicated system that's all tied together. Depends on the magnetic field. It depends on the solar inputs that we have to constantly observe so we can see what those inputs are to the system. Um, and then we take all those inputs and the magnetic field and everything and throw it into these big models like TYCM and try to see what's happening and use that to understand some of these phenomena. Um, and all this is still obviously ongoing. All right, and I haven't even really touched on like connection with the magnetosphere, although I think earlier in the week, some of your previous lecturers said something about that. But, complicated system, isn't it? Um, I mentioned IRI earlier. Here's a, just a quick discussion and link to that. Um, IRI is a nice model that is a combination. It's sort of a semi-empirical model. So, it actually inputs a lot of data. MSIS is the sort of atmosphere equivalent. MSIS stands for something you guys remember? Mass? Yes, thank you. Far that Mass Spectrometer and Incoherent Scatter, which sounds like an atmosphere model, right? It's, it's the sources of data that go into the model. IRI is obviously much easier to understand the acronym. So, from IRI, you get data from ionosondes that measure the ionosphere, incoherent scatter radars, which take full profiles of the ionosphere, a couple of very old, long ago topside sounders, ISIS and Alouette. So, those are essentially like an ionosonde that beams downwards and measures the topside of the atmosphere. Down, they can, they can basically measure down to the peak, whereas ground measurements can measure from the ground up to the peak. And then lots of INU measurements as well. So, they take all of this data. [Music] Uh, correlate it with solar activity, etc., to produce a model that you can then use to get a profile for any location and time. But it is absolutely model-based. The model gets updated regularly, and there are international meetings where groups get together and talk about improvements. Um, I briefly mentioned the plasmasphere. I sort of, you know, when I teach this stuff, sometimes I talk about the plasmasphere in the ionosphere section and sometimes in the magnetosphere section. It is really the, the connection between the ionosphere and the magnetosphere, where the, the ionosphere is essentially bound thermally. It's dominated by the thermal pressure. When you're in the plasmasphere, it's a cold plasma, and it is dominated by magnetic pressure. So, the plasma now becomes confined to the magnetosphere as opposed to just being confined geographically to the Earth. You can also, uh, define different definitions of where exactly the plasmasphere and, uh, actually, I don't know if I've, I might have less material than the time we need. Gravity waves, gravitational waves, way out of my expertise. I think these are microscopic perturbations in in gravity. So, yeah, gravitational waves coming from like astrophysical sources. Whereas gravity, gravity waves on the plot? Yes. So, so this is actually a fairly common, uh, uh, point of confusion. Yeah. ATM. Yes. So, gravity, so for everybody's, uh, knowledge, gravity, you know, gravity, when they talk about gravitational waves, this is the astrophysical stuff that's happening from black holes, etc. Impact on our system is, you know, negligible. Gravity waves, keep pressing the wrong button. Gravity waves shown here are, uh, atmospheric waves that are generated by thunderstorms and other sources that, you know, propagate essentially like, like an acoustic wave up through the atmosphere. They grow in amplitude with altitude. Um, and then, yes, they absolutely slosh around the atmosphere and the ionosphere. So, very evident in the lower ionosphere, for sure. So, they have an impact in that they can be observed. You can see the structure from the gravity wave propagating through the region. And then they, they tend to break in that altitude range, sort of 150 kilometers, and deposit energy and momentum there. So, they are a source of energy for the ionosphere, source of momentum, um, that is, you know, very, very big area of study right now. Yeah. Um, in fact, is it ACE? Um, Mike Taylor's mission? It's not ACE. AWE. Yes, the Atmospheric Waves Explorer is a, a new mission on the ISS, uh, PI'd out of Utah State, that is that is doing essentially a global study of gravity waves. Another question over here. Oh, yeah, sorry. So, uh, IRI is the main model that, that is used to, um, subtract the, uh, ionospheric error from the communications. Iris? I, yes. Um, I wouldn't necessarily say it's the main model. It's, it's one of the models that we can use to generate ionosphere profiles. I want to know how, what is the efficiency of this during the disturbed geomagnetic conditions of the model? Yes. When you say efficiency, you mean like the accuracy of the model? Yeah. Uh, not particularly accurate. Reasonably. It's okay, but it's not great. No. I mean, if you were to use the IRI model as your source of correction for GNSS, for example, I don't think it would do a very good job. I'll say a little bit more about how that is done, um, but it's much more data-driven than model-driven. Yeah. One more. I just wanted to ask about the, like, the equatorial anomaly. You talked about electrons, you know, drifting upwards with the E cross B drift and then going back down. What about ions? What are they doing? Yeah, that's a great question. The ions don't tend to drift because of their, because they're heavier, um, and so they tend to be more collisionally tied to the atmosphere. So, they, they, they're sort of stuck to the atmospheric neutrals. Um, electrons, being lighter, are able to sort of drift along magnetic field lines or across magnetic field lines much more easily than the ions. So, you do get this sort of charge separation situation happening as well. Get like a secondary electric field from that. Um, yeah, definitely.

Okay, shall I move forward in the slides? All right, so radio wave propagation. As I said, being in an engineering department, I like to talk about the effects. So, let's look at how radio waves are. So, so this is actually a little bit both of how we measure the ionosphere using radio waves and how the ionosphere affects radio waves, you know, used for communications. Um, so I'll get into touching on these things. You, you've probably seen the basics of plasma oscillations and plasma frequency, but I'll, I'll revisit that quickly and how the index of refraction, collisions, and the effect of different sources of energy sources of ionization.

Okay, so normally I would walk through this slowly. Not today. Very basics. If you've had, how many have not had a plasma physics class in your curriculum? Everybody's had plasma physics? So, everybody's seen this? Nobody's not seen this? Okay, nobody's just being shy and doesn't want to put their hand up. Um, so I don't need to go through this. This is great. You all know this stuff. Oscillation of plasma leads to, uh, this equation for a harmonic oscillator, and you get an index of refraction of the plasma that is given by one minus Omega P squared over Omega squared. Okay. So, the key takeaways, of course, from this are that there's an index of refraction in the plasma that is frequency dependent. And at a certain frequency, it goes to zero. And at lower frequencies than that, it becomes imaginary. So, radio waves with a frequency above the plasma frequency can propagate. And radio waves below that frequency are reflected and/or absorbed. Okay, that's the fastest I've ever done that before.

So, reflection occurs, like so. As we said, the plasma frequencies are related to the electron density. Radio waves above the plasma frequency, which is shown by this guy, can propagate through the ionosphere. And essentially, it's because the electrons can't respond fast enough to that propagating radio wave. So, the frequencies that are reflecting here in the, um, in the E region are on the order of megahertz. So, you want, if you want to propagate through the ionosphere, so satellites, etc., you have to use frequencies typically over 100 megahertz into the gigahertz. Radio waves below the plasma frequency are quote unquote reflected. As you can see from this nice qualitative picture, they're not really reflected. They're actually more like refracted. And they have a bending path. And, um, we can take advantage of this. So, so on the one hand, if you're trying to communicate with space, you're out of luck. But if you're trying to communicate with some system far away, you can actually use the atmosphere as a, essentially a reflecting medium. So, this is what enables over-the-horizon radar. And over-the-horizon radar typically uses tens of megahertz frequencies, which can take advantage of the F region of the atmosphere and propagate very far.

Okay, so there's a picture of this. For over-the-horizon radar, you'll typically have like a single skywave. So, you're communicating, say, from a transmitter in Boston, bouncing off the ionosphere to some receiver further down. At lower frequencies, you can actually communicate long distances with multiple bounces off the ground and the ionosphere. So, so VLF waves in particular, reflect below about 100 kilometers or like 85 kilometers, and they can be used to communicate around the globe. So, Navy, there are Navy transmitters operating in the tens of kilohertz, which take advantage of the D region ionosphere and propagate globally. Like we have, I, my group runs VLF receivers. We have receivers all over the world. There's a transmitter in Western Australia, and we can see it anywhere on the globe. Very cool.

I want to quickly talk about the index of refraction because this is important for the propagation. You've all seen this before, right? But as you propagate from one medium to another medium with a different index of refraction, your ray will bend. And if you look at this in a wavefront picture, you can match wavefronts along the boundary with the slower propagation speed in the higher index of refraction medium. And that essentially is what looks like a wave propagating this way and then bending sort of towards the normal, right? In the picture on the right, where the other, the second medium is a lower index of refraction, less than one, you actually get bending away from that normal boundary. And of course, there's the equation that determines the angles based on the indices of refraction. All right, hopefully, this is all review. What happens in the ionosphere? As you increase in altitude, you are changing the electron density, right? We're at the bottom of the ionosphere, we're going into the D region, and then the E region, and you're getting this index of refraction is changing. So, what we can do is we can divide up the ionosphere into layers like so, and treat each sort of discrete boundary as a different refraction. So, you're getting a wave incident at the bottom of the ionosphere, it refracts slightly in a lower index of refraction away from the normal, and then more and more progressively away from the normal to create this bending ray path. And at some point, as this continues, it will completely turn around and start to come back down. So, the picture here now from the ground to the ionosphere shows this process of a wave propagating, refracting, refracting, refracting, and then ultimately turning back down to the ground. So, it's really a continuous refraction process, it's not a reflection. But with the geograph, the geometry of this problem, as well as the time difference, you can actually determine a sort of an effective reflection height for this wave, as if it was a hard specular reflection off of some altitude. And so people often say, yes, there's a reflection off the atmosphere, and you can, you can, you can even define a reflection altitude based on this.

All right, so this will, like, like I said, in the VLF, this will happen repeatedly. It'll refract, reflect on off the conducting ground, and then do that same process again and continue to bounce. Okay, so the frequencies I mentioned a little bit earlier, sorry for the, sort of messy writing all over the place. In the F region, the peak electron density, remember Omega P equals root of NE Q over M times epsilon zero, means there's a relationship between the peak electron density and the peak, the critical frequency in the F region that can vary from a few to tens of megahertz, again, depending on day, night, mostly day, night, and solar cycle. So, at nighttime, down to three megahertz. Daytime, typically up to like 10. And then when there's a lot of extra ionization, it can get up to 30. Um, the, as I said, higher frequencies can go pass through the ionosphere. They will be slightly refracted. So, you want to use this sort of low tens of megahertz source, single-digit megahertz for the over-the-horizon radar or for sounding the ionosphere. If your goal is to measure the ionosphere from below, you transmit a signal between zero and say, 10 megahertz, and look at all those frequencies as they're reflected back to the ground. In the E region, the density is lower, so the critical frequencies are lower. But as I said, sporadic E increases that density dramatically. So, there are cases where you are trying to measure the F region and you're transmitting at, say, four, five, six megahertz, and then sporadic E shows up, and the F region disappears completely from your, from your sounding observation. And what's actually happening is that there's a huge increase in the E region density that's blocking the radio wave from reaching the F region. So, you're getting reflection from the E region, but nothing is making it to the F region. In the D region, we can't really define a critical frequency because of all the, well, primarily because of high collision frequency. This is no longer accurate. You're all familiar, hopefully, you're all familiar with the Appleton-Hartree equation. Hands up, Appleton-Hartree equation. Hands up if it's not your favorite equation. Oh, it's all your favorite equation. That this is a very simplified form of the Appleton-Hartree equation. The Appleton-Hartree equation, in short, defines the index of refraction in a plasma. This is the very simple form with no magnetic field and no collisions. So, super simplification. In the D region, we have a lot of collisions, so the index of refraction actually requires the full Appleton-Hartree equation. We, it also, that equation can define quantitatively the absorption that we get through the D region or through the atmosphere. So, we'll see that in a little bit as well. And I talked about this before about how lower frequencies reflect from that region. And here's a picture of VLF waves bouncing around in the ionosphere.

Okay, so really brief waves in plasmas. I probably should put this a little earlier. Quick summary, of course, here are Maxwell's equations, which you can convert into frequency domain by converting d/dts into j omegas. And so, to define propagation of waves in plasmas, we simply need these two equations, maybe in frequency domain, and this equation, the Lorentz force equation, which is actually just F equals ma in the ionosphere, where you've got m times acceleration of electrons is equal to a sum of forces, which can include Q times Z, QV cross B, collisional force, damping force, pressure gradient, heat flux, other components that you can add to this equation depending on the region of the atmosphere that you need to model and which terms are important. Ultimately, this is an equation that defines the currents in the system. Like n times Q times V, sorry, n, number density times Q, charge, V is current. So, when you solve this equation for V, you can actually convert that into current, and this becomes an equation for the current densities in the ionosphere. So, now I have two equations for the propagation of waves, and this other equation for how those waves interact with currents, the atmosphere, and those are the equations that we use for wave propagation in this region. So, go through all the electromagnetic theory as you had before, including that extra equation, and you can ultimately solve for the index of refraction, just like you would in Physics 2, but it's a little more complicated.

So, here is n squared, the index of refraction squared, which is 1 minus X over something. And if Z goes away, and if Y goes away, if I drop that term and I drop that term and I drop this whole mess, then I simply have 1 minus X. And X is Omega P squared over Omega squared. So, 1 minus X is that equation. Okay, in this equation, I'm really glad you guys haven't seen this before because I love explaining this. Um, in this equation, X is essentially my electron density because X is Omega P squared over Omega squared. So, it's frequency-normalized electron density. And a bunch of coefficients. Y is the magnetic field. This Omega C is the gyro frequency, QB over M, you've seen that before, normalized by the frequency. So, it's the magnetic field normalized by the wave frequency. And then Z is collisions, the collision frequency, again, normalized by the wave frequency. So, X, Y, and Z are electron, this plasma, magnetic field, collisions. Easy. So, plasma shows up in this. Collisions are typically going to have an i in front of them. Collisions lead to damping. Damping is the imaginary part of the, of the refractive index. Um, and then Y often is seen next to some sin(theta)s and cos(theta)s because you can imagine the propagation relative to the direction of the magnetic field is important. So, theta is the angle between the K vector of the wave and the Earth's magnetic field. All right, so this is a whole beast, by the way. This is the simplified form. This is the Appleton-Hartree equation for electrons only. If I throw in ions, you can imagine now we've got a term for ions, for each of the ion species, and each of the gyro frequencies, and each of the different collision frequencies. So, this can grow into a horrible mess. Okay, but it's fun. So, like I said, this is the index of refraction. All the stuff I told you before is still true. If the wave frequency is, um, below the plasma frequency, critical frequency, then we're going to get 1 minus something positive, so we're going to get a negative number, and the index of refraction is going to become complex, imaginary, in fact. And so you get absorption and/or refraction. You don't really get propagation in that sense. The, the big term has to be less than one for this to be a real number and therefore have propagation. So, magnetic field plays a role. The direction of the magnetic field plays a role. Collision frequencies, we name it. Um, you can take this thing, this is n squared. If you could solve this, you can't really do it analytically, but if you could solve this for the real and imaginary parts, the real part of the refractive index will tell you the propagation speed, right? Velocity of propagation in any medium is C over N, where N is the real part of the refractive index. The imaginary part defines absorption. It gives you an e to the minus alpha Z term, right? So, we, if we could break this down into a real and imaginary part.

you could actually look at propagation speed and absorption. We can simplify that a little bit, and so some steps have been skipped here. But if we actually solve for the imaginary part of the refractive index and simplify, you get this equation. And this equation now defines the absorption. So dA is the change in amplitude, and dL is per unit distance. So this is the absorption per unit distance through the ionosphere. Uh, this version of the equation has been put into dB per meter. Uh, this coefficient is just the product of a bunch of constants. And that absorption now is related to the electron density and the collision frequency, and a little bit the magnetic field and collision frequency in the denominator. Um, so but primarily you think of this as the product of electron density and collision frequency. When there's more electrons, you're going to get more collisions, or sorry, you're going to get more damping. When there's more collisions, you're going to get more damping. So um, sorry, real quick. This again is sort of a profile of the neutral atmosphere, and neutral atmosphere is directly proportional – I should say the other way – the collision frequency is directly proportional to the neutral density: more neutrals, more collisions. Uh, this is an electron density profile. And so if you take the product of these two things, you can kind of get an approximation of where absorption is going to occur. So electron density is increasing with altitude, neutral density is decreasing with altitude. We end up with an altitude range here where absorption is dominant, and it's mostly in this upper D, lower E region, kind of 90 to 105 kilometers. Yes, sorry, can you say that again? I didn't mean – what do you mean by – oh yeah, yeah, no no. The, the, the, the coefficient here, this 4.6, yeah, that's rec – calling the preactor. Yeah, it's, it's based on just those physical constants. It's not empirical. It comes out of epsilon, mass of electron, etc. I have the derivation somewhere if you're interested. Um, other questions on this? So all of this was to sort of highlight that absorption depends on these things. Absorption falls out of the Appleton-Hartree equation, the equation for the index of refraction. Um, and it's the imaginary part of the index of refraction that leads to absorption. And where that occurs is in this altitude range where the product of electron density and collisions is maximum. Okay, so this is where our ground-based, you know, HF waves are going to get absorbed and therefore attenuated as they propagate. And if I have a big sporadic E event and ne goes way up in this region, then I'm going to get even more absorption and more loss of that signal. Okay.

Um, I have a little bit on the collision frequencies. I should have said earlier, you know, we're primarily – the dominant collisions in the ionosphere are between electrons and neutrals, and between ions and neutrals. Um, so I, I apologize, I just sort of assume that, and you probably didn't think of it. There are also electron-electron collisions and electron-ion collisions. Uh, but the, the collisions with neutrals are going to dominate because of the fact that we're still in a very weakly ionized plasma; there's a thousand times more neutrals than there are ions. Um, so electrons are going to collide with neutrals vastly more frequently than they are with other electrons. Um, it's not obvious to figure out sort of how to get collision frequencies, but they – I'll just highlight that they depend on the density of neutrals. So this is the average collision frequency between in N2; it depends on the density of N2 and depends on electron temperature, and this is a more empirical equation. Uh, you then get collisions between electrons and O2 as well; it depends on O2, depends on temperature. Add those together, and you get a collision frequency. And this is the collisions between electrons and neutrals per electron. Um, and that's why the absorption increases with electron density; electron density is not built into these collision frequencies. All right, I just answered the question at the bottom. Uh, there are – this is actually from one paper – but there are numerous models for collision frequency. We're trying to, like, you know, again, sort of best fit some observations to the physics that we think is going on. Um, but there, these are, these are things that are very, very hard to measure.

Uh, so here's ultimately D region absorption. Um, what I'm plotting here is actually just some electron density profiles, a collision frequency profile, and these profiles are for different, uh, sort of ionization scenarios. They're not real scenarios; they're simulated electron density profiles during precipitation of different electron energies. Uh, and then we're looking at, for those different energies here they are in the legend – uh, what does the amount of absorption look like in dB per kilometer? And so this is really simply plotting that equation from a couple slides ago. Uh, so different energies get, uh, deposited at different altitudes, leads to absorption at those altitudes, and so on. Um, there are systems called riometers in high‑latitude regions that monitor this sort of thing; they measure this absorption. Um, and this is a riometer up at HAARP in Alaska. Um, the way they do this is by – there it's a passive system, it's not a radar, and it is measuring cosmic noise at about 30 MHz, uh, which is reasonably constant, with a diurnal variation. So that cosmic radio noise is just being monitored by this system, and the blue line is the kind of the diurnal variation that we would expect to see. When there's big events that produce precipitation like this and then enhance absorption, you'll get a plot that's got little dips in it relative to the diurnal curve. So they look at the difference in the actual measured cosmic noise versus the diurnal profile that they expect, and that tells you the absorption in the D region. And this is sort of a way of monitoring that, uh, that, uh, this phenomenon.

Um, other sources of, uh, perturbations to this region include sudden – well, there's a phenomenon that is described as a sudden ionospheric disturbance. And a sudden ionospheric disturbance is particularly an ionospheric response to flares. Uh, flares – solar x‑rays – just like electrons get absorbed in this altitude range in the D region, and x‑rays have, you know, more than enough energy to ionize neutrals. So they're leading to an enhancement in the electron density in this altitude range, and that enhancement in the electron density leads to higher absorption, and um, can actually, again, disturb communications. Uh, so same process shown here, except in this case it's actually the flare, x‑ray flare directly from the Sun. Now x‑ray flare hits the atmosphere everywhere on the dayside. So this is, uh, much larger region that gets perturbed compared to, say, uh, you know, an auroral event or electron precipitation event. Um, and any sort of communication through that region will get affected.

Um, related to this – what happens when you have a large x‑ray flare like this? Um, okay, have to talk about this real quick. So we've, we've talked about – I mentioned the, um, the critical frequency in the ionosphere, which defines the lowest frequency that you can use, um, to communicate through the atmosphere. How do I want to say this? Uh, the maximum frequency we can use – oh yes, okay. So for over‑the‑horizon radar, I was kind of describing this picture backwards, right, compared to this. Uh, when you're trying to propagate through the ionosphere, you want to use high frequencies. When you want to propagate over‑the‑horizon radar, you want to reflect off the atmosphere, so you actually want to use relatively lower frequencies. There's a maximum frequency you can use, and that maximum frequency is the critical frequency in the F region. But there's also a minimum frequency, because if your frequency is too low – uh, this is a simplification of that earlier equation where we drop the gyro frequency, just assume that the frequency is relatively high compared to the gyro frequency – um, if your frequency is too low, this term gets very large, and now you're getting absorption and loss of that signal simply by, by nature of having a lower frequency. So this plot is actually showing you the lowest usable frequency due to absorption just to have enough signal, and the maximum frequency based on the F region, as a function of the diurnal variation, 0 to 24 hours. So in between there is what's called the usable frequency window of a few megahertz for over‑the‑horizon radar. Now say we get a really big x‑ray flare. X‑ray flare increases the electron density, uh, increases this absorption even further, and so it's increasing the lowest usable frequency. And if that lowest usable frequency then becomes higher than the maximum usable frequency, now you can't do over‑the‑horizon radar at all. So the flare can lead to this, this phenomenon where there's actually no ability to communicate over‑the‑horizon.

All right, okay. Um, little bit on higher frequency radio waves. So I've been mostly focusing on stuff around the plasma frequency. Um, but now let's see what happens with higher and higher frequencies. So if I get into – if I start talking about GPS, remember GPS is at about one and a half gigahertz, so we're way above the critical frequencies of the ionosphere. Uh, these signals will propagate through the ionosphere even under the largest, um, disturbance conditions. Um, but they are still, still affected by the plasma. And very simply, the way to consider this, ignoring the magnetic field and ignoring collisions, you still have an index of refraction for any frequency that is related to the electron density in the ionosphere. The frequency here, omega, can be much, much, much higher than omega_p, but this is still a nonzero term. Um, what the GPS community does is takes this equation and expands it in a Taylor series, converts omega to f, and then drops the higher‑ordered terms. So you're really looking at a now a one plus some constant over f². And so now this is a small perturbation to the index of refraction. That small perturbation to the index of refraction – uh, remember, index of refraction defines the phase velocity of the wave. And effectively, from the spacecraft to ground communication from a GPS satellite, that effectively changes the path length. It changes the perceived path length for that wave, as it's slowing down through this region of the atmosphere. It's almost – you can think of it like it's traveling further. Um, and so they consider this as a change in the ionospheric path length, delta L, given by this frequency, um, related to the electron density, which then gets converted into a TEC. So this is again sort of integrated along that path. So you've integrated – one over meters – um, and you get an effective change in the path length due to this sort of electron content. So consider the scenario here on the bottom, where I've got a normal environment with an index of refraction of one. Here's a signal that's just propagated five wavelengths. In an index of refraction slightly less than one because of the negative sign here, um, those five wavelengths – those same five wavelengths will propagate a little bit further, and so there's a tiny difference in the effective path length. So I think GPS really cares about path length; the distance between the satellite and the ground is what's important for figuring out position. So this is how the ionosphere leads to position errors in GPS. Uh, I don't know if I'm going to talk about how we correct this. You guys know much about how – anybody know how they try to correct this path length? There, there's one very simple solution. It works very well up to a point. No? What's on a GPS satellite? What's – what's – you've got F? Yes, thank you. You use more than one frequency. So with more than one frequency, this is – you can turn this into two equations with two unknowns, where the unknowns are TEC and delta L, and you can solve for both of them. And you essentially – you're using one frequency to determine the path length there, and then correcting it with the second frequency, something like that. So that's what they do. Dual‑frequency GPS is much, much more accurate in positioning because it's got this sort of correction. There's move – they're moving now towards three‑frequency GPS receivers, L1, L2, and L5. Um, that's not super typical yet in your, you know, your handheld GPS systems. Um, but they still – this, you still end up with about a 10‑centimeter best‑case error even from dual‑frequency GPS.

Okay, so we showed you some of this before. This is just another example of a map of the ionosphere with TEC units. In this picture, you can actually see a whole bunch of receivers on the ground. Um, so what, uh, ionospheric scientists do is they collect data from all these receivers. They get the slant TEC between every receiver and, um, satellite. They try to convert slant TEC into vertical TEC to get a vertical profile of the electron density. Um, take all that data and interpolate it and so forth to get nice TEC maps of the globe. Um, this has actually led to some cool science. This is pretty old now – 2001 – but I really love this example. Um, where they're using – so a lot of ionospheric scientists use GNSS signals now to actually study the ionosphere and study even the plasmasphere. Um, this is a really cool case where there's this, this sort of tongue of additional ionization in the GPS map. So all these squares of color are again GPS measurements of TEC. Um, and this sort of extension over the, over the lakes and into Canada here was observed. Um, and then relatively quickly they were able to, to, to figure out that that tongue in the ionosphere was a mapping of this feature called the plasmasphere plume down into the atmosphere.

Is there a comment or question? Okay, that's right. So this – so this okay – so this plume – the plasmasphere is, you know, nominally circular, but there's this – there can sometimes be this enhanced plume feature, which is on the – I always get this wrong – dusk side. You think about where the sun is. This is the dawn, dawn side over here, 6 AM, dusk side. So you get enhanced plasma densities forming this sort of finger way, way out into the magnetosphere, and, um, in this particular event they saw that plume essentially map down into the atmosphere, causing this enhancement in the atmosphere. So, um, all based on this, this GPS TEC observation.

All right, cool. Okay. Um, I don't know if I'm talking about this too much. Um, I wanted to briefly talk about a couple of the missions that are going on, something I do in the class that I teach. Um, I talked about the, um, this fountain effect before, and, you know, it gave a pretty good explanation for how it arises. In some of the animations you saw, it doesn't look exactly like this, does it? So this is what a model might say the anomaly should look like, and here's data from the TIMED mission. There's a lot more structure; there's a lot more interesting stuff going on. Um, so this was one of the main goals of the ICON mission: understanding drivers of ionospheric – so the questions I've written here, these are the science goals of the ICON mission: understand drivers of ionospheric variability, explain how energy and momentum from the lower atmosphere reach the environment, including gravity waves, and explain how drivers create extreme conditions during geomagnetic storms. So here's a picture of the satellite. Um, the ICON mission has a bunch of instruments on it. Um, we talked very briefly about these optical emissions. One of the main ways ionospheric scientists study the ionosphere is through these optical emissions. So this satellite has a bunch of optical instruments: Michelson interferometer, FUV imager, EUV imager, as well, and then some in situ stuff: ion velocity meter, RPA, etc., um, to measure and study the atmosphere. So this nice picture showing the satellite is also showing the airglow from the ionosphere – it's that excitation‑relaxation photon emissions – um, that they can use to study the structure of the atmosphere. So that's ICON. Um, I will skip over some of this stuff.

Here's a really – I really like this diagram of the ICON conops. Um, here's ICON at three different times in its orbit crossing the magnetic equator in red – that might be the geographic equator, yeah, it's the geographic equator. Here's the magnetic field lines, so there's the magnetic equator. Um, so as the mission flies, one of its instruments, um, is looking in this direction, in at this region of the ionosphere, and so that's mapping down to where these magnetic field lines sort of reach the ionosphere. So it's looking at that sort of, uh, the dumping ground of the equatorial anomaly. Um, the other instrument – not shown – MTA, MTA, MTA is looking this way, and MTB is looking this way, it's not shown. So at T equals 0, this guy's looking at this region. At T equals 7 minutes, the other interferometer is looking back at the same region. So they get two cuts, seven minutes apart, looking at the same region from different angles. Uh, at this three and a half minutes in between, you've got your in‑situ measurements measuring here at the equator, uh, and then the UV and EUV and FUV imagers looking towards the limb and observing that same region. So at three different times, the satellite sees the same region from three different perspectives. Um, so that's the sort of basic conops of the ICON observations. So you can see how the stuff I described about the equatorial anomaly really ties into this observation; they're really looking at that region at the, the, the whole – the edge of this anomaly.

Okay. Uh, so the animation I showed you before – they made another animation of this that actually includes the satellite and the fields of view. Uh, so this kind of highlights the same, the same idea. So you'll see as the, as the color comes in, you can see the fields of view better, but it's showing the fields of view of those three instruments and how they kind of look at different parts of the environment there. Uh, so the anomaly is coming in very, very slowly this time, and there's the instruments staring at all that stuff through a real orbit simulation, of course. See the orbit processing ever so slightly getting closer to the magnetic equator. Now all right, cool, right. Uh, there's another – I'm going to skip this video. I'll, I'll send it to you. It's a little PR video for the ICON mission. It's not going to tell you anything new, so uh, you can, you can look it up on NASA. I'll give you the link. Um, okay, questions here? Otherwise, I'm going to transition to last and different topic. Okay, talked about Earth's ionosphere. Uh, let's talk a little bit about comparative ionospheres. Uh, I use these two because they are very different from each other but similar to the Earth in different ways. Um, so I think they provide really nice comparisons. Also the two that we know the most about.

So let's look at Jupiter first. Jupiter is a great big gas giant planet, you know this. Um, its atmosphere – it has an atmosphere, it's, it's a gas giant, but how we actually define the atmosphere is totally definable. There's a – the altitude here is relative to one bar, where one bar is similar to the Earth's surface. So you can think of this as an altitude, even though the atmosphere does extend below that, below zero. Um, Jupiter's atmosphere is mostly H₂. It's a hydrogen atmosphere. Uh, so you would expect that ionization – UV from the Sun is going to reach Jupiter, it's going to ionize H₂ and produce H₂⁺, and it does – a little – no, it doesn't. Doesn't – it does, uh, hit H₂ and dissociatively ionize it into protons and hydrogen atoms. So that's your main production mechanism of electrons and of protons in Jupiter's ionosphere. Those protons then charge exchange with H₂ to create H₂⁺ and H, so you do sort of temporarily get some H₂⁺, but then H₂⁺ after it's created reacts with the neutral H₂ that's still in the atmosphere and produces H₃⁺, uh, and, uh, neutral hydrogen. So you look at the profiles here of the Jupiter atmosphere, and this is the H⁺ profile – so that's the protons going down here – sorry, the laser pointer's very tricky to work with – um, and then there's the other profile here which is actually the H₃⁺ profile, like so. And the, the, the solid line between them is the electron density. So your dominant ions are actually H⁺ and H₃⁺; there's really not a whole lot else.

Now on Earth, how do we actually measure this stuff? How do you get a profile of the Jupiter ionosphere? On Earth we've got our ground‑based sounders, we've got our topside sounders, we've got in‑situ measurements, we've got all sorts of stuff. On Jupiter, the really the only measurements are these, um, occultation measurements. So you've got a satellite – obviously I didn't draw this picture – uh, that is orbiting around the back of the planet, uh, or maybe it's coming out; it's either the ingress or the egress of that observation. Uh, Earth is way off to the left to our receiver. So we've got a radio receiver all the way back here at Earth, all the way back here. And the satellite could be Galileo, could be Juno, is flying around Jupiter and transmitting signals back to Earth. Um, as it, as those signals pass through the different layers of the ionosphere, they get absorbed, they get, uh, they go through Faraday rotation, they get refracted a little bit – Faraday rotation means the polarization changes as it propagates through the atmosphere – um, and our receiver back at Earth can measure those changes: absorption, Faraday rotation, refraction, etc. And from all of these slices through – we, you know, we have to assume kind of a uniform ionosphere around the planet – you can back out a profile. Uh, you can probably guess from this picture it's not trivial to do that, because each slice is going through different altitudes, and so it's sort of integrating through these sort of strange cap‑shaped caps, right? Um, but it's doable; that inversion is possible. So you do that inversion, you get an altitude profile. This is a picture from Saturn, of course this is different, but Cassini did the same thing, uh, going around Titan and around Saturn and measuring the atmospheric profiles of Titan and Saturn as it sort of went behind that planet. Um, so I throw this in here as a nice illustration of the process. We're not paying attention to Saturn.

Um, so here's some actual altitude profiles made by radio occultations from Galileo back in the mid‑90s. We've had very few missions to Jupiter, so you work with what you get. Um, Galileo – again, the ingress is initially coming in behind the planet, and then the egress is when it reappears from behind the planet back into view of the Earth. Um, and so you get ingress and egress ionosphere density profiles. So these are electron density profiles, uh, reaching up to about 10⁵ per cm³; it's actually a very similar density to Earth's ionosphere. Um, the altitudes are quite a bit higher though, as you can see – they're up here at about a thousand kilometer altitude. Um, and there is some significant structure; there's lots of altitude structure here. Uh, you also see that there's quite a bit of difference between the ingress and egress profiles. Uh, so different sides of the planet, or even just different times – these observations are made at different times. Uh, there's obvious – we expect there's going to be ionosphere variation, but it's hard to get enough data to really look at what's driving that variation, right? Um, so there's lower layers. Some of the papers that published this suggested that some of these thin structured lower altitude layers could be due to gravity waves or other types of processes, um, as opposed to just ionization Chapman profiles, right? Question? Well, it's probably not physical, is it? Um, you know, it's, it's getting low, the low, very low densities at this point. Um, obviously there's uncertainty in the measurements. Unfortunately, they didn't put error bars on this plot. My guess is if you put error bars, they would extend above zero. Yeah, so it's probably just measurement error. Yep.

Um, other thing I wanted to point out: the altitude. So look at this altitude now compared to Earth. This is way up at a thousand km altitude, the peak of this ionosphere, compared to Earth's peak at 300 kilometers. What do you think drives that much, much higher altitude of Jupiter? Two things – nobody? It's the atmosphere, I'll tell you that. So what are the two features of the atmosphere that are different? It's lighter; it's hydrogen, so the whole atmosphere is extended to higher altitude, uh, and therefore ionization is happening at higher altitude. Um, the other factor is temperature. The Jupiter atmosphere is significantly higher temperature than Earth's, and so kT over mg means we have a higher scale height; everything is just stretched out, so that pushes all the ionization to higher altitude. I didn't include the atmosphere plots, um, but they're there.

Okay, this is really cool. Jupiter has a strong magnetosphere, much stronger than Earth's. Um, you learned probably learned about that when Fran was here: Jupiter's magnetosphere. Um, just like Earth, you've got a kind of a dipolar magnetic field. It's in a similar orientation relative to the sun. Uh, the, the magnetic pole and the geographic pole are perpendicular – roughly perpendicular to the ecliptic. So given that, the fact that our, the magnetic field's very similar, we should expect a lot of the same stuff: sporadic E, the equatorial anomaly, etc. We can't observe all these things – we don't have the instruments out there – but the equatorial anomaly in particular has sort of been observed. So again, here's the process, right? You've got rising, uh, electron density which falls back down the field lines, creates enhancements – so here's actual observations of the electron density as a function of latitude at two different altitudes, at 2,000 km and 3,000 km altitude. So there's a minimum at the equator and there's a peak about 30 degrees north and 30 degrees south. Uh, the different squares and triangles are for high and low solar activity. You know, they've, they've limited measurements of this, so they're piecing together – what, 12 total observations – but they paint a pretty good picture of this same phenomenon occurring at Jupiter. So that's cool.

Okay, I will jump to Mars. Um, so same thing – any atmosphere that's near a star that's got EUV is going to have an ionosphere. So we get ionization of – so Mars' atmosphere is primarily CO₂, what is it, 96% CO₂ and the rest nitrogen. So largely you're getting direct ionization of CO₂. Um, and the, there is chemistry, but CO₂ ends up still being the dominant ion. So most of what we're looking at here is CO₂⁺, and electron density. Um, the ionosphere then fits the Chapman layer really well, because the CO₂ is the dominant ion – elect – yes, oh, thank you, O₂⁺. I will write that down and I will update these things. Okay, so you end up with O₂⁺ as dominant ion. I don't mind being corrected; I appreciate that. Um, O₂⁺ is a dominant ion, electrons. Uh, you do get a pretty good fit to a Chapman layer then. And so these plots are actually showing you the M1 and M2 regions of the ionosphere, sort of equivalent to E and F regions, and the Chapman layer fits – in blue, it's sorry, in black and red there – the solid lines. This is obviously your daytime profile; here's your nighttime profile. This is 10¹¹ electrons per meter cubed, which again is about 10⁵ electrons per centimeter cubed, similar density again to Earth and Jupiter. So that peak density ends up being similar here. Uh, the two plots on the right and left, I believe, are simply different times, so you're seeing some variation in the altitude and the density, etc. And then occasionally maybe a D region. Um, and again, notice the altitude. So here the altitude – the altitude of the peak is way down at about 150 kilometer altitude. Same questions: it's not the mass in this case, because – if you've got CO₂, it's going to be heavier, so it's going to be a little bit of a lower atmosphere. Uh, it's a lower density atmosphere, so that pushes it to lower altitude, and temperature is definitely lower, so all that's pushing the ionosphere to a lower altitude.

All right. Um, here's some plots of the, uh, Mars ionosphere composition. You think these are measurements? Don't we wish. No, of course not. Uh, this is from something called the M‑model, um, and so it's again a model of the ionosphere. So you've got your – uh, and the two plots here are 60° latitude. Um, I think, I believe they're low solar conditions and high solar conditions. So you've got electron density profile, uh, and then all the different ions. Um, you know, this is great because I should have – I should have noticed this myself on this plot. Here's your dominant O₂⁺ ion; there's a little bit of CO₂⁺, there's a little bit of O⁺, and various other ions. Um, all again related to what happens to be in the atmosphere and therefore available for ionization.

Okay, so, uh, you do end up with about 90% O₂⁺ and about 10% CO₂⁺ as the dominant, dominant ion sources. What else do we have to say about Mars? Um, this is where I should have reviewed the slides before I came. So we ionize CO₂, uh, we get CO₂⁺. CO₂⁺ reacts with atomic oxygen, produces O₂⁺. Um, and then the loss mechanism is the recombination of O₂⁺. So that's what's giving us our primary loss mechanism. This, uh, recombination – dissociative recombination of O₂⁺ – one of those atomic oxygens ends up in an excited state and, uh, relaxes back down and emits a photon in the 5577 wavelength. So there's a natural green line, uh, airglow in the Mars ionosphere. There is a little bit of N₂ in the Mars atmosphere, which gets ionized, does the similar processes that Earth – reacts with atomic oxygen, makes NO⁺. So that's where the NO⁺ in Mars comes from.

Okay, so observations of Mars ionosphere: we've got better observations than we do for Jupiter, for sure. I haven't actually updated this with MAVEN stuff; I should do that. Um, back in the Viking era, you had the, these, um, instruments descending through the ionosphere making in‑situ observations. So this is – are you guys familiar with the retarding potential analyzer? Who's heard of this instrument? A couple people, not too many. It's a pretty neat instrument. So this is an in‑situ instrument that's flying; the spacecraft is flying in some direction, and ions simply enter this aperture due to the ram motion of the spacecraft. Um, you then have a series of grids, uh, set to different voltages, which will – certain ions with certain mass and charge will get essentially, uh, uh, turned around, right, depending on the polarity and the amount and the voltage on these things. Certain ions can just get rejected from the system, and other ions can get preferentially accelerated down to the detector. So by adjusting the voltages, which you can do very, very rapidly, you can select different ions, uh, to measure at the detector. So this is how this very simple instrument with just a collector can actually give you some composition measurements. Um, so that's what they've done here. Uh, there's some solid lines for the theory, uh, just based on chemistry; some dashed lines of the Viking 1 measurements. There's your O₂⁺ profile, your CO₂⁺ profile, and your O⁺ profile. And unfortunately, no error bars. Um, so this is one way that we actually get, uh, direct ionosphere profile measurements from Mars.

The other way is to do radar. And so similar to Earth, you can transmit from below. You've got something on the ground with a lot of power and a power source. We don't have that. Mars doesn't have that; we have not yet landed anything that can do an ionosonde from the ground on Mars. Um, but orbiters can do this. So orbiters, um, orbiting Mars can transmit, um, in this frequency range, a few MHz, and they basically become a topside sounder. Um, so this is actually showing you – these are spectrograms showing time, um, time delay on the y‑axis and frequency on the right, on the, on the x‑axis. Um, and converting that to apparent range. And each of these sort of ionospheric echo structures – this is essentially your ionogram for Mars, which can be used to infer the topside density. So you take this ionogram of what's the time for different frequencies, turn that into a density versus altitude plot with the little diamonds, and fit that to a Chapman profile. Um, so this is the example from Mars Global Surveyor, here it is now actually compared with the in‑situ Viking measurements – not taken at the same time, of course – um, and showing actually a pretty good agreement of the atmosphere to the Chapman profile.

Right, cool. There's solar cycle variation on Mars. Um, this is from Mars Express and it's showing you just a variety of topside profiles taken at different times. Uh, so there's four different dates shown here. And, uh, declining phase of the solar cycle, the lower phase, increasing phase of the solar cycle, and then the peak of the solar cycle. And sort of as expected, at the lowest part of the solar cycle you have these low density profiles. The, the solid profiles here are the same for all, all four to compare, and the gray lines are the actual measurements. Um, so here's the sort of minimum ionosphere, here's a maximum ionosphere, and some stuff in between. So significant solar cycle variation, as we would expect.

Do the E sources? Um, and then there's actually been some observations during flares as well. Uh, so this is from a Mendillo paper, yes, 2006, again using Mars Global Surveyor. And they were doing – in this particular case they were doing the, um, the occultation measurements, not the direct sounding measurements. So they're, they're doing Mars Global Surveyor is doing occultation measurements to get ionosphere profiles by transmitting back to Earth. They're doing it at a much higher – at a higher frequency, so they're really looking at Faraday rotation and stuff. So they get a whole profile. And during this flare, which is the red profile – the green arrows are what I've drawn in – you're seeing this huge enhancement in the electron density primarily at the lower altitudes. And again, this is what we observe at Earth: the x‑rays penetrate the atmosphere to the down to 100 kilometers and below, that's where they get absorbed, that's where they ionize and increase the electron density down at the bottom. So these plots are the change in electron density in percent units. So below 120 kilometers you're seeing 100% or more increase in the electron density. Um, I look at this plot and I see big enhancement all the way up to 120 km. To me, that says soft, soft x‑rays. These are actually fairly lower energy x‑rays; the higher energy x‑rays get deeper and deeper into the atmosphere, they ionize way down at 70 kilometers or, or lower. Um, so this tells me that these are mostly what we're looking at here are the effective soft x‑rays.

Okay, so I think that's the, that's the end of my comparative ionospheres discussion. I'm well ahead of time, so we got lots of time for discussion, questions. Um, and my last slide here kind of does the comparison between Earth and Mars – uh, sorry, yes, Earth and Mars. Did I not include the Jupiter one? Um, so in a lot of ways it's very similar to Earth, and then in other ways it's very different. Uh, Mars – the atmosphere has no stratosphere, so therefore there's no ozone, there's probably no ozone layer. Um, it's mostly CO₂. Atomic oxygen in the thermosphere, same as Earth. The scale height of the atmosphere is a little bit higher but pretty similar. Um, and so those similarities and differences in the atmosphere help lead to and explain the differences in the ionosphere. There's a peak density that is similar, but it's at a little bit lower altitude. Um, mostly O₂⁺ due to this reaction. Um, but similar to Earth, there's variability with solar cycle, solar flares, effect on radio wave propagation, etc.

All right, and that's it. That is the last slide. So I am well ahead of time, talking too fast, and I'm happy to have lots of questions and discussion. As Tanya knows, this is probably the first time I've ever finished early. What do you guys think? Yes, questions. Thank you.

Um, from your, your first talk you showed, uh, uh, two comparative images of the Mother's Day storm at mid‑latitudes, and I was wondering if there's any, um, like, um, method of transport from high latitudes to mid‑latitudes. Yeah, there definitely is. The, the, the transport though between latitudes – um, it's first of all, it's getting a little bit out of my expertise, but I, I do know this: it's a phenomenon that happens relatively slowly over the course of days. So you can have enhanced ionization at high latitudes. There's, uh, the one of the phenomena is called MSTIDs – you've heard of MSTIDs? Now, mesoscale traveling ionospheric disturbances. So you get disturbances at high latitudes, and they will propagate in the ionosphere down to mid‑latitudes, like over the US. Um, but the time scale of that is, is relatively slow. Um, that is a phenomenon though that people are, are you know, well aware of, very interested in, study frequently to understand the propagation of the whole system. Thank you. Traveling atmospheric disturbances? Well, the TIDs are more of a latitude propagation, not an altitude propagation. But you're right that the Joule heating in the high‑latitude regions leads to increase in the atmosphere density, right, raising of the atmosphere, and that's, uh, one of the triggers that sort of – you know, think of it like pulling on a string – like that creates the wave that then propagates to lower latitudes. Yeah.

Um, so I have two questions. And one is, uh, how are the equatorial electrojet and the E‑region dynamo related? Oh, that's a question that's outside of my expertise too. Yes, the dynamo, the dynamo – I don't understand. I'm going to just tell you right off the bat. Yeah. And then my other question is, you talked about how, um, the something was mapped down onto the ionosphere. What physically is meant by "mapped down"? Because like sometimes, uh, I hear it a lot when it comes to like, oh, the magnetic field lines are mapped down onto lower parts. What does that mean? Yeah, yeah. Um, I wonder if I can, if I can find a good picture that would describe this. Um, anywhere – any of my slides that have a magnetosphere in them – you could use this for example. I want a bigger magnetosphere picture. So when we talk about mapping, we're largely talking about magnetic field mapping. And when we say mapping, we're actually saying like the connections of magnetic field lines. So think about the magnetosphere with its great big dipole. You could start with just the dipole field and, uh, say for example just go out to like – this is where I was talking about mapping, right? Yeah, um, I need the third dimension here to show you what we mean. These, these blue arrows are supposed to be kind of out of the page and then coming back down into the atmosphere, and following magnetic field lines. All right, yeah. Is this where, where you wrote down that note? Probably, yeah. So consider that this picture is plasma in the equatorial region of the magnetosphere. And so way out here at, you know, in the, in the plume, I'm out there at like L of 6, I'm at Earth radii. Um, there's a magnetic field line out here which is vertical and maps back down to the Earth's atmosphere at some latitude. For L of 6, it would be like 75 degree latitude or something. So the phenomena occurring at L of 6 out in the magnetosphere or in the plasmasphere is going to connect to the atmosphere along that magnetic field line. Um, and the reason is because plasma can move along magnetic field lines very easily, right – gyrating electrons – but doesn't move across field lines as easily. So there's often a mapping of the phenomenon happening out in the magnetosphere down to the atmosphere directly along magnetic field lines. Thank you.

Yep, yes. The magnetosphere – to return to steady state, to relax. Yeah. Um, we so – it depends on, it largely depends on altitude. Um, the, the question was: how long does it take the ionosphere to sort of relax back to normal? Um, if you have a flare, say you had an impulsive flare, uh, instantaneous, right – they're not actually instantaneous, they have some time profile, but assume that it was instantaneous so we could actually see the temporal response of the atmosphere – the ionosphere. Um, you know, that flare is going to ionize a bunch of stuff, and then immediately chemistry is going to take over, and recombination is going to be the main way for it to relax back to normal. So the time for it to relax depends on those recombination rates. Um, but also depends on the concentrations. So if you're at – an x‑ray flare that produces ionization at a low altitude where there's a lot of neutrals available for collisions, it's going to relax much faster. Um, so down at 60–70 kilometers, the relaxation time is like seconds or less. So really at those altitudes, you're actually measuring the temporal profile of the flare itself. Make sense? Because the flare, the flare itself is longer in duration than the recombination time; it's almost responding instantaneously relative to the flare. At higher altitudes, the recombination time can get up to like minutes. Um, but really not more than a few minutes. So even there, if the flare lasts for tens of minutes or even hours, um, which is pretty common, uh, the, the relaxation time of the atmosphere is, is faster than the flare itself.