09:01:52 Okay, so just to get started I want to introduce our first speaker today Luther Schmidt's. He does PhD in space plasma physics and later moved to UCLA, where he is now a senior research scientist, and also the group leader for Lh transition studies on
09:02:08 He's known for many contributions in LA transition, physics, which you'll introduce to us today. And he's also an accomplished artist.
09:02:24 Today he will speak to us on transport barriers in magnetized plasma. Go ahead. Look,
09:03:01 So this talk is about the fundamentals of transport barriers and magnetized class mass we have heard a lot about atmospheric and Planetary flows, and these are basically two large degree, two dimensional turbulence properties here, and
09:03:24 I basically will mainly three, the fundamentals of edge transport barefoot formation in a magnetized plasma. This is off great practical importance.
09:03:35 And also, is meant as an introduction to the second talk to the pitch, create space transport barriers that are characterized by staircases and connect to the main topic of the workshop, more fundamentally edge transport barriers and enable high confinement
09:03:52 motor age mode infusion plasmas, and this is operating regime that is characterized by about effective to improvement in thermal energy confinement.
09:04:01 So that's a very substantial improvement in terms of the potential size of a fusion power plant that can be much more effective livan and effectively build fusion plasmas can also form internal transport barriers in the core plasma, that are not discussed
09:04:20 here so we will really concentrate on the edge and previous talk that you had two weeks ago by a GM diff party has introduced staircase dynamics in kinetic plasma simulations already.
09:04:34 The following talk by Arash avant to discuss their case observation in the HB area of fusion class mind more detail.
09:04:42 So this is a brief outline. After short introduction of edge transport barrier phenomenology and the high confinement mode.
09:04:50 We look at the low to high confinement more transition, essentially the formation of the transport barrier and more detail and turbulence reduction via flows here is a very crucial element in the relevant physics there.
09:05:17 Then we look at flux gradient relations histories effects and so on. And finally limit cyclists feedback cycles that regulate turbulence suppression. The associated long range flow correlations.
09:05:20 And then finally, a brief look at the Reynaud stress phenomenology in the details and spectral condensation.
09:05:29 So, magnetic confinement devices can have different forms and shapes, the most known one is the Toronto confinement in token marks here the magnetic field is mainly in the right direction, but there is a plasma current flowing in the right direction.
09:05:48 And that essentially imparts a twist on the magnetic field lines so you have an anger of the finish line here that it's not purely through it but also to sit in the pool either direction.
09:05:59 That's very crucial for the Troy equilibrium.
09:06:11 The force is that in the plasma, so so you have physically nested magnetic surfaces and then you have the boundary surface the last close.
09:06:14 Magnetic surface here indicated in yellow outside of this last close flux surface stiff the field lines and open, open and interface with the diverted plates.
09:06:24 So it's very important to understand that in Troy to classmates at the relevant temperatures conditions are very infrequent and the particle dynamics is mainly driven by drift flows.
09:06:47 And the equation that is shown here on the bottom is basically the radio forced balance equation. So one important term is the pressure gradient here.
09:06:46 The other important term are flows that can be intrinsically generated or externally imparted by momentum input for example, by launching neutral Particle Beams into the plasma.
09:06:58 And basically the electric field that is perpendicular to the flat surface here in the radio direction is determined by basically the balance of the pressure gradient term and the v cross be term here.
09:07:11 The party gets actually drift perpendicular to the electric fields with the cross be drift. And this is true for electrons and ions, although the species FA different Lamar API.
09:07:22 It's also important to understand that alarm or API, are very small compared to any microscopic dimensions of the device so I anomaly I typically for fusion parameters or point 121 centimeters and the electron l'amour it is much smaller than that, but
09:07:40 10 minus three to 10 minus two centimeters. These are the shorts to throw it a direction here and Apollo direction in the radio direction, that's the coordinate system views throughout the talk.
09:07:49 So, basically we launch auxiliary heating power to heat up the plasma to thermonuclear temperatures and there's a large video heat flux that is lost from the core plasma to the edge here really eventually makes it past the closed flux surface region and
09:08:11 flows power to the magnetic field onto the inverter. And this is just the cartoon it shows the two confinement states that have been found at low.
09:08:18 A couple of power, we have the so called download state that is characterized by Jen to temperature in density gradients, and then pass the certain auxiliary power so the control parameter is really the cupboard power to the plasma core.
09:08:34 Just this this heat flux has to come out to add.
09:08:37 And then at some critical power, the plasma essentially transfers into a high confinement state the so called h mode that is characterized by very strong gradients at the edge pressure gradient temperature gradient and density gradient.
09:08:54 And that allows speeding up much higher temperature and pressure in the car, so it's very attractive from a fusion point of view.
09:09:01 These are actual measurements of transport barriers in the the 3d plasma here, and we show here the particle density, the electron temperature and in the eye on temperature.
09:09:12 There is a difference in power here the Keystone and blue has about 2.8, megawatts captured externally from neutral Particle Beams, and the high confinement cases 7.8 megawatts, but you can see that the difference in temperatures and pressures much more
09:09:27 than a factor of two and a half in power. So what that means is that basically the couple of powers much better confined, the energy that has been covered to the plasma is meant that are confined.
09:09:39 And this is basically accomplished by this edge transport where you can see the very steep gradients here in the particle density and also in the temperatures and the core actually which is the temperatures here that thermonuclear of thermal nuclear relevance,
09:09:53 relevance, but the density is about an order of magnitude smaller than will be needed for for actually creating net fusion power here.
09:10:02 There's also an indication of an internal value formation I will not talk about that in any detail here but there can be additional barriers that can be generated in the interior of the plasma.
09:10:15 So, when this was this phenomenon of the DH mode or the edge transport barrier was first experimentally discovered in the Asterix upgrade took a mark in about 18 1982.
09:10:28 And soon afterwards at the 3d it was found that the physics of the edge is in the last few centimeters of the last close flux surface really determines the dynamics here now and in particular it was found that a Jeff Lewis forms, very close to last cruise
09:10:43 flux lives in about one centimeter. You can see you the difference in blue are the Elmo data that have a very shallow feel for failure, positive flow in the scrape of layer, positive flaws in the core, and then slide to reverse it here in the region.
09:11:00 And this becomes a jet flow that is much stronger here about six kilometers per second.
09:11:06 After the Lh transition and concomitantly the turbulence in the HB show the density fluctuation These are a millimeter wave back scattering measurements have decreased by a factor of two.
09:11:19 So, the energy flow from the car to the edge presumably has been SUBSTANTIALLY reduced here. And this is actually the crucial ingredient to transport better information and you can see here that as an example the density gradient Stevens from the red
09:11:35 blue state to the orange red state, as this transition occurs in the fluctuations are suppressed.
09:11:43 Now also, it's important to understand in this jet flow configuration here that the shearing rates, the the radio variation of the flow increases here on the core side and on the edge side and typically the increase on the edge sites across the last plus
09:11:59 flat surfaces even larger. So the sharing rate is a very crucial ingredient here for the physics.
09:12:06 And soon. These sheer phenomenology is also discovered in dryer kinetic simulations. You can see here that the turbulence is actually stratified and very much extended along the magnetic field lines so the parallel reef number long the magnetic field
09:12:22 line is much smaller than the radio and the colloidal reef number VC basically that fairly small scale Eddie's have formed and their self organized flows that were found in destroy kinetic simulations that we are very much reminiscent of zona flow jets
09:12:45 and the bat that occurred the boundary and planetary atmospheres here. And basically, when we think about localized check shows, we also think about Korean hemorrhoids instabilities.
09:12:54 So, in this case here the magnetic field is still cheered at the edge and you can actually see the shearing here in these allegation of the turbulence pattern along the magnetic field sign, see if this localized jet fuel at one particular areas, but the
09:13:10 But the magnetic field is shared and the shearing prevents Kevin Helmholtz moods from growing basically because the resistive layer is typically smaller than the crispy shear layer, and the free energy that would be required to Dr.
09:13:26 Kevin hemorrhoids instabilities is just not large enough to really take over the fluid dynamics.
09:13:33 Soon after the first experimental evidence, the theoretical framework of sheer civilization and to quench First, put on farm footings and pet diamond was very much involved in the bush 1998 paper in physics of fluids here.
09:13:48 And it was basically found that the crucial parameter for sheer standardization of sheer credentials turbulence is that the shearing rates defined basically as the radio derivative of the Crosby velocity, be larger than the Airbnb correlation rate of
09:14:04 the turbulence.
09:14:05 So this is basically the, the correlation of turbulence that exists in the absence of sharing.
09:14:11 And there are several physical effects that were found in simple vortex or simply edit simulations here.
09:14:18 One is that the accurate density contours become the correlated from the flow contours here. So this is basically a simulation that has a strong flow in the positive direction on the inside negative colonial direction the outside.
09:14:35 The head is still there no stress becomes finite and the deep the density fluctuations D correlate spatially from the velocity fluctuations.
09:14:43 Another way to understand the difference in transport is to simply look at the correlated across the flow that that is carried along the vortex if you have a vortex to this radio the extended.
09:14:55 This flow has a certain Gaussian profile but if you tilt the vortex and extend it in a polite direction shrink it in the radio direction, the flow profile, the intrinsic correlated flow profile is much reduced.
09:15:10 And then later on. It was also found that another criteria for sheer stabilization is that the cheering rate exceed the maximum linear growth rate of the unstable modes in the system and this is work that was done by balls at all, and published 1998
09:15:29 was better measurement measurements we had a little better glimpse at the localized and the dynamics at the edge was high temporal and spatial resolution and this was again done with microwave beds next scattering in about 2011.
09:15:45 And here we compared to Location One is in the inner Shelia in the outer Shelia about five centimeters inside the last close flat surface. The second location is about two centimeter inside the last close Fox, so very close proximity, about one and a
09:15:59 half centimeters apart, and the turbulence suppression here, or curse visit about hundred microseconds so very, very short time scale.
09:16:09 And this occurs, exactly when the MBND correlation rate of the turbans This is the local engine, the correlation rate meets the sharing rate so the sharing rate is increasing here, the flushing rate is increasing, and the the correlation rate of the turbulence
09:16:24 is decreasing and when the two rates are essentially the same, that's the exact moment when we observe turbulence suppression.
09:16:40 There's also a spatial dispersion in that the suppression is first observed near the last close flux surface. And then about one milliseconds later in the inner Shelia about one and a half centimeters further inside the criteria very similar that the
09:16:51 correlation rate decreases the flow sharing with increases. And this allows them the pressure gradient and the density gradient to substantially increase and create the confinement condition that is leading into the pedestal that forms that two plus much
09:17:08 more sophisticated char kinetics simulations have looked at the time evolution of the turbulence from linear instabilities all the way to the set saturated nonlinear state, we compare here to simulations one resolve the cross species that was externally
09:17:24 imposed, and the lower two frames are the equals b share case, these are provided cross sections here so vertical cross sections to the Tacoma.
09:17:35 After the initial India instability face, we see that radio streamers form here in the upper left finger, both in the car and also in the edge. And that, of course, is equivalent to large media transport of charged particles, along these Eddie's to the
09:17:52 phone from the inside to the outside.
09:17:55 And then even in a saturated state we have more complicated, Eddie structures, but we have still three months that essentially extend from the Middle Ages, all the way to the, to the edge of the plasma.
09:18:10 Conversely here in the case with equal speech here, the streamers already constraint.
09:18:16 Shortly after the linear instabilities have grown. But then in the nonlinear saturated state, the edits are much smaller, and there's no communication from the core to the edge anymore.
09:18:29 There's basically localized Eddie chains to propagate the cross be velocity, but no large scale energy exchange with the edge anymore and you can also see from the color scale that the fluctuation the saturated fluctuation level is much lower than in
09:18:42 the news noshir case.
09:18:44 Another important element of transport barrier formation is histories is.
09:18:51 So, initially when you increase the heating power to the core plasma, the pressure gradient increases. At some point venture civilization becomes effective in in the edge.
09:19:03 There is an unstable region in the flux gradient relationship here. So, at this point, basically, the plasma transitions within a very short time to a much higher pressure gradient state that is basically characteristic of each mode here, and this unstable
09:19:20 region of the histories IS curve is not accessible. Conversely, however when we go back and we reduce the heating pole to the core, the plasma follows a different branch, and then essentially from the, the, much lower power transitions back into the air
09:19:40 modes. battery confined state here. And this is the reasons trace was actually traced out in the SEMA tokamak so when the power was increased the points that are shown here on the, on the upper part of this Teresa's career fair obtained.
09:19:54 And then eventually the plasma jumps into a higher Canadian state h Morton as the powers reduced we don't trace the same histories is called back but we basically can follow it to this unstable point here and then transition back to our mode.
09:20:10 If the, the powers in the march know that does not necessarily have to be histories is here. So this is a state that is characterized by limit cycle oscillations better class market and essentially in a reversible manner transition from one gradient condition
09:20:26 to a much higher creating condition here at the same heat flux, as long as the heat flux is not substantially increased above this point.
09:20:35 And this is basically leading to limit Cyclops solutions that fellows experimentally observed in many situations where the heating powers close to the marginal power, and it can be associated with electric field or solutions to to flows, or due to the
09:20:53 pressure gradient and the latter case is shown here where the gradient lengths, basically is modulated. And then as the gradient increases turbulence intermittently flares up deteriorates transport and the gradient relaxes back to the state.
09:21:05 And this process is basically repeated and when you will have the power close enough to the marginal the necessary power you can actually maintain this oscillation for many hundred milliseconds here, or even seconds.
09:21:20 So this is very important in terms of the general feedback characteristics of the transition.
09:21:27 The. When we look at the fundamental physics, a little bit more indeed till it turns out that provider flow is driven by Marina and stress, and this is one of the important feedback loops typically early in the Lh transition.
09:21:43 So we have turbulence that is of course driven by the pressure gradient that drives below the floor via the Reynaud stress so this is the source term here and then the competing damping term is the provider fluid flow damping term.
09:21:57 And then the flow is an ingredient to the radio momentum balance here so increases the radial electric field, and in turn the radio the electric field, she has the turbulent Eddie's apart.
09:22:08 So this is one part of the important feedback cycles that have had cycle that happens during the transition.
09:22:16 Then as I already mentioned the greater pleasure opinion is of course very important ingredient to project green is also part of the radio and momentum balance and contributes to the electric field.
09:22:26 But the pressure gradient also drives turbulence and in turn the turbulence by critical gradient phenomena and the turbulence model modulator moderates the pressure gradient.
09:22:36 So the other part of the feedback cycle has basically a closing to actually been treasure breathing and turbulence and then as also the pressure creating and interacting with electric fields modulating the turbulence via the cross be sharing effect.
09:22:50 So these two feedback cycles to typically synergistically work together.
09:22:58 The right side feedback cycle that I mentioned first is typically initiating the transition. And then as the pressure gradient starts to increase the left feedback cycle takes over.
09:23:12 And this was all seen very nicely here in limit cycle oscillations close to marginal input power where we have the ultimate state Here we show here the cross be velocity and the fluctuation level.
09:23:23 There is a well formed that is very shallow here and the possibility then we get limit Cyclops situations where the well and the sheer at these task close flat surface here and on the insight or two centimeters inside increase periodically and our modulated,
09:23:38 and eventually the cross be Shelia becomes very wide, and much deeper as you can see from the much larger use here in the contour plot. And that's when we have reached age mode here and there's no more installations there's basically just a solid permanent
09:23:55 transport barrier now.
09:23:57 So this can all be depicted in the limit cycle here where we essentially go from the animate state periodically around the cycle here and then eventually end up in the age mode state where we have much larger flow much larger fellowship in a much lower
09:24:15 fluctuation level here that is about effective two or three lower than the state.
09:24:22 This is just a depiction of the sheer, the shearing rate as we go through the same cycle is the same data then I showed before and almost we have a remnant of sharing here at the last close flat surface.
09:24:36 Then we have periodic modulation here during the limit cycle isolation phase the sheer increases on average though, and then becomes very large and is permanently sustained engagement phase and we can also see here the inner Shelia does limit cycle oscillations
09:24:50 here. And then eventually begat strong shear and initiate earlier also here.
09:24:57 When we look at the dynamics in more detail. These are now.
09:25:04 Emerging results the Felton has been commissioned spectroscopy imaging these are eight by eight centimeter windows in the Polaroid plane. This is the last close flux surfaces so so this is the Florida direction here, we can see that originally in the
09:25:19 Alamodome the ad is basically traverse the Shelia, it's a very big Shelia at this point. And they can actually communicate effectively from the core boundary here to the edge to the open field line region.
09:25:33 Eventually, there's a spectral condensation process, taking place. The wavelength becomes longer the edits become organized.
09:25:57 the point in arena it's trust strives for order flow in a, in a very profound way. And this is very reminiscent of the earlier simulation that I showed you where we saw the, the correlation between the identity and the potential surfaces car the flow
09:26:07 surfaces. And the turning of the ad is is basically what transfers of energy from the turbulence, to the flow after the turbulence respectfully cascaded to larger scales.
09:26:20 And then, this essentially depletes the turbulence energy and eventually we end up with a situation where there's no turbulence in the Shelia there's turbulence in the car and turbulence in the scrape of the outside, but there's a turbulence fi reach
09:26:35 and here in the spatial region read a jet still occurs and this is basically equivalent to each mode.
09:26:42 here in the spatial region where the jet flow occurs and this is basically equivalent to each mode. So when we look at the spectral cascade cartoon here there's a both an inverse cascade to largest kids and also the forward cascade to the viscosity scare where we
09:26:53 where we have damping here, and the gradient thrive in inserts energy into the turbulence at some intermediate scale that is typically 10 times dilemma is 100 times the normal radius so it's it's lots of kids that are much larger than the long way, especially
09:27:11 because it is scale damping is comparable to the number it is. So we cannot basically look at to energy conservation equations, the other equation here.
09:27:23 Basically, is the energy balance of large scale collider floor threatened by the way no stress, and then by flow damping whiskers for damping for the most part.
09:27:35 And then the second equation is for the high frequency flow energy that is driven by linear growth, and then D correlated by other turbulence by other processes that are related to target and saturation, and also depleted by Reynaud stress.
09:27:50 And when the, the flow source here to the turbulence given by the linear course rate minus the correlation rate becomes smaller than the damping rate of the large scale that the transfer into the rain on stress basically the Reynolds for into the low
09:28:09 frequency flow. Then we have basically condition where the turbulence energy can be effectively depleted and the turbulence can cease to exist, direct evidence for the large scale thrive have access symmetric flows that are broadly and throw it to the
09:28:27 symmetric was also obtained experimentally, and we look at correlations on two sides of the tokamak we're now looking down on the, on the tokamak here, this is the direction we have to measurement systems here, we look at back scattering of microwaves
09:28:43 on one side and the other side, we find that there's originally an Elmo, no flow correlation at all. And then as the limit cycle oscillation emerges receive beginnings of a flow, increasing the flow correlation.
09:28:59 That is not related to the limit cycle of solution frequency.
09:29:01 oscillation frequency. And as the limit cycles solutions are valid developed just before the, the final transition to a sustained h mode. This flow correlation becomes quite large.
09:29:11 So what this really means is that the the flows that we are measuring here. I actually symmetric, they have a period of Nm of zero, so they're basically access symmetric modes that span the entire magnetic surface, and we're not really looking at the
09:29:25 same field line here we're just looking in the same flux surface so that would not be any correlation that can be mediated by the shorter turbulence skills at all.
09:29:35 So basically just summarizing here, the characteristics of the hX transport barrier formation and magnetized plasmas, we need a threshold in heating power that depends, in practice on plasma density iron mass, the geometry of course, the flow perpendicular
09:29:49 to the magnetic field is strongly enhanced that plus my boundary between the very narrow radial layer, and the kosher physics ingredients is that the flow Shia dh is enhanced and turbulence just inside the boundaries surprise is in hundred microseconds
09:30:04 to one milliseconds typically common signatures need a power threshold for ion very informational limit cyclo situations, this is caused by to interact and feedback loops between flow and turbulence and the pressure gradient, there's typically is the
09:30:20 reasons and threshold power, and the stages of barrier formation are basically that there's an increase in Reynaud stress via turbulence inverse cascade respectfully pronunciation.
09:30:29 There's a local increase in the n m equals zero flow the flow at the edge.
09:30:34 There's a local increasing the cross species and turbulence six suppression, and then finally we get bifurcation to a higher edge pleasure gradient is increased die magnetic Florida, driven by the project reading.
09:30:48 This is the age mode.
09:30:50 And then as the turbulence suppress reach and violence, we built the pedestal and the pedestal pressure and increase the pedestal height and width.
09:31:00 And just in summary, transport barriers crucially improved terminal confinement infusion plasmas sheer flow at the bus plasma boundary locally suppresses turbulence strong evidence for no stress radiated excess symmetric flow is found generated by a spectral
09:31:21 condensation and interacting feedback cycles determine the Lh transition dynamics and power threshold in detail. There's quite a few open questions of course and transport Dahlia physics, for example, is the physical space killing off the critical heat
09:31:39 to the trigger barrier formation, what is the role of the seat flow sheer. Can we quantify spectral condensation in real life through either plasmas. This is work that is very much stood at the beginning.
09:31:43 What is the role of ion versus electron heat flux and triggering the transition to the edge barrier and what is also the role of these different components for the threshold.
09:31:54 And finally, what is the role of multi skier turbulence flaws and the ratio of languages to the gradient scale.
09:32:01 And then other 3d turbulence effects we have seen that the turbulence is largely 2d, except for the thriving mechanisms for the the 3d effects are really important.
09:32:12 But what are the 3d turbulence effects beyond linear instability physics. Once we look at electron on any adversity and so on.
09:32:21 And then finally of course from a practical perspective can we met, manipulate sheer flows and reduce the power required to trigger confinement barriers in each mode, there are some initial indications that yes, we can of course, we can inject tar file
09:32:36 a neutral beams that launched an Android a direction, and also via 3d magnetic fields that break the field is symmetry the flow symmetry, and it took them up.
09:32:45 Or for example by increasing the edge pressure creating via frozen fueled pellet injection all of these methods has shown have shown some initial promise to decrease the poetry.
09:33:00 And finally, so this talk was meant as an introduction, looking at single transport barriers at the edge the next talk by Chauvin will discuss staircases in much more detail.
09:33:11 And with that, thank you very much for your attention.
09:33:15 Thank you very much for a nice introduction there