 Oh, so we were at the quite a single list here is James. By the way, Helicity is an unfortunate word, which is not the same Helicity as the Helicity on Taylor actually so they are using the same word but in this case Helicity means the MNN of the mode. Sometimes it gets some confusion, but so this is why we call them Helicity was a single electricity. Now, scar six in this kind of the of the spectra were observed in the control room in intermittently in the experiments but basically ignored and I was a PhD student to have looking at spectra and looking at the software to see tomography and I had an island there but I was thinking it was an error basically. So, it is rather after actually giving and looking at this statistically these ideas and be convincing yourself that it was not an error but they're still actually something real. It was actually analyzed and we it was seen that this most were real actually so the mode was illegal and so one mode was dominant and was increasing. I think we had the, the, the best that was a single city experiments and regimes were at the highest current obtaining in our effects, but especially in our effects more than I will show you tomorrow, which was the way to get cleanly to high because our effects was struggling against the, the problem of the lock it modes that was interacting locally with the first world not allowing to obtain the low the sufficiently low resistivity to allow to increase the loop voltage and the increase the current. So, whenever we get to this high recurrent the regime at high lung this number we obtain examples of just like here so you see a 1.5 mega amp discharge in which the mode one seven remains sustained for a significant fraction of the discharge and looking at it statistically the persistence so the fraction of the time the discharge remains in quasi singularity grows as long as the longest time when the temperature basically increases. And there are some back transitions to image but we get less and less frequent. So what happens is that it is not only a magnetic things, but it is also seen in tomography. So, once I begin to do and to look at the soft x-ray tomography together with magnetics and correlating with to the two measurements. We're seeing that the position of the structure of scene in the soft x-ray tomography which is located in one poloed location. It was a randomly appearing in different locations from shot to shot. And this was related to the fact that the modes were locked in different locations, some from from shot to shot. In our effects model, we were able to make them rotate during a single shot to slowly. And this is an example shown here in which actually the phase of the mode as measured from the outside and the location of the old point actually or the hottest point of the soft x-ray tomography seen here actually they match nicely. That was a one mega amp 1.1 mega amp so it was kind of an intermittent qsh but still so we have the magnetics and the soft x-ray tomography that was one of the first convincing evidences of qsh helical ones. And then growing in terms of current, we found that there were actually two kind of structures. So, these nice structures, which were located in helical structure located inside the plasma, which were occurring in different angles because the diagnostics are located in different poloed locations. So soft x-ray tomography is 90 degree apart from the Thomson scattering so in one case was up, in the other case it was out. And remapping this kind of things, it turns out that it was actually helical, we were same helix, the same helicity, the same mode number n as the mode measured by the magnetics. But what was found whenever we went to the 1.5 mega amp regime is what in some cases the Thomson scattering, this is a measurement of temperature along an equatorial plane, were much wider than what we used to see in the 1.1, 1.2 mega amp regimes, which is a narrowware. And so we had two kind of structures, so the wide structures and the small structure, and looking to the Poincaré plot, but I will in the next lesson guide you again to this kind of Poincaré plots done only using the dominant mode. It turns out that the wider structures corresponds to states which are purely helical, so these are not island anymore, so these are called single helical axes, so these are the formed cylindrical structures. Well, the narrower one were related to real islands in the sense of one that you can compute with the formula of small island widths, and these are the two main transitions, and we will see later how it depends on the mode amplitude. And another important thing that was related to this kind of structure so the RFP was not actually axi-symmetric anymore. There was an equilibrium associated with this kind of structures and at first the computing numerically following the field of lines and then adopting the tools typical of the stillerators so whenever the equilibrium is 3D, we were able to see that the Q profile is not monotonic anymore in the helical structure, but it has a maximum, so it's ironical because actually you want to avoid a maximum, a minimum of the Q, but you end up having a maximum of the Q whenever you get to the higher currents so it shows you that things are really nonlinear, the thing is in the regimes that you are studying and so the presence of the maximum Q, it is actually intrinsically related to the helical state, and I guess it's confirmed whenever we were using VMEK and giving you the, which is the equilibrium code of the the stillerator, giving us constraints, the measurement of the pickup coil, so the helical component and the flux and the current and so on and so forth, and the Q profile to which it converges has a maximum where, which is characterized by the fact about the number seven, which is the actually the periodicity of these helix is not resonant anymore. And curiously actually, the Taylor v conjecture came to place actually some colleagues of us asked our data and they tried to find the following idea which I find interesting actually. So if you remember Taylor's theory supposes that you have your plasma confined in a perfect conductor, and the whole elicity now the elicity in the sense of Taylor so A cross J, the total integral, is concerned that you minimize the energy and analytically you obtain the BFM. What these groups, Dennis and others suggested, say, imagine that the plasma is separated in different regions and the minimum number of region is two. And you prescribed the helicity and energy separately on this regions, so it is depicted here basically so the idea is that you are the your your conserver, the flux outside and the helicity outside the flux inside the elicity outside, and you have to specify in this basically, where the, which is the flux of this determines the region, which is, which is actually separated from the other so impressively you assume the presence of a transport barrier, which is actually an answer. But if you end up, and now it is not analytical anymore but you have to use a minimizing code, which allows you to compute the minimum energy, given the constraint of concerning the elicity on these two separate regions. There is no doubt that the minimum energy is exactly the single axis, the single helical axis states or the double helical axis states that are found experimentally and there are some examples here and there is some actually residual chaos or whenever they are going to trace the elicity that is obtained by their code. So it means that there seems to be something in the details theory also in the helical states. And so, this is very recent actually result and something which is worth looking at and thinking to. It was basically with the end there is many more things but actually I'm summarizing. And so what we have shown in this first, this first part was that the RFP is a strongly paramagnetic configuration, which required the reversal, but it is not consistent with on slow and the fact that it has been observed experimentally it depends on the fact that the plasma wants to become helical or want to become 3D so develop some instabilities and this can be explained or described in terms of an universal curve in the F theta plane with some dream empirical best of function model which are different kind of explanations so which gives us some glimpse of ideas just to describe the experiments but basically we had to rely on the disco resistive simulations and on global modes so this is what we deal with. And one of these global most actually was responsible of the transition from the multiple elicity to the quasi single elicity states which in itself then split into so the quasi single elicity. The axis whenever the amplitude was not high enough and then the single helical axis. And one of the point is that this can be described not only as a small perturbation but as an equilibrium. So I'm a helical equilibrium so the RFP was born axis symmetric but it in the end it can described as a helical equilibrium with a maximum in the safety factor. So this actually some references of what I've in which you can find much more details about the RFP because we are there are the three reviews and some early pinch research in the old books and few books which may be useful for this part. I immediately switch to the second part which is on the transport, in which I am basically building on this on the two topologies and seeing which are the properties of transport, which in a sense are very, very well connected and so how can you get out of here, which are pretty connected so distinguishes between equilibrium and transport is some somewhat arbitrary in a sense because they are interrelated. Okay, transport but it would be better say it is transport and topology because actually topology changes the transport properties overall actually. So in a nutshell, and so if we had to do this lesson in a few minutes that would be the main message that the core transport properties of the RFP are described in the framework of stochastic fields generated by global modes but the point is that the phenomenology is so rich but it cannot be simply in terms of amplitude of magnetic fluctuations so per se so there's much more richness in regimes and in some transient experimental conditions, there are experiments in which this stochasticity is disappearing, but it happens only transiently and so now I'm going through just to show some examples and now a few slides in which I will recall something probably you are very familiar with about basic stochastic transport. I will show what we did on transport in multiplicity just to see how the basic stochastic framework works in that regime and then I will switch to the quasi-singularity regimes in which transport actually is more complex and meaning that you have to distinguish regions and so the same modes that plays for transport they also plays for topology and so it's not so easy to draw a simple scaling load. And the last part I will briefly show some results from on transient results in which you are in some experiments in which these modes are switched to very low level. Now you'll probably all know about the Chirico stochastic instability parameter which means which tells you whenever you magnetic field becomes stochastic. Now I recall it just to show that it won't work in the quasi-singularity state or at least it needs to be modified it always work but we have to be dealt with some care. So the basic idea as you all know that if you have to neighbor island opened by no matter what kind of resonance perturbations can be a magnetic instability, a field error, a very fine scale grain turbulence no matter what. If they overlap, so if the distance, the half distance of the two islands is less than the distance you have distinguished these three regimes. Whenever they are not overlapped they are actually only distorting field lines, even if inside the island there may be some transport and so the island may be flat itself so it may in any case influence transport. So they are barely touching magnetic field lines are weakly stochastic and there may be some remnant structures and actually I will show you that we have measured some kind of this kind of structures in some regimes. Whenever they are much greater than their distance in principle in the region of a fully stochastic regime you are and then magnetic field lines wander stochastically and they flatten every every gradients. This is the regime in which register Rosenblut actually derived its famous formula which has been used for years and whenever no direct the thermal diagnostics available and it was used as a scaling just to assess the transport. Now, in the case of the RFP, the resonant global modes, in fact, the three modes are the one responsible for generating this stochasticity. And due to the Q profile that I've shown you if the amplitude of the modes is sufficiently high these islands may overlap, especially in the region near the reversal surface in which we have a packing of the rational surfaces. And so it is more and more easy to overlap and to get the silicon criteria going much higher than one of this figure I will show you later on. Now, the point is that which is basically the mechanism of the stochastic transport it is based on the stochastic instability of the interjectories. I mention it because actually it has been used by our colleagues and by my group also just to map directly the field lines and to compute the the the diffusion itself because actually here in the case of register Rosenbluth it suppose that the average displacement is described by a diffusion formula which is valid whenever you have a fully developed turbulence. And so it is an approximation that can be done there are plenty of regimes that should be taken into account but the idea is that you have this divergence. This is exponential divergence of lines basically and so you have this this coefficient so for an experiment this is a number and this is a coefficient that skis with something that you have to work then to compare with our with our measurements. And the point is that whenever you have the field lines that are actually diffusing the particles will follow because actually transport along the lines is much faster. You can do it to the six times typically one the transport perpendicular, and then you have this scaling formula in which if you assume that the transport is local, which is a strong assumption, in any case, but in the fully developed turbulence, you can do it. The coefficient depends basically on the scaling of the of the fluctuations to the square to some autoregulate auto correlation length and to the temperature of a particle so the lower the radial perturbations the lower the transport and the scaling is basically that the experimental were measured, we're trying to seek this kind of dependence, and also the transport is low is the field is weekly stochastic. Now, with the advent of a high resolution special diagnostics we tried to basically compute the effective coefficients and compare with stochastic theory. So, by carefully measuring temperature density, reconstructing the profile of the current with the models that I've shown you in the first lesson, we were able to obtain estimates and profiles of chi effective with with so called power balance technique so assuming so say stationary condition, and that's an example is shown here, basically in the in the core. There is a huge uncertainty so this is shown here what you see that the uncertainty by varying a little bit with Monte Carlo varying the various parameters were such that the estimate was meaningless. Minimum near the near the core, near the edge, and this is typical so the RFP confinement that is basically minimum in an edge region which is nearby where the reversal surface is located. And there is a region on which you have some chi here so the chi core, where there is some residual gradient clearly these are multiple electricity so some strong turbulence. The number compares with the register and rosin both and our colleague in medicine basically reconstructed and recomputed the magnetic field lines, starting from the Eigen functions so the radial perturbation reconstructed with an m hd this code. They did it to resist you we did with a linear analysis in any case in both cases we had to rescale this kind of line of measurements in order to match the external measurements so we had to rely on the measurement of the magnetic field perturbation at the edge and feeding these kind of lines inside the field line tracing code. A Poincaré plot like this one was obtained and by the way in the paper they do not actually notice that there are there's an n equals six island here and later on they admit that this is a qsh but they focused on the region in which fields are stochastic and in fact what they did was they did a power balance just like we did in our effects. And so comparing obtaining an effective value with with with a similar uncertainty which is the gray area due to the fact that whenever the temperature does no gradient it's difficult to estimate the effective. And we compared that we've stochastic in two ways by the simple application of the register a reasonable formula so using the square of fluctuations and estimated the auto correlation left with a field line tracing. And it is shown here basically so it basically is it is in the gray area in the region where the the Chiricov parameter is rather high. It doesn't work inside into the core whenever actually there is some actually uncertainty but there is also the remnant islands, the qsh and it doesn't work at the edge. But in this case because they were not using eigen functions to deliver to obtain stochasticity in that region in any case I will show that the q equals zero act as a barrier so there cannot be stochasticity, unless in some to go to a localized region. So the message here is that in multiple electricity the transport is a scouting in between, not in the core and not and not and not in the edge. The fact that it works but not that much. It was also retained that when looking at the scaling with a magnetic fluctuation so in other effects that we were able to gather the chi effective averaged in what is this written core in the paper relates to half radius so basically where the Kaiser is meaningful. And by considering the dependence with respect to several ensembles and in which the longest number could be estimated. It turned out that there was a scaling dependence with this number minus point 77 simultaneously. It was also possible also to measure the scaling of the magnetic fluctuations so minus point eight in principle if the retches the rosin blue to hold the chi, which would be minus 0.36, which is weak. Actually, that was thought the motivation why RFP doesn't work as a scaling for reactor in MH, but experimentally actually it is much steeper than that factor of two basically. That's 99 so in these ensembles there were some qsh hidden inside so it tells you that whenever you do some scaling without knowing exactly what is inside your data you can mix up things and obtain different scaling laws. So it was a first time that indication that there was a change of regime so scaling should be always taken with care. Transport in the, let me close it. Transport in the edge is not stochastic and that was proved with some direct insertable probes by our colleagues in medicine. They actually measured the parallel flux q parallel fluctuations they measured the radial field so directly so without me not be mediated by some Fourier analysis. And it turned out that the inside the reversal, it was compatible which was what's coming with the theomic flux coming from from the core, while outside it was not. It was negligible basically so other mechanism so electrostatic fluctuation were responsible for transport outside so the q equals zero surface act as a weak barrier in a sense. Why don't you. But the point is that even in image, the transport in the in the axis symmetric, the transport in the edge part of the discharge is not is not symmetric. This is a figure taken from a paper in which the magnetic magnetic profile is taking from a visco resistive simulation by the special code which is located in part of that just to illustrate someone asked me which was the structure of m equals zero modes. And this was actually an experiment actually a full experiment so it's a it's only only theory. So using all the modes. Pre point career plots are shown here. And so in the first in the first row, it is a point career plot used performed by using only the m equals zero modes produced by this mode, which is a cylindrical mode. The same because it almost do not show do not do any chaos because actually Chirikov does not does not apply whenever all of the modes are resonators on the same surface but you have a modulation so you have several rings with different shapes, and they are there. The second, it is also very interesting because whenever you do a point career plot with only m equal one modes, you still see m equals zero structures or islands. And these are due to the fact that this m equal one modes interact themselves with the equilibrium and so there is some structure and as these modes are phase locked as I shown at the beginning, all the phases tend to be aligned in this code. They are aligned in zero. There is this barrier effect, due to this m equals zero structures in everywhere but where all of the m equal ones are pushing the lines, the magnetic field lines away and so the this is the region in which the lines can escape from inside to outside. And the last one is a point career plot in which both of them are present so in the multiple electricity we have remnant time equals zero islands and through the x points of these islands there are some islands getting out there with some different kind of connection, connection length and up to 2006, these were only, say, numerical calculation but some measurements were performed later on and in a regime in which are effects operates at lower current allowing us to insert the probes inside the machine. It was possible to measure simultaneously with probes and with the Thompson scattering an m equals zero island, an edge m equals zero island, which is shown here so here you have a point career plot showing in red lines belonging to this island, and this is performed at the time at the Thompson scattering fires, and the temperature in this line, it is fairly flat basically and corresponding to the location where the island is located while outside is much higher because it's going higher to work toward the center. It's also allowed to measure the electrostatic flux in terms of the particles and reaches a Rosamble of key some estimate which is lower than the measured stock, the measure electrostatic flux. It's a question of that in the edge outside the reversal transport is electrostatic is not stochastic anymore, and also power balance was actually performed whenever a gradient was there with numbers in which which were such that Chi over D was of the order of a square of a ratio between me and I onto electrons so consistent with stochastic. There are many ways to take a ways of transporting multiple electricity. While whenever we took about the quasi single electricity things are different. A paper that anticipated this factor was actually probably seen 2000 so seven years before discovering actually this is a single helical states and the idea that it brought about is fairly simple so it tried to say okay let's take let's let's take numerical this co resistive simulations which gives us a single electricity. It used to be but they had this kind of simulation but they were thought as a of academic interest because actually no one ever so single electricity pure stationary in the experiment and so they took the field as obtained by the simulation and they tried to compute the up to apply the Chiricov criterion and so it is shown here in the is taken from the paper, so it was an n equal 11. It was not a perfect simulation actually it was not realistic because the electricity was not like like the one of the experiment but it is the idea that matter. It was a significant strong overlap so Chiricov was way higher than one in a couple of region, but then they tried to do some field line tracing in this case and the field line tracing was still showing some order. So the n equal 11 was still remaining here so there was bonds of chaos, but the modulated with an n equal fun when equal 11 and so region of chaos separated from inside to outside and when they took the spectrum and practically so arbitrarily say reduced by a factor of 10 only the dominant mode and so basically reducing the Chiricov parameter and so going to a less chaotic situation according to a standard to a standard idea. So we ended up in a Poincaré plot like this one which was way more chaotic, we having saw only some remnant of the 11, the n equal 11 here in white and some n equal eight here. And kind of a paradoxical effect and the explanation of the paradox was actually explained in terms of the topology of the magnetic field as generated by the dominant mode alone. So, if you if you discard all the all of the others and you perform a Poincaré plot by using only the dominant mode, it turns out that whenever this dominant mode is low. It is on the left and so it is actually generating an island which is characterized by an all point an x point and there is also an all point which is the residual magnetic axis of the equilibrium. As long as you increase the amplitude of this mode, the two, the all point, the all point of the magnetic axis of the original one say of the unperturbed one and the x point gets near and near and at a certain point they coalesce and they merge together. And you obtain what it is called a single helical axis so and this is the why reducing the field or generating more cows because the presence of an x point now for the guys who belong to the Hamiltonian club to which I do not belong. They think that it is very common to understand that whenever in the orbits there are x points, this is very prone to cows so whenever you have some perturbation this may grow while whenever the x point is expelled from your system. It is more resilient to cows and this is what seems to be happening also in the experiment. In fact, this transport barriers, as I mentioned at the beginning of the double axis and single axis were actually found in the experiment. And while at the beginning we had the Thompson scattering measurement showing just like in this black curve, which was actually only one or from one part from one side of the magnetic axis of the island of the chamber. It happened that sometimes we had this wise with wide things and extending way above the magnetic axis so from the from both sides, and when correlating with the amplitude of the dominant mode only. It turns out that there was a threshold so thermal structure wide thermal structure were obtained whenever the mode was above a certain threshold. Actually, this began to occur to be observed. In the last part of the of the of our effects modding which some of the technology we're beginning to fail. So now the things are patching because actually some campaigns have something now since some other campaigns are some other diagnostics. So, whenever we had a new diagnostic and a new campaign, it turned out that the situation is even much more complex than this and this is a very, very rich and recent paper. In which it turns out that not only the dominant mode determines whenever you have a wide or a narrow structure, but also the secondary modes, but not more modes are equal. So by analyzing and so performing a lot of point care plots and looking at the structure with and correlating with the amplitude of the most turned out that we're constructing much better than equilibrium. Also what we thought to that they were double helical axis structure actually they were already shocks so it seems that the transition from a thermal point of view. The structure remains narrow, even if the x point has been expelled and only at a certain point. It's still wide and why it happens. It happens because the innermost resonant mode remaining because in the Q profile that as I mentioned has a maximum so the seven is not more there, but the 89 in our case are the ones which are still there. They decrease to such a level that they are not stochastic anymore they can allow the structure to widen and so this is this points here so this white structure are correlated to the fact that the n equal eight and equal night amplitudes are decreasing as long as the amplitude of a dominant mode is increasing. So, these cases are the ones that are when what we show. So, even if we have this magnetic wise huge structure, dominant mode so in a sense stochasticity stochasticity is still playing a role, but in a complex way, it's putting this way. In fact, whenever you do some power balance also in this, in this case is so remap the temperature not, you're not a systematic anymore but you have to remap in this helical structure in helical coordinates of a single helical axis, and you see the minimum which occurs where where the barrier is located, it do scales with secondary modes. So this the dominant one should be taken off and so it in a sense it reminds the ratchets that are scaling but only concerning the dominant mode only the most relevant for the location where the barrier is located. And so, okay, this is a summary of what we have some we have observed so dominant modes matter but dominant plays a different role sub dominant plays a secondary role and we all the others determine the transport. Now, let me conclude with a few slides on the current profile control techniques, in which our colleagues from medicine tried to switch off to reduce the second wave in stochasticity by switching off all of the, all of them are by driving current from outside. And as I mentioned, the idea is that if you drive some political current instead of relying on the plasma. You do it from outside. The vrfp can be sustained without relying to the it's self organizing mechanism, be it multiple city or single city or what else and clearly in doing some ad hoc simulation this resist even with you had this. You are this current and you do a point correct lot you clearly end up that these modes are stable and so transport is expected to be much better. But clearly this is a doc this is not in reality. Now our colleague tried that now this is a busy busy slide, but they tried with the different approaches so they tried inductively they tried with electrostatic insoluble chrome currents also with waves. The most successful one was the one we inducted which unfortunately is transient and also in our effects we did it and it is called the oscillating polar current drive, the field instead of going down and then ending the discharge. It is repeated clearly there is a good part in which you have the field. The current is driven in the right direction and then there is a bad part in which actually you charge it. But they do it worked. At least in the low current and now there are many over but you can find in the radio but now I'm focusing only on the most successful one which was the past. The current drive and the first the measurement that they did is that as expected, whenever you are you drive current from the outside. The flow is matched. So they measured the parallel current and the ate a j square, while in the standard case, as in the parallel big pinch as I showed you the first, the first slides and the first lesson, they are unmatched so there is less. There is not much less in the core and differently at the edge in the PPCD case, at least in this transient phase they are pretty much matched so no current is required from the plasma and in principle no dynamo field is a is required. And this is a time trace here basically so you see that the beef I is reducing in in time so there's a pass there. The difference is that the root me square of fluctuation so global most do decrease during that good phase, and while they recover whenever you are in the anti PPCD phase. And these modes go down to such a low level that by tomography I was in the control room that time I remember that I saw the traces there. You do not stimulate the qsh, which happens often but in the case in which you do not happen you do not stimulate it. Multiple tiny islands appear in the fluctuation pattern beating because they are rotating at different velocities and clearly indication that the magnetic chaos is very very decreased. While in the wild in our effects, typically the PPCD which is the oscillating the oscillating part of this kind of the behavior was such that the dominant modes was decreasing and the secondary most decreased and the dominant mode increasing and getting the higher temperature. And our mystic colleagues also actually sold that temperature significantly increase the chi clearly go down to say 10 square meter per second and concerns electrons while irons are pretty much unaffected. So this is something to be understood when they add some kind of different experiments and trying to have to increase the ion temperature. And it found that the temperature scaled with amplitude of the most located clearly near where they are more densely packed to where some residual magnetic chaos was still going on. And I think that's it because actually I squeezed a little bit too long. So in essence, Stochastic Trampost still apply to the RFP in a multiple electricity. It's an important loss channel in quasi single electricity actually it still is stochastic but the various modes have different roles in changing the topology. And so the dominant mode the sub dominant modes and all of the secondary modes so still scaling but who knows we maybe we are in a in a regime in which something else is going to change because actually as I show transport it's not actually so there is this region of the locket modes, which may connect the edge of the wall, if the amplitude decreases and these connections gets closed, who knows what may happen. And what would could what can happen was shown by transiently by this current profile control techniques in which actually these modes are decreased the transiently and showing that I can read can be reduced to very low level. And closing it was there so many things to say. Thank you. So, any stochastic question. Yes. Okay. Thank you. Let's say the city. The point. This is the exactly the point that we are struggling with, say, for the experimentalist. Discosity is a number they plug it, they do their simulation that's okay and then they tell us okay measure it. And that's the definition obviously because they actually the various kind of say approaches. So our colleagues in medicine have done is just taking, not looking at the magic code but looking at the breaking curve of the most, because they have the most rotating but they tend to be connected to the plasma there is a bad talk balance between them. The flow and the breaking by the shell I will talk about tomorrow about the talk balance and the locket modes. And by measuring this curve. It depends on the amplitude of the of the viscosity parameter and in some cases it seems that it can be better represented by stochastic viscosity. And so it is not Braguinsky, but then it is the perpendicular one, the parallel one, and not really expert. And so the point that we are eager in our effects mode to start again experiments because from the beginning, we were forbidden this kind of experiments because most were locked from the beginning so nothing rotates so you cannot measure anything. So to in principle, these most will be rotating so we would now we have much better diagnostics. In principle, we can measure and estimate to this viscosity. Okay. Yes. The global modes. The most but actually they are very most dynamic modes so the m equal one and usual modes. Yes. Okay. What's the question. I will be wrong. In space. Yes. Yes. Good point. All of the simulations typically are zero pressure. So, all of the special simulations are still pressure they are trying with six pixity with other codes to introduce pressure and transport. But it is a nightmare of all in stability is that we have to stabilize that the depths code has some pressure, but for sure it is isotropic. Whenever you switch on beta, there are so many ways that we're going on that I've seen that they are not using so often. Basically, all of the mystery results that they have found so far are zero beta. Yes. Yes. We are curious to watch. So the point is that the we are building an experimental database and idea so in some cases in MST, they seem to be to have some behavior which reminds of it G's or, and they are doing some kind of kind of zero kinetic simulations, but we do not have such such a solid database or experimental evidence is that we can say, okay, we are getting into that regime, because actually what they what we have tried to see is that the gradient of the temperature even in this gradient normalized gradient scale with a secondary the global secondary modes, but this is how whenever you lose your key you look below the lamp whatever you see so because this is what we measure. So we will have a wider array of pick up sensors and set up a sensor so we will look at the wider, say, and HD fluctuations are lower lower times case and we will try to see but so far. We have some indirect evidence in the. There's a couple of figures in the review in which maybe the effective Chi maybe consistent with some kind of gyro kinetic computation in the very edge of the figure probably. Any other questions. It's not. Thank you. Thank you. So, somebody reminded me that I'm supposed to be talking this afternoon. So what I will try to do then is to give you. Some kind of.