 Hello everybody and welcome to the free online version of the future research lecture. My name is Alp. This is a YouTube channel called Der Plasma And we are in video number 19 We are in chapter 3 parameter limits for fusion plasmas and you might remember that in the last video We talked about the stability beta limit rising from ballooning instabilities in this video We will talk about an additional limit additional density limit so topic of today's video is in additional density limit Which rises only in tokamaks on additional density limit in tokamaks and this is really a severe limit an important limit because exceeding this limit in the plasma density May lead Well usually it's May lead oops, sorry, sorry for the typo may lead to disruptions and You might remember from video number 15 that disruptions is Something we want to avoid especially in a large-scale fusion experiment This is something which was not theoretically expected or something, but rather experimentally observed And found so experimentally observed and there usually there exists or other the stable parameter ranges where The tokamak can be operated without crossing the density limit is summarized in a certain type of plot so the stable Parameter ranges parameter Ranges where a tokamak can be operated Without exceeding the density limit is summarized in I'm pretty sure I'm pronouncing that name wrong in a yugel diagram Maybe it's more like you Jill Probably and you Jill came up with that in 1983 and what is it that diagram so on that diagram we plot? oops, sorry We plot One axis one over Qs Which is basically as you remember proportional to the plasma current and on the other axis We plot the so-called Murakami parameter that is M bar is equal to N bar are not over B Phi That basically then is the plasma density So it's the if you want you can bring it down to the plasma current versus the plasma density and machine parameters Know how does such a you do a yugel diagram looks like Here you can see one. This is as I said we have Here one over the safety factor against this Murakami parameter And you can see all these crosses here or symbols So these are partly diamonds open diamonds and crosses these are stable discharges Performed in the jet Tokamak, and you can see there are a few boundaries. So first of all, there's the boundary towards lower Low values of the density so this boundary basically is a low density limit this is a low density limit and You can explain that by the first dimension Explain that by the fact that if you have two little Electrons in the beginning when you start to when you're trying to start your discharge You're basically only accelerating these electrons and there are two little collisions to little interactions with the gas to ionize it So there's no ever ever lunch process. So this is why this limit is also sometimes called runaway limit runaway limit Because what you're basically doing is accelerating a few electrons and these electrons are getting faster and faster. They are so to say they are runaway Running away, so they're getting faster and faster without delivering the energy to to the plasma So then we have a limit at one over Q equal to point five here and That limit is something which you might remember this is a limit against external kink instabilities So this is the limit at a Safety factor at the edge that this is should be larger than two to Get stability against the external kink mode Against the external Kink mode something which we discussed I Think three videos ago and then We finally have this kind of this this line here basically So this one and this is the phenomenological as I said experimentally observed a phenomenological density limit Which is not completely understood So if we exceed that limit if you exceed the density we might get a disruption, which is something we want to avoid So this is a phenol Mino Logical density limit which is not Complete Completely Unless stood Meaning it is still subject of active research Okay, let's have a closer look at the density limit. So the density limit So first of all, we will have a look at a circular Talk about meaning at a plasma having a circular polar cross-section and There we have the so-called and then the so-called usual limit applies and that is the density is Equal to the magnetic field over The safety factor and are not and this is oops, sorry And this is for Circular talker max But that I mean talker max having a circular Poloil cross-section that is the usual limit or you go in it. I don't know and if we Include the shape so non-circular cross-sections. We get a different limit So including So-called Shaped cross-sections and whenever we read something about shaped cross-sections. It means having non Circular cross-sections And cross-sections here refer to polo cross-sections then We get a different limit and G which is for green walled That is IP the plasma current over pi and a squared and that is the Green wall Limit this is an important limitation for talker max basically Okay, as I said and this is important. This is why we have to repeat it here a Disruption can occur can occur if we cross that density limit and This has been not fully understood, but there is an experimentally deduced causality so there is an Experimentally deduced causality causality That goes as follows so in the beginning before the disruption occurs in intense intense radiation from Region at the separatrix is observed The separatrix and this happens as I said also observed before just before we reach that density limit That radiation is called math This is a math Mafia is short for a Multi-faceted asymmetric radiation from The edge and what that is is that If we have an increase in radiation so a lot of radiation coming from the plasma Then what happens is that the temperature drops due to the increase in radiation So the temperature drops because the energy content of the plasma drops due to the radiation a drop of the temperature Resides in a drop in the conductivity So conductivity drops that leads to a modification of the current profile and You might remember That a modification in the current profile then you drop in conductivity can lead to the occurrence or appearance rather of tearing modes and You hopefully remember that tearing modes then can finally lead to disruptions And this is something we want to avoid Now can we understand the density limit? Yes kind of so it from a physics point of view it makes sense so understanding the linear Dependence one over Qs Proportional to end so that the Yeah, the inverse of the safety factor is proportional to n which is And that there's a linear dependence between these two well as it's written down here As observed in the experiment. So yes, we can understand that From some simple considerations First the omic heating in a toka mug Which is the heating due to the current driven driven by external coils By the external transformer rather so the omic heating is due to resistivity and That scales so the power of the omic heating OH omic heating is Proportional to the square of the plasma current Then we have the radiation losses So radiation losses and the radiation losses P rad They scale with the squared density with the square plasma density and this math develops Starts to develop when the Omic heating power or the radiation of the plasma when they in those two are the same at Oops, sorry at one position in the plasma Usually at the plasma boundary, this is where it happens and then Keep in mind that the safety factor at the edge that this is basically proportional to the Magnetic field be phi the toroid is a strong toroid magnetic field over the plasma current and Then we can put all this together Which tells us then that we have start with the inverse of the safety factor, which is as I have just written it above the plasma current IP Proportional to the plasma current over the magnetic field and This is as I have written in the as I've written here oops, this is then proportional to the square root of The power the heating power Over the magnetic field again be phi and This is Then proportional as I have written it here to the density Over the magnetic field and a viola. This is the linear scaling as we observe it experimentally and then to add to the other parameters they come into play when we want to compare um different Experiments so comparing of different experiments And being able to plot them on one scaling. This is why we You do then edit in our dependence and this gives us then finally the we want density limit as we had discussed on the previous slide Now the interesting thing is and you might have guessed that from the headline or the title of this lecture Is that this is an additional density limit occurring only in toka max? There is no such Severe density limit Installators no such severe density limit instillators. This is something important to keep in mind Now why are we interested generally in higher density? So as a reminder as a reminder the energy confinement time and the energy confinement time scaling according to the so-called isso4 scaling Tells us that the energy confinement time scales with the plasma density to the power of 0.54 Meaning a higher density is beneficial because it results in a higher energy confinement time Now also instillators the density cannot really get arbitrarily high So but the story is a bit different than instillators. So what is happening in instillators? so instillators They Observe or you observe instillators a radiative collapse terminating the plasma terminating The plasma of course much less violent than in a toka mark where you have a disruption which often the terminator plasma What happens? During this radiative collapse when the density is getting too high. So Radiative collapse basically is that the power radiated away from the plasma is or exceeds the heating power Which Results then in a sudden decrease of the stored energy of the in the plasma stored energy Resulting in a sudden termination of the plasma basically the point however here is that the Radiated power is usually Due to impurities usually due to impurities That means this is something we can control we can modify so we have an influence on that and this kind of radiative limit is referred to as the Pseudo limit or sometimes also to to the Radiative density limit you will find Both these expressions in in literature So we have this pseudo limit or the radiative density limit occurring in a oops. Sorry occurring in a stellar radar and This is as I said something different to a toka mark because in contrast to Toka mark We can push this limit higher. We can push the density higher by for example wall conditioning wall conditioning Which reduces the impurities which allows us to get a cleaner plasma or in general by adapting Different experimental Experimental scenarios and this these are methods which allows us to Achieve higher densities so we can Push the density limit much higher in a stellar radar. This is why this is rather an Operational limit depending on the scenario you're running in your stellar radar and not such a severe thing as in a toka mark Okay, that's it for lecture 19 for video number 19 where we talked about an important additional density limit in toka max This was the so-called green walled density limit something which is not completely understood thus being still topic of active research I Told you and this is important to keep in mind that when we pass the density limit We usually get a disruption in the toka max something we want to avoid Interestingly enough this limit does not appear in a stellar ater in the stellar ater. We have something slightly different We get a radiative collapse if the density gets too high because usually then the radiative Power increases as well the power radiated away by the plasma, but we can reduce that by tuning the operational scenario or Sorry in general tuning the plasma Chamba for example by proper wall conditioning. So this is not Such a severe limit as in the toka market we can push stellar ater's too much higher densities Okay, that's it hope to see you in the next video