 Hello and welcome to video number 36 of the Fusion Research Lecture. We are in chapter 6, Turbulent Transport, and in the last videos we talked about turbulence, turbulence in plasmas, turbulence measurements, and how this turbulence is created. And that this turbulence is responsible for the majority of the transport, which is actually observed in fusion plasmas. In this video we will talk about a way to reduce the transport. So topic of today's video is basically transport barriers. So we will talk about transport barriers. So what are transport barriers? So transport barriers are basically narrow radial regions, narrow radial regions with a strongly reduced, strongly reduced diffusion coefficient and also with a strongly reduced thermal diffusivity. So the particle diffusivity, the diffusion coefficient d and also psi, just for the thermal diffusivity, both are strongly reduced. And they are reduced because the turbulent transport is actually reduced. So it's a strongly reduced turbulent transport. And what you see in the experiment is that the local fluctuation level in this narrow radial region decreases. So the local fluctuation level decreases. And this leads to a steepening of both temperature and density profile. And that is what is depicted in the figure on the left-hand side. So you can see on the top, these are radial profiles of the electron temperature. And on the bottom, these are radial profiles of the electron density. You can see two colors, black and red. Black is before such a transport barrier is created and red after such a transport barrier is created. And you can strongly see that there is an increase in the overall temperature and in the overall density. If such a transport is created and that in a certain radial region, the profiles are strongly steepened. So this is basically the radial region in which the radial profiles of both density and temperature are strongly steepened. And this leads to a major increase in the confinement time. So it leads to a major increase in confinement. And what you observe basically is that the energy confinement time tau e increases by effect of 2 due to these transport barriers. And this is why such a scenario where you have a transport barrier is called high confinement mode. This is why it's called high confinement mode or short just the age mode. And this scenario without a transport barrier is called the L mode. So L mode, low confinement mode refers to this scenario without a transport barrier. Okay, a bit of historical, a few historical notes. So the situation in the late 1970s and the early 1980s basically was such that it was known that the energy confinement time decreases with further increasing power. Decreases with power with the heating power to the power of minus 0.57. And it increases with radius and with plasma current. And just applying these scalings, it was realized that much, much bigger tokamaks than the current latest tokamaks at that time were needed to achieve fusion. So this requires much bigger tokamaks. That was sort of a problem because much bigger also means much more expensive. Luckily, however, the first transport barrier then was found, which lead to a tremendous increase, a significant increase in confinement time. So the first transport barrier, so the first age mode was found in 1982 at the Aztecs tokamak. So the predecessor of Aztecs upgrade by Fritz Wagner. And he nicely explained at that time that he once gave an overview talk and he said that when he first found that age mode in his data. So I think he was a post talk at that time. Then the directors, his bosses basically told him, no, this is not what you think it is. This is just some kind of instability and this is nonsense. He really had a hard year, he said, presenting his results on conferences because people were not really believing what he showed them. But obviously it was worth his fight because it is an improve in confinement time by a factor of two, as I said, which made a huge difference for the overall performance of fusion devices. And this is why people had such a hard time believing him because it was just like it was just so much better all of a sudden. And of course, you're skeptical at the beginning, but Fritz Wagner said that he was also skeptical in the beginning about his own data. And of course, it relies on the age mode. So it relies on the age mode to achieve its peak performance. Now, when we look at the profiles, we see that the temperature profile is what we call stiff. So the temperature profile is stiff. That means is, well, we will see that in a minute. It is a stiff, it is sensitive to the edge temperature, to the profile, sorry, to the temperature of the plasma edge. And the temperature at the plasma edge, which we also call this region pedestal, I will highlight, I will more explain that in a minute. The temperature at the pedestal has a huge impact on the overall eta performance, the overall eta performance. So what is the pedestal? So if we draw, if we look again at a temperature profile, so this is T. And then if we here say this is R, then let's for the temperature use this use yellow, then the temperature profile might look like this. I don't know, like this, then going down. Here we have the plasma core. And then this region here where the profile basically goes down to zero. So this profile, sorry, this region, this region is called the pedestal, the pedestal and the temperature at the top of the pedestal. This is the so-called pedestal temperature and also pedestal density. And this on this is by the way, this is the width of the pedestal, sometimes abbreviated with the data and the height of the pedestal is then this one here. And on the right hand side, you can see a figure which shows the fusion, the gain of eta capital Q as a function of the pedestal temperature. Estimated with various models and all of these models agree with that respect in the looking at the general scaling that the higher the pedestal temperature, so the higher the temperature at this point here, the higher the Q factor is of eta. This is why I said the pedestal temperature has a huge impact on the eta performance. When such a transfer barrier is formed, a reduced fluctuation level is observed, as I said initially. A reduced fluctuation level is found in the pedestal region. This is depicted here. So on the left hand side, you can see various radial profiles of the density at different time steps. So this profile here is recorded when it was still in L mode shot. And then you see this is a transition to the age mode. So the profile steepens and steepens until we have a fully developed age mode, so a strongly steepened profile. And then you can see on the right hand side different time traces taken in this region where the profile steepens. At the beginning where we have a full L mode, so this one, you can see how there's a strong fluctuation level. Then when the age mode starts to build up, you can see how the fluctuation level decreases until we are in the fully developed age mode scenario where the turbulence level has been strongly reduced, has been found to be strongly reduced. Well, this sounds all very fine, but there are some problems with the age mode. So let's talk about the problems. So what are the problems with the age mode? And problem number A is basically there is no detailed predictive understanding. There is no detailed predictive understanding of the transition to the age mode or of the threshold to achieve the age mode. And this is of course a problem and meaning there is no detailed predictive understanding means that we cannot fully capture this in modeling, for example. So it is known that sheared plasma flows play a role. So it's more like a phenomenological understanding. It is known that sheared plasma flows due to a radial electric field times the magnetic field. So due to the E cross B drift, they are believed to play a major role. Why? Because they have been found. They have been measured. So on the right hand side, you can see the radial electric field as a function of normalized radius. The black crosses are from an L mode shot. And then the red crosses are from an H mode shot. And you can see this strong increase in the radial electric field here, reaching values of minus 450 volts or 400 volts per meter. So a very high value, which then leads to an E cross B drift, which leads to a sheared plasma flow in that area. And this can help to decorrelate turbulent structures, something which we talked about in the very beginning of this lecture, which can help to decorrelate turbulent structures and thus reduce turbulent transport. And these sheared plasma flows, as I said, appear if there is a gradient in the radial electric field, of which it is unclear, fully unclear, well, not totally clear, I should say, how this is created. I'm clear how it's created. Since we have a radial electric field, it is generally believed that some kind of plasma current flowing inside the plasma must be responsible. It's basically different in the flow between electrons and ions. So B, the next problem is very similar because there is no, the understanding, let's say, there's no full understanding of the pedestal physics. So understanding pedestal physics in general is very challenging, thus getting a predictive model for estimate the height of the pedestal, which, as I showed you, tells us something about the Q factor would be very helpful, right? But this is something which we do not have at the moment. This is very challenging due to the huge variety of both temporal and spatial scales being involved. And spatial scales being involved. What we have, however, is instead of like a predictive, detailed computational modeling is we have scaling laws. And but these are very robust scaling laws, which we use to predict or to get an estimation for the width and the height of the pedestal. And on the right hand side, you can see in an example for that. So this shows the measured pedestal height as a function of the pedestal height predicted by a model called EPID. And you see that for a number of different experiments, going from jet over to D3D, JT60 upgrade, Alcatraz Cmod R6 upgrade, compass and eta. So spending a very wide range of experiments. The problem with this model is, for example, that this is the pedestal height in terms of pressure. So here we do not differentiate between density and temperature. But this is a very robust scaling, which is mostly used at the moment. But it's just a scaling. And then C. Another problem is so-called etched localized modes or short elms. So what are these? So during the age mode, you have seen or have shown you that we have an increase in the gradient of density and temperature. So the profiles become steeper. This means that there is a decrease in collisionality, decrease in collisionality. Thus the bootstrap current increases. And eventually with the increased current and also increased plasma pressure, we reach a macro stability limit. So eventually a macro stability limit is reached. Well, eventually it is reached. And what then happens is a so-called etched localized mode, an elm. And that basically is a periodic relaxation of the gradient. If you look on the right hand side, you can see temperature profiles, radial temperature profiles. We just look at the black dots at the moment. These are two scenarios, black and red. But if you just look at the black one with the higher temperature, you can see the pre-elm profile. So these are the field circuits looking something like this. And then post-elms. So after such an elm has occurred, you can see that the gradient has been relaxed if you want. So it has been flattened down a little bit. So these are elms. Now they are of course a problem because relaxing the gradient means that there is a release of bursts of energy going on. Something which can be very harmful for the diverter. So large elms can basically erode the diverter. And for eta, this is a big concern. So problematic for eta, problematic for eta. And on the right hand side, on the right hand side, there are two figures. On the top it's a photography. And here you can see the actual impact of elms here, making visual damage to diverter plates, to target plates here. At the bottom you can see the spatial profile of the plasma-facing structure. This is before it was installed. So without any plasma exposure. And then after 50 elm pulses, you can see how the profile of the structure has clearly changed. So plasma material was clearly eroded and taken away from that. This is something of course we have to avoid. Now luckily there is a solution for that. And the solution, there are basically two solutions. One is try to make small elms. Why small? Because small also means... Why small? Because then you have less energy impact by how to reach that is by making them more frequent. So we are actually trying to trigger elms. We are trying to make small and more frequent elms. And this is done for example by pellet injection or also by magnetic perturbation. So that you are trying to deliberately trigger elms. But instead of having one big elm, you have a number of small elms. Something with what the wall material can withstand. Then there are other scenarios where you try to actually achieve an elm-free H-mode. Where you do not have any elms at all. Sometimes this is also called quiescent H-mode. However this might have the problem that impurities might be accumulated in the plasma center. So mostly you might have some kind of combination of these two solutions. Okay, that's it for this video where we talked about transport barriers. Which are narrow radial regions where we have a strongly reduced turbulent transport. Leading to a steepening of density and temperature profile. Residing in an overall increase of the energy confinement time by roughly a factor of two. This is why the corresponding scenario is called high confinement mode or H-mode. And this is something really important for modern fusion devices for Tokamak's at least. We talked about also the problems of the H-mode. That we do not have a detailed predictive understanding of the transition from the L to the H-mode. Or of what determines the threshold for that. That the pedestal physics to understand them is very challenging. And that we have these as depicted on this slide, the edge localized mode. Something which can erode your diverter but there are ways to deal with them as outlined here. Okay, that's it for this video. Hope to see you in the next video.