Accelerating Fusion through Integrated Whole Device Model of Magnetically Confined Fusion Plasma

okay uh we're ready to uh continue here uh yep my name is Ben jorns I'm in the aerospace engineering department where I research plasma potion systems and low temperature plasmas and I build just embarrassingly simple models compared to what we're learning about here today so it's a real privilege to watch This research and it's a real privilege to introduce our next speaker Professor amitaba bhattacharji who comes to us from Princeton University also my alma mater where he was I'll speak up a little bit more okay yeah um I'll move that up uh who comes to us from Princeton University where he's the head of the theory Department from 2012 to 2021 before joining that he held a number of prestigious positions including the Paul professor of Space Science at the University of New Hampshire professor of physics and astronomy at the University of Iowa and associate professor of Applied Physics at Columbia University a copy of his textbook rests comfortably on my shelf and has dog-eared pages in it his students and doctoral colleagues have just had an impressive number of contributions in the field including over 300 refereed Publications he has served on the board of American and physical Society he was a chair of the aps division of plasma physics APS topical Grant group in plasma astrophysics founder the senior editor of the Journal of geophysical research space physics from 2006 to 2009 he's a fellow of the American physical Society of the American Associated advancement of Science and the American geophysical Union his research interests are wide and varied including Humanity connection turbulence kinetic theory free electronic lasers and complex plasmas and he was recently recognized by one of the most prestigious Awards in the field of plasma physics which is the James Clerk Maxwell price and plasma physics so without further Ado please welcome our next speaker [Applause] thank you Ben for that very kind introduction somehow when you say all those things it doesn't seem like me I'm very pleased to be back uh in my alma mater where my education in plasma physics actually began but somebody in the department of nuclear engineering a much revered faculty member in the department and for me personally who was an inspiration professor ziachatsu who passed away a few years ago but I owe my great love of plasma Theory and non-equilibrium statistical mechanics to Professor rakshasu's very inspiring lectures Professor dudistat was in those days a faculty member in the department of nickel engineering as well and he had very interesting lectures on Neutron transport theory that I also learned from and I can go on and on about the many wonderful colleagues in the department of nuclear engineering who taught me a great deal and after I learned from them all I could I went to Ben's institution to complete my doctoral studies and I'm very pleased to tell you that the circle keeps getting more and more completed with more and more students colleagues who circled back into this University and continue what I think is a very strong link with this campus so it was my hope that Doug koti will speak before me and I have no desire to steal his Thunder nor do I think I ever can he is the director of the exoskilled Computing project which has provided a very major impetus to the project I'm about to describe I will not try to substitute for all that Doug will tell you the the previous speaker already introduced to you what a revolution it has been for the application projects to have Frontier at Oak Ridge and Aurora about to become available to many of us in Argonne but let me begin with one project in the access skill computing project that Doug leads which is the whole device model of magnetically confined fusion plasma otherwise known as wdm app if you make a mistake and permute DNM it can end up being wmd and I want to emphatically stay away from that uh the uh the main thing that I want to suggest to you is that Fusion program which as you know is experiencing a very major Resurgence both in the doe office of Sciences as well as through private investment has come to the point where modeling using supercomputers play a very important role I believe in actually choosing the next design of a fusion power plants not that it can ever be a substitute for experiments but we can't build thousands of billion dollar experiments we have to be selective on what we build and I therefore think that computer simulations will have to be a major guide in our choices so this is a project of accelerating Fusion through whole device model a magnetically confined fusion plasma it's a group I lead as Pi and C.S Chang from the Princeton plasma Physics laboratory is a wonderful co-pi to work with this is a multiple institution group composed of National Laboratories Princeton plasma Physics laboratory as I mentioned already Lawrence Livermore National Laboratory Oak Ridge National Laboratory Lawrence Berkeley National Laboratory and universities uh University of Texas at Austin once at Boulder University of Colorado the University of Utah RPI University of New Hampshire and even a private company Jubilee development which is part of this Enterprise is an astoundingly talented group and a lot of the progress that I'm about to describe to you is attributable to the early career and mid-career people who dominate the program now and I speak for them I'm very fortunate to be associated with them words of wisdom from one of our heroes in physics and he had amazing foresight about a lot of things and even though he was a very fundamental physicist himself he says something important that he thought that what will be important in the 21st century will be the integration of knowledge provided by complex models to understand predict and control the performance of fusion experiments and he was a big fan of fusions but he made his comment more generally and when he said I think the 21st century will be the century of complexity we have already discovered the basic laws that govern matter and understand all the normal situations we don't know how the laws fit together and what happens under extreme conditions there is no limit to the complexity we can build using those basic laws and you will see in my talk an example of exactly that what he had in mind so if one thinks of a whole device model hierarchy and you ask yourself what does it mean to say that you have a whole device model because models can have various levels of description and the way I like to think about it and this is a nice cartoon due to Jeff candy of General atomics is that at the Apex of this pyramid you have what you might call a basic first principle simulation uh this will take the fundamental equations in my particular case of plasma physics and that generally means some sort of a kinetic model from which other fluid models are derived by taking moments a well-known procedure in most books in statistical mechanics especially non-equilibrium ones leadership class Computing facilities are out there at the very Apex to give those answers which because they are determined by fundamental equations could be thought of as definitive values if all things are right but those are often very expensive Computing models but what do they actually provide and why are they so Central there are a whole lot of reduced models that we can actually use to model plasmas and they would fit in to the second category and these are often faster to run and they can often if designed suitably can be quick enough that you can run a laptop or even a small workstation and in some cases if you're fortunate can be synchronized with experiments they often have coefficients in them that one fits phenomenologically a very valuable service but the coefficients that you obtain in doing that uh should be one that should be derivable from first principles and it is in some sense that Holy Grail that one is really after these intermediates scale models have enormous applications particularly if you put in machine learning artificial intelligence and you automate them you can run them and produce large Computing data sets and obtain from them what you think would be the very best ones so there is no process by itself this pyramid really needs all its levels in order to be a fully functional entity and not all of which may require excess skin computing but access skill is at the Apex of it and in some sense provides ultimate computational validation of a lot of phenomenology that goes after and therefore when I emphasize fundamental principles of the access scale please don't think that that is uh uh in any sense dismissive of what lies below without which we would not be able to have the detailed verification and validation program which is the heart of a lot of computing now plasma physics especially Fusion physics is a poster child in many ways for the new office of advanced scientific Computing research and that is because at every stage of our game the hunger for supercomputing facilities has been so great in Fusion physics that every time the department of energy has given us more computing power we have actually done more physics with it so it isn't that our physics was solved at the level of gigaflops we had incomplete physical models because we couldn't do enough for example if you look at the fusion literature about that time you will find things like electrostatic ion physics in simplified cylindrical geometry pretty much chewing up all the computers that there was then came the era of the turf flop when we could do five dimensional iron scale electromagnetic physics in a Taurus we're beginning to tackle the edge but we couldn't do it any more than electrostatic and we couldn't do electromagnetic problems came the error of the petaflop when we could actually do both ions and electron physics uh and however with rather incomplete separation of scales the exit Club era really brought home to us and that's the era we are in now where we can actually do five dimensional I want to explain to you what five-dimensional you might think because when you think of kinetic models you generally think of three spatial coordinates and three momentum coordinates that's really makes six dimensional phase space when I say five Dimensions what do I mean I mean that there is a very strong magnetic field about which particle gyration is so rapid that you can average out that particular time scale so the angle Phi which tracks the motion of a Charged particle what a magnetic field is averaged out then in coordinates you can actually have five D phase space and that is what is called the model of Gyro kinetics that's been enormously useful in Fusion plasmas as well as an astrophysical plasmas and space plasmas for Rapid representation of plasma particles which have the advantage of exploiting the fact that the Llama radius of the particle is a lot smaller than the system size so when you get to the error of the exit floor is where we are having five dimensional electromagnetic study of plasmas now we can make them eater relevant eater is the big uh fusion plasma experiment as you know uh had been cited in catarash France with eight Nations and a huge budget 20 billion dollars which should have its first plasma it has been delayed and it has project river runs but it's a major engineering feat and if you haven't been to kadaraj I urge you strongly to visit I have not seen a more spectacular experiment that is being built um I wish it would have done sooner and I wish it were done less expensively but that's a separate issue so what we are looking at today is to try to model each and great plasmas using our whole device model Beyond we have whole facility because the science is where the focus of this particular project has been but if Fusion is to become a reality we have to integrate that with the entire infrastructure that goes with the engineering of fusion reactors a lot of which has things in common with what also took Vision to work and so there's a lot in the nuclear engineering we don't inherit the radiation problem and so we are fortunate that Fusion is still classified as a green technology by people who know but on the other hand the infrastructure that we engineering infrastructure that we know that nuclear engineerings have excelled at is also something that we would like to learn from and it is in the combination of Science and Engineering that the feasibility of a Final Fusion facility will be determined and that lies Beyond we're beginning to do some of that work in the extra flop era and we must but we also look to the next era of computing so what is it that is the vision of wdmr what I wanted to tell you is that this is a seven year project that comes to end this year as Doug will tell you and the most challenging part of the problem was actually to produce a kinetic description a first principle's description of the plasma in a Taurus and what had happened in the fusion Community is the problem at the edge and the problem in the core are somewhat different problems even though they obey the same kinetic equation if you just try to use the same equation in the core as well as the edge you actually run into very major computational challenges so people have tended to separate the core and the edge for reasons that I'll give you into two separate models what wdm app tries to do is to produce a synthesized model which does the first complete model of the plasma integrating code with the edge whereas The Edge is described by the full distribution function and its non-equilibrium Evolution near the edge which happens at a much more rapid time scale the core which is much more Collision less the background distribution function doesn't evolve all that much but the fluctuations on it evolve very rapidly and even though we have the same equation underlying it the versions of the equation that we integrate in the core and the edge are somewhat different the core equations are an approximate form of the full equations and it has its own algorithm the integration accomplishes that and this is tightly coupled as I will describe to you on top of that you have all the challenges of plasma material interactions radio frequency or neutral beams MHT behavior of the whole system energetic particle physics all of these are to be added as special modules to this core whole device model and my work primarily today that I'll be describing for the whole group is our success in having achieve that integration so far now just to show you why I think this is a big deal I'd like you to look at the core plasma simulations of the code Gene and the edge plasma simulation for the Codex GC which had been there in the community for a very long time predating the inauguration of the exoscale error and if you look at it the code is actually evolving on a slower time scale with very different spatial structures than the edge which is much more rapid and at very different kinds of structures the separation of time scales is a crucial asymptotic parameter that separates core physics from Edge physics The Edge physics requires a full F description you cannot linearize the F around some background and in Delta f whereas the center one you can the integration therefore of a Delta F algorithm with a full F algorithm is what was the major challenge for this whole device model furthermore the left results are actually coming from a Continuum code which actually integrates that pdes directly whereas the right hand side is from a particle in cell representation which is equivalent in mathematical terms but the techniques required are very different so what were the principle wdm app goals when we started out on this seven year Journey first of all the demonstration and assessment of a whole device model gyrokinetic physics and experimental transport time scale in a challenge problem for pedestal formation in a in a fusion plasma I'll explain what the pedestal is in a moment we must do so we were told by the ECP at a figure of Merit no less than 50. because if you look at going from say Titan which seems ancient today to the frontier there's a factor of eight involved already eight to ten depending on your problem in terms of sheer computing power so if you took the same code and you scaled it you could say naively you get a figure of Merit of 10. that's not enough you must have enough algorithmic enhancements in order to get to 50. you'll be pleased to know that we

have met that guideline and more but I'll save that for a little later in the talk and I'll tell you a little bit more about it just to tell you that we just ran on Frontier and we have achieved a figure of Merit of 150. which I think Doug is very pleased about he never tells me that in public but every now and then we need threatens to take my funding away there's always a wink in his eye about the fact that we've finally met there for him that he set us up to do and we have furthermore we wanted to set up an integration framework which we call end-to-end framework for Fusion integrated simulations which I hope will provide a framework that will bring in other codes not just the codes that we are talking about here that's our aspiration now I must forewarn you that plasma codes are not like climate modeling codes in the sense that in climate modeling they've achieved the ideal uh quite a bit of what I would call plug and play in some Frameworks where you can bring in codes and I would call them in the recoupling mode in the sense that you don't need to really couple distribution functions for the codes to speak to each other here what we are really talking about is sharing particle distribution functions across the core and the edge which is a much more detailed level of modeling so what is this challenge problem that we told the ACP project we will solve this is actually the heart of the matter for each of Performing and meeting its Fusion goals it wants to operate in what is called the high mode abbreviated as a h mode where the pressure profile is expected to have this this pedestal and then a rapid uh going to zero near the edge the maintenance of this pedestal depends on critical plasma parameters and heating power and so on so forth and the prediction of the pedestal height and weight is one of the primary inputs into ether modeling going forward that is what we have targeted to predict for eater using realistic eater parameters so that's a much larger volume but it also must predict this has not been done before and so what have we done what we have done is this is sort of gives you an Insight in how we proceed it so we have one code HTC which is the edge code in the plasma which is a particle end code is in fact the only full Edge code that is now there which is highly performant on gpus and has been shown to be highly performant on Frontier that is coupled to a core code of the kind that you saw in the movie gene or any other code we have also one Continuum code and a particle in cell code that we bring in both we brought into the project one for the explicit purpose of coupling the other for risk prevention and we are actually trying to do this fom that I told you about the figure of Merit with both classes of codes with XGC so we proceed typically in two steps first we do xjc xdc modeling where xdc is doing Delta f at xjc runs in F if we can't get that to work there is no way in which you can remove XTC in the core and bring in another code and get that to work as well so we do that as a first step then we bring in gene or gen which is a core code to couple them and we have done this now successfully and very quickly the coupling accomplishments between XGC and Gene is that we have done linear and non-linear electrostatic adiabatic electrons and circular geometry we have done it with realistic d3d fusion plasma device and calculated pedestal gradient we've also done more advanced electron models which we call Kinetic models and the challenges to address between the chords has been one of variable time stepping the time integration and the field equations which are common that basically Maxwell's equations that we are solving in the entire domain while we are coupling these this is an enormously complex problem this is a result from XGC and uh Gene as well as a couple runs all showing together I'll show you more detailed quantitative comparisons and you can see that we have been able to reproduce reference runs from this coupled code in a robust way here is our a movie of now XGC gem coupling where Gem is now being running in the core a Delta F particle in cell code and what you will see here is a region which is we deliberately put in the coupling region because that is the hardest part of the simulation domain where they are actually joined together with a buffer and what you see is the development of an instability the iron temperature gradient instability tracked by The Edge core on the one hand and the core code on the other until it runs to saturation and let me take you to the results if you think of the fact that the HTC code is a particle in cell code which has noise in it and the Continuum code is one which has very little noise in it you will find that the agreement in linear growth rate is really good but what is more impressive is that we have been able to converge in solutions for the couple system obtaining an agreement on heat flux or thermal flux prediction which is a very important prediction for eater which is an agreement to less than five percent for given the presence of statistical noise in the pick codes and the absence of it in the Continuum codes which have their own challenges it's a striking agreement and below the experimental bar that's actually measurable we had a contract with the ECP this is a four one three point three week project in the doe and I don't know whether those numbers mean anything to you but people who run at Major facilities experimental facilities know what those numbers mean it means you set tight Milestones you meet all of that if you don't you will have a price to pay it's just not a very negotiable entity so you set reasonable conservative milestones and you make them I'm pleased to tell you that the project has met all its Milestones so far and we have survived the scrutiny uh so one was the mere challenge of getting the figure of Merit right and as I told you already you're comparing now full Frontier at 1.6 extra flops compared with the figure of Merit which was at the 27 better flop machine and that has to be greater than factor of 50 and there were two measurements that was required of us one is that we should show that HTC itself which takes up most time in the coupling is it self-performant along with the others but the performance of HTC was very important and the other is that the coupled code also performed at a very high fom and that has the coupling in it and that coupling could slow you down because the time skills of integration between the core and the edge are very different well I don't want to bore you with the definition of the fom and just to let you know that the F there's one thing that you should know that unlike many other projects in the ECP Fusion had a very major challenge there's never been a couple code before the ECP started so the model we started out with was really the XGC fom uh that we had on Titan that set the Benchmark for us now we had to produce a much faster a much more performant code later on let me not go into the details of the fom this was all determined in close consultation with the computer scientists and applied mathematicians who make up the ECP project by the way it's one of the drug is not here so I can tell you it's probably one of the most competent and demanding officers that we have ever dealt with I said both with a great deal of pleasure because it's very very nice to be able to deal as you heard from the opening talk this morning with project directors our project managers who are keenly interested in the science you do and actually ask you searching and probing questions to see how well you're doing we certainly have had that in this facility so here is our report now if this is barely six weeks old we were given 10 days on Frontier to run with wdmr and what you're seeing here CPU only MPI and GPU aware MPI and the talk that you heard this morning on data sharing and others is extremely important and as he told you and rightly so the data management is a very very important part of the Enterprise it's not just computing and we've had very significant help from Oak Ridge National Laboratory in terms of having a group which built the framework which does a lot of the in-seater data management and you're seeing GPU aware NPI CPU only MPI we learned by running that these things do affect and we achieved uh form of one 150 with each other electromagnetic making predictions this was not a problem run to saturation because we didn't run it for as long as it would take we didn't have the time to run it in 10 days because a lot of the notes crashed this is running phase of getting a booting a new machine is a hazardous Enterprise and we are the guinea pigs in that we went up to 6000 nodes but we couldn't get and that was the most that was made available to us and that's the number we are reporting and with XGC and Frontier uh similarly reported about 136 Factor fom uh I'm going the wrong way so what does this mean for Fusion Energy Sciences the eater whole volume simulation that took 150 days on Titan before ECP can now be performed on one day on Frontier for both wdma coupled code or XTC and for those of you who haven't visited Frontier I strongly urge you to do that if you go and stand before one of the shells of Frontier it's amazing to imagine that the computer that is now being phased out which is next door Summit which also occupies the floor that power is now contained on one shelf and if that doesn't give you Goosebumps I don't know what will you're looking at a really amazing machine with amazing capability and you have to wonder that if you don't rise to the challenge of making full use of the machine your competitor will so my rule in thumb is never argue against super computing learn how to use it you will turn it to your advantage in complex problems and if you don't then we are the loser for it super Computing doesn't solve everything but super Computing does give you enormous power to get to answers and complex problems that you can't get otherwise and I'm a pen and pencil theorist so uh what I want to show you is a I know this is a little bit of a high level talk uh but I wanted to convey to you the complexity of the task and I'm not doing justice to all the wonderful pieces of physics that love to spend time on and if how much time do I have okay I'll get into some really interesting uh fundamental physics in in the five minutes that I have I think that's very kind thank you so what I want to talk to you about is this um General framework it's an extra skill framework that has been bled from Oak Ridge which actually sets up how we've developed a general framework for coupling codes and as you know the dream of wdm app is not only to get kinetic coupling to get a whole device model but also to Bringing other pieces of Science in and so this is actually a workflow if you will it facilitates easy integration to analysis and visualization tools components Frameworks and the unique features are in C2 memory based data movement exactly the kind of things that you heard the legend does and I would love to find out how one can actually use Legion which we haven't used yet and today was a learning day for me in that respect but also exactly the points that were emphasized how we move data around and we are using some of the older tools Cocos is a very important tool for us and this turned out to be a very important tool for us to interface fortrans C plus plus codes couple them and run them on FS 2.0 and our goal is to actually make at the end of this period f is 2.0 available to the fusion community but using of this framework will require people to actually get extra skill resources that can only be gotten through insight and other programs that you have to compete for and we really hope that people who want to use this framework will now what I want to talk to you about is something which is a little bit more physics that is what we have done towards whole device model of a chocolate plasma but the question that you can ask me how are you going to use all this and what problem in Fusion are you going to solve and obviously we have targeted either eater will if everything goes according to plan exceed Q by far 10 not just one it's a complex machine but there are two problems in running tokamax and the two problems in choco Max that are the subject of intense research this is what keeps Tokamak Fusion people up at night which is that they need a plasma current system is beautiful it's actually symmetric that is a great strength but access Symmetry by Maxwell's equations required that you must have a current flowing in the plasma Colby equals J most people who do electromagnetics know this Central equation and you insist that if it is access symmetry then you must have a current flowing through it you have no two ways around it that current is the source of many instabilities that can disrupt the plasma the other is that current also needs to be driven so if you want to get to a steady state machine you have to really not run the current in pulse mode but run steady state and these are the two principal challenges that took my people face if the current disrupts is well known from French super chocolate Max that you produce a beam of runaway electrons that when it hits the plasma can melt the plasma locally and the control of that disappear of the disruption and mitigation is one of the major challenges lineman Spitzer who actually uh started the fusion program did not go with the access symmetric way his idea was and it was probably the most beautiful idea in Fusion physics he said he wanted to build a device without a plasma current which he called a figure eight accelerator and his Ingenuity was that if you take a Taurus a donut and you twist it and make it into a figure eight you will destroy its access symmetry it will become fully three-dimensional magnetic field but that magnetic field from field topological considerations can produce the complex magnetic field that you need for a fusion plasma which combines a toroidal field as well as a colloidal field it was a topological intuition years ahead of its time Quantum mechanisms later on found this to be what they call the berry phase and I don't go into the history of that it's a favorite topic it would take another hour but he got this idea on a ski slope he liked to climb mountains and when he couldn't have mountains he climbed buildings there are stories about his climbing the graduate college at Princeton overnight and it's very nice practice and the police had to chase him down not to do hazardous things and this is the only equation that I'll actually show you in the whole talk forgive my theory inclinations it turns out that why stellarators have had a real Resurgence so the complexity of steriliters were always that there were three-dimensional magnetic fields and they require complex topologies if we write on the lagrangian which every physicist likes to do for a Charged particle you will find that the answer depends on the vector potential a which is fully three-dimensional but then if your gyro average that lagrangian you come to a remarkable fact that the lagrangian depends not on the vector B but on the magnitude of B this actually raises a very interesting possibility what if your vector B is fully three-dimensional but really the lagrangian that controls your particle depends only on the magnitude of B so if you can make the magnitude of B dependent on only two coordinates they may be somewhat special coordinates and the third coordinate will be ignorable and that by noise's theorem is going to give you a conserved quantity which will confine charged particles in the axis symmetric Taurus that symmetry is out there for you to see it's the Phi coordinate and it is a very nice momentum conservation law that goes with it the ties the charge particles to Magnetic surfaces in the steroid of a three-dimensional magnetic fields there is a hidden Symmetry and that hidden symmetry comes about through this and what people therefore figured out very ingeniously is how to build three-dimensional magnetic fields which have the property that the magnitude of B depends on only two coordinates it's called causes symmetry and causes symmetry has opened up a whole new area of research not really infusion plasma physics but broadly more mathematically and what you're seeing here are things that have been built at Madison in fact with the magnetic field as you can see this is as a helical uh the Madison experiment had a helical magnetic field but if you follow along a fear line you actually find if you go along that the bee is actually constant along those field lines and this has actually been built and plasma contained and the most spectacular version of something that is close to causes symmetries the wendelstein's stelerator in Germany which now this is from a science paper in 15 which has been built according to computer models has remarkable confinement of particles and has met every specification required of it and that was designed 30 years ago now we can do a lot better and what happened is about four years ago Jim Simons who as you know is a mathematician and actually has the Silence Foundation which supports long-term research I actually persuaded him along with a very talented group of people to start what we call the hidden symmetries and fusion energy project which essential goal was to develop a sophisticated computational product which will very rapidly design stelerators using state-of-the-art Computing tools we developed as a result of this the science optimization code which uses the full power apparel computers is a multi-institutional international team because Simon's unlike the doe actually funds people in UK Germany and Australia and together this group has done marvelous things including Purdue using designs that have shown that particle confinement high energy particle confinement exceeds that of even accessymmetric devices because the flexibility we have in three-dimensional geometry through quasi-symmetry gives us this control and now we we are actually in the process of doing magnet designs so what I want to tell you is the entire power of the wdmf framework now has ready for it to build stellarator relevant whole device models that I hope will be the next challenge that the wwm app model will take up my conclusions and thank you for your patience that I believe wdm app will deliver a computational tool of unprecedented power exploiting the full potential of Frontier on Aurora this has met every Milestone exceeding the fom 50 Criterion by a factor of three and I hope we will do better as we have more and more of Frontier available to us we focused here on two primary goals which is coupling of core gyrokinetic code and Edge Auto kinetic code and performance of the couple code and the development of a user-friendly extensible framework for code coupling in wdm app further development of wdmf for stellarators and other Concepts I hope other people will do in the years ahead and I should tell you that Hawking's Vision that the science is extremely interesting and complex systems you have emerging facts that you don't get from each of the individual models is coming to pass and integrated with engineering we hope will enable the first principles modeling of fusion power plants of the future thank you for your attention [Applause] thank you for that wonderful talk and we have time for a couple questions okay there we go um I was wondering if you could kind of talk about the coupling in terms of um like looking towards coupling other codes in the future like some tips and tricks for kind of some major pitfalls you found that are kind of important to avoid I can tell you that the challenges are different depending on what type of codes you're trying to couple in our case we have some mathematicians who are also involved in the problem and therefore we did some simple problems first like advection diffusion systems and things like that and one of the things that you faced right away in order to control your time is what level of data are you going to exchange between the two domains the core domain and the edge domain that's one the second one is when you're solving Maxwell's equations do you have just each domain solve its own field equations or you have one field solver for the entire domain we found that the numerical instabilities when we actually do the field solves in each domain separately it was anticipated by this mathematical work which on advection diffusion equations but the physicists as you know they go Way Beyond the scope of a simple advection diffusion problem that they tried it out and surely enough we understood that this was something that we had to do in the process we uncovered a few more things for the applied mathematicians to now prove theorems about on what can the stable algorithms we will actually have then it came to the question of F and what you're really doing is that you're actually merging codes with different time steps on the left and the right and if there are issues of phasing of information you can introduce Furious phases that will actually decorate the turbulence and make you feel that you're doing better at controlling turbulence physically then you're actually really doing and this is a numerical artifact that took us time to get over it was all cured because we had nice reference models where we saw this was not happening is tricky business and hydrodynamics people told us that this was something that they had tried in the area of neutral fluids and they had a lot of trouble with people in Livermore in particular and very good people at that Phil colella and a whole bunch of other people who had tried these sort of things we found a way around many of these difficulties and getting those quotes to be robust is another big challenge so I just mentioned to you two things now if you couple a kinetic code with a fluid code there you can actually you have boundary conditions to worry about because they're going from a higher degree of system to a lower degree then the Fidelity of the boundary conditions coming from the left and how they match on to a kinetic code you have to do multi-scale methods which really score screening in time it's called time telescoping techniques that we have to implement and those have been pursued to in the program but in the main project we still haven't coupled this couple code to say an MHT code that's a task for the future lots to talk about perhaps our coffee thanks thanks for a nice talk um I had a I was a little bit unclear about use of the phrase first principles you do seem to be coupling different chords operating at different fidelities to me first principle is some underlying physics that you cannot go below right so is this first principles or let's say a common terminology in your field no no when I meant first principles I meant first principles in other words if you open chapter one of a plasma kinetic theory book you will find what you would see a variant of the boltzmann equation if you and I agree that the bols 1 equation is a fundamental equation of kinetic theory that we are talking about the same thing the gyrokinetic model is actually derived from the boltzmann equation with only one rigorous mathematically justifiable operation which is that if you have a very strong magnetic field you average out boltzmann and get rid of the rapid gyro phase motion which you end up with are what are called the gyrokinetic equations those are the five dimensional equations that I was talking about now every fluid description in plasma physics is derivable from the gyrokinetic equation from first principles so I think if you solve the gyrokinetic equation in a strongly magnetized plasma most plasma physicists would say that is what would be a first principle model and the coupling of the two codes that we are talking about here are done with the same gyrokinetic equation it just says that the core we make a further approximation that Delta F the variation from the total left is smaller than F0 whereas in the edge the total f is integrated they are then coupled would you agree with me that that's first principle enough okay okay so this is no uh yeah I I I I don't know because I don't know the terminology in your field what I was going to say is that uh the there are reviews of modern physics articles where people have shown this using hamiltonian methods and so on and so forth where this has been this state of the art has been worked on and refined where you're right though if I am if I actually interface a kinetic code with an MHT code there are mixing models and you are absolutely right because the mhd model is a fluid model it doesn't have detailed kinetics in it but it was the coupling for the whole device kinetic model that I was referring to as a first principles model [Applause]

2023-04-15 12:30

Other news