 Okay, so let's continue. So I will try to give a summary actually of this last part of the course related to planetary ionosphere. Now, I had quite maybe a long introduction but I will maybe skip some slides and anyways it will be uploaded on the website presentation so you will have it. You will have all the slides. So I mentioned in the morning that there's two interfaces with the solar wind. So the magnetopause an external interface and the internal one internal one is the ionosphere. And actually, the ionosphere it can be is one of an example of a multi MHD approach actually the solar wind we consider the plasma as one fluid. But the ionosphere is different. We should for the MHD equation, we should write them for each ion species that we have. Also here, we have an additional term really, which includes actually the iron or the collisions between the species that we are considering. And in the continuity equation you would see here that we have two terms, the S are the source terms and the sources are related to well usually photo ionization, or the energetic particles and the last terms. They would be related to the chemical reactions or the recombination or charge exchange actually. Maybe very quickly, some history about the ionosphere so ionosphere was discovered in 1901 by mostly in Italian Marconi, who actually was performing first radio signal transmission and across the Atlantic Ocean actually. And he could perform this experiment successfully so the ionosphere was kind of discovered accidentally actually and many years later on. The success of his experiment was interpreted by the presence there should be a kind of conductive layer in the atmosphere that is making this experiment possible. And while in 1926, the word ionosphere was invented to characterize this layer in the atmosphere. Okay, how do we measure I mean they are the ionosphere we knew the altitude of the atmosphere this kind of plot is called I don't know. And basically by transmitting a wave kind of train of waves at different. Let's say a frequency, because they get reflected by the ionosphere, we can kind of estimate the altitude of the ionosphere. So the y axis is the altitude as a function of the wave frequency. And you see, so this is the signature of the reflected waves from the ionosphere and most of them are between 400 and let's say 600 kilometers so that's the altitude of the ionosphere on earth actually. And you would, you can see that above six megahertz above this frequency. There's, there's no reflections of the waves. So the waves just propagates and go into space. And that's, that's actually what we call the cutoff frequency of the way. So all the waves which are lower than this frequency will be reflected. And this phenomena, I mean the reflection of the way we can it happens from earth but also can happens from space. So there's lots of in the electromagnetic spectrum for instance the very large wavelength waves they are also blocked by the atmosphere and reflected into space. Okay, so as you all know the atmosphere plays a very important role in our communications and GPS signal and also because it's a, it's made of charged particles. It's very sensitive to any kind of changing of the magnetic or electric conditions in space. It doesn't want to move. Okay, so here just a profile actually. So the altitude profile on both figures in the first one of the neutral gas so of the atmosphere and the second plot is of the plasma density. And here the red curve is the density of the neutrals and the blue curve is the temperature of the neutrals. And these different. Well, at this different altitude, we have the different layers of the atmosphere troposphere stratosphere middle sphere and these different layers are actually controlled by the changes of the temperature in the atmosphere of earth. However, this is the second plot here it shows the profile of the ionosphere of earth. And now the structure of the atmosphere of earth is not controlled by the electron temperature, but more by the electron densities. And here you see the different. Well, at least here we have three layers region F, E and D. The solid line is the atmosphere during daytime and the dashed lines is enduring the night side. And you see of course as expected because the atmosphere is formed mainly by photo ionization due to the EUV solar radiation during the night time the electron density is much higher than the night side. But then we still have a relatively important electron number densities in the night side and that's because of the rotation of the earth and also the transport of the plasma from the day side to the night side. And so there are two basic requirements to form the ionosphere. Well, first you need to have a neutral atmosphere, and the second requirement is the presence of the source of ionization of these gases. And this ionization can be due either by photo ionization so from the photons and or from energetic particles coming from the solar winds or from the magnetosphere itself. So this is just an example actually of an ionization by absorption of extreme EUV light with so on the atom here, the oxygen, which would give a positive ions plus a free electrons. You mean for the oxygen the atom. What are you talking about mono atomic oxygen just yes, mostly oxygen. It depends on the altitude actually. Yes. So, is so it's just the composition of the atmosphere of. So it's basically the atmosphere I can show this plot. Yes. They are the dense. Yeah. You see here this is the profile of the density of the neutral atmosphere. I mean, I this year we don't show the composition, but the density is much higher at lower attitude than at higher attitude now. I'm, let me show. Yes. I mean, or it's going to be. So this is kind of here I'm showing just the neutral density in Earth's atmosphere. So. So at least what so the dioxin is the density is really important. So let's say at this altitude, but then due to lots of photo chemical, well, this photo dissociation and chemical reactions, then mono atomic oxygen can be as well produced. Because they are transport of. Yes, but I mean it's lots of processes that take into account. Okay, so I talked about photo ionization. I can skip this. Now, okay, so photo ionization is a kind of a source of the performing the ionosphere. Now we have some other kind of reaction that from which we lose actually this positively charge ions and one of them is recombination and recombination always happens. And that's when so ions are lost by recombining so. So they will just gain an electron and this will produce an atom plus release of energy. And an example of this is what we call air glow, actually, an air glow is just the lights that we you observe, which represents basically they are no sphere. And it shouldn't be confused actually with auroras, which is formed with a different kind of process. So air growth is very different from the northern lines or the auroras. And then you can have dissociative recombination when you have splitting of a molecule into atoms and excited states. So why actually the profile of the ionosphere is, I mean the shape is very particular as I showed you there is a peak in the ionosphere at a certain attitude. Why is it the case. So, actually, this is because it's, and I will show it to you here, maybe more qualitatively because so it's like this because it's the super super position actually of the attitude dependence of the particle density and the flux intensity. So, I showed you before so the actually the neutral particle density and the profile decreases exponentially as a function of height. Okay. I can show using like barometric row low actually that the this is the expression of the neutral particle density, the profile and assuming an ideal gas and isothermal temperature. density here is written as a function well certain and zero density at a certain reference let's say height, and then the big age here I don't know if you're familiar but it's the so called scale height and is a function of the temperature well the mass. And the scale height is basically it reflects the vertical width of the atmosphere, because how can you define what is the width of the atmosphere. So we use this quantity to characterize the different let's say with or layers. Yes. Yeah, yeah, yeah, yeah. And surprisingly it works really very well actually. It's better always to start very simple and they say that when you go to up to a month. When you feel something pressure. Yeah, basically when you pass some flags. Yes. scale, some portion of the scale. Because we go to your. Higher. Yes. Yes. Yeah. So this is how. So this is how the density of the particles varies the function of the altitude due to gravity mainly the density of the neutral especially is much higher at lower attitude than at higher attitude. Now how would you think the flux and density would vary. Would it vary the same way or. So it will vary in the opposite way actually. So the intensity of the solar radiation with decrease. Going down in altitude. Okay, and you can see it directly here. So, actually, the combination of this density profile on the intensity of the solar flux is actually gives the ionization kind of rates of the ionosphere. So at high very high attitude, the density, the neutral particle density is very low. But then, even though the intensity of the solar radiation is very important, but we don't have much neutral to to ionize. So, well, this is why the ionization rate is lower at higher attitude. And at very low attitudes. Now, the density of the neutral particles very high, but then the intensity of the solar radiation is very low. So that's why as well the ionization rates. So there is an optimum attitude where the ionization rate is maximum. And that's what gives actually kind of this profile of the ionosphere. Okay. And then the ionization rate while the intensity would change, but then the profile would say the same but of course the intensity was. Yes, yes, of course. Exactly. Yeah. Yes. Yeah. So this is mainly so and the solar flux is actually given by this formula here, which depends on the solar flux outside so at infinity here, which is the solar flux outside the atmosphere, and then it depends as well of course on the optical depth. Now, I will skip some slides but this was actually in the 1931 is Sydney Chapman actually, who proposed a very simple mathematical model to explain the formation of these ionized layers in the atmosphere. And of course there are some assumptions I will skip. So, so if we consider only one type of gas, one. Well, and that the atmosphere is horizontally stratified so we consider very simple geometric geometrically the problem. And then we also consider only monochromatic radiation so only one wavelength, and that the atmosphere is isothermal so that the scale height is constant as well so basically you can think that we are only considered one layer and the kind of the ionosphere. Well, you can actually show that the, the iron production rate for a given the neat angle so the neat angle is the angle between the vertical direction with respect to the direction of the sun. So if the neat angle is zero. This is here you get the maximum actually. And that prime here is a kind of reduced a scale height. So is this. Well, yes, so it's it's kind of the altitude with respect to a reference altitude. The maximum iron production rate so at the neat angle equal to zero, and then time the so exponential these well valuables, and the ratio of so this I write the iron production rate is this formula is what is known the Chapman function. And so this is an example actually here the y axis is the altitude. The axis axis is the ratio of the production rate over so the normalized one over the maximum iron production rate. And from this also from this formula you can get as well the ratio of the density over and zero as well. So normalized kind of electron number density is produced. So you can fit. I mean this for a given the neat angle, you can get this kind of different profile of the atmosphere. So for the neat angle equal to zero here you get the maximum ionization rate at well this attitude but then changing the neat angle. Of course it will be lower at 90 degrees. Okay, I can, I mean one also important thing I wanted to talk about is the ionospheric currents. And that's very important because actually they are not here. It's coupled to the whole magnetosphere by providing some, let's say electrical conductivity channels, and this plays a very important role actually in space plasma since the ionosphere, it will connect. The different regions, electrically. And so this would play a role in the energy transfer and the momentum from one region to another. So if we take the classical arms low. So in the absence of magnetic field, you have here the current is simply equal actually to the conductivity of the plasma due to the collisions times the electric field. Now if we add a magnetic field. As you know so we obtain the generalized arms low, and here the formula is a bit more. More complex, let's say, so it is related to the electric field, but then we have here the electron velocity across be. So if we are parallel interaction parallel to the magnetic field, then this term goes to zero and here we have what we call the parallel conductivities, or we obtain the field aligned current so the currents that are aligned with the magnetic field. But if we are perpendicular to the magnetic field. It's not as simple as the first one here we can get two types of conductivities. In both cases we are perpendicular to be now here the conductivity becomes a conductivity tensor actually. And in the direction parallel to the electric field we have what we call the Peterson currents, and in the direction perpendicular to E we have what we call the whole currents. And this illustration. So, these are illustration of the different conductivities or different currents. So we have the field aligned currents, the Peterson currents, and the whole currents, and this will actually connect to the magnetosphere with the ionosphere. And it kind of will close the current system in the magnetosphere. Yes. Yes. Yeah. Yeah, so that's how actually. So, kind of this whole system is connected to with each other through. Yes. Yeah. Okay, so they almost use an hour solar system so actually all the planets, except one, they have ionosphere and except mercury mercury has a very thin ionosphere. But we. So it's basically, it doesn't really have an ionosphere it has only an exosphere so it's kind of the upper layer of the ionosphere. And also the moons around planets they can have by the atmosphere. Also around comets, they can have ionosphere and the rings of Saturn as well they have their own ionosphere actually due to the photo ionization of the charged dusts and the dust as well. Let's talk a little bit. How long do I have. Okay, yeah, yeah, yeah. So, yeah, so I will just give you an example of the, how we can measure in situ actually, or we could measure in situ the ionosphere of Saturn. And I will focus actually in the final phase of the Cassini mission, which started between April 26 until September 2017. And here on board and for this I will show your measurements from the Langley probe. So again, the Langley probe is this instrument which is on board the spacecraft. And during this final phase, actually, it was completely spectacular because for the first time Cassini so performed for 22 orbits, and it crossed actually the gap between the planet and the main ring. So for the, this is maybe a video. So for the first time we could actually sample in situ this region here between the rings of the planets and and and Saturn. And also we could measure in situ for the first time. So you can see it crossed as well and or in this region. Okay, and then here you will see the different flybys or the different orbits during this final phase of the mission. You can see it here. Yes. So every week there was a one crossing of this gap between the planets and the rings. Yes, every week. Yes, every week we had one flyby. Yeah, but because this is the video. And so with the Langley probe, we could take in situ measurement in this region here very close to the planet and the rings. So we could measure, we could measure in situ the ionosphere of Saturn. So this is an illustration of all the orbits. The final orbit, it actually crossed. It actually was just the end of the space mission with. And so it was just it, it plunged into the atmosphere of the planet and then it just evaporated in inside center. Yes. So this is the control kind of crash of the instrument action of the spacecraft. And this is all the 22 orbits, and you see that this is, let's say the closest approach at the closest approach, the orbits they cover different altitudes from Saturn. And this is, I mean, in this region here, the closest, the innermost rings is called the D ring. And the D ring is very dusty ring very thin transparent ring. Now I will show you a real image taken by Cassini actually. This is a real image. And it's basically kind of the same of this one. Yeah. And this is, this is the highest altitude of the orbits when it crossed this region. This is the D ring, and you see some of the orbits they even they crossed even inside the D ring. So with this measurement we could also probe in situ the D ring region. And it was kind of risky because the, the, the scientists, the engineers, I mean, they oriented the spacecraft in a way that the, the high gen antenna was facing the, the dust and all facing the ring so to protect the instrument, but it was very risky because we didn't know what to expect actually. And it went really very well so for the first time we could also measure in situ with the rings of Saturn's, at least the innermost D ring. And again here I'm showing you the Langley probe instrument, which was actually developed in the Institute of space physics in IRF in, in, in Uppsala Sweden. Okay, so here I'm showing you one example so off the first. So this is the altitude profile of the electron number density for the first proximal orbit proximal orbit. So this panel is the electron number densities and this one is the electron temperature. And let's say there's lots of information on this curve. The blue, I mean all this part of the plot is the inbound. And then the, so in the northern hemisphere, and then the magenta line or the pink one is the outbound portion of the orbit so this one is in the southern hemisphere. So the dark blue curve here it represents the electron number densities inferred from the Langley probe instrument. The red curve is the iron number densities inferred from the Langley probe. And so we also consider the ionosphere as a quasi neutral medium. And this is you can see it here actually the iron number density and the electron number density they are coincide very well. And then the black curve here is the electron number densities but estimated from the upper hybrid frequency, the cut off frequency of the upper hybrid ways actually. And just to show you here an example. This is a spectrogram of an energy spectrogram. A frequency time spectrogram actually off the wave during this proximal orbit. And you can see very broad band emissions but more importantly above the electron cyclotron frequency, you can see here very narrow band kind of emission. And this was actually at the upper hybrid frequency. And from this basically formula we can estimate the electron number density. And this is the electron number densities inferred from this upper hybrid frequency. And it's, it's very well, consisting very well with the Langley probe measurements. I mean the large scales, I mean there's a small offsets here but at least the very small scale variations. But it's very well consistent. Now you see this is the closest approach here at the lower attitude, and you see that's the ionosphere of Saturn, at least below 4000 kilometers is about the density is very high about 10,000 1000 for this case particles per CC, and the temperature is very low is about 0.1 EV so it's a very dense and cold ionosphere. You can also note very clear a symmetry between the inbound and the outbound in the profile. And you see here very sharp decrease actually in the electron number densities here. Well, but here there was a data gap, but it's consistent for the other flyby, and, and a local increase in this region. So this was, this is really very nice because this actually related directly to the ring shadows. So the a and the bearing are opaque to the EU B solar radiation. I can show you. Yes. So this is Saturn, again, one of the orbits of Cassini, and on the color here it shows the the electron number densities. So these are the rings. The first rings, the D and the series are very transparent to the UV solar radiation. But this is not the case to the B and the a ring, they are very opaque to the UV solar radiation. And so below in the southern hemisphere, there was a shadow actually because of these trains. So of course in this shadowed region, there's much less ionization. And so we have much less electron number densities. So it was very, and in between these rings, you see here there's what kind of a gap. It was discovered by Cassini, so the scientists. So, so that's why it is named the Cassini division, and it's transparent to the UV solar radiation and that's why we observe kind of a local ionization in this region. So it was very nice that with the lightning probe, we could actually observe this. The presence of this a and the bearing shadow. And also we could study the effect of this a and the bearing shadows on kind of the transport in the ionosphere of Saturn. Okay. I will just I will show this and then I can stop. So here I showed you only one example of the ionosphere of Saturn. But of course, we want to try to construct a standard ionospheric profile for Saturn. We want to combine all the proximal orbits. So these are all the orbits of Cassini and Saturn, the y axis is the altitude as a function of the latitude here, and the color bar represents the electron number density. The crosses here represents the closest approach of Cassini to to Saturn, and it's in the southern hemisphere basically is a minus five degrees. And also, here you can see it very clearly the clear asymmetry between the northern hemisphere and the southern hemisphere. And this is, as I said, due to the ring shadowing effects. So, if you want to construct the kind of ionospheric model for Saturn's ionosphere, we need to exclude these effects of the rain shadows. So we just focus on analyzing all the electron number density profile in this box here so basically around equatorial latitude between minus 15 and 15 degrees. So we, so we can compare these electron number densities profile between the northern hemisphere and the southern hemisphere. So this again the y axis the altitude as a function of the electron number density the color. Okay, let's forget about the color bar so far. In the northern hemisphere and then in the southern hemisphere. In the northern hemisphere, you can see well that the electron number density increases increases at as we go down in altitude. And you can see that the density goes up about more than 10,000 particles per CC at the closest approach so it's very high very dense ionosphere actually. Note that in the northern hemisphere, the, the profile are kind of organized. So above 4000 kilometers except this orbit here, but I will tell you why the profile I mean the variation is kind of constant with the altitude, then between let's say 2500 kilometers up to about 4000 kilometers here the profile look like variable and more kind of structured, and then below 2000 kilometers the profile becomes smooth again. As if we have kind of different layers here in the northern hemisphere. Now if we compare to the southern hemisphere. This is not the case actually at all these altitude. In the region that the profiles look like very structured and variable and not at all organized as is in the northern hemisphere. So why is it the case to understand the difference between this northern and southern hemisphere profile. We have the what is called the magnetic L shell values. The magnetic L shell value is the distance on so the equatorial plane, where the magnetic field so crosses the equatorial plane. Okay, so if an L so very particular L shell value here is about 1.11. And that's where the D ring starts actually. Okay. So all the color colors. So, yellow or red represents actually basically the crossing of the D ring by the magnetic field. So when we add this information to this profile, you see that well in the northern hemisphere. The ionosphere. So, this yellow color is only above 6000 kilometers, which means that in the northern hemisphere above 6000 kilometers, the magnetic field is actually or the atmosphere is coupled to the magnetic field that crosses the D ring. But in the southern hemisphere. This actually happens at all these different attitudes. So this actually showed indirectly the role of the magnetic fields in kind of shuffling, or the structure of the ionosphere, but also it, it implies the important role of the my magnetic field in facilitating the coupling actually between the rings, and the ionosphere of Saturn. And we have this clear asymmetry with between both, basically because the, the whole magnetic field the dipole magnetic field of Saturn is shifted towards the north. So we have also an asymmetry in the kind of the structure of the magnetic field. You have current along the. Yes. Yes, yes. And I mentioned this profile, this particular profile here, why this is the electron number density, why for this one is much lower than the other ones. Actually this, this profile is one of the cases where the casino was very close to the jury. And so, when we look at the landing probe data. We could see that for this case, actually, the electron number density was very low, because the landing probe could indirectly measure the presence of negatively charged us. That's why the electron number density was lower. So this is basically the landing probe observations. The y axis is the bias voltage as a function of time, and then the current is shown in the color bar here. So when we compute, it's not very clear here. So when we compute the different number densities. So the red one is the iron number densities. Okay, the red curve. And this is the closest approach in this region. And let me check because I forgot. And the electron number density let's look only at the red curve and the blue curve, the electron number density is given by the blue curve. And the iron number density is given by this red curve. And you see, the iron number density is not equal to the electron number density. And we know that the plasma is quasi neutral in the ionosphere it should be quasi neutral. So this means that we have additionally negatively charged dust that corrects for this quasi in neutrality and that's how indirectly we could measure the presence of the negatively charged us. So, then of course, so we took all so the profile in the northern hemisphere because here we don't have any effect from the rings of Saturn, and we can kind of construct average ionosphere or standard ionospheric profile of Saturn. And based on this only this observation we can kind of categorize the ionosphere of Saturn's in three different layers. So above 4000 kilometers, the profile look kind of constant between 205 2500 kilometers and up to 4000 kilometers, the density kind of increases exponentially. And then below 2500 kilometers the profile becomes more the game. And we compare this average profile to the profile of the final plunge of Cassini that actually covered continuously all these altitude ranges. And then we see that it's quite comparable actually the profile where above 4000 kilometers quite constant in this way in this layer we have lots of variations, and then below the profile becomes smooth again. And then for these different layers we can fit this kind of layers, and we can estimate the scale heights as well in these different layers in the ionosphere of Saturn. And I forgot to mention, okay, let me. So in this below 2000 kilometers. Here, the, the, let's say, we will have well chemical equilibrium processes will dominate because we are, we are at very low altitude. And in this range, we would have the diffusion kind of equilibrium processes that would dominate. Maybe these variations could be due to other kind of waves. Other kind of transport processes but it's very difficult to say with these data and then above 4000 kilometers at very high altitude the ionosphere starts connect with the plasma sphere. One last thing maybe I wanted to show yes. That also, I mean, we could detect you see here there is one peak. This at very low altitude at 200 kilometers from Saturn, but this doesn't mean that this is the main peak of the ionosphere it could be one of the peaks of the ionosphere. That's it. I think I'm done. Thank you. I wanted to go talk about the ring channel effects but I think I can stop here and but it will be in the presentation. Okay, I'm thirsty actually so just drink water. Yeah, I was. No, I think just maybe the order in which they discovered them. I think maybe a was discovered in the beginning. The D there's the F ring the earring and I miss one but there's, I think it's just the order. No, no, no easy. Yeah, actually, yes we do have, but I didn't show it here because we have no next. Maybe I can add some references I mean I, there are already some references but, of course, here I only talked about the Langley probe. Well, maybe I could have talked about other instruments as well, but we there was also magnetometer on board the spacecraft and we could measure in detail as well. The magnetic field the internal magnetic field of Saturn. I forgot the value but it's a very strong field actually, but yeah. Yes, yes, it's much stronger than earth. What I only remember is that you know the, the inclination of Saturn's rotation axis is actually very well aligned with the axis of the magnetic fields. And there's no inclination actually, and they could calculate the angle which was 0.00 something so extremely low so it was perfectly aligned actually with. So the, so I show the electron currents actually increases exponentially with exponentially and then at some point, it saturates once the potential of that we apply it balances the potential of the plasma that's. Yeah, yeah, yes, yes, yes. Yeah. Yeah, exactly. And the velocity. Yes. One more mobile because the slides are. Yeah. Yeah. Exactly. That she's more expert than me on language. Yes, for this one. Yes. I think well for this case we are really measuring nanometer size grace so extremely small and the speed of the space was very high I forgot how much so this. At the closest approach, yes, they dominate, but not all over the space. Yeah. Thank you. Thank you. Okay, I have lots of future project but I can tell you, at least for now what I'm, I mean, my background was really solar wind turbulence that's what I did in my PhD but then in my postdoc and so far I'm doing much more planetary kind of or magnetospheric related kind of processes. And now I'm actually mostly involved in the mass spectrum analyzer instrument that I present you so I'm kind of doing instrumental calibration as well for the Beppe Colombo mission. Yeah. Yeah, you're welcome. Thank you. Yes. Yes, we can get out with now maybe a five. We have like 15 minutes. Okay, that's a challenge. It is a different lens, like the easy one, rock and roll, heavy metal or jet. Jets are going to be. We can do the chorus to them. Yeah, okay. So you needed the projector? No, no, no. All the same school.