 It should start. Okay. Then I got it. Okay. So, in a nutshell, what I'm going to do is to tell you that the reverse film pinch is an MSD equilibrium configuration, but you have studied in the books, in magnetic confinement, which is found essentially in two limiting states. An axisymmetric reverse film pinch state, which is the one which used to be known since 2000. And the newly discovered helical symmetric reverse film pinch, which is new actually, which is covered in the last review basically. And all of this realize of the fact that the steady state inductive omics sustainment of an RFP is not possible in axisymmetric geometry. Whenever you get it in place, then it will diffuse away. And so no way, it cannot be really axisymmetric. So some kind of 3D geometry is required in order to keep it sustained. Now the point is the plasma self-organizes itself with some outside help that I will clarify to reach stable conditions in two ways. So in axisymmetric geometry, well, the 3D, the required 3D geometry is supplied by some MSD turbulence or MSD modes. These were the old ideas which provide sustainment. But with this view in this approach, the plasma is intrinsically chaotic and with models confinement basically. While in helical geometry, only a single saturated MSD global mode can deform the plasma and provide the degree of 3D geometry required for sustainment. This is basically ideas and now we will go through. Now what I'm going to touch in four parts. So about the basic axisymmetric RFP properties and some terminology just to understand what is the bibliography about the axisymmetric RFPs. And then the second part, I will deal with the experimental phenomenology of global modes and in the multiple HDG and we require single LST regimes. Now let me start from the name of the configuration. This is basically is too obvious that you have already started, but the reverse pin pinch inherits is named from the old Z pinch effects. So the old Z pinch experiments in which we had that you had the self-construction of unidirectional currents due to the current that you are induced in discharge. And so you are just this very high beta because possible to be obtained in this discharges due to the fact that the plasma confines itself from J cross B beta was very high. So it was very promising, but unfortunately it was very violently unstable. And what happens is that in the high plasma currents and non axisymmetric deformation of the plasma currents grows exponentially and eventually terminates the discharge. And this is happening on the time scales of the Alfven waves, which is in the time scale of the microseconds for the time being for the size and densities that were available at that time. We are in the sixties basically and they had to develop the diagnostics very fast in order to see what was going on. And what I'm showing here is the first ever picture of a of a king mode actually in the aldemastone old pinch. And it was actually King instability, so it was an M equal one deformation, but there were also M equals zeros M equal one and M equals zeros are modes that are still affecting RFPs, but not this kind of ones. The time scale is important because actually the microseconds was such that it was very into an electrical engineering laboratories in which they were able to develop a very fast discharges. In fact, the Padua was an electrical engineering department. That's why they actually developed to took the RFP research. Now, in order to stabilize it, another simple thing that you can find in textbooks is that the idea was to add an external toroidal field. So a moderate toroidal field actually in order to to try to see to stabilize this more this ideal mode based on an ideas that were available at that time. And by using by analyzing what you can do with on with on slow, you can write down the equilibrium of a of a pinch, which is driven by by the simple of the simplest to actually transport coefficient to have been developed in the fifties in the forties. So they were ready available. And now, in order to build a simple analytical solution, but you can do it yourself. You can ignore your pressure. So you are in force three conditions that in the pressure coming elected the electric field is only actual. So we are looking at the station steady state solution. And this is something that you can find in the fight. New new text to book. And it is the stability that you're you're equipping depends on one parameter. Basically, it is proportional to the electric field you apply. And it is inversely proportional to the resistivity. And clearly, the toroidal field at the edge is the parameter but the experimentalist control by changing the current in the in the toroidal field course. And you have a simple ODE what you can that you can integrate numerically. So what happens in the pinch basically you drive the current by increasing the electric field or whenever it heats up the the resistivity decreases and keeping the the value at the edge constant because it is in the coils that you are applying. The plasma begins to produce a much more toroidal field inside as long as the current grows. So the pinch is paramagnetic. And this is one of the characteristics of the toroidal configuration and also the reverse pinch. So the reverse pinch produces much of its fluxes with a small value of toroidal field at the edge. This means that you can do it and you can sustain it without superconducting coils. So this is one of the advantages of RFP. But it shares and it inherited from a stabilized pinch research. Unfortunately, what happened is that even if there's some improvement was obtained still the pinch was already unstable. And this is due to the factor very, very fact that in any case the q profile of a pinch is always characterized by the presence of a minimum, basically. And the presence of this minimum is such that you can have some resistive interchange or ideally interchanging stability can take place. And the Sweden criteria of stability is always always violated because the q prime is zero. And the fact that it must behave this way is very simply due to the fact that in the center it should decrease due to the characteristic of the currents and in the edge it must increase. The only way in which you can obtain a solution to be a parent paradox is basically to have heat to reverse basically. So the idea was okay so we can decrease continuously and increase in absolute value at the edge here. Or the other solution to solve the pinch was actually to as you probably already have seen in the last days increase the toroidal field very high. So relying on a complex technology of very high toroidal field coils and which is the tokamak basically. The point is that in order to get this configuration you have to let the toroidal field invert its direction after the discharge formation. Because actually very p is nice for idea stability but it is not consistent with oms law and now I will repeat it the various time this kind of figure just to give the the the flavor what's going on because instead state as I said the electric field of a pinch is totally actual. And so it can drive current in the toroidal direction only or axial direction. And if you have the mhd equilibrium which is driven by the oms law as I said the speed resistivity the current in the toroidal surface in particular which is with q equal zero is such that it is totally toroidal so basically the electric field is orthogonal to this line. And so it cannot match it cannot drive any current you see here basically the comparison of the parallel current of a simple pinch with the 8j the 8j term they do not match for and so the RFP cannot be obtained in in a steady state. So the idea is that in order to obtain at least transiently an RFP and that was in the tested attempted in the 60s by okawa is basically to change rapidly the toroidal field at the coil after start up whenever you are already you are your pinch which is in the unstable phase but the loop voltage is high enough so that it still survives and then after a while with a perfect timing or with an optimized timing you reverse the current in the toroidal field coils and so the field is going your way around and in this way you hope that the plasma will keep frozen this configuration. Another variant was also to drive a parallel current so to increase the the reversal and so also reversing the loop voltage so that we have also the current in the direct in the opposite direction. It relies on the time of diffusion basically so it was very much empirically at that time basically so you are to do it fast in fact in the old pinches it was so fast that the current was only flowing in a in a in a sheet. What happened in the last pinches is that the current penetration is anomalous and so instabilities actually takes a place and so they make the current penetrate but the essential is the fact that you have to change the toroidal field during the start up phase with a timing to be understood. Now applying these two recipes which is basically reversing the toroidal field after the discharge or the pinch setup and reversing the toroidal the colloidal current in order to allow the reversal to obtain actually in 68 it was reported the first results by the Zeta device actually it was not an FP device it was a device that was actually built in the sixties to to test the pinch configuration but in the end of its life it has been modified actually so they had condenser allowing them to reverse the current very rapidly and they also use winding in the opposite direction just to have a loop voltage sent in the opposite direction and they were able to obtain during their discharges actually it cannot be read very well but it was in the milliseconds range which was big at that time because actually all of the small pinches were in the microsecond range and so this was a big machine for that time and they reached up to 500 kilo amps in few milliseconds in other facts this is the start up time but at that time that was a whole discharge and it was very turbulent so the second trace here shows what was the derivative of the Rogovski signal so basically the current was fluctuating wisely due to some kind of instabilities they called them very turbulence but whenever they applied the reversal and of toroidal and colloidal fields basically we obtain a reduction a significant reduction of these fluctuations so the so-called quiescent state which lasted as long as the reversal and the easy decrease was remaining there and that was the quiescent period that actually encouraged all of the RFP research came which came after that and there was also I forgot it was measured actually that the the toroidal field at the end was reversed point is that it was not occurring in all pinches because not only Zeta but also all over all another couple of devices tried they obtain reversal but they do not obtain quiescence and it later on resulted in the fact that even if you reverse actually what we are seeing here is the Q profile but reversed so the outer side is on the left you need to have a programming and an edge that allows to have the Q monotonically decreasing so that it is not unstable to this is an interchange where in other machines very likely the Q was still having a minimum there and so allowing to be to the instabilities to grow and that depended on recipes of the first world materials so they used to be there's some timing there probably they used to have the quartz so insulating instead of metal and they were not very clean they were filled filled errors so all of the things that actually made these charges very short motivated by this success in there were several generations of RFP experiments going on basically the first one was the HBTX which was built by the same people from Zeta actually it was a much reduced budget it was a very small machine what you see here is the minor radius and the the height is the the major radius just to give an idea so Zeta was very big actually it was kind of comparable to modern ones while all the 80s these pinches are reverse filled pinches were kind of short the second generation was in some sort of intermediate and the last generation which is actually when I'm talking about and whose results we have summarized in the last review has comprised this four ones actually KTX is the last one which is a Chinese experiment which began operation in 2015 but they are still struggling to obtain an RFP but we have some trouble talking with them and well the various generations had a different timescales so but some ideas about the RFP were born having in mind the experiments and the experimental findings of these small machines and so when we talk about relaxation when we talk about dynamo they were thinking about some kind of experiments now they have been adapted to different experimental findings but it is useful just to to give a look at the past and see what an RFP looked like at that time now that they spent some time recovering what it was let me just tell you how we describe an equilibrium parameter an equilibrium we use some kind of parameters and so the RFP equilibrium is basically represented in terms of measurements that you can do outside so electromagnetic measurement the first the first parameter theta is called the pinch parameter and if this is an inherited from data data pinch research it changes is meaning a little bit so whenever I was looking at very old papers theta was meaning a slightly different so it was it was connected to what was the toroidal field applied before the discharge while whenever the discharge is get longer and longer it became the the flux being produced during the plasma but in any case it's a normalization of the plasma current to the flux to the toroidal flux which is measured and produced by the plasma and theta now after the data pinch or after the theta component the new parameter which characterizes the RFP and which was not present at the time of a data pinch is the field reversal which is F and which is very present the edge value of the toroidal field normalized to the average value so after plasma breakdown so whenever you are in vacuum this number is one while theta is zero because the plasma has no current and another important parameter is the safety factor q which is the ratio of BZ or BZ clearly on q you will lose the information about the flux the flux which is being produced by the plasma now characteristics of all of the RFP experiments from the old ones up to now is that they they can be described their time evolution during this church can be described by the F theta diagram the F theta diagram means but no matter how big or small is your RFP machines also their pinch and the time trace of the F theta parameters on this plane will eventually get to some kind of universal current so at the beginning you are here so basically no plasma no current the toroidal field applied from outside is exactly equal to the to the average so one zero then the current grows the plasma begins to be paramagnetic so it produces its flux and it goes somewhere here and you see here the first characteristic that characterizes the RFP is that whenever the current grows so you have to go to high current you cannot scale simply to more small current because in order to have it reverse you have to go above some kind of threshold and in this case in case of normalize the coordinates and theta is 1.4 1.5 now whenever we are talking about the old experiments the small one they were characterized by this violent instability because actually whenever you use which on the plasma theta is equal almost zero it is unstable because it is a Q profile with a minimum and then the first idea that came to the people was okay let's go fast if we use condensers that goes faster than the instability we can make the plasma grows so fast that it will go burn through say the unstable the unstable period and then we will go in the the reverse stable quiescent phase but whenever you do it so fast you had so profile current profile so concentrated in the edge but they tended to be with very high theta low f and so they tend to violently relax to a curve in f theta so depending on how you adjust the timing of the reversal of the toroidal field of the toroidal field it turns out that they were always referring to some kind of curve in this f theta space and if you start up was such that you were getting far from that curve then with a very fast time scales was relaxing there so the time relaxation was invented at that time I think while machines, bigger machines which cannot go fast because you cannot go fast on a more small machine tended to stay on that curve for a whole start up and here cast the name of self reversal of the machine rfx and rfx mod actually do exactly the same thing so these are time traces for more more recent from rfx mod they all trace the same trajectory in the start up phase from 300 kilo amps to 1.5 mega amps so this is very very general and such a behavior was empirically observed to depend and to be described by the so called Bessel function model which is very simple in the cylindrical geometry again you take your equilibrium msd equilibrium you take it without pressure because in the start up phase the pressure is negligible the plasma is conducting but it is not playing that much role and this implies that the gradient of B is proportional to B so the current is proportional to the current to the field everywhere but you allow it to in principle be different from surface to surface but if you far assume absolutely empirically at that time but this constant this mu is not radically depending but it is constant it gives you a solution which is unacceptable from an experimentary point of view because it tells you that you are a finite current which is flowing into the edge so there is something to adjust but still if you work out the details of this equation in cylindrical geometry it turns out that it is analytical so it is the Bessel functions hence the name basically which all depends on one parameter which is the proportionality between the current and the current field and also in this case if you increase this number above some kind of threshold you obtain a solution which resembles the RFP actually it was recognized that it was resembling also to the pinch so it dates back in the years and it was inherited from some astrophysical papers in which these force free fields were used to describe this kind of astrophysical phenomena I am presenting the Bessel function model before the explanation of it because actually when I was a student it was confusing me a lot so that's why I prefer to do it this way but probably someone would not agree with me but from in fact they were lying around for a long time so empirically as an experimentalist I am happy I have something which represents my data I take it I buy it I am an experimentalist to explain why now in fact we were unhappy about the fact that mu was constant at the edge and so it was empirically modified and so allowing it to be constant in the core and decreasing at the edge so if you work out the details you obtain the alpha data zero model which we are still using today these days just to represent the equilibrium in order to do some kind of say remapping computation idea stability and so on so forth and at first the justification very very course justification of why is it could be is by introducing the concept of stochasticity and introducing the first time I will give you some basic ideas later on in the lecture on transport but may at this stage we only need magnetic field which is stochastic if the lines wander radially instead of describing nested the torey so basically it cannot sustain a pressure because the pressure is equilibrated along these surfaces this would justify why the current is proportional to the to the field and as the current is divergence free basically and as this mu constant should be should vary perpendicularity to be the only possibility is that whenever you have a region in which you have stochasticity mu should be constant along that region but if you have a region outside which is not stochastic anymore then you can allow to change and so this very simple argument about how this alpha to the zero and mu profile can be going to zero at the edge it was satisfactory for us but for the for the theoretician it was not satisfactory which is correct so and now I have touching the Taylor's theory which is still at the center of the debate in these days and people in fact are calling this conjecture instead of theory and so Taylor basically tried to borrow experiment ideas from theory to explain this BFM and the fact that this mu profile was constant and so his relaxation theory trying to prove why the BFM works so effectively basically still as I said called a conjecture and I will say why in a few minutes now the idea is that in the plasma there is a conserved quantity which is called the magnetic elicity now I am not an expert now this elicity is difficult to visualize unless you see some nice picture it is the knottedness of the field if the plasma is completely ideal all of the flux tubes are conserved so if you stretch twist them this quantity on every flux tube is conserved but this is ideal and the plasma is not ideal there is a tiny amount of resistivity so its conjecture is the fact that whenever you have the resistivity you have the tearing of lines so you are still again some kind of stochasticity so that the flux tube do not retain their individual character and so each elicity on each flux tube is not conserved anymore but he assumes that only a global elicity is conserved this is an answer basically so let's say that the plasma will reach at the end of its evolution it will tend to get to a state in which the energy is the minimum so the magnetic energy is the minimum so that the elicity is conserved so that the elicity is conserved so that the elicity is conserved so that the magnetic energy is minimal but keeping the magnetic elicity conserved so it is a constrain minimization so once you charge your system because you have some kind of loop voltage some of something going on by a very simple variational Lagrange multiplier argument you obtain a solution which minimize the energy keeping the constraint of the coke bfm so your lagrange multiplier is this bfm so now i'm clearly really over simplifying it but that's basically it so the fact that given these answers you obtain the bfm then the fact that the bfm represents pretty well your experimental data your experimental profile was taken as a proof because actually if you increase the data mu below no above a certain threshold it reverses and so this is usually presented as the proof of the Taylor's theory and more and then he elaborated more on that and i told you that if you want to get some more result no more detail on that we are very nice presented in some let me go back in some lectures by Dalton Schnack that he published in 2009 he spent a few lectures in going to the details of how it was obtained and which were actually the delicate point which cannot be proved and actually as yet there is no rigorous proof of the Taylor's theory even if it has been measured in fact i've seen a second in a second paper Taylor actually raised some arguments about the fact that helicity should decay at a different speed in terms of a lumpins number which rules the msd turbulence different from from the energy and actually this was measured in msd and in some particular conditions actually you do see if you measure the energy you through measure the helicity you can do see that the energy decreases and the helicity is conserved but still it is an heuristic argument because actually the point is that Taylor had in mind micro turbulence so small scale while we will see later on most of the rfp dynamics can be explained in terms of global modes so they are not cascades they are not going from big scale to small scale still some of the arguments are applicable but still there is some there but probably professor swadesh know much more than me about that point is that the rfp the Taylor's theory does not tell you anything about dynamics so it can give you only the minimum state of which toward which the system will will go but how are you going to go there and also how is it being to sustained so the the issue of the the the lacking poloidal current is still there so what is driving the poloidal current in the edge in the in the reversal surface and here comes another idea which is parallel to the idea of of Taylor which is the concept of a turbulent dynamo or the dynamo field which is about in the same years basically and the idea is that okay let's imagine that you have your rfp plasma which has some kind of turbulence and which can be split in two parts so you have your equilibrium b zero and the fluctuating with some part with some zero average average in space or in time so undetected and undefined and if you if you write down your arms law actually it turns out that your arms law has a new term so at least the the zero part of the arms law not the fluctuating part there is a term which is order zero so which is fluctuation times across fluctuation velocity fluctuation magnetic field and so arms law is modified by turbulence a generic turbulence and so you have an additional term which is the right term that you need to drive the poloidal current if you if you rfp with dynamo field is something that you see in the literature every every time basically point is that whenever you do some kind of statistical analysis or statistical description of your of your turbulence you have to do some kind of see simplifying assumptions at that time no i'm not going to go into this details by assuming that the msd turbulence had some very simply homogeneous isotropic properties an alpha dynamo effect what was brought borrowed by by astrophysics can be introduced and basically in astrophysics you have flows in the core of the of the stars of the planets that are that are driving the material and also generating magnetic field and it turns out that gimlet was able with this alpha dynamo effect we very simplifying assumption to obtain the bfm again and so in principle this is also a proof of the fact that gimlet theory is correct because actually with his assumption about turbulence and alpha dynamo effect he obtained a representation of this field and also there was some kind of time dynamics but the problem as i said is the factor that it borrowed ideas from astrophysics in which the flow determines the magnetic field while in the rfp beta is very high so flow and field is very tight together so there is no back reaction so from this theory the idea is just to come out the idea that there exists some msd dynamo so there is some dynamo field and in fact that's why the global modes are responsible for the sustainment are sometimes termed the dynamo modes now without dynamo field what happens is that an rfp actually would decay it's another way of saying what i've already shown you several times so there is no electric field no ohms law that can sustain an rfp but in the second generation rfp devices actually the plasma was there so it didn't know but it was there so it can be sustained for as long as you apply loop voltage if you do classically so actually i'm not going to in the details of the solution of the pda of transport basically but the parametric pinch with with time dependence of induction which is done by karaman in 84 it states that if you have an initial rfp configuration which is depicted here and you let it evolve classically under the resistivity and the flow which is pinching basically the the rfp will decay away so it will get more and more deeper it eventually will will be lost so in cylindrical geometry axisymmetry and with a pure omelow without a dynamo field rfp cannot be sustained recognizing the fact that there were not poloidal currents some experimental technique have been explained tested just to see if we can replace from outside the missing current and so it has been attempted by our colleague in mst in medicine to use the inductive field to induce poloidal current or using insettable electrical guns or or waves and the idea is just depicted here so if you drive some parallel current and you change the mu so the parallel current in principle you can try to mimic what was actually done by zeta basically so they reversed the the poloidal field and the toroidal field and this is what the the ppcd i will talk about that later on just to mention mhd was not the only possible solution about what drives this poloidal current there was an idea brought about by the american colleagues at 80 40 that it is fast electrons again there is stochasticity stochasticity make this electron flow along these lines and if they are in a number in a sufficient number they can drive the very quiet poloidal current there were some measurements in the old experiments showing that actually fast electrons so electrons with energies typically of the core were in the edge they were not typical of the temperature measured edge but in rfx by tracking the trajectory of a frozen pellet injected into the plasma and they computed its its deflection it is deflected due to the fact that but whenever your frozen pellet is in the plasma it is bombarded from the ion side and the electron side and by the difference of these two parts there is a rocket effect by and you can be quantitative and you can compute the deflection and the deflection if the fast electrons were there the fast electron required to drive the current that you need it would have been deflected too much so the deflection was there was a lack of deflection and so that's why in rfx the kinetic dynamite theory is not applicable so probably also in high in bigger these experiments but in the smaller who knows it also it depends on the density regime so so the final explanation of why the rfp self reverses was a numerical simulation so basically instead of doing analytics you try to use the full transport code the full visco resistive code and what i'm showing here i'm not an expert in this field but what is instructive is looking at the very very first simulation which was based on the same code which was used by western and sex to simulate the the tokamak so tiff and they try to do what try to see what happens in plasma in a pinch and let it evolve with some arbitrary choice of energy losses but the idea was that let it be unstable let the mode grow but this mode grows so fast that as it was in in a con flux conservate it reverses the field and so some reversal is obtained and this reversal is is sustained later on by several over modes which comes on so it was not actually an accurate simulation but the idea was that global modes could play the role of the the the makes the turbulence actually and from this on actually all of the results all of the research on rfp was basically based on the investigations of global modes and so now i'm going to to give you which is the phenomenology of the global mode so i'm starting from the basically the what is contained in the in the in the rfp review in the last rfp review global modes which in rfp are the m equal one and m equal zero as in the old pinches basically and these are basically m equal one and several n modes which are resonant into the core so there's a bunch of modes whereas a bunch of resonances of m equal one and m equal zeros are all resonating at the reversal surface and this magnetic flux these were called you will see also very in this global most also named magnetic fluctuations and this is due to the fact that it was discovered in the 80s basically that they were due to global modes because they did the correlation analysis of several pickup coils and trying to figure out the global structure with with a full respect now it's obvious that you take multiple measurements you take a full analysis and you you get the mode at that time was not that obvious and they are resonant mode also not dubbed dynamo modes or tearing modes tearing because actually they drive islands this is a simple example taken from the west and you probably already know that resonant mode with a real field different from zero at the at the resonant surface again drive an island basically and so a tearing mode and we will have some experimental examples of this kind of islands seen in rfps so global modes in rfp tend to manifest themselves in two different ways of the of spectrum basically so in multiple electricity we have many global m equal one and m equal zero most this is a time trace of an rfx mode discharge for example in blue we are high-end modes and in red there is a dominant mode basically what happens is that in some regimes all the modes are together similar so there's lowly decay in spectrum areas here and in some cases they tend to grow and remain high and so it gives you one mode dominating over the others and these are called single quasi single electricity and we are widely different phenomenologies the multiple electricity phenomenology was studied basically in all the all the charges in the all the experiments and the quasi single electricity is emerged emerged only in from the nineties over 2000 basically multiple electricity tended to have non-linear phenomenas between these modes they manifested themselves in terms of increasing and whenever they add increased together they tended to induce a sort of crashes dynamo so they were not stationary solutions and these connect these events were also connected to the regeneration of flux so it is called so called so if this kind of behavior in multiple electricity is important because basically most of the production of the mst experiment is based on ensemble averaging of measurements along reproducible this this dynamic reconnection events and this is due to the fact that there is a cascade of these modes which interact and they tend to increase and then they release this is some kind of reconnection events there is some kind of release of flux and so on in particular as I mentioned earlier there were measurements of electricity and energy during assortment in order to verify the Taylor's conjecture so the fact about during a relaxation event the electricity is concerned while the energy is decreased and within the experimental uncertainties in that particular case this is really happening also during this sort of during this sort if they had to measure the dynamo field and so by directly measuring the fluctuation of velocity and fluctuation of magnetic field we were able to compare it with the parallel current and the parallel electric field and they matched pretty well so in multiple electricity also you can have an mst dynamo which comes from these global modes which are which are defined and measured another characteristics of the multiple electricity is the fact that all of these modes tend to phase lock together this is another non-linear behavior which makes more complex to deal with them and they tend to be not to be remain near the resonance but they are global mode they also deform they also deform the last closed surface and as they are lining up together all together they tend to deform in a to rather localize the region which tend to interact with the plasma oh gosh we tend to interact with the plasma and you see here that if you look with a camera from the to rather view you can see some kind of helical interaction and this actually was kind of difficult to deal with in our effects especially now i've seen that it is 55 now i think it can stop here and let the second part of the 11 so because otherwise it will be too long okay sorry thank you yes yes because actually whenever you have you in this current you need a small one so just like in the pinches so you need a toroidal field delivered from the outside so the seed is actually required but it is not big it is not dominant so you have a more small toroidal field from the outside so the the coils are not that huge and then the plasma produces much of this toroidal field inside through n because at n equal one n equals zero and the various n depending on the q profile basically so yes and n equals zero basically it means some kind of rings i will show you something in the second to second lecture so it is not a it is not a helix but it's some kind of yes some kind of rings just yeah so the fact that it does not scare so if you increase a parameter it changes shape and so you do not apply the same tools even if you can but the root cross b in a helical case it assumes a different meaning right i mean the plasma is kind of trying to do it so okay and that can be what's the role of the parameter for u s color here what's the role i make it still the reverse in current actually in in zeta they were trying to reverse the zeta just to help the the current and to keep the q without the minimum and in some experiments in msd they see that the whenever they are decreasing the current and if they apply a further part of a further toroidal reverse in the electric field they reduce the amplitude of these modes basically so i'm not sure when i ask you a question but you can discuss later it's still a magnetic configuration right so you know the magnetic field is just an important part in any other you know you said the magnetic field is produced differently its behavior is very different that's it yeah yeah but what i'm thinking is uh there is a toroidal magnetic field so for that toroidal magnetic field it also induces some kind of current maybe just out of the toroidal whenever it changes so another reverse magnetic field that opposes this change yeah we may have it depends on we may be on the conductor if you are gap so if you have no gaps so yeah in transient it's a nightmare because yes sure right so for the time being what was the externally applied to then the toroidal and the magnetic and the toroidal magnetic fields are connected they're not independent yeah there is one goes as a less information zero the other goes as a function one of the same parameters so there's a deep connectivity they're not independent parameters like the one system i think okay all right so i will just make one interest to all of you please try to be here five minutes before the other five minutes after life okay so i believe that the magnetic field allows us to start things in time and it's just being respectful to