 Hello everybody and welcome to video number 12 of the free online version of the fusion research lecture My name is Alf. This is a YouTube channel called Der Plasma and today is Sunday We are in chapter 2 magnetic field configurations and you might remember in the last video We started to talk about the stellarator and how we achieve a twisted magnetic field line in a stellarator We will continue to talk of the stellarator in this video and as a reminder I'd like to distinguish the classical stellarator the heliotron torsotron something which we did in one of the very first videos But it's definitely worth to be repeated here since this is an important differentiation so on the left-hand side we see a drawing of the classical stellarator This is a classical stellarator on the right-hand side. This is drawing of the of a heliotron Also called torsotron torsotron and the In the case of the classical stellarator you can see here the helical coils winding around the torus one two and then here we have three and here another one four and The current in the helical coils flows anti-parallel with respect to each other. So the helical currents are Flowing anti-parallel with respect to each other In the heliotron or torsotron on the other hand you can see here the helical coils winding around the torus These are two coils in this case here right and In this case the helical currents are flowing parallel. So here we have the helical currents flowing parallel with respect to each other Now you can see that in the case of the classical stellarator We have additional torsotron field coils depicted in blue in the drawing and these are required due to the fact that the helical currents are flowing anti-parallel. So the classical stellarator additional torsotron field coils are required additional Additional is written differently I guess additional Toroidal field Coils are Required as we discussed in the Heliotron or torsotron Instead additional vertical field coils are required. You might see it in the drawing above These are the green colored coils and these are the ones which are required here. So additional This time I've written it correctly additional vertical field Coils are required Okay Let's take a further look at the difference between these two types So here you can see two drawings on the left hand side a classical Stellarator on the right hand side again heliotron or torsotron and in green you can see the coils Sorry the current flowing with the coils and the current flowing in the coils the left hand side You have currents flowing anti-parallel in the helical coils see these arrows here depicting it and The additional toroidal field coils which are required. So these Ones and On the right hand side you can see in the case of the heliotron or torsotron current flowing in one direction and the additional Vertical field coils which are required for that. So to Quantify the periodicity of stellarator and torsotron we introduce small numbers So it's usually it's quantified by small numbers small L is used to quantify the poloidal periodicity So of symmetry so the poloidal symmetry of The magnetic field so basically The number of periods into that direction the periodicity in the poloidal direction is usually denoted with a small L And a small m is used for the toroidal Symmetry of the magnetic field so for the periodicity into the toroidal direction for the number of periods in the toroidal direction And in the example above In the pictures above there on the left hand side First of all, it's a three-fold symmetry into in the poloidal direction and in the classical stellarator This requires obviously apparently two times L meaning six helical windings six helical windings in the case of the let's say at the Classical stellarator at classical stellarator Whereas in the case of the heliotron or torsotron it only requires aliquids to three helical windings Well, yeah at the heliotron or torsotron Torsotron So an example for a classical stellarator was the original Wendelstein series for example An example for a heliotron is LHD the large helical device Which is a very large stellarator in in Japan it was the largest stellarator for a long time until W7X came into operation and Well heliotrons are actually a bit easier to build because you have fewer coils and thus also reduced forces between these coils But you're kind of less flexible with your magnetic field configuration Okay, let's have a look at the residing shape of the flux surfaces So the magnetic field in stellarators consists basically of multiple fields These are depicted on the left-hand side So we see three different structures three different symmetries or three different multiple fields if you want and as I've said the Magnetic fields In stellarators in stellarators Consists of multiple fields of multiple Fields which are generated by currents by by the helical currents or currents in the helical coils in the Helical coils and The shape of the multiple fields or well or the the multiple fields the structure of that reflects in the shape of the flux surfaces so the multiple fields the configuration of the multiple fields or the structure reflects in the shape of the flux Surfaces you can see three examples on the left-hand side an eloquence one stellarator and the center and eloquence two and eloquence three and you see this type of symmetry when you go around poloily in these cases An important thing to be note is when you are Bending or when you are deviating from the linear stellarator which might be useful to describe it analytically But when you bend the linear stellarator into a torus What you eventually have to do to describe it properly then a few things are happening first of all There is a loss of the helical symmetry. So you lose your helical symmetry loss of helical Symmetry and That means that the proof of existence for flux surfaces is no longer limited analytically possible as we discussed so that means the proof of Existence for Flux Surfaces is no longer possible Meaning to check for the existence of flux surfaces. We have to do something like a punk array plot. It's no longer possible well analytically of course I meant by that analytically and This is why we have to prove Or check for the existence of flux surface surfaces. Sorry differently. And as I explained a Poincare plot is usually used for that Either numerically or experimentally because you can of course also check that in the experiment Okay, a very important Aspect in stellarators are the helical coils which are actually hard to build. So helical Sorry a bit hard to read Helical coils in classical Stellarator Sorry Problem with my hands this morning stellar Raiders Just all Heliotrons are hard to build and They are hard to build because when you think of the high field side the coils can be very close together but they cannot overlap so to say right and Then you have to build the helical coils inside of the two royal coils and This can be very annoying. And so this is why a few years ago somebody The community came up with a very interesting approach. These are modular coils So let's first or to understand that let's draw a good drawing where we unfold the coils So here we have the toroi. Sorry the polo direction So this is the polo direction here. We have the toroi direction toroi direction Now we are first looking at the toroi coils in this example. So let's assume Since the toroi coils opposite us going in the toroi direction, right like this One two three four and then down like this one two three four and then like this and Another one one two three four down like this and The current flows of course in these coils everywhere in the same direction like this for example like this and Let's now have a look at the helical coils in Such a accelerator if we unfold in this plot where we unfold the toroi and the polo direction It looks for example like this and then one two three like This for example and then one two three like this and then another one and And another helical coil and another helical coil and Since we have here is the example We look at we take a look at the example of a classical stelerator Meaning the current flows for example in this direction then here in this direction in this direction In this direction this direction and in this direction Now what we want to do is we want to replace this classical concept with modular coils so replace With or by By probably so quite proposition replace by With I don't know with by modular coils And this would look for example like this We would just try to get to the same current path meaning you would need a coil Which is flowing with the current flowing like this like this and then like this and Then we need another coil where the current flows like this down Up down up like this and then another coil where the current flows like this these And Then again current flowing like this this and these are the modular coils so yellow are the modular coils and that was a very important a very big breakthrough in stellarator research so that was a big break through in stellarator research so and the first example for that was W7AS the advanced stellarator so the advanced concept basically means to use modular coils which allows for more flexibility it's easier to build so that was really an important thing okay what else is important in stellarator research there are a few things and one is of particular importance so very important in stellarator research is the optimization of the configurations the configurations for symmetry this really is an important topic I will explain you why that is the case in a minute the optimization of configurations for symmetry okay it is important because to make it simple we know from the Noether theorem the very general property that symmetry implies conservation laws so symmetry implies conservation laws this is something very important and here for our magnetic fusion device this means this means that we might have better particle confinement something very important it also means that we have better control of the plasma over plasma rotation plasma rotation which is important for control our plasma which has effects on transport losses especially on turbulent transport as we will see in one of the later lectures turbulent transport and this is why it is so important in stellarator research to always try to regain or restore some kind of symmetry because I told you when we bend a linear stellarator into a torus we lose the symmetry so this is why in stellarator research we try to regain or restore symmetry such that we will have some type of quasi symmetry in the end so we have some type of quasi symmetry and I will show you three examples in the next slide what do these quasi symmetry expressions in general mean well it's the structure of the magnitude of B on the flux surface which is important so the structure of the magnetic field on the flux surface is the important quantity this is decisive and not the symmetry in real space this is something important to be aware of and there's a nice paper by an boozer from 1983 where these things are discussed so this is an important statement and let's now have a look at a few of these quasi symmetry cases and here one example the H is accelerator which is an example for a quasi helical quasi helical symmetry and the example shows the H as X stellarator a photography on the left-hand side the magnetic field strength color coded on the right-hand side the stellarator is located at the University of Wisconsin medicine in the US and what does this quasi helical symmetry means it means that the magnetic field strength is approximately constant along a helical trajectory along a helical trajectory and this means or has the effect that the the experiment exhibits tokamak like meaning good transport properties and good neoclassical transport properties now that is the expression neoclassical just means that we have a total magnetic field and don't worry we will discuss that in a future lecture one of the next videos actually but neoclassical here just means that we have a total magnetic field and having a quasi helical symmetry means we have tokamak like neoclassical transport properties transport properties and that is of particular importance for the confinement of fast particles so of high energy particles and of course when we talk about high energy particles we're always thinking about alpha particles and we need the alpha particles to be well confined because we need them to deliver their energy to the plasma and in a classical stellarator these particles as we will see are very fast lost in the magnetic field okay that was the HSX stellarator then another one is the quasi axis symmetry example okay quasi axis symmetry and this is again an experiment in the US so the NCSX stellarator which was however closed in 2008 immediately after the construction has been finished for a few reasons right in the drawing on the right-hand side there's first well it's first a drawing of the experiment you can see it was quite a big stellarator because here you can see the typical engineer physicist standing next to it it was built in at the Princeton plasma physics laboratory on the right drawing of color code of the magnetic field strength again and here quasi axis symmetry means that we have a magnetic field being approximately constant along a toroidal coordinate along a toroidal coordinate and similar to the previous example this is predicted to have similar good confinement properties as a tocamax unfortunately this was never put into operation as I said due to a few problems during the construction phase budget problems and the magnetic field coils are a few problems that's actually a long story another example is the so-called quasi omnigenious symmetry so the quasi omnigenious pretty sure I'm pronouncing it wrong omnigenious symmetry and again on the left-hand side this is a study so this is a model so such a stellar it has not been built this is a model color code a magnetic field strength you can also see the coils there and what this symmetry implies is that the displacement of the particle orbits from the flux surfaces is minimized now you might be wonder why the flux where the party is deviate from the flux surfaces as we will see in a following lecture if you follow a particle around a tocamac or a stellarator you just follow it along its trajectory you can see that due to drifts the particle will locally deviate from the flux surfaces and this is minimized in the quasi omnigenious symmetry so the minimization of the displacement of particle orbits from the flux surfaces is what quasi omnigenious symmetry means now it is actually in principle similar it is in principle similar to W7X which was however which was drift optimized so to reduce also losses by particles due to drifts as we will discuss again sorry in a future lecture so similar to W7X with the difference however that the quasi omnigenious symmetry has a small aspect ratio so it's more compact has a small aspect ratio oops aspect ratio usually has no end there small aspect ratio and also a significant a significant bootstrap current now a bootstrap current or the bootstrap current is a current a toroidal current flowing in the plasma and W7 which is generated by the plasma itself and actually W7X was optimized to minimize the bootstrap current but the quasi omnigenious concept has a significant bootstrap current in contrast to a typical stellarator where you do not have a strong toroid current flowing so overall it is a much more compact design and an interesting candidate for a potential future experiment let's say and before we talk more about of the different type of stellarators that exists I here for a nice drawing and the major point is that various that various quasi and then whatever symmetry concepts exist and it is not yet clear which is the best of those stellarators so you can see this drawing a few examples we talked about so these are usually notice all color code of the magnetic field strength here you can see W7as this is W7x then we have the TJ2 stellarator here then LHD Japan's largest stellarator then NCSX we talked about that HSX and then QPSS which is only a study and also Heliotron E and CHS and you can see they look all quite different so as I said it is not yet clear which is the best stellarator okay so that's it with video 12 where we talked again about stellarators we talked briefly in the beginning about the difference between classical stellarator and Heliotron or Torsatron we talked about the advantage of a modular coil of the modular coil concept and that this was actually a big breakthrough and how this is achieved and mimicking mimicking the toroidal and helical field coils by modular coils and then I told you a very important topic in stellarator research which is the optimization of configurations for symmetry and that the structure of the magnetic field on the flux surface is decisive and not the symmetry in real space and we talked about a few examples finishing with this kind of overview plot here showing a few different stellarator concepts and as I said it's not yet clear which one of those is the best that's it hope to see you in the next video