Transcription
Okay, so I want to move on to the ionosphere now. I'm going to skip a couple of slides because I want to talk about interactions and some fundamentals pretty quickly. But I think one of the most important things you can remember, or you can take away when it comes to the ionosphere, is the fact that the ionosphere is formed in layers. And so it's important for you to understand why there are layers in an ionosphere, and that's produced by different production and loss processes, and if necessary, the action of diffusion, that is, gravity, which also acts on the charged particles.
So, you know, I'm just going to describe the Earth's ionosphere. Actually, the production and loss processes and the things that are going on in other planetary atmospheres will be, normally, covered by Luke, I'm sure, on Monday. But, but for now, just to point out that the E layer and the F layer—I should also point out that I think there's a lab about production and loss processes that produce layers in the atmosphere—that lab's on Monday, is it? Okay, so you'll be able to sort of play with different production and loss processes in order to see what their effect on the composition and altitude is. Yes, yeah. So you'll learn a little bit—sorry—oh, sorry. All right. Yes. Oh, the delay. Oh, yes. Okay. Well, yes. All right. Know that there is a delay. It's not very strong, and it involves the absorption of energetic particles and very high energy—much higher energy—photons that get deeper into the atmosphere. So, but the principle layers in the Earth's ionosphere—that were layer was first seen was the E layer due to a radio wave bouncing across it—and it was called the E layer because "E" was used for the electric field vector that was reflected off this layer. And then subsequent layers were observed above and below it, and they got the names F and D and so on. But there's a difference in the chemistry and the production and loss processes. And the point I want to point out is that some of these layers are—the equilibrium is established between the production, photoproduction, and the loss—and other layers are produced by an equilibrium between the production and diffusion and gravity. That is, the production, photoproduction, creates the plasma; the plasma builds up in pressure, and it continues to build up until the pressure gradient opposes gravity, and then you get an equilibrium.
Okay, so those are—there are two kinds of layers: E and the F1 layer, a chemical production equals loss layers; the F2 layer in the ionosphere is produced by a balance between the photoproduction and diffusion. And you can look at this—just do an exercise in your head, maybe after the lecture is over—look at how you produce an F2 layer by ionizing O, and look at how you get rid of the F2 layer by recombining with N2, and ask yourself, as you go up in altitude, how quickly do those processes drop off? One of them drops off as the scale height of O, and the other one drops off—that's the scale height of N2—so which one drops off most rapidly? Right. So the loss process drops off more rapidly than the production process. So as you go up in altitude, the density should just increase forever. So if you just had photoproduction and chemical loss, you would predict this density in the F2—I would increase indefinitely. But if it does—now you start creating a very large mass that now has to—has to cope with the gravitational attraction of the surface of the Earth—and so now you get a balance between the—between the pressure gradient in the gas and gravity. That's what I call diffusion. Yeah. Oh, oh, yes. Okay. These are—these are just the reactions, but not the reaction rates. The reaction rates will determine how rapidly these densities are created—are destroyed and created—will depend on the rate. So here in the—in this layer, the F1 layer, you produce O2+ + N2+ + O—O− + + N2+—lost O2+ by this reaction, N2+ by these two reactions. Yes. Oh, sure. Yes. Well, that's because I don't have—I have not included the chemistry of atomic nitrogen, right? So there's other chemistry that—that is incomplete here. I just looked at the production and loss of the ions, not of the neutrals. Okay. Okay.
A word about equilibrium in a plasma. You've all heard—had the benefit of the lectures by Dr. Liang Bo C at the beginning, and so the thing I want you to remember is that in a plasma—the ionosphere is highly magnetized—the particles gyrate around the magnetic field. So the perpendicular motion of the gyrocenter—and motion of a charged particle perpendicular to B—requires a force perpendicular to B. Okay. If you go parallel to B, then the gyrocenter motion of a charged particle moves just as if the magnetic field were not there. The part—the gyrocenter is free to move along the magnetic field just as if the magnetic field were not there. So if there's no external forces, then parallel to B, the plasma just moves in response to a pressure gradient and gravity. So it looks just like a neutral gas parallel to B. I'll talk about perpendicular to B in more detail later. So parallel to B, there's an equilibrium between the plasma pressure and gravity, just the way there is in the neutral gas. But the plasma, of course, consists of ions and electrons, and so the pressure for the plasma is NK TI plus TE, and when it's in equilibrium with gravity, it falls off with altitude according to a scale height, and the scale height looks like this and contains both the ion and the electron temperatures. You can refer back to your notes on Dr. Gumbel's from Dec to again—we'll see on that—but that's a scale height of the ionosphere. Okay. Um, this is just reference to an international reference ionosphere. I don't have any homework associated with this. But similarly, you can go to the same address you can see here, and you can investigate what the ionosphere looks like from measurements. So when you get done with your lab on Monday, looking at various Chapman layers, you might go to the IRI model and look at the model ionosphere and compare it with the Chapman layer calculations that you did in the lab and see whether—where the profiles look the same and where they look different, and why you think those differences might exist. So, well, here's a question about production and—and loss in a photochemical equilibrium situation where the photoproduction is equal to the chemical loss. Then if you know something about the loss rates—which we can calculate in the laboratory—we can observe, and you can observe the total density, then it's possible to discover what the production rate is. And so again, just from the simple argument or a simple understanding of photo—of this equilibrium between production and loss, you can derive one parameter that's very hard to determine—that's the production rate—by just knowing what the total density is, which is fairly easy to measure, and—and calculating or discovering in the lab what the reaction rates are for the recombination.
Okay, so now I want to talk about some fundamental principles, and these are the principles I was talking about at the beginning that I believe if you—you're dealing with a plasma—maybe it's a stellar plasma, the interplanetary medium, the plasma in the Sun—doesn't matter what I'm going to tell you now applies equally, even though I might personally use it in the ionosphere thermosphere; it applies in the magnetosphere, the interplanetary medium, the Sun, and interstellar medium and so on. So, and there are conservation theorems. Okay, so the first one I want to talk about: conservation of mass. So in the neutral atmosphere, conservation of mass—you—you've probably seen these conservation theorems before. Everybody knows about this structure for a conservation theorem, right? In a given volume. Yeah. Everybody either knows or—no, they should know. Right. Yeah. Okay. Go. So this just says, if I look inside a volume, the rate of change of the density—mass density—in that volume is determined by whatever can change that mass density in time, plus if there's a flow of mass density through the volume, and a difference between the flow in and the flow out, that will change the density in a volume. The change in the density is either a change in time or the change in the flux. And if this is the neutral gas—since I'm not creating or destroying any neutral particles—that sum of these two things has to be zero in a neutral gas. That's a fairly straightforward—I do want to talk a little bit about this derivative following the motion. Everybody familiar with this derivative following the motion? Or—again—know that you should be. Yeah. So there's a difference when you're looking in a fluid, right, whether it be a plasma or a neutral—you can do two things: you can look remotely on a fixed volume in the fluid and say what's happening, or you can take a little fluid parcel in a volume, and you can sit on that fluid parcel and you can move with that fluid parcel wherever it moves and ask what's happening, right? If you sit on the parcel and you move with the parcel, that's called the derivative following the motion; that's denoted by this D Rho DT here with the straight DS. If you look remotely in from the volume, then you have to take into account both changes in time and in space, and so there are two components to this D Rho DT here—this change in time and another term here, U dot grad Rho, which is the change in the density that you experience along the direction you're moving, right? Makes sense. Okay. So so we can write this in—in one of two ways. In the neutral atmosphere, it's generally assumed that the—that the fluid is incompressible—grad U is zero—and so if I put grad U is there in zero in this term, it just says D Rho DT is equal to zero. That means if I'm a little packet of plasma or a packet of neutral gas, when I move around, there ain't no change in my density because I'm incompressible. In a plasma, we have exactly the same physics, except we can create plasma by photoproduction, P, and we can lose it by chemical losses. So in a plasma, the conservation of mass equation for the number density in a volume contains production and loss and the divergence in the flux. In the neutral atmosphere, adjust the divergence in the flux. Okay.
Of the next conservation theorem is conservation of momentum. Okay, so maybe you'll recognize this. I don't expect you to do the math. Okay, I just want you to recognize that when you look at conservation of momentum, you need to list in your head the forces. So here are the forces in a neutral gas: there's a pressure gradient force, the Coriolis force—because the planet is rotating—it's a rotating medium, gravity; there's viscosity in a fluid, and that neutral gas—if it's in the atmosphere, in the upper atmosphere—can collide with charged particles, and so those collisions with ions—that's another force. So these are the forces in the neutral gas. Okay, and over here is the acceleration term. Now you'll notice I put these derivatives following the motions on—sitting on a parcel of gas and just asking what—what do I see? In a plasma, the Coriolis force and viscosity are very small. Okay, just a word of warning about "very small" to all of you: when you're doing analysis, it may well be that terms are small compared to these other terms, but always when you're doing a term analysis like this, you need to make sure—ask yourself: can any of these terms ever be zero? Do they go through—can they go through zero? Because if they can, even these small terms that you might be trying to neglect might be the only guys in town if the other terms are zero. Okay, so just be careful when you neglect terms that you make sure the other terms really have finite and large values. In a plasma, we can generally neglect Coriolis and viscosity, but we have electromagnetic forces. So is the pressure gradient—it's common—is gravity—it's common—here are collisions with the neutral gas—now because the ions are moving—and then the other force observed by a plasma is the J cross B force. Everybody okay? Happy with this nomenclature? Okay. So the forces in a plasma are the pressure gradient, the electromagnetic force, J cross B, gravity, and collisions. And what you'll see is that this term involves the neutral-ion collision frequency and the velocity difference. This term here involves the charged particle-neutral frequency and the velocity difference. So these two terms are the coupling terms; this is where ion-neutral coupling comes from, right, in the collisions between the ion and neutral gas. And then one final note for those of you are in the interstellar medium or the interplanetary medium or in the Sun: most of those studies come by looking into the medium and not sitting on the plasma. So you don't look at the derivative following the motion; you look at the derivative with respect to time, and that term there has the derivative with respect to time plus this term, V dot grad V—a change in velocity along the velocity. This is generally referred to as the inertial current inertia. So sometimes this DV DT will be over here, and you would take this inertia term and put it on the right-hand side, and now you have all the forces, and one of the forces you'll consider will be inertia. Okay, I just written that like this. So if you're a plasma person—okay—you're looking in the Sun, in the interplanetary media, in the interstellar medium—you look at all these forces with the exception of this guy, right, because it's a collisional—it's plasma, and we don't have to worry about collisions. Normally, we're going to be far enough away from the—from the—from the body that we don't have to worry about gravity, and so we'd consider inertia, pressure gradient, and the electromagnetic force. So this is exactly the same equation you use—yet I use it too—even though we're an astronomical unit apart.
And then finally, conservation of energy. So I'm not going to write the equations because I don't want to fuss with the—I don't want to distract you with the details. I want you to recognize that the collisions between ions and neutrals also exchange energy between the particles. So if you look at the terms that go into conservation of energy in the neutrals, the electrons, and the ions, they contain collisions between the ions and the neutrals and the electrons and the neutrals. So coupling between the plasma and the neutrals also exchanges energy between the species. Okay. So now I want to look at the results of those—those interactions, and just invite you to do—is a simple process, which I think you may do in your everyday lives when you're doing your research, but just to be aware that you're doing that. And so what we normally do would take the conservation of momentum equation, and we would assume a quasi-steady state, and this—we take the DV DT term and say, let's assume that's zero. Okay. When that's zero, what you're doing is you're equating all the forces—you're saying the system is in force balance. So the plasma is moving at a constant velocity; everything in the system is behaving in a quasi-steady state, and so all the forces must be in balance. In a plasma, for example, is the force balance equation for the positively charged particles: the pressure gradient, gravity, is the electric force and the Lorentz force, collisions with the neutrals, and—well, is that the term I've divided up into collisions with ions and collisions with neutrals and the ion velocity. The reason I do that is just to point out that there are a lot of forces that are independent of the velocity and then forces that are dependent on the velocity. Okay. So good question. So in the ionosphere where you have ion-neutral collisions, the inertial term is very small, and so I've neglected inertia. In the magnetosphere, solar wind, stellar—I would need to be there—this collision term would not be there, but the inertial term would have to be in there. Okay. So the point I want to make is that when you have forces that are independent of the velocity—now you can see that the plasma moves perpendicular—experiences a force that's perpendicular to the direction it moves in B and have four sets in the direction in which it moves. Okay. So if you express the velocity in terms of that force, and you'll see—hey—you put a force parallel to B, the particle moves parallel to B. But if you—perpendicular to B—in response to a force, the particle moves in the direction of the force and in a direction perpendicular to the force and the B field. So the other thing to remember—and this is very important when you go to quasi-steady state and you look at this force balance—there's no causality exposed in these equations. There's no—this electric field right here produces this motion; all this pressure gradient produced this motion—no causality when you take out the D by DT term. It just tells you these forces have to be balanced; it doesn't tell you how that balance takes place. I'll come back to that, but that's a very important thing to remember. Okay. But what does this all mean? What this means is that the velocity of charged particles is dependent on the charge—see this nu over Omega term here—the Omega here—it depends on the charge of the particle—well, that—the velocity of the charged particles is anisotropic—that means the velocity of the particles is different parallel and perpendicular to B, and it's different in two directions mutually perpendicular to B. Okay. What does that mean? That means that any force applied to the plasma drives a current because it moves particles in different directions, and the currents are different in different directions. So the current parallel to B is different to the current perpendicular to B in the direction of the force and different in the direction perpendicular to B in perpendicular to the force. Okay. So this is just a picture—I don't want to dwell on it too much—just to show that if I take a plasma and I push on it with a force this way—I push on the ions moving in this direction—in the lower ionospheric atmosphere—when I push in this direction, the ions will move in this direction. If I push on the ions in the upper atmosphere like this, then you move in that direction. Okay. And so the direction in which the plasma moves in response to a force changes as a function of altitude because it depends on this ratio here—the ratio of the collision frequency to the gyro frequency—though if you look at the electron motion in response to an electric force—this is here—this is how the particles move as a function of altitude, and this is how the ions move as a function of altitude. At the highest altitudes, they move in the same direction at the same speed, so there's no current. Low altitudes, they move in different directions at different speeds, and so you drive a current. The other force would be at the collisional force; you look at the collisional force, then the ions move in the direction of the force at low altitudes and perpendicular to the force at high altitudes. The electrons, however, pretty much magnetized, they spiral around B, and so very low altitudes they move in the direction of the force, but above about 100 kilometers, they don't move with response to—in response to—a neutral—to a mechanical force. A neutral force can drive a current at all altitudes above 100 kilometers. So this is—this is more for reference here. So if you wanted to take away—and you decide you want to do a quantitative calculation—then you can take this away from you—the relative motions of the particles in response to a force are embedded in this value we call the conductivity or mobility of the plasma. And so there's a nice mathematical expression that allows you to determine the current in response to the force when the current is expressed in terms of an electric force, E, and there are two quantities here: one is called the Pedersen conductivity—everybody heard of that, right?—and the other one is called the Hall conductivity. But Pedersen and Hall conductivity is kind of useful if the force is an electric force, but what if the force is gravity or neutral wind? Then this—you've either got to re-derive all the equations, or you can use—Rod Hill—as is—Chi Chi—and you can take the force and simply express the force as F cross V over N nu, where nu is the collision frequency, and take that expression and plug it into this here, and now you'll get the current from that force. So if the force is charge-equivalent forces—charge independent—not an electric force, then just replace a perpendicular by F cross B over m nu. So if the force is gravity, for example, just gG cross B over m nu, plug it into here, and that's the current.
If the collisional force mmm new and new, you and just put it in here and plug it into there, half the current, okay? So I did the algebra for you, and there's a little cheat sheet. Okay, so um, facts about the conductivity, about this mobility. So this is a plot here again; it's it's kind of a takeaway that I want to give you.
In the Earth's atmosphere, in fact, it almost any planetary atmosphere with a magnetic field, the Hall conductivity is in a small layer. It exists at the lowest altitudes in the atmosphere, and because that layer is always normally in chemical equilibrium, photochemical equilibrium, when you turn the Sun off at night, and that layer goes away, and so the Hall conductivity is dramatically reduced. The Pedersen conductivity is distributed in these two regions in the Earth's ionosphere; two regions because there are two layers, the E layer and the F layer. The E layer is greater than the F region during the day, but the E layer goes away at night, and so the F region has the greatest conductivity at night.
If you look at the conductivity parallel to B, the mobility of the plasma parallel to B, it's many orders of magnitude. You can see the difference; in the scale here is 10 to the minus 6, and the equivalent scale here is 10 to the minus 2. But the direct conductivity parallel to B is 10,000 times bigger than the conductivity perpendicular to B. What does that mean to you conceptually, not I have to do calculations? It means you can think of the magnetic field; if you can draw a magnetic field line, they go—that is a copper wire in the plasma. So the Hall conductivity is the Hall conductivity responsible for the disappearance of the F1 layer; so those are related. So the Hall conductivity, it principally occurs in the E layer, okay? And the E layer rapidly recombines at night when you turn this off, and so the Hall conductivity is reduced rapidly in there, in the atmosphere of any planet, because it decays at night.
The F layer, in the F region, the F1 layer is also in photochemical equilibrium, so that layer also goes away when the Sun goes down. And so any conductivity associated with charged particles in the E region and the F1 region is rapidly reduced at night. In the F2 region, where the principal processes are photoproduction and diffusion, then the density doesn't decrease so much because you turn the Sun off, but the density can be replenished by diffusion, and so the conductivity in the F2 layer is retained, but it's retained in a region where the ratio of the collision frequency to the gyro frequency is much larger, and so the Hall conductivity is much smaller in the F region. Okay, so is another little animation.
Parallel to B, the neutral gas moves the plasma in the same direction as the wind. So as I said, that the charged particles behave parallel to B just as if the magnetic field were not there. So if there's a force along B, and the particles just move along B, and you can ask yourself what are the other forces? So what will happen is, in response to that force, the particle will accelerate, and it will accelerate, and the particles, the charged particles will will pile up in this region of acceleration, and they'll do that until the pressure gradient and the gravity and the collisional forces balance. So you can push on the on the gas, and this is parallel to B, right? So there's no J cross B force. I push on the gas, and as I push on the gas with a with the neutral atmosphere, the gas will move until it's supposed by the pressure that builds up because I'm moving it and gravity, if gravity exists.
Perpendicular to B, the neutrals will will move, will collide with the plasma and start to move the plasma. And what are the other forces perpendicular to B? In that case, the plasma will accelerate until the pressure gradient increases, gravity increases, and the J cross B force increases. So remember, when I push on the gas with the neutral particle perpendicular to B, the plasma can move in the direction perpendicular to the force. So what will happen if I'm if I'm just a neutral particle pushing on it on there ions? I can continue to push on the ions until I'm a tilt; my force is opposed by some equilibrium force. That equilibrium force is the J cross B force, the current that's produced because I'm pushing on it; that current produces a J cross B force that opposes the original force that I'm applying, and when those two forces are in equilibrium, now I just move at a constant velocity. So this concept of force balance can be used in a very simple way.
So here's just a simple exercise. Let's suppose I have a neutral wind that's blowing in one direction at this altitude here, and in the opposite direction in this altitude here, in an inclined magnetic field. The wind's blowing this way, and now the wind's blowing this way, and here's the magnetic field. Then parallel to B, there's a component force in this direction, and up here there's a force in downward in this direction. So as a result, if I started with a uniform plasma distribution, just flat like this, what I'll do is take this plasma and transport it down; would make this plasma and transported upwards, and I'll continue to do that until the forces that I'm using to move the plasma are opposed by the pressure gradient. And so the plasma density will move from that equilibrium distribution to this distribution like this, where the density increases and decreases, and this pressure gradient opposes this force, downward force, and this gradient in the pressure opposes this upward force. Now I have I'm in equilibrium; the plasma stops moving, but I've made a layer; in the ions used to have it equilibrium distribution of plasma, but now I got a layer because I've got winds that have this wave-like profile in them, and waves are in the atmosphere everywhere.
And if you look at the plasma density as a function of altitude, this is from the Arecibo radio radar, and you'll see traditional E region here. Now you see a layer; see this layer propagating down; is another layer down here. So these layers are prevalent everywhere in the ionosphere, and they're produced by this wave-like motion in the neutral atmosphere. This wave-like motion in the neutral atmosphere in Crete produces these plasma layers, layers in the plasma; that's the one of the first products of ion-neutral interactions that you'll see if you observe the ionosphere from below. No, this is altitude; yes. So this is plasma density; I guess the scale is not on here. These are these variations in the density are on the order of 10%; you're right; yes. So when you if you get this information from us from sounding, this information actually produced by scattered signals rather than a sounder, but that you're right; when you sound, you sweep the the frequency, and the certain frequency is reflected at a certain number density that corresponds to the refractive index and the plasma; yes. So it's virtual; yes. So what you do is you send out a pulse of the radio wave, and and it propagates up to the layer; it gets reflected and comes back down, and so you look at a time of the timing and you and then you take the the speed of light and you can convert that to a virtual distance.
So the other thing you can see in the atmosphere is, if you put magnetometers on the ground, your scent you can be sensitive to currents overhead, and if you look at those current systems, you can see them current and effective current circulating anticlockwise in the in the ionosphere near 120 kilometers. This is a so-called Sq current system, so low-quiet current system, and it's produced by the mechanical force of the neutrals on the plasma, and that drives a current; we just saw that just from their simple considerations. And so if you know that current looks like this, and then you can ask what kind of neutral wind, what kind of neutral relative neutral-ion velocity would I need in order to produce this current, and you can do calculations like that, and there's this is the wind systems that result from trying to reproduce this current system, and the wind circulated in this manner like this, and I'm not going to go into the details here, but if you had a heat source near the equator here, means local noon, you can perhaps imagine how the neutral atmosphere would circulate in response to a heat source here; it would move away from the equator, turn over, come back in these two big circulation cells like this, he's a Hadley type cells, and this circulation produces a neutral collisions—I'm not very good with this pointer—produces I neutral collisions and currents that are distributed in this manner. So this current system here is a direct result of the ion-neutral collisions, and if you look into that into the plasma, you can deduce fairly straightforwardly that the plasma moves with respect to the neutral gas, and what's in force balance is the collisions between the ions and neutrals and gravity; those are the two forces that are applied to the plasma. Okay, there are large-scale motions that result from that in the ionosphere.
The one thing I want to lead you through is just a simple little force balance consideration. So if we look at observations of the plasma near the equator, we see it moves up during the day and down during the night. There are some deviations that I don't want to dwell on here, but updrift is upwards during the day and downwards at night. Okay, so this is a very simple picture; who's up during the day, in midnight it moves to the west during the day and towards the east. These are simple plasma motions. So we can look at these plasma motions in terms of electric fields; velocity E cross B over B squared. Remember, this isn't force balanced, so it doesn't mean this E field would produce this velocity; it means that the velocity and the electric field coexist, but what is in balance is the force that produces this motion and the currents that flow in the system. So what's in balance is the collisional force with the neutrals. So let's say the plasma is moving upward, and the neutral atmosphere is stationary. So what direction is the force from the neutrals? Nobody actually wants to say downward, but everybody's looking down; you assume everybody's happy with the force being downward. Okay, so the plasma is moving up; the force that it feels from the neutrals is working down; that force has to be balanced by the current, all right? So well, what is the upward force I need from the current? Just gave it away; what's the force I need from the current? So I need an upward J cross B force to make the force balance. Okay, so what direction does the current have to flow? I see at least one person pointing their finger in the right direction; so the current has to flow this way; it has to flow to the east. Okay, so so this is a simple force balance; the current flows to the east, and the plasma moves up. Okay, now it's certainly possible for me to say, hey, well, I'm going to have that current produced by an electric field. Okay, so now in the in the F region, what direction is the electric field have to be in order to drive a current to the east? Like field has to be to the east, to right? So if the plasma across B drifts and the plasma and it goes to the east, what direction is the plasma move across B? Oh, right, which is that's right; it was moving up. So I can certainly take this current that's flowing to the east and tell you, hey, it's consistent with an electric field that flows to the east such that the velocity plasma is moving up at across B, all self-consistent, but the forces that are balanced and the J cross B force from this current and the upward and the collisional force on the plasma because it's moving up, and you can apply these principles everywhere. Okay, so this is a homework exercise; I'm going to have you look at it's a thought process, Oh calculations here, just a thought process about force balance in a plasma. Okay, yeah, alright, let me just draw on the force balance just one more; one you can see the results of our plasma move of that force because the plasma is moving up and it moves up perpendicular to B everywhere. So now let me just pose you a question: if the plasma is in this region here at the equator and it's moving up in this direction like this, what would you predict the velocity in the plasma will be right here? Right? I will entirely Oh perpendicular to B; we know that has to be force balance, right? So we know that the J cross B force, which is in and out of the board, has to match you the collisional force, which is along the negative direction of the arrow; is that there's a force in this direction; what would you predict the velocity of the plasma wouldn't be? We thought on that. Okay, so if we worked the equator, yeah, there was a the forces were perpendicular to B at the equator here, or would you predict the velocity would be? What direction? Allowing people got to be in the direction of the force, right? So here we have plasma forces all right in this direction up and down, and they're perpendicular to B, and so gravity is perpendicular to B, and so all the motions are perpendicular to B, but in this you off the equator here, now J cross V forces in this direction, the collisional forces in this direction, but gravity is up, and now the gravity has a component parallel to B though. Now in this region here, now I have a gravitational force down in this direction that has a component parallel to B in this direction. So now the forces are perpendicular to B and parallel to B, all right? And so now if I were to—this is a calculation—but now if I were to look at the plasma motion that results, you can see perpendicular to B at the equator, sure it's moving up and down, but away from the equator; in fact, at this location here that masti is almost horizontal because it has a component perpendicular to B due to the force to the J cross P force and collisions, but a component parallel to B due to gravity. So the motion of the plasma, the forces in the plasma redistribute the plasma, so you can see signatures of the forces present in a plasma by just looking at the plasma density, and this is just some an example, two examples of what the plasma density looks like, and you'll see some of the pictures like this when you look at calculating the density just from the forces that are present in the plasma.
One interesting feature from from this, just because there's at least one person here who's dealing with climate, there's some very interesting variations in the density, the change in longitude that coincide with boundaries between the continents and the oceans, and these signatures here are signatures of currents driven by waves that are produced by convective disturbances on the surface of the earth. So this is a relatively new discovery that we're still trying to figure out, but it's these are what wave-like signatures that are produced by convective disturbances on the earth, and they affect the ionosphere in much higher altitudes.
So I want to finish by just talking about the effects of relative motions between the ions and the neutrals in the plasma, and they show up in these two places: in energy balance and momentum balance. So when there's a relative velocity between the plasma and the neutral gas, there's an exchange of energies in this between the species such that the ions can be heated to a temperature that are in excess of the neutral temperature. This phenomena is called frictional heating. In addition, this relative ion-neutral velocity here exchanges momentum between the ions and the neutrals such that if the ions want to move at speeds greater than the neutrals, the neutrals impede the motion, and if the ions want to move at velocities that are smaller than the neutrals, then the neutrals apply an additional force to the art of the plasma to try to get it moving. And these relative motions, this energy difference in the temperature also shows up in the chemistry because this recombination of O+ with N2 is dependent on the temperature. So if you increase the temperature of the species, they can recombination rate goes up. So I want to introduce you to an interesting feedback mechanism here. Suppose you have a velocity between the ions and the neutrals that's different, then ion drag will try to set up the neutral; if the ions are moving faster than the neutrals, the ions will try to set the neutrals in motion; this will decrease the velocity difference between the ions and the neutrals, and there's a timescale associated with that, and that timescale is depends on the neutral-ion collision time. On the set at the same time, the ion motion through the neutrals produces frictional heating; this frictional heating depends on the ion-neutral collision time; depends on how frequently the ions strike the neutrals, but this frictional heating increases the recombination rate, which reduces the ion density, and that reduces the efficiency with which the ions can collide with the neutrals because there's not so many of them. So this reduces the ion drag, and so this is a self-limiting feedback in the ion-ion neutral coupling, which is very gratifying because you don't want to have a situation where the bulk dynamics in a fluid is unstable; this tells you that the bond dynamics is always stable.
I'll leave you with this plot as this is a very nice plot that shows the signatures of all these energy and momentum exchange. This is a plot of the ion motion seen high latitudes; this is this two-cell circulation that Fran referred to in her talk here, and you'll see that simultaneously this motion is being imprinted on the neutrals; neutrals are moving in the same direction of the ions here and here; there's a location here where the ion and the neutral velocities don't agree, and in that region where they don't agree, you'll see that the ion temperature is highly elevated; this is the energy exchange. So this region here is a signature of momentum exchange; ions and neutrals moving together; this region here where the temperature is increased is a signature of the energy exchange between the species, and you'll notice also that where the energy exchange between the species increases the temperature, the number density of the plasma is reduced; this is a signature of the chemistry that results from the interchange between the ions. Oh, this one plot here where you can measure the temperature and the density and the motion of the species can be completely interpreted in terms of conservation of energy and conservation of momentum. Um, I think I'll skip that and just show you what this one feedback picture. So here's another picture where the ion drift is very very large; measured ion drift goes up to almost four kilometers per second view, and you'll see that's associated with a large increase in the temperature and a corresponding decrease in the density here. You can see a large velocity, the ions with respect to the neutrals; frictionally heats the ions and changes the chemistry, so the density is rapidly decreased, so now that ions and neutrals become decoupled.
So here's what I want to leave you; this is my takeaway; I just want you to read these these following two pages, and you can read them as I'm talking to them, talking to you, or you can just take them and just mull over them at night, as I want you to be able to what leave this school and say, hey, there was a couple of lectures by Heelis on ion-neutral collisions; what did I learn? What is the takeaway? So there's a lot of examples, and there's some details I've given you, yeah, but these are the essential features that I'd like you to recognize about the ion thermosphere-ionosphere interactions. What the upper atmosphere is; the upper atmosphere is this transition to where a plasma is completely ionized, and you can think of it as collisionless to where the ions and neutrals mixed together, and collisions between neutrals and the plasma become important. Okay, the lower ionosphere is in chemical equilibrium; that is, if I just consider how I'm making them and how I'm losing the plasma, that tells me what the plasma density is, but in the upper atmosphere, I have to take account of how the plasma is being moved around in order to understand how the density changes. The lower part of this region is an anisotropic electrical conductor, so it's a conductor; it's capable of driving of closing currents, but how those currents get closed depend on the conductivity, which is anisotropic. Okay, so that makes it complicated, and in the lower part of this region, the neutral density is so high that it can move the ions and electrons around with pretty much no effect on the neutrals; that means the neutrals can drive currents, move the plasma around, and the neutral is they're so big and heavy they don't care; they just push the plasma around, and the plasma drive it can drive currents in the plasma, but no large effect on.
The neutrals, and then this: the points I've just made about the relative motion between the plasma plasma in a quasi-steady state parallel to be the balancing forces are pressure gradient and gravity. Okay? If you have relative motions between the plasma and the neutrals, then you exchange energy between the species, and that energy exchange changes the reaction rates, changes the chemistry, and it and it changes the heats the plasma and for the neutral gas. This energy exchange heats the neutral gas and changes its motion. Okay? So this is my sort of state of the art, of the art for you. So many of you dealing with the Sun, many of you dealing with the interplanetary or interstellar mediums. Every planet will have some kind of conducting medium; it'll either be the surface of the planet or it'll be the region where the ions and neutrals in the atmosphere interact, and where that occurs, there are many interlinked processes. There are big pictures here. I'm going to call this upper-lower atmosphere coupling. There are places here where you have to consider how the plasma and the neutrals are coupled, and then there's this last region that Luke will dwell on a little more: how their ionosphere and atmosphere are coupled to the magnetosphere. The thing I want you to remember, or snow tiss, is that all these circles, even if you are living in this little box here or in this little box here, all these circles intertwine. So you can't fully appreciate what's going on in this box without knowing something about what's going on in this box and something that's going on in this box. So my message is just to learn the basics, how to apply the fundamentals, but recognize that everything is coupled together, and that that you can benefit greatly by gaining a little knowledge of what's going on in these other boxes. [Applause] I'm around. I hope you'll—love you—dwell on this a little bit, and if you have questions, then come talk to me. My email is on on the front, so you can email me if you have questions about anything that's on your mind scientifically.