 Hello everybody and welcome to video number 16 of the free online version of the fusion research lecture We are in chapter 3 Parameter limits for fusion plasmas and you might remember in the last video We talked about the external kink instability and in this video. We will talk about the internal kink instability so whoops So in internal kink Instability will be the topic of today's video For the internal kink instability we set the separatrix to be fixed meaning we set the perturbation at the separatrix of psi at a to be 0 Which is the same as saying as I just said that we have a fixed separatrix separatrix then the Or analyzing the energy principle or applying the energy principle. We then find that such perturbations So perturbations of the inside of the plasma and generally stable for mode numbers m being larger than 1 for M equals 1 this implies as you might have guessed already that there is an unstable mode And this is unstable If the safety factor in the plasma center so qs at 0 is smaller than 1 over n and For n equals 1 this means that We get an unstable mode because We then have the condition that qs we can get an unstable mode. Sorry that qs at the center has to be smaller than 1 for instability, so this is a Condition for Instability and Since usually we have a safety factor in the center of the talk amongst being Smaller than one being on the order of 0.7. We have such a mode there so usually the safety factor in the talk of Mark the typical talk of Mark is on the order of 0.7 in the center and That means we have such a one one mode which is unstable Or that generally one one modes are generally unstable and typical talk of Mark's in the plasma center and those modes or these modes have a special name and they are called or these modes, let's say have a saw tooth shape Thus are they thus they are also referred to as a saw teeth So they have a saw tooth shape in the time traces of temperature and Plasma density as you can see in this Time in these time traces So you see two time traces in the top from the Aztec's upgrade talk of Mark and it's time trace in the center This is the one where we look at now and the time trace at the plasma boundary And this is a soft x-ray radiation being proportional to density and temperature You can see how the soft x-ray radiation increases in the plasma center, then it suddenly drops This is what we call a crash and it increases again It suddenly drops and it increases again It suddenly drops and so on and this is a saw tooth like behavior so here We have so called saw tooth and stability what this is basically is as we just Talked about a slow increase The slow increase is related to the finite or to the diffusion time of The plasma current to the diffusion time of the plasma current Because it takes a while for the plasma current profile to evolve Spatially, this is what we meant. We have a finite diffusion time. This is why we only have a slow increase in the soft x-ray radiation And then a sudden decrease a sudden crash afterwards and obviously this has some kind of a periodic behavior so this is a periodic behavior and it limits or imposes a limit on the temperature Density and also on the plasma current peaking and it is sometimes all in principle It's also a relaxation instability because it relaxes a bit the plasma pressure now This instability can be good. So it can be good oops Can be good Because it can transport in a burning plasma where you have fusion reactions going on it can transport the helium ash outwards So it can help to transport the helium ash Outwards and this however only good as long as it is controlled as long as It is controlled Because these saw teeth instabilities can also trigger in principle ntms something which we already talked about in video number nine To correctly describe the saw teeth the sorties to Correctly describe them so a correct Description Requires Actually to take into account resistivity, so we require finite resistivity So we have to say goodbye to ideal mhd here Because what we observe just before the saw tooth crash so before the sudden drop of the soft x-ray radiation in the center rotating rotating one one island in The center so this is just before The crash and as you know islands require finite resistivity The all the details about or the physics Details about this saw tooth behavior So I have a not fully understood and still subject of active research both in the experiment as well as in simulations Now since we talked about finite resistivity we can start to talk about T-ring modes T-ring modes, so if we have finite resistivity Stivity this And well if we allow for finite resistivity and then apply the energy principle analysis it yields that for Mode numbers m being larger than one There are unstable King modes Which can appear and those king modes are referred to as T-ring modes so T-ring modes are basically King modes where you allow for finite resistivity, so where you no longer have the case of ideal mhd And since we have finite resistivity, of course as I just said already in the last slide it means the formation of Magnetic islands are possible now formation of magnetic islands Just as a brief reminder, we already talked about islands, but it's good to just repeat it here if we have here a radial coordinate and into this direction Cedar the pole oil angle then We might have something like this so well Can try to draw it a bit nicer a Bit more symmetric something like this an island structure Yeah, and so flux surface configuration encapsulated in the background configuration where we have here the x-point Here is another x-point of the island the center we have the old point and Why islands a problem you might remember islands are problem Because they allow for radial transport with the velocity of the parallel transport now by that because Here basically on this flux surface All these areas are connected and they are and with the configuration without an island They would be radially separated which means slow transport. However, they are now no longer radially separated They are connected via the magnetic field lines Thus we have now the fast parallel transport into that direction so Transport just as a reminder transport along the field lines is fast and thus Basically have the same plasma pressure around an island This means we have the same Plasma pressure around the magnetic island and This means we get a flattening of the plasma pressure profile so this means we get a Flattening of the plasma Pressure Profile across the old point of the island Let's make a drawing of that situation so now Here we have the plasma pressure oops the plasma pressure p Small p here we have a Radial coordinate then the plasma pressure profile without islands Might look for example like this So this is in the case with no magnetic island With magnetic island It might look like this So we have the same increase coming from the outboard side and then however We pass the old point of an island where we have the same plasma pressure and then it increases so This is the example with an island Here we have a magnetic island and this is a profile across the old point and As you can easily imagine this is bad for confinement because the plasma pressure profile drops there and well This one here would refer to the width of the island W and as a conclusion islands are in general bad for confinement now This is not the end of the story. It can Become even more problematic To understand that Let me please allow me to make a brief preview on the topic which we will discuss in a later lecture That is the boot strap current. We have the boot strap The boot strap current This is a current which is generated by the plasma itself. So it's a safe generated current which is driven by the plasma pressure gradient in combination with collisions between Particles which are Trapped the magnetic field configuration. This is like trapping similar to Particles from the Sun which are emitted from the Sun and then trapped in the magnetic field of the earth Which can then lead to the northern lights or the southern lights So collision between trap particles and particles which are not trapped in the magnetic field configuration Those are called passing particles Again, this is something we will discuss in more detail in later lectures For now, it's just important to know that the boot strap current exists And it is basically a safe generated current by the plasma and the boot strap current is proportional to the the square root of the inverse aspect ratio over the Polo magnetic field and then the radio plasma pressure gradient. So the larger it is the larger is the boot strap current Okay, now what can happen here? So if we have due to the Turing mode appearing a local change in the plasma pressure gradient Then this will result due to the resulting change in the boot strap current and the perturbation of the plasma current Perturbation in the plasma current as you might remember from the chapter from the video where we talked about islands Leads to the formation of islands Now islands as I just explained on the previous slide leads to local change in the plasma pressure gradient and so on and so on So basically what we have here? oops is something like a self Amplifying system. So this is a self Amplifying system and can thus be dangerous Now this kind of mechanism is called a neoclassical Turing mode. So this I've just illustrated here what I've just drawn here. This is called a Neoclassical Turing mode or short NTM and It is called or the the expression neoclassical just refers to the boot step current being involved We will talk about other neoclassical effects later on Neoclassical just means basically that we have a toh royal magnetic field and I should probably add that This is not in all cases self amplifying, but it is self amplifying if the Seed magnetic island with which it started is Large enough. So if we have just some small islands These will not all lead necessarily to NTM's Now, let's have a look at an example from an experiment something we already talked about. So Here you can see an island Structure with a three-fold symmetry. So here one two three Three islands on one flux surface. You can see the resulting Electron temperature profile on the right hand side first of all the unperturbed profile and then the perturbed profile with the open circles where you here have the Cut across the open of the island you see the overall decrease of the electron temperature and Due to the self amplifying mechanism the potentially self amplifying mechanism of the magnetic islands of the NTM's Sorry of the NTM's NTM's can finally lead to disruptions and this is why they are so dangerous so NTM the neoclassic attiring mode can lead to disruptions disruptions were discussed in Towards the very end of the last video and from that you should remember that a disruption is something we want to avoid At a large scale experiment They do not necessarily lead to disruptions. They could also saturate at some large size at some large size, which is however also problematic because this means the overall plasma pressure is reduced and Not only is the plasma pressure reduced, but because the plasma pressure is reduced it also means the Plasma beta is reduced. Therefore, you have a less efficient experiment. Basically, it's the confinement is worse There exists however techniques to handle these NTM's and one example is for example Well, one example is for example. Yeah, what is that? Sorry is to Trying to replace the current which is missing Remember when I said that a local change in the plasma pressure leads to perturbation in the current to Reduction the current now if we would be able to locally replace the current by for example Adding the missing current in this Position here on this position or in this position Then we could restore the original profile and this is actually Precisely what is done and this is done by local microwave heating. So microwaves can locally Deposit the energy and then drive a current very localized Trying to restore the original profile and thus getting rid of the NTM's This is something which has been successfully demonstrated in our sex upgrade and in the D3D talk amok and it is something which Such a system will also be installed in eta exactly for this purpose to handle the NTM's Okay, that's it for this video where we talked about the internal kink instability You learned about the saw tooth instability About tearing modes and we talked in detail a bit more detail Let's say about the neoclassical tearing mode an important instability Which can however be controlled or be mitigated by localized current drive by microwaves for example That's it hope to see you the next video