 you need this I don't know whether you do I usually don't like no no I know how to do this for the recording it's better use the mic offer the recording so I better I do okay then you Daniel Daniel Achille come tomorrow. Yeah, but you can introduce her. I think that we should begin, and hopefully the house will be completed soon. So, welcome to the second week. I believe that somehow in the post it is making a fusion application. So, I'm using the data in that, it's a really wide physics, the first week of the world between fusion. And we will be talking much more about the genuine theories, and perhaps there will be greater emphasis on, not perhaps, definitely greater emphasis on carry on the situation. And let me introduce the actors who are using this week. Professor Dany and Dennis. Nice meeting you. And here again, one of my students that I used to be. Long time ago. Longer than we want to remember that. And then we have Sergio, who is a student of the University of Calabria. She's from the Palace. And we have to be helped. There is hiding inside the room. And David is. In addition, and leaders in and all of these people so I believe we are going to do a lot. And then this week, you will see less and more of that. But I'm there. Anything you think you want. And you want to have some session into one of your. So we are ready to start this session this morning. We are going to have a search of the video from Calabria. He will be given the first stop. A couple minutes. We are going to start this session this morning. We are going to have a search of the video from Calabria. He will be given the first stop. A couple minutes. Then we'll have a coffee break. And after the coffee break, we'll have the second stop. And after him, and then after this morning. So that will be that resume. Our conversation. Then I remember that. With the coffee break in between. With the coffee break in between. And we'll have a coffee break. I'm sure there will be coffee break here. would I want to remind you to bring your doctor as soon as possible so that they will be there by the end and that will be for the day they will be in some costal grounds of exception. They have students having a FAS. Okay. So that pretty much resumes our session today. So let me introduce, it is my pleasure to introduce Dr. Sergio Servillo from the University of Calabria. Thank you Daniel. Thank you Professor Jean for this for inviting me to this prestigious school. I'm very honoured to be here and I will try to do my best. Oh yeah, yes. Sorry to interrupt this. Yeah, I think so. Recording is already recording. No, no it's wonderful. I mean please, this is an example of how you should interrupt me constantly. Okay, no, no that's not true and you stop. Okay, anytime. So in this, okay. So this course is going to be divided in three parts. We will do really in a Galilean way. First we observe things, we will look at the observations, see how the space plasma looks like and then extract features and think in the way we would like to model it. So observation first always in our hand, right. We look at the data, the real data, then we will go back and think about the questions and then we start from scratch. In the first part of the course we will start really from scratch. I will introduce you the basic really tools to do simulation codes. Really a blank piece of paper and we do like program blah blah blah, okay. Of course we will not have time to do a real numerical course on this, right. But I will like to show you just the basic tools and then we will jump very fast from the basic tools, we will build a code, we will simulate the astrophysical plasmas, okay. This will be pretty much the first part. In the second part we will go more into the observation, really observe, we will observe the simulation and compare one to one with the spacecraft analysis, okay. This is really the main thing we will do through all of the presentation. And then in the third part we will learn something about the solar wind and export it to plasmas that are very far away, like supernova remnants, black holes, and we will conclude with objects that are plasmas that are very very far away. So basically we start from observation in the solar wind and the solar wind is a nice laboratory, it's a prototype to understand stellar winds, right. And then thanks to our model we will try to extract information on the on other objects. So in this first part I will really show the main properties of the spacecraft and then I will introduce the numerical techniques. We will use both fluid models, that's the field where I come from, I come from hydrodynamics, I'm an hydroglyke, but then we realized in solar wind that really you need of course a magnetic field, then you need the magneto-hydrodynamic to describe it, or maybe all MHD, but then we realized that really the plasma is not really so collisional, there are a lot of collisionalness effect and therefore we need like kinetic models to simulate, to understand some features, not all of them, most of them can be interpreted via MHD for example, but if you want to understand fully the small-scale termination of turbulence then I would argue that you need a full self-consistent kinetic model. Okay in the third part we will go from global to local simulation, what does it mean? Well when there is a weather forecast for example there is large simulation of the earth, okay, and then you need to know coriolis force, the impact of like, you need to know a lot of ingredients, right. Then the computer passes local information to other modeling, another higher level, refined level of simulation, so you simulate smaller domains with more physics, that's what we will do, we look first at the global heliosphere with the MHD global simulation and then we will do local simulations of turbulence, because with local simulation of turbulence you can really go to higher resolution, extract the maximum of information thanks to simulation, okay, that will be our, it will be a weather forecast for the heliosphere. So it is a plasma, a plasma is an ionized gas, I guess, where charged particles really interact in a very complex way via electromagnetic forces, most of the universe as you know is in this state of very ionized charged particles, but observations are somehow limited, we wish we can observe everything in a plasma, we try in the heliosphere with missions, but really you can probe small pieces and have only certain details or by looking at imaging you can extract some other information. What is certainly true is that most of this plasma here is highly collisionless, a part of some regions like the lower corona where there are some friction like and the collisionality is high, but if you consider the amount, the volume of the universe is mostly collisionless, it means that the density is so low that really particles do not collide and therefore this will have strong consequences on the modeling, okay, this is really the good time if you want to enter space physics, it's really the good time to do it because there is a tremendous amount of data today, it's the golden age of space physics, there are, this is just, is a partial covering of spacecraft that today are or the past flight around the earth at one astronomical units or closer to the sun with the new missions now like Solar Orbiter and Parker Solar probe, many other here with people involved in missions and there is a lot a lot more going on, for example there are very exciting space missions now going close to the sun, but in the future by using other techniques like Ilioswarm, they will have like constellation of like kubesat, kubesat of data to extract information about magnetic field and particles, now we will see why in a little, so really there is a very large amount of data in some other projects, we do study this amount of data even using artificial intelligence to extract information, for example because it's really, you need to mine a lot of features from a very large databases, but you have to be careful with that because there maybe there is an overcrowding of information coming from this, right, so you have to select few things that you are interested in and this is the solar wind, you see there is a shiny happy sun which is emitting the the wind and the solar wind speed at one astronomical units is very fast like 500 to 700 kilometers per second, so it's very fast and this is very important because if you look into a river flow and the flow is going very fast and you look at the river for while it's going through your camera, if you measure in a point of the flow and the flow is going very fast on average, then you can apply that you can apply the Taylor-Frozenin hypothesis, it means that any signal in time is a picture of the signal in space, okay, because if the fluctuation level is very small compared to the mean flow, it's not really varying while it passes through, so any time recording it's a picture of what is happening in space. Yes, absolutely, but essentially you go to here and you have a probe here, a satellite and this is like a fluctuation going very fast here with this V0 much bigger than delta V and this is like delta V, if this condition is verified then each time sequence, this time here, this is my time arrow, can be transformed into a, actually it's going the other way because there is a mirror effect, if you think a little bit about that, it's not immediate, you have like an image in space, okay, if you record time series here then it's so fast it's not, it's frozen, assume your it's frozen, it's not exact, it's an approximation, then you are like extracting a piece of space one day, okay, this is a very important point on this because if you do this and you measure time series then you are extracting little slices through your turbulent setting, this is really true also in engineer hydrodynamics and it's very old hydrodynamics thing, right, can be proven that is correct, then you, if you measure the magnetic field as a function of time, this will be the magnetic field as a function of space and here we have magnetic and velocity field, you see, you, we measure in the solar wind really, I wish it works but it doesn't, okay, it doesn't, if you're okay, okay, in the meantime I will continue here because here we have V and V, the first thing you see is that it's really highly fluctuating, it's like random, it looks random, the second thing you see is that they're really aligned and therefore there is a coupling between the magnetic and the velocity field, so this is telling you that your velocity and magnetic field are not really the couple probably there are some physics principle that make them like aligned and this is the typical of alphanic turbulence where there are correlations between velocity and magnetic field, so if you do the power spectrum then on both, you will see a nice thing that the energy as a function of frequency, careful now because frequency it means k vectors, so the energy as a function of k really decreases fast and there is a power law, when physicists see power laws we become really excited, okay, because it means that there is a law behind which is regulating that that flux and here the idea, we will see it in a moment, here is like there is an analogy with hydrodynamic and the slope was like 5 minus 5 thirds, which is really something well known, so from observation really this is very old observation you see from the 60s from marine explorer, from this old observation we extract the field is very random like, there is alignments between velocity and magnetic field that are like wave-like activity and there is a power law spectrum of different, the energy is distributed over different, a broad range of scales with a power law, three things, so probably there's turbulence, structures and waves this is a very old picture that probably you have seen already, if you are familiar with with turbulence, the idea is that if I have, if I shake my coffee in the morning, okay, and I shake it fast, I will see the, I will, I'm injecting energy from the large scales, which is like my steering scales and my steering scales are this one and the the vortices couple and produces smaller vortices and then eventually this goes on, vortex splits into two and so on until you reach dissipative scales where friction between molecules is happening, this is typical, the typical Richardson-Turbulent cascade where you inject energy at one scale and it goes down at small scales and is ubiquitous, is the universal process and no matter, this process is very universal, it can be, it can be in fluids, plasmas or other media, in particular with this, in this phenomenology, in the framework of this phenomenology, you can predict from hydrodynamics that the k vector, the energy among scale is distributed with a power like k to minus five thirds, so there is a power law which is really well observed, if you write, you google it, k to minus five thirds will be in hydrodynamics, plasmas, in helium, in whatever, so of course it's much more rich than this, but the calculation when I do it to my students, it takes well be one hour, the hypothesis, they may take three or four lessons before you arrive to that, but the calculation is very basic, right, it's something like contained time scales and can be obtained very easily, if you are interested then maybe in a break and someone of you is interested to revise this classical result from Kolmogorov, yes, why not, that's an exact, absolutely, this is crucial because then if you learn the way that you obtained this law, maybe one day measuring something different with another timescale, you can obtain your law, okay, and this is my wish for the students, right, that's a PhD, that's the purpose, but okay, suppose I do in hydrodynamics, I pump some turbulence from the a sphere, okay, like the sun, and this turbulence is going away, so if the medium is adiabatic, temperature will decrease like power like minus r to minus five thirds without the distance from the sphere, will go very fast, will decrease the temperature as I move far from my injection, right, if I do in solar wind and we will, with this technique we can measure the temperature at different distances from the sun, really doesn't match at all with adiabatic, so here it's a break, strong break with fluid dynamics, with adiabatic fluids, it means that your wind is eating much more when it goes away, this is crucial and on this they built space missions, the space mission that you see today, they are partially want to answer this question, why the temperature is so high, it means that the heat flux in the plasma is zero, it means that your pressure is supposed to be like rho to gamma, okay, it's like an adiabatic disclosure for your internal energy, okay, really a fluid like compressible flow, but here you see the energy drops very more smoothly, why is this, probably because there are turbulence and wave like activities that eat more the plasma, for example, ion cyclotron and other effects, but when we think that this is another good point, when we think about landau denting, we see a plasma which is very magnetized, we perturb it with little fluctuations, oh it doesn't have to be a magnetized, I'm speaking about just about magnetized plasmas and it's very well well behaved but is in the perturbative regime, okay, small fluctuations usually to do the your landau integrals, right, to do so you imagine some wave like that perturb your plasma, you do your recipe, the mass can be even challenging sometimes, but observation tells us that first this level of fluctuation is very high, delta f over f is not order epsilon, it's not minimal, it's order 2, 200 times, okay, when you go to your perturbative limit, first thing, second thing, the plasma is really an homogeneous, if you take the difference between two points here, you see it's very easy, I have a time series f of t with my python code and I do f of 1 minus f of 2, then I do f of 2 minus f of 3 and so on, I can measure differences, the differences are difference in time, but really with this hypothesis our difference in space are gradients, we are measuring gradients when you do compute the increments and the gradients are tremendously large in solar wind, it means that this flow is high level of fluctuation is very turbulent and it has spikes, sharp gradients that pollute your database and they're localized, you see they are not all over the place, they are really localized in regions, so these are ingredients, but so we are extracting ingredients, turbulence, power loss and gradients and anomalies in temperature and speaking about the anomaly in temperature, if you go to MHD, MHD assumes like a collisional Maxwell-Boltzmann equilibrium, okay, your distribution function is a Maxwellian for MHD, is a single Maxwellian for the basic MHD, I'm not speaking about multi-fluid with different temperatures, for the basic MHD case you have a single Maxwellian with a single temperature, it means that if you go to your Vx, Vy and Vz space, your velocity distribution function, your f is going to be a sequence of spheres, my f will be proportional to the density to one temperature and to my bulk flow, a single isotropic scalar, okay, but if you go to the solar wind and measure, you can measure velocity distribution functions now with high cadence and high resolution, we don't observe this, we observe that our distribution function as different is really something like this, is very distorted as different temperatures and in particular from the pressure tensor, you can measure the pressure tensor with respect to the mean field and you will see that T parallel and T perp are much different from one, it means that your MHD for different betas should all stay on this line, this is a scattered plot of the data between beta and temperature line isotropy, yes? Is the Brazilian plot, we call it this? Oh, this is a big question, okay, this is a tremendous question in the expansion, there are many, we will have time later to answer to this, we will show some with the simulations, we can recover this, okay, we can understand this, it's a very important point but it's too early now, this is just to look at stacking from the data, if you look at this, you have, because you are familiar with this topic, so for the audience it's better to arrive to the point step by step, so here you scattered plot of the data and it's telling you that the identity is here, the center, it means that more or less the solar wind is a beta order one plasma with temperature and isotropy on the order of one, but the anisotropy varies a lot, so there are regions with temperature and isotropy, like 10, any regions with, where the ratio between the two temperatures is 10, so imagine you're in the center of having a sphere, you have an ellipsoid with a temperature which is like 10 times the one on the transfer direction, or regions where you have like T parallel over T perp bigger than one, okay, you have all of them, so this is a coverage of 10 years of data, it's very statistically relevant, it tells you that your solar wind has anomalies and here you can see some, we are showing some plasma instabilities that probably you are familiar with, like the mirror instability or oblique fire rows, there are many instabilities in plasmas, but this is for protons, weybel for protons is highly suppressed, for electrons you must better go to higher relativistic plasma to see the weybel to be very active, of course it's crucial for far away objects, but in this one here you can see that the plasma nicely stays bounded by these instability regions, what does it mean? It means that really the plasma, if it enters this region here, if you put your plasma here will immediately establish some isotropy and emit waves, so we'll go through the instability process and emit waves, so you never observe it because it's stable with respect to that instability, doesn't mean that the instability is not happening, it means that it's modulating your plasma, it's very active because the plasma cannot cross this otherwise immediately will produce local instabilities, so turbulence is a very rich fauna of entertainment with fluctuations and kinetic effects, we cannot overlook this important property here that the plasma needs more temperatures and more and kinetic effects to be described, to understand all of these ingredients we need simulations, so you can choose one of the steps to understand the results and any of it has limitations, if you really have infinite computational power you can go to an n-body problem, write the Liouville model for your plasma in the phase space and good luck with that, or you can integrate, lose some, when you integrate the n-body problem you lose information on the, because you coarse grain your system basically, and then you arrive to a glass of Maxwell system of a question, which will be our best friend and this is a course, okay, when you couple the glass Maxwell equation with the evolution of the velocity distribution function in the phase space, okay, integrating this you can go to, you can arrive to two fluids equations for example, but when you do that you assume something on the pressure and you're losing some effects, if you really want to do something large with high resolution and understand the, with maybe with an easier model, which is always very good, you can integrate the fluid equation, make assumptions to fluid equation, obtain m hd equations, if you really want a zero level model, you neglect the magnetic field and you do a navier stocks of your wind, okay, you cannot neglect anything more than that, if you want something reasonable, that's what Eugene Parker used to say, you at least you have to start from navier stocks, okay, we will skip the Liouville part and body part and we will integrate our equation and we will work with this system, which is pretty impressive because it couples distribution function, which depends on the three position in space, three directions in the velocity space and time, so it's a seven dimensional problem where fields and particles are hidden in two years in this velocity distribution function, the densities and the velocities are the moments of this distribution function and they are coupled through the Maxwell equation to the original equation there, so basically we want to simulate turbulence in a reasonable box with some assumptions on the boundary conditions by solving that equations and I will say that there are two philosophies, the first is the Eulerian approach, just really take that equation and solve it in a seven dimensional space, I mean six dimensional space plus time, okay, that will be unfeasible probably up to 20 years ago, but now it's feasible, okay, with our computational power, what is the advantage when you solve directly the equation you see, the advantage is that you don't have a really noise, you have numerical errors but you don't, you are exactly solving the system, but of course it's very computational demanding, if you try to allocate a vector which is already seven dimensional in your computer, it will freeze, okay, you don't do that at home, okay, just do it on supercomputers, when in the way I'm trying to, I will explain you, the second technique is very interesting, it's a trick, is instead of solving the equation of Vlasov, it does a Monte Carlo of the Vlasov by integrating I say fake particles as a sort of like these particles are elements of the distribution function, we integrate the particle trajectories and try to reproduce the velocity distribution function with a Monte Carlo technique, okay, so in this way it's very cheap because now you don't solve any more seven dimensional equations, but you solve a question in 3D space, but with billion of particles, if you do some quick-hand calculations you can see that you gain something, but you lose on the precision, you produce noise, particles in cell codes are very noisy and we have to deal with this. So since it's a basic course and many of you probably are familiar with fluid or MHD plasma models, I thought it would be interesting to see the basic steps to build your own code in one case or the other, so this will be our, at least this will be like coding for beginners, okay, the first part and really as an example I will not start from the full Vlasov Maxwell, indeed you can use a trick instead of using the Vlasov equations for both protons and electrons, you can say that electrons are much lighter and you can treat them as a fluid and forget electron inertia, this is called hybrid Vlasov Maxwell where you essentially you close your system with a ohms law, a particular ohms law in the electric field, this saves you a lot of time because then you have to solve only for the protons this, okay, it's a lot of memory saving, but really we can to show you the basic steps to build a code, we can do a simple 1D, 1V that means that one velocity and 1D in space, Vlasov Poisson system where you neglect even the magnetic field and you use a very reduced system because if you know how to simulate this equation then you can easily implement it to other dimensions and you can go back to the first one, okay, so as a template for our simulation we will use the Vlasov Poisson in 1D, 1V, so it's a simple two-dimensional plus time of course where the system is written there, so the Vlasov equation is very important, it's very interesting because it's a very, it's essentially a hyperbolic advective equation where you have to just choose the boundary conditions and really you, if you forget the transport in the velocity space, in space is like really an advection equation, very simple, the basic equation of advection where you have F and the derivative of F, it depends on V which is a coordinate now and the derivative of F, okay, and you want to integrate this, first thing you need three steps, you need to discretize velocity space and the x space and the velocity space, okay, discretization, of course we normalize equations and then you have to create an algorithm, of course in each point here since we want to work on a lattice and we need to compute derivatives, in each point you need an approximation to have the compute the derivatives, of course there are many refined ways to do this, with eye order, with like a superposition of Fourier modes, spectral and so on, really I will go with the basic, so since you will have these slides they will send it to you and the thing is recorded here, I thought I will write all the steps, I will not go through now because it becomes boring otherwise, but you will keep this as your notes, right, if in case one day you want to understand where finite difference comes from, because everything starts from finite difference techniques and finite difference starts from a Taylor expansion, okay, this is the simple formula that you obtain this when you, and there are different ways to do that, but if you try to mimic to solve the Blasov equation with a simple finite difference technique, it will blow up immediately, it will create a lot of problems numerically, it is not stable because it's too complex, if you want to do any, there's a lot of non-linearities, so really what you want to do for example is to use this trick, it's called upwind schemes, upwind means that just really the name is, if I'm computing a derivative in the x direction and the thing, the plasma is moving along the x, I use the points backwards with my Taylor expansion to compute the derivative, this is more stable, it has a larger small scale diffusion and it's more stable for your scheme and it's very well used, this is very well known for example for more refined volume, finite volume techniques, okay, using this upwind scheme, so if you use this upwind kind of method, your equation becomes stable, you can integrate, now this was simply 1d Blasov without the term in the velocity space, you see, now we tested that, we know something which is stable in that simple verified fake configuration because it does not exist, of course you need to keep all the terms for Blasov, right, but then since you learn that this technique is stable, you apply this upwind technique both in the velocity space and in the physical space and in the velocity space, okay, something is moving in this phase space to compute derivatives, you always look backward and this stabilizes things, so you can combine, this is like a typical splitting technique that we use in my university, my group, where like you really advance the velocity distribution function first in space and then you do one step in velocity space and when you do this, you use the points backwards behind the wave which is propagating the characteristic, with a characteristic velocity, so you really move along the characteristics and if you want the solution from one point in this phase space to another, really you are doing like with two steps, moving first in physical space and then in the velocity space and with very small discretization meshes, then you can arrive really with a fairly good precision to the final solution, of course you need to test this with waves, with templates, with test beds, we call it, so you need to have some tests and verify it numerically and this is very, very powerful and very robust numerically, that's what we will use for the Eulerian case, but the Eulerian case is not so difficult because it's very expensive, then you need to create vectors in multi-dimensions and it's going to be very expensive numerically, really the trick is to use the particle and cell techniques, I use both, I do work like 50% of my life with one and the other, I see the advantages, I think sometimes I prefer one or the other, but this is very interesting, especially if you want to study plasmas where you produce high energy particles, if you want to use, simulate a plasma which is pretty thermal, then I would use, I would recommend to work with Eulerian Blasov because you have higher resolution in the velocity space and the plasma is well localized here, but if you're working with like cosmic rays or the very energy particles and you produce very high energy electrons or relativistic electrons as we will do at the end of the course, then I will recommend more of this because the particles can really go too far away and here you can not really use a finite volume to describe your plasma, that's the main philosophy I will say. So how to do that, well instead of solving that equation, we solve these particles trajectories in the phase space and so we go into a Lagrangian world, we solve it here is a total derivative, of course it's not a partial and we solve this equation in the phase space and there are a number of techniques as before, there are stable and less stable techniques, usually the Adams Bashford or the Boris technique is very good for integrating particles. So what's the trick here, this is an example, okay we need to integrate particles to reproduce this F, but we also need to solve Maxwell equations, so the Maxwell equations will be solved on a lattice, on a grid in physical space in X, Y and Z, okay because Maxwell is what it is, right, it's a series of partial differential equations for numerics on a lattice with a time evolution, so our electric magnetic field will be on a fixed grid in physical space, while the particles will be free to fly in the continuum, even not on the grid points in the continuum, they will fly around in this phase space, moving both in X and in V, so this has to be done, can be done in a serious way and this is very, it was a very smart one, first you like start from initial condition, upgrade the fields by using moments of the VDF, then once you upgrade the fields, the fields will interfere with particles, then you upgrade the particles, then the particles move a little bit, you recompute the moments, the moments will make the fields upgrade and then both of them, okay, except one works in a meshless space because the particle can fly for free in the continuum, and the other one are defined on a grid, of course you immediately see the problem in doing this, is that particles are not located in your mesh, here the meshes are in blue, can really go everywhere, but you know the fields only in the blue regions, so to advance particles you need the fields here, therefore you have to interpolate, the interpolation is a big problem because for each interpolation you introduce an error and this error is propulating your system and it's like it's making your system very noisy, that's where it comes from, okay, so how can you also the error of the interpolation, but also the fact that you have a finite number of particles to reproduce your velocity distribution function, you really to be a pure Blasov you need to have like an infinite number of particles, of course this is infeasible and anytime you have a finite number of particles you will have more noise because you want to reproduce f by integrating in the velocity space, by doing a local coarse graining, okay, you have particles, like I have a bunch of particles here in a little cube and each particle is in a single position because my cube is is elementary, it's very small and each particle has a velocity, one is pointing there, one is there, I have like 10,000 particle in an infinitesimal volume, I want to reproduce f, I do an Instagram locally, I'm here, I reproduce my velocity distribution function by bidding particles into little sub cubes and I can reproduce f in a single point where there are a lot of particles, okay, this is again probably creates a lot of noise, it's very noisy and it's damaging our numerical element, there is no walls in my in my in my talk because we are studying the plasma which is flying away from the sun and you will see in a moment why I'm not caring about boundary conditions, we will see in a moment by the hypothesis of homogeneity of turbulence, we will see but so far now we forget, of course if you want to study tokamak plasmas you have to be very very aware of what is happening, for example in the scrape of layer of a tokamak devices or close to the diverter, there actually there is also pollution from neutrals which is coming in actually with some students we studied this with fluid like models but really we will not care about more laboratory plasma problems, okay so far, okay in a little, so here in each slide I'm not mentioning you during my talk because I'm trying to show you the just the steps but again with the slides you have the literature on this from important seminal papers, okay in green in the green with in this kind of in here you can see I also report the basic literature on this on each step so you interpolate and just in case you want to interpolate something it's important even if you work on a completely different subjects like doing like tracing of passive tracers or things like this it's good that you know the basic the basics of the algorithm that are on this simple slide this is a typical tree linear interpolation which is very pretty precise I will say in case you want to interpolate the motion of a single tracer in the in the continuum whenever you know the values on a lattice okay I'm sure most of you will deal with this so of course you if you want to do this calculation once we built two codes so far one Eulerian and one with this Monte Carlo particle Lagrangian way if you write your code I know most of you will go back now and write your code and if you try to run it on your laptop it will just not move okay before it does a it does a reasonable time step on your little laptop or your cell phone or your or your computer really this is not efficient is not really going too far you have to wait really a lot so what we really need to do is to see we have a lot of information here we have a vdf which is seven dimensional and we are all we have a lot of particles so really to have a reasonable amount of noise is too much for a single computer then we go to multigrid to multi processes processors usually we the basic the basics are here for the good parallel parallelization you can use two philosophies to to make your code parallel even go using like open mp directives like is sort of like adding some flags to your cycles to accelerate the processing this is more like hardware like but I prefer this one this is the most efficient one is by using mass message passing uh informations um how it works well instead of solving a single my problem which has a number of points in xyz for example on a single computer I divided the domain through processors okay I divided my domain and uh into number of processors this is the basic one for example process zero is the in the first centimeters of my volume process one in the in the cloud in the neighbors one and so on I give it to each one of these processors the same number of points for example and each one solves the equations locally of course but when you use these kind of directives processor two doesn't know anything about processor one nothing to be very efficient they have to work really locally okay if you work with local operators like finite differences so each one of them works locally but they don't know anything of course we know that for finite difference if we want to approximate delta f dx this is going to be f of x plus delta x minus f of x minus delta x divided two delta x and of course sometimes I will arrive in the I will encounter this problem when one f is definitely one processor and the other one is in the neighbor but the other one doesn't know the other right okay for processor zero I will hit a boundary when I need extra an extra slice to do so of course we have to send the messages okay like lovers okay one sends the message one sends the information this row of data to the next processor the other processor receives this and send back the message like a whatsapp okay they send this message they communicate this they store the extra slice and then they can do the calculation and move on this is very efficient it's very fast it's really you have to wait until the two processors communicate so this is one of the first thing I do with my my PhD students it's just to train to do this and to learn how to think in different processors it's very difficult you have to spend some time at the beginning it's just a philosophy a processor doesn't know anything about the other as can just collect it and spread informations but you don't have to collect and spread too much otherwise your computational slows down you want to keep it very very very light so if you do so and suppose I have a problem that takes one year on my laptop I can arrive to solve a problem in like 15 20 minutes on a supercomputer depending on the number of processors okay it's very powerful otherwise you cannot use the kinetic simulations to understand plasmas uh with mhd i will say you can still do reasonable simulations even in a single cpu so what's the result of my scheme well uh this is one of the simulations where at the beginning there is a counter streaming plasma flow it's a full plasma this it's a plasma made by ions and electrons with like my is is my full seven-dimensional blast this was very expensive on a supercomputer in the States and uh basically the public because okay you cannot see it here but essentially there is a shearing flow like the one with the produces a Kelvin elements okay and this is the current of the of the electrons it's like the more or less from the Maxwell is like the the the carl of the magnetic field is is telling us the gradients of the magnetic field as you can see if you wait a little bit it's a lot of instabilities triggers locally both secondary Kelvin elements and also tearing tearing like and also also relay Taylor they observed in this locally you have a lot of instabilities while the cascade proceeds and at the end to answer your question you will see that there is a pattern here which is which is pretty much like a van Gogh van Gogh paint with no boundary condition the band the system locally forgets about your shear so this is what we call it like if you take a small box here we call it like a homogeneous turbulence there is no preferred direction there are more this is everywhere and this is very convenient because once you have a homogeneous turbulence there is a trick to solve the questions and you use periodic boundary conditions imagine you have a system that does not prefer direction no mean gradient is pretty becomes pretty much homogeneous therefore I can use my periodic boundary condition I don't have to care anymore about this so even in a case where boundaries count like in a Kelvin elements at the if I wait enough I go to a turbulent regime I'm pretty much and I want to do a local analysis right for what I understand like what happens on the box scale no you have to impose some boundaries and there is there are solutions also for for full particles but if I'm interested in the in the nature of turbulence locally then no I can yeah I'm almost done actually so I will skip this which is about global image the simulations but you can now we can start to do global simulations of turbulence by using full particles in cell this uses a hybrid blossom electrons are like fluids and this is like the magnetosphere with full peak so there is a wind flowing in this direction and from mhd from simulation of mhd was pretty much everything well known everything well be able there is some turbulence but it's symmetric if you send some solar wind through an obstacle with mhd you don't see too much surprises but if you do it with a code which has full particle full kinetic physics you see some anomalies and the anomalies are on the fact that there is a mean field and particles behave differently when there is a mean field and here you start to see an influence more turbulence here because there is a mean field which is perpendicular to the shock and particles like are accelerated there is a foreshock and producing local instabilities and there is all that beautiful blasts of models and probably lambda damping also an ion cyclotron a lot in this foreshock so things change if you think like do large simulations yes and again here we see this same so again to go back to the point before really this is a zoom in of this large scale peak simulation it becomes pretty homogeneous again even in interaction with a shock before was a Kelvin Helmholtz yes homogeneous that the level of fluctuation are statistically the same all over the volume there are the anomalous turbulence will be like this here a lot of fluctuation and here quiet this is an homogeneous turbulence homogeneous is when I have fluctuation on the same level everywhere in the same that yes pretty much yeah for example think about a system where I have like a boundary layer in the boundary layer there is a lot of energy close to the boundary far away that the level is so that's an example of anomalous turbulence okay which has you have to take into account the boundary conditions so since I have few minutes then we can extract to understand the turbulent cascade from global simulation we can do a zoom in and essentially I think I can continue this later you can do simulations locally of blasts of turbulence with high resolution and I will I will stop it here for the for the break thanks mm-hmm yes in that in the for example in the shock turbulence interaction yes there's a mean field which is the field from the sun it's the field coming from an exterior like a device okay that mean field creates a lot of differences you have turbulence that becomes anisotropic anisotropic means against that starts your vortices instead of being nice spheres without elongate along the mean field doesn't contradict what it was saying that you can have vortices of different sizes everywhere but just they flip they align with the mean flow exactly exactly there's a preferred direction that's the plus maybe there's another question yes okay okay okay the power load the Kolmogorov load says that your energy spectrum your energy at a k which is proportional to them you can decompose a field with a Fourier transform and you take the amplitudes of these Fourier modes the energy is the amplitude square okay the energy as a function of this k vector from the Kolmogorov load was like to k to minus five thirds okay but in when the things I was showing before we were pretty plotting as a function of frequency we like like e of f as a okay it's related to the Taylor hypothesis okay x is equal minus v zero t where v is the bulk flow so you see this is related to frequency this is related to the k vectors immediately you can obtain one direction one one to one it's linear right it just goes through v zero so either you can use k or you can use frequency frequency is related to t it just there is a velocity which is the velocity of the flow okay it's you can but it's because of the initial one that's why I spent like few minutes on this because it's the mother assumption of all the measurements that my flow is frozen linear m h d no for linear m h d there is no cascade for linear hmm I think we may need some more time to chat about this no you can have spectrum yeah it's very a large amplitude but from linear theory you can have some sort of cascade of like like wave wave like interactions that produce some very steep flow that do not match the result though okay in both independent do not interact the quasi linear one there are some we are weak coupling that can produce it it would be a good chance to do right all the and address all these many questions that were filled out so so if you want to yeah I I just want to make this uh first of all I'm uh okay trying to produce a video you agreed to do what I was trying to do so that could take some more time I had I was able to I was going to give a short lecture and okay so I'm so let's write uh uh take me to the state of of let's write the blossom equation of one-dimensional nothing without any force okay no forces it's just a convection and then my initial condition is I think it is zero some f is some function of the last okay so from this little problem I want you to show that when you try to construct the density all right demonstrate to me land of damping there's no force nothing the sort all right which is and in fact we find out the origin of land of damping is basically a very large number of modes the different phases right mixing together all right so that there and this will also tell you what are the conditions required on g you will you will have to tell me when will gv what class of gv will give you land of damping okay obviously if gv is going to represent the distribution of article right well let's let's make it going to zero at infinity right I mean it will make sense so so you will figure out this is a very trivial and a very profound problem and I all I want you guys to struggle even if you don't get there but the struggle itself will be worth of that okay all right go ahead and have some people okay on JP's funeral of plasma physics it was okay I think I saw it I I didn't really I know a lot I will okay okay and I'd like to yes yes yes I will check but I mean is it this year right it's an analytic isn't this year 2022 2021 okay okay we'll go do have a look before you go yes absolutely good I hope that the level is this is the level you were asking okay I was I was going to do the comagour of I will I assume the recording it was on pause I did it I did okay okay fine so is it recorded now yes and I guess it's not how to do it oh it's a oh now it works yes oh wow oh it's not a laser is it it's not effective for what for this slide slide slide oh really that was yeah I just no I don't think it works yeah but this is just for the laser right yes fine okay thank you so yeah yeah I was two slides later actually to reach the main part of the first part of the course now we will simulate little boxes where the site is smaller than typical gradient sites so we will assume a constant b homogeneity and we will forget about the large scales so there is a recipe to do this of course we can start when you have a mean field it introduce a nice entropy it means that the turbulence develops more perpendicular to the field so it's a good approach will be to use a 2d simulation with the mean field going up so we are looking at the plasma like this the mean field is pointing to us and look at the vortices that develop with a full glass of model that's what we will do we will use boundary conditions and some here there is some recipe for the our Eulerian simulations one thing we have to fix is the level of fluctuation with respect the average field that's important because on solar wind is order one half order one just to again to stress that is a system which is far very far from being linear it's a very large amount of it's not order epsilon this delta b over b on the corona where I have to say that one of my first paper was the one by Daniel when he wrote the simulation of a reduced mhd with Pablo on the corona corona then if you have a strongly magnetized then system then delta b over b is order epsilon very small with a strong mean field and that you can see really a lot of turbulence there but this is different now we are in the solar wind we will set up this simulation how to set what is the initial condition that's a good point actually if you want to study a simulation study a homogeneous turbulence is to fulfill you want large-scale vortices like really my steering coffee I want to build a coffee of plasma and I inject energy only at large scales so in the Fourier space this becomes like injecting energy only at lower case okay I put as initial condition this with random phases I back transform I have a random nice field if I wait enough and then I start my blast of simulation on a thousand and thousand of processors and at the end that's what I produce I see a sea of islands they reconnect that's what turbulence is with and there are strong current sheets in between them so this is a typical plot of turbulence if you do the Fourier spectra of this field you will see nice analogies with solar wind this is the typical blast of simulation with the we are simulating this part here you see the spectral index is comparable with observation plus we see that the electric power power spectrum the power spectrum of the electric field as in the observation have as an enhancement with respect the mean field this can be related to the all effect where because the all effect it has a j cross beta is well established in the literature in the literature that the all effect produces more high frequency electric field okay probably with you have dispersive waves sorry okay yes yes that's what I was saying in the solar wind they have the still are the doubt if it's like kinetic alphan wave regimes or whistler regime and I don't want to enter this debate because they are both possible they can go with physics why not lower average plasma no no this is kinetic is the branch from no no no this is not at all actually it's the opposite I know order order one plasma is here is less than one so it's they have all the branches are all active and it's turbulent so careful with kinetic alphan waves because still there is a big group today trying to find waves in plasmas but if you do a dispersion relation of this simulation as we demonstrated in 2010 there is no waves you don't see any dispersion relation if you drive turbulence to be the you see all the waves okay let's say that there are all the waves and no and no waves okay because you have the most of the energy is in structures what we really see in these simulations is strong current sheets now and the reason for that is that the employment of the kinetic alphan wave comes essentially from the property of the system and elements for the if for instance electron mass was taken to be zero then it will become a vector fraction so most of the time what that means is that it is created but even in electron or some finite ion law will be used all right sorry no problem so in this second part we'll really look at the result of our kinetic simulations what is what do we see we see that there is a contact between the simulation we can reproduce the spectra of observations but with simulation you have much more you have the full face space you can really look at everything now with with observation you are just related to this one decad with observational constraints and noise and errors but now at least we can discuss a little bit more with simulation we can speculate let me say okay so in this second part we will look do a local analysis and then since we saw something strange in the simulations we go back to the new missions so you see our pathway we started from from observation very old turbulence we repeated with our simulations with simulation we see something strange unexpected we go back to the new missions new missions i mean mms for example the one of the latest missions in a with very high resolution measurements and we see if there is a gain link with reality between for our simulations so we always hear about magnetic reconnection so magnetic reconnection magnetic reconnection must be there somewhere somewhere must be there what is magnetic reconnection well it's a change of topology where there is a very efficient conversion of energy which is embedded in our in the magnetic field and then is transferred to particles with either with flows or with acceleration or eating you see flows acceleration and eating three things the connection is a conversion from magnetic energy there is a reservoir of energy in the magnetic field that exchanges with particles that can accelerate and move to kinetic and non-termal features as we will see so but this is a very basic cartoon and since we were a child and here is my daughter actually we we always know that when you do magnetic reconnection you have to have a nice box with nice boundary condition no noise at the beginning very little 10 to 10 to minus nine percent of noise you perturb the current sheet you follow the recipe it's very orthodox we're very well behaved if you want to study the connection and see all the tearing instability you have to do it in a proper way with well known boundary condition and there is a really a large amount of works on this i will not enter not even enter the discussion on this we will do it a non-orthodox procedure we will produce turbulence and then in here we will look for local magnetic reconnection we will not care about initial condition a boundary condition at all we will produce a very high this is a very high simulation we are resolution simulation by Pablo Dimitruk like 32 000 square m hd with the a lot of current sheets so at the beginning i was a younger student looking for a reconnection in turbulence and i was very discouraged by this i mean oh my god here there is no be no reconnection it's very difficult to find reconnection here but but if you zoom in this box and you're going a local frame you start to see something like looks like reconnection with the field lines that touches strong current sheet and therefore if you want to study reconnection from the other perspective when you are in a fully nonlinear regime you have to jump into the local frames here and imagine that you are in a landscape of mountains and the mountains of peaks that are the eyes of the vortices and subtle points that are the passes between the subtle points are the passes between two peaks and two valleys okay so imagine here you are in a landscape with google map and you want to measure this you can study the asian matrix of the magnetic potential you study the asian matrix and you find maximum and minima and by definition reconnection is a course only at the x points where you have subtle points where there are current layers very strong so you jump here and you can measure the reconnection rate as the electric field at the x points so you do that systematically it's a network it's a neural network with islands that merge interact repulse it's a complex family of islands that are interacting and each one there are spots where the connection is occurring and in each spot you statistically can measure the reconnection rate so there is no not a unique reconnection rate in turbulence but there is a broad distribution with very very large numbers values so there are regions that are very quiet yes a magnetic island is a close torus in 2d something like this and that this is the direction that iso surfaces of the magnetic potential are the field lines by definition the eye is the null point of the magnetic field so positive if your vortex is your flux rope is spinning this way negative simply the other way exactly in that sense okay since it's homogeneous turbulence you can have you see it in turbulence the vortex is spinning one side and the other side same is for the magnetic field remember these are like 2d cuts so these are there is a current here and therefore sometimes this current sheet this this flux rope will encounter another one which is spinning like this when they are and there are two filaments with the same polarity you know what is happening right from physics courses they attract that's really the first cartoon that Giovannelli an Italian living in Australia thought about reconnection probably something when you have two field lines two flux ropes that encounter attract because of the force and then in between them you have a layer this is the basic mechanism the basic cartoon you have when you have in mind 2d reconnection I will say two one and then you zoom in there and again you have the nice hold a nice tearing like properties but here we don't care about all the process to reach to every connection we are looking just at one snapshot measure the current sheet the the reconnection rate and then here we model it with a modified structure modified sweet Parker in mhd and nicely there is a good agreement with with a a nonlinear stage of reconnection because it's fully nonlinear the process we don't really follow the the the each single one of them it would do a statistical analysis and it's the question is that is this now related anyhow to observations right our obsession is observations okay so before doing this we went to a technique that now is called I didn't know this virtual spacecraft technique in 2067 we did invent think that if you you can send a spacecraft you have a turbulent regime and turbulence in the solar wind is like flowing through your probe now you can do a Galilean transform and in mimic you can mimic the solar wind by flying through turbulence so we will mimic solar wind measurements by flying sending us a virtual spacecraft through our turbulent field okay this yellow path here is my spacecraft which is flying through my box okay in this way you can really mimic mimic the the the acquisition of data okay and if you do the statistics you can measure increment increments the statistic from the simulation are these lines here here there is a comparison with observations really the the the the increments are not maxwellian i mean the increments are not gaussian you see the gaussian is typical of random numbers if you take difference of two number numbers and you do a distribution you will find this but if you do it with simulations or observation you will find very large tails it means that these tails are unexpected something like extraordinary something like explosive okay something like intermittent so the question now is like we kind of invented this simple technique to measure this intermittent see these intermittent structures you have a time series okay that b you can just take the increments but you can normalize to the rms value to the average of the mean square displacement so if is a gaussian these values should say around for this plot around eight with random numbers because it's random numbers are bounded but everything that is extraordinary will go behind this and it makes you identify a a a singular structure okay it's very statistic i have a sample box i know the distribution of the random numbers for this and thanks to this distribution i can select the extreme events is a self adjusting threshold to to identify the the events now we send us our spacecraft our virtual spacecraft with this green line here throughout my probe and the blue regions are the reconnection regimes the connection a singular structure locally that we identify by a means of studying the action of the matrix as we were saying before while the open circles here are the peaks of the of this pvi measurement this technique is called pvi when you set the threshold and as you can see there is an excellent match for the strongest parachute you don't catch all of them of course you have to catch it really nicely going through your current layer but for the strongest one maybe 90 percent works so why do we do this because then once we build this we can go back to reality this is a simulation this is the solar wing we can do distributions and they for very small scales they really look nicely as you can see there is a departure at very large scales between data the red and the measured one why because at very large scales you are starting to feel the in homogeneity of turbulence our box was a local box we are simulating local conditions we cannot simulate like really all the solar wind so that's why there is the mismatch but the statistics are small scales it's similar it's very encouraging so then we went back with Jack Gosling which was a very famous researcher in the field of magnetic reconnection in solar wind and it was very skeptical of this no no you cannot identify a connection you do that you need my idea of reconnection you need to use a look at flows at peaks in the densities he has a he had a lot of recipes for sweet parker like reconnections and say no your model is not going to work indeed but then he did like so much that we co-authored some papers because for the strongest events we were able to identify you see this is our there was a pvi series here was able to identify this you see there is the peak that was identified the same current sheet that came from like more physical like reasoning so our method was statistically statistical but for very high threshold it selects the physical reconnecting sites so discontinuities the strongest discontinuities very likely in the solar wind can be sites of reconnection where if you do some statistical averaging of the temperature it can be demonstrated that these current sheets are hotter something strange is happening here we have current sheet that produces locally short gradients but locally these gradients are hotter than the surrounding plasma so you are producing eating of the solar wind and you can observe it here with from 10 years of data some study i will not spend time on the statistical details but all of this was mhd and mhd is cheating because it's using resistivity and viscosity and our plasma resistivity the collision the collision and parameter is zero i will say in solar wind is negligible collisions where so what we thought in the years is like why don't we repeat the same experiment instead of m with mhd with our good blast of code so you repeat it again what you found is that of course the picture in space is very similar this is very encouraging for people that work with mhd because you still will have islands reconnection and all of these nice things nothing weird happening is there but what you see is that you can measure the temperature anisotropy something that you don't have it in mhd essentially locally you can go jump into a point here and you have the velocity distribution function f x and t and from this you can measure my temperature tensor or my pressure tensor and this is everything but maxwellian it means that the plasma near to the x points is becoming non maxwellian the novelty with respect to mhd is that my plasma local is becoming strongly non maxwellian now now we see the pieces of the puzzle that come in together in a little this is an example there are regions where my my distribution function is not a nice sphere as a mhd guy will say it's more or like of a potato it's a potato elongated with some directions with three axes as we are very weird potato yes this is still a 2d simulation in a little bit we will see the 3d simulation what's t parallel then or it can be t parallel it can be larger under one than t perc or vice versa this is just the the answer to your question there are regions where where you have t parallel smaller than t perc you see and here regions where my distribution function is aligning with b you have both okay why not there are regions probably where there is a mirror miscibility locally regions probably where you are like ion cyclotron or other things why not so then we go to the 3d of course we want to do the 3d took some time to go to the 3d because now this is a seven dimensional simulation of turbulence and you zoom in here you see these are like vortices in glass of turbulence and you have current sheets that are are like these pancakes red pancakes and the anisotropy are like nebulas close to this this uh uh current sheet so this is what is happening in 3d you start to observe the production of a beam because of ion cyclotron resonances you have compressive wave excited ion cyclotron you see now it's plasma physics again we can do now plasma physics locally maybe qualitatively and we don't really follow instabilities but you can see that there is a production of a beam which is observed in the solar wind constantly so then along the mean field you have the particle resonate with your field and produces this field aligned beams okay now there was a somewhere before a guy that was asking me how do you build that brazil plot there okay okay in each point you have a new simulation in each point you have your pressure tensor by using the uh vi i will say ti j v j this is sort of like i don't remember it now uh some sort of like projecting this you can build the parallel and per temperature you can measure it right in each point you have two scalars ti parallel and ti per so each one of this point is a point in this diagram you can do it in the solar wind or you can do it with your simulations now to cover all the solar wind you can now you do it with a single small simulation what you do is to take little volumes all over the heliosphere with varying the plasma parameters and you can cover the full phase space that's a trick okay instead of do a global simulation you do a lot of local simulations this is probably a very very very quick what is your initial distribution function maxwellia is your experiment with a maxwellia yes but we have forces with with respect to your nice experiment which i i encourage you to do it because it's very extractive we have forces yes uh electrons at this level are still our fluids we repeated this but on this simulation yes that's hybrid but we yes can you can yes not for the simulations but we repeated this with also with electrons and they have another they have other physics in okay it's different this is only for ions temperature okay so now this is the 10 years of collection this is our simulation which okay yeah it's not really looks like identical but the main feature are uh you can see some main some analogies with the you see this some segmentation here what the which is due to the fact that we have local finite simulation if we if we had infinite power we will we will like we may cover all this phase space more continuously but there is a strong analogies and this here you are measuring this pvi signal which is telling us that close to these boundaries the plasma is unstable with respect to kinetic instability it's very very very exciting because it means that the plasma near current layers is unstable with the physics that we know it is an an an homogene it's unstable in an inhomogeneous medium because the this region here it has a strong magnetic shear so it's not the typical homogeneous instability that we studied on test books right is an instability that is acting on an inhomogeneity okay so but this this is not the end of the story and this was nice because at that time we were doing this but they were also building a new space mission which is called like multi-scale uh MMS and at that moment they were going to very high resolution in the velocity space and we saw since we have the full velocity distribution function we can invent a new parameter okay when you have vdf for ever for describing a maxwellian you just need density temperature and bulk flow then you can have higher moments like temperature and isotropy but it's not the end of the story you can have it flux which is like you can have costosis so you can have a lot of differences so we kind of invented this parameter which is we call it epsilon there's never any better name which is the difference point wise between the your video and the associated maxwellian you take the difference between your video which is a potato and the little sphere there the associated sphere why do you do this because in this way you measure the correction of a fluid to a fluid approach everything that is not in the maxwellian is some extra non-fluid quantity okay it's some local entropy if you want it's related to the correction to the velocity distribution function so this perturbation are completely non-fluid non-mhd so you with a single parameter you can look at this parameter and as you can see epsilon is i close to the current sheet because epsilon includes like anisotropy it flux costosis all the moments of the velocity distribution function so locally the current sheet is not producing just anisotropy it's producing everything it's making your plasma very far from equilibrium local in a single spot yes absolutely no you will see this is really a good question no no not at all and this is the answer that you anticipated just the this slide because if you want to speak about eating i'm very conservative on this i never speak about eating or dissipation with vlaso vlaso and dissipation are two words that really disturb me because vlaso is an ideal model and really if you want to do it you have to have collisions dissipative mhd fine dissipative boltzmann fine dissipative vlaso not fine because it's ideal so we did very recently you did the boltzmann simulations where we solved the same equation and we added a collision operator what we see is that now really is unfortunate that close to the current sheet here there are spikes of this dissipation thing is now this is very blurred but from here you can see that in the current sheet you have high dissipation this is the demonstration that really dissipation is occurring that current sheets chroma kinetic world but you don't need to compute this complicated integral here that i didn't even expand it because it's too complex you just need to compute our epsilon here this epsilon is the modification to a maxwellian is i close is very high at the carnation so is this true in spacecraft missions probably it is this is our mms spacecraft which is flying through the bow shock and the bow shock is a lot of there is a lot of kinetic effects so here is maxwellian your plasma when you cross the bow shock it becomes really non maxwellian and my epsilon it has a large spike here this is my epsilon parameter so this epsilon is localized in space and why because now we go back we go back and forward between measurements and our simulations we are both now we are now in a in a regime where we can compare di directly with data we are flying our satellite through turbulence this is from simulations and this is what is happening there are regions where you starts to produce a beam here i was playing a little bit and then it looks like a mushroom then you have a beam then you have multiple beams while you fly through turbulence you have different distribution functions so at some point you can see if this is true looking at the spacecraft data so we took this magnetospheric multi-scale mission which has very high resolution velocity distribution functions and we fly we have recording we are recording one the data from magnetic field you see it's very turbulent there is compression and there is a lot of turbulence here but also in each point of that we have a cube of velocity distribution function which is like 64 cube resolution pretty much it's not bad it's a lot of data and this is how the distribution looks like in a in a real plasma this is data in one point the plasma is like it looks more like a distribution function looks like more like a vortex with multiple beams and something like you like is spinning you see this is a cut with two three beams multiple anisotropies there is an isotropy in the core and in the beam or something that we really don't understand fully yet what is happening this is in a single point and it's varying indeed now we are doing a movie finally a movie with the observations this is real data you can almost hear in the wind flowing through your probe and while it flows is measuring the velocity distribution function which has a lot of different you see there are regions where it becomes crazy with beams crescents like then it becomes more quiet then like then you have also pancake like distributions you have also like hazelnut distributions you have like what's the torus like distributions ring like you have a really a variety of structures in the velocity space is like your distribution function is free to evolve in this phase space steered by turbulence something really novel and then we thought okay we describe this velocity distribution function this is a new aspect of turbulence we don't have turbulence just in the physical space we have turbulence also in the velocity space so imagine about something about that to do that we went back to the 40s of course and there is a lot of giant literature on this most of this literature is on gyrokinetics people in gyrokinetics really love the ermite projection we thought to capture fluctuation in the velocity space we can use ermite and ermite basis we can decouple our distribution function by use a orthonormal projection with ermite basis it's similar to what we do in the physical space with Fourier ermite is my new Fourier okay and what we observed for the first time is that if you project your velocity distribution function with ermite modes you can again my m is like the wave numbers for for the is like my k vector in each point you can project your distribution function and measure the fluctuation in the velocity space and what we observed is that there is a power law mode zero is the density m equal one is the bulk flow m equal two is the temperature m equal three is related to the heat flux each m is related to the order in the closure of the fluid moment which is beautiful if you think about a tokamak plasma because people like have multi fluid models with a lot of moments in tokamaks for example if you want to do simulations and here is a real plasma and we are measuring the ermite spectrum and it has a nice power law here and we were very puzzled about this so since we I really love Kolmogorov we went back to the Boltzmann equation and make the three assumptions of Kolmogorov one about the transfer rate which is constant characteristic scales and some conservation laws that's what you need to do Kolmogorov three things you do this and you will obtain p two minus m three alps if is the electric field dominating or m two equal minus two it is really magnetized we we had this very qualitative prediction for the spectrum indeed this one m two minus three alps is the is the one we observe in the data in different regimes this m minus three alps and this is simulations from different groups that they obtained this either one or the other depending on the time scales you can flip to sort of like a Kolmogorov phenomenology so really the energy is flowing where are we staying now in research in this field the energy is flowing from large scales in the velocity space in the physical space to small scales in this new phase space it's a phase space cascade we imagine zero no m equals zero for how it's defined is everything is m equals zero it's not so there is no phase space turbulence for m hd okay that's really to make it's the and your epsilon is the integral of all these modes because epsilon it has the is by definition the integral of all this energy extra energy free energy okay is energy in the velocity space so this is my take-home message for the i think no i didn't finish i have time yet right yeah yes i have it so for the second part i have a we can say that magnetic recognition emerges local in turbulence and we started with m hd because it's really well behaves it gives a nice pattern and we can go to very high resolutions locally it is occurring we don't know how locally this is reconnection reconnecting sites are like stable they can disappear they can produce secondary tearing for example and it sometimes it appears if you have very high resolution some of this tearing produce high tearing like locally for a little bit they vanish you have to follow them with a camera and you can see that if they produce a secondary islands but then they get absorbed in this mess which is turbulence is very chaotic and we had to make contact with the reality with this virtual spacecraft because we want to use our simulations to understand real data so we fly through this through the simulation and we verified one simple thing is that for if you fly through turbulence you measure only gradients of the magnetic field that's what you can do from a single spacecraft if you have multiple spacecraft then you can do multiple like direction currents but from a single spacecraft close to the sun for example you can just measure gradients these gradients are broadly distributed like in the simulation the strongest one have all the nice properties of reconnection so probably reconnection are like magnetic discontinuities are reconnecting sites all of them probably some of them are more more strong some more than a more steady state some of them are like more flashy you know they disappear there with their small reconnection rate if you want to understand more then you have to go to the kinetic do the analysis with the kinetic simulation so you will see that you are not producing only shears of a magnetic field in turbulence but you are producing temperature anisotropy local to the current sheet with thanks to the blast of support from simulations and but moreover very recently we discovered that really you don't produce just an isotropy but your distribution function produce all the possible corrections in a sort of like cascade in this phase space so in this part that i anticipate a little bit the last part of since i have like 10 minutes i will anticipate the a little bit last part of my lectures where we will now uh we understood a little bit a little bit what is happening in turbulence by means of Eulerian simulations and Eulerian simulations are very good when you want to describe temperature or correction in the thermal region of your velocity distribution function so if your velocity distribution function and you take a cut here is something like this fine your your Maxwell Eulerian code can describe this and can describe all the fluctuation in this velocity space this is f of b but if you want to look at electrons and you want to look at the really want to drive your system very hard or you want to study your the same system probably more in a compact object for example or in a supernova eminence uh if you have high tails in the velocity distribution function then you will have your vdf will produce very very picked distribution here if your vdf will produce high tails if you accelerate particles and therefore if you want to study acceleration of particles the Eulerian simulations are not the best you want to do it with a Lagrangian way so we repeated the same experiments with the other technique we introduced this morning instead of doing Eulerian blast we repeated exactly the same with peak codes to see what happens to particles if they are accelerated where they are accelerated and and we did the look at diffusion and acceleration of particles in a turbulent regime that is like solar windish like solar wind like in the in the parameter setting of the solar wind but then there is another important property of the wind as we saw this morning the wind is flowing it is not going like free in your heliosphere it encounters objects like our plasma sphere right a magnetosphere so there are there are these obstacles and interaction with these obstacles produces shocks or when a supernova remnants explodes for example it has turbulence around so you see now one particular feature which is common to all of these systems is the interaction of turbulence with shocks that's the last the second part of this of this sequence of lectures that we will introduce we will the idea is to study shocks not only like the typical ranking jugoniot conditions but having a nice shock and shouting like turbulence against it like like sending a turbulent field against a shock with mhd and with especially with kinetic models that's a that was the motivating question why do we always study shocks with like nice mhd global codes but locally we see something strange what is happening when you study the interaction of a shock like the heliospheric boundary layer with the surrounding medium this actually this starts from a was very like inspired by a work by genitzank where he was drawing some cartoon of a shock interacting with little vortices that go against the shock what do they do to particles this work was mostly on diffusive spot particle acceleration is very very well known except uh till two years ago nobody did it with a self consistent kinetic code you have to build think about a strategy i have a shock and i want to send first i want to see the effect of a shock on particles as it as it stands alone okay i have a smooth shock it goes away it accelerates particles we know this with drifting acceleration or many mechanisms like can be uh many fermi like mechanisms then i send like one percent turbulence then i send 10 percent turbulence then i send 100 percent turbulence what's the difference when i do this experiments it's a uh a thought experiment you do it first but we did it with the kinetic physics i will observe the some analogies again then we establish analogies with the observation in the last part i will speak about something i'm working more actively now with like supernova remnants that explode interact with a shock and or the problem of a dynamo this is a actually even four years ago we were speaking about probability of generating magnetic field from shears i was a very puzzle to into the 2018 meeting here at the press previous school about possibilities of producing magnetic fields it was a nice talk by professor mahjong and by the reason there was another talk on produce new production on the role of shears on dynamo like problem what i was thinking about is what if we do the same experiment but with a collision less plasma imagine you we study turbulence with zero magnetic field and we initiate at this turbulent motion what happens in time with zero magnetic field if you do it with m h d if you don't have a seed you will never produce magnetic field there is a theorem you can see it from equations actually that if you don't have a seed of a magnetic field you never produce produce it this is very common to people that do laser plasma interactions they see production of a magnetic field when they they produce they send a beam of particles on a target they produce magnetic field in a collision less way we will do the same with by using turbulence and finally i produce i built up a group in my university of calabria where we match all of this that we were speaking about before with the compact compact objects we have simulations of black holes we will show you some at the last part some simulation of black holes dynamics collision of black holes first in vacuum and now we are adding like studying plasma physics when in the neighbors of the orange horizon event so okay okay in the in the vicinity of black holes we do local simulation of turbulence with highly relativistic plasmas so that will be pretty much the way we will abandon i think i have a few minutes i don't know if i can i can stop it here because 45 minutes yes yes question time thank you okay so um you can give me for asking these questions okay so i'm scared now my intention is that once you go past magnetic magnetic the concept of reconnection makes no sense it's it's a totally stupid concept okay because what is reconnecting in what fluid the moment you act sufficient for the city in the iron question all right b is no longer frozen in me what is frozen in b plus current you mean like about relativistic regimes and you go to the electron motion give it some velocity electron speed is not the fluid speed no not at all different from the current so either the current and the your physical quantity which is to be frozen in the in the fluid does not mean no okay or the fluid in which it's getting frozen has no redefined physical velocity so what the hell is reconnecting with what you're saying i got it i'm saying himself said this in last year of his years of his life that magnetic lines don't exist according to him no no no but that's a different this is the as matter of skates yes so the question is one should really eliminate reconnection into these things the language and use the energy exchange process oh sure you can write down yes all right yeah you can really talk about the things totally independent of the totally absurd concept of reconnection we did it but but the nice accident and this is i'm sorry now you to repeat this to you that that nice accident is that if you do this if you measure the transfer rate of energy is occurring nearby this current sheet that probably are connecting one yeah but then need to be moving with any physically relevant speed okay so that's the whole point here is what is really happening is that there are three or four forms of energy that suppose oh yeah yeah the thermal and connect right yes one can write a fully self-consistent system in three energy evolution okay this is fluid like but then reconnection according to me really introduces extremely strange concepts which can disguise you into the interpretation of data okay especially it's a topological it's a topological company that's the point you needn't have any change in topology and still have energy tests no no so for the whole point is that we have to go away from the language of pure energy because it makes no sense for that any time any time you have past particle any time you have the velocity period drop look at the mode of electricity to the lamp yeah but careful because with mhd you lose the main ingredient of that with that's the divergence of the electric field okay number of the facts which will make the concept of e-correction somewhat meaningless and imposing it on you know energy exchange is we understand yeah version of one form of energy we do understand and they can take place absolutely without any so-called change in topology topology of change can take place nobody is talking about it but it cannot be the dimensional notion of reconnection but you have seen so far that at the x-point you have x-point and there is happening a connection by definition you have seen that this is a topological constraint and creates local patterns where there is an energy production energy exchange now with your language this locally the reconnection is these are active regional of energy conversion no i can say that there is a local region yeah the tendency for the magnetic energy to be converted to to connect energy absolutely because that's what we have in the in the system there's a different region yeah yeah but i don't see contrast to what i don't see any contrast to what we have just seen right not to your results it's an interpretation okay see the the point is why bring reconnection and it has been a 70-year industry yes yes nobody understand anything about it so what you do is you take the msd notion then it's a very connected activity but the connections are destroying the entire reconnection process okay so the point is that why won't you move away from the language of interconnection it's uh it's semantic i do then don't you think it's semantic i don't mean no no no i mean this is this is very it's the point of my talk actually it's good that that may be that they should um oh yeah yeah yeah for sure that's that's another story yeah i think it's a nice profession for there's a question there and then you yeah it's uh they come together and as you can see this this region will squeeze and by definition you have to form a current layer which everything i spoke about was about current sheet okay this to keeping because in the first experiment we did we had resistivity it was mhd and here j is sufficiently large we have we have a strong ohm electric field okay e this which is dissipative is that there is a peak there and you can make all the street parker like that's a black box was actually like in plasma courses with field lines that came in flows that goes out there is a budget of energy indeed sweet parker which is the connecting the picture of sweet parker it's a conversion black box it's a conversion box it's a black box where magnetic field enters and goes out as backflows because particles are accelerated there is a flow of velocity here it's really a perfect conversion machine but you need eta j now the problem is that eta is zero in the universe in the in the in the physical in the in the solar wind but so your ohm's law becomes like of course you have to keep like u cross b this is the general ohm's law then plus the altar and then there is a magic term here there is one term that many people they overlooked the past years and that was bad that make the concept of reconnection obsolete and is the divergence of the pressure this is my favorite because it's like people that do fluids they forget about this don't do it because because this is the divergence of pressure here it can have a strong component you see parallel to the magnetic field that can really break field lines let's call it reconnect or really matching field lines or converting energy okay this tensor it's not isotropic not at all it is absurdly no that's a problem and then we have like all the terms like on the order of d e so the divergence of current there is a yes yes yes but this one we measure that emissions this is ready to do everything I said this morning and if you measure this is like my sort of like proportional to my epsilon because it's like it has an isotropic in I can really do that's the probably is the most the largest one in the magneto sheath and solid winch so this is a lot of effects for mhd only for mhd we went crazy on this point I anticipate you I know your question is the excellent question people will suspect that you see all the tearing more the tearing in linear phase we don't that part is completely eaten destroyed by turbulence because the characteristic time of the tail or of the tearing is on the order of nanolinear times so if you these vortices are shaking with a frequency which is higher than that characteristic time so that part is cancelled is useless I will say that although it's a exact it's a beautiful example I do in my courses again plasma I spend hours and hours to do the tearing because we need to do calculations but in that our numerical experiments is gone most of them are like in a crowd of reconnecting which is not steady state and the value of the reconnecting this reconnection rate is almost zero because they are too flashy they appear and disappear they are not steady state it's so low that you didn't see it in that plot I was selecting the strongest one for the strongest one that's all but why we are we interested in the strongest one because the strongest one has a very nice topology and this topology is important because we can identify in space data and we can see these structures here to be very active for particle acceleration then there is like 90 percent of like quiet unstable secondary silent reconnecting like mud okay okay oh that's another really that's really a an homogeneous pattern your a CME it's a very large scale or a cast on the sun it's a very large scale and homogeneity we are not describing that we are starting homogeneous turbulence that's a singular okay but people's there is a big question on this maybe not all of the times there are other effects like vortex productions locally that can trigger and break the field lines to me I mean it's a it's another problem it's like extreme events very large scale extreme singular events this is more I mean it's more present in homogeneous turbulence that's like extreme events yeah a connection of course three-dimensional then you have to go to the 3d reconnecting world where like you have kind of spines null points the connection that's a completely different topology than this so really I don't know what is happening there from the kinetic point of view but it will be interesting to see all right just those you know they do much more uh in the category of what I call the catastrophic okay oh I think so, yes. Perfect. Can you hear me well like this? Yes. Yes. Yes. Yes. And the pointer is. Professor Lina Adi from the portfolio technique. Not the professor, but he can just say that. From the portfolio technique and she will follow the technical problem there. These will be her. Yes. Thank you, Daniel. The pointer is not working or is it this one? Yes, it is. Okay, it works on. Oh, okay. Perfect. Okay. So thank you, Daniel, and thank you again, Professor Swades and Professor Daniel for this invitation. I'm very, very honored to be here. It's actually my first time to be to attend ICTP and also to give a kind of courses in school. So I'm very happy and I'm very honored. So for my courses or the talks, so I will be more speaking about in situ observations fields using fields and particles data in space plasma. And basically so from the title it's a bit different from what is actually on the schedule. So it's, I will describe you or present you some of the underlying processes that pray an important role actually in the solar wind magnetospheric coupling. And basically I will show you some examples using or some example of studies using space observations. And during the talks I will show you some results and these studies or results of course were done with huge collaborations with my colleagues and many, many collaborations. So, so I will be. So the course will be split into three parts. In the first part, I will just describe you how do we observe actually space plasma. Because, well, Sergio presented as well some solar wind observations, but how do we make actually these observations. In the second part, I will talk about an example of an underlying processes in the solar wind, which is turbulence, and well, Sergio presented or talked about turbulence more on the kinetics case, but I will talk more of the turbulence in the energy space or the large scale. And the last part, I will talk more about planetary ionosphere is actually focusing on Saturn's ionosphere, because it's a very particular one. It actually interacts with the rings of Saturn's as well so it's very different from Earth or other planetary on us here. Okay, so, and actually for so I will start now with the first part. How do we observe space plasma. And as you know, when they are in space or in the universe or if we take the solar wind. It covers a large range of parameters and wavelength and energies. So we cannot have. It's very difficult to build one instrument that will cover full range of frequencies, or full range of wavelength and that's why when we develop a spacecraft missions we need to put many different instruments. Sometimes these instruments they measure the same quantity so I will present you today, different kind of instruments that will be able to measure the electron number densities. And that's very important because we need to have independent measurements of the same quantity, but also we need to have complimentary measurements to cover the full range let's say of the frequencies. So for the first part, and please interrupt me when you have any questions. So as you all know the plasma, it makes up over 99% of the visible the visible matter of the universe. And here I just like actually to show you this very recent image taken by the James Webb Space Telescope, which the so called the pillars of the creation actually and this was measured using UV light. So you can see here, these are the columns of dust. There's also gas and there's also plasmas. So this is in the interstellar media, and closer to us in the solar system of course we have our star, the sun, and here, which emits continuously this non-collisional plasma which we call the solar wind. So what's the name of this monster? This one. It looks like a monster. This one, yes, three monsters. It's like actually it's like horses, I think is, or dinosaurs if you want. And actually this, the first image of this nebula was taken actually in the early 90s and 1995 by the father of the James Webb Space Telescope, which is Hubble Space Telescope. Well, I could have shown you the differences but you can see it online. So how do we observe, how do we make measurements of the plasma in space? So there are two kinds of measurements. You will hear, speaking of remote sensing measurements, and this is basically we make the measurements distantly, remotely, and these remote sensing techniques, it helps getting the general, basically the general and the global properties of the system or the object that we are measuring. And remote sensing instruments or measurements are extremely important because of course the interstellar medium so far we could, we cannot measure it in situ yet. So remote sensing instruments are very important and complementary to the second type of the measurements, which is the in situ measurements. Why do we call them in situ? For instance if we take the solar wind, we consider the solar wind as a perfect laboratory actually for studying collisionless plasma. And in laboratory we make in situ measurements actually. So that's why we call in situ measure we directly measure the properties of the plasma locally. So that's the equation of the spacecraft. And from the in situ measurement we can get much more detailed measurements or gets the plasma parameters, for instance the electric field, the magnetic field, and the electron number densities or the ion number densities, and so on, that we can use in the equations and so study the different processes that we are interested in. I won't have the time in one hour actually to speak about all kind of remote sensing measurements and all kind of in situ instruments, but I will present you a few examples of a remote sensing techniques, and also a few examples of a remote of in situ techniques or in situ instruments to do the measurements or the observations. Okay, so regarding the remote sensing observations. Of course, one of the most famous instruments are the imagers. So, the images are very important because well we can get the images of the objects that we want to study and here I really wanted to show you this example of an image of the Saturn, taken by the Cassini spacecraft and it's actually one of my favorite images taken by Cassini of Saturn. So Cassini was NASA mission. It was well built to explore Saturn's and its environment and its moons. It was launched in 1997, arrived to Saturn in 2004, and then ended a couple of years ago in 2017. This is a very nice image because each so this Saturn was image behind. So the sun is behind the plane and Saturn was in the ninth side and took this beautiful spectacular image of the planet. So you can see the planet, it's range around the planets. And also, you can note so here we are at the night side observing seconds, but you can see some lights in the northern hemisphere on the surface of the planet and this is actually the reflected lights from the rings onto the surface of the planet. So you can see here, as I said, the rings I will talk about a bit more the rings of Saturn tomorrow, but you can see this kind of bluish ring around the planet. This is actually the E ring. And the E ring is very particular because it's made of plasma and dust particles generated from one of the icy moons of Saturn, which is called Enceladus and you can see here dots. And this is actually the moon, and we discovered with Cassini that this moons ejects continuously charged dust and organic materials and water, and while it's orbiting around the planet it will form this kind of nice ring and we call it E ring because of the name and E ring for E. Okay, so I just, so this is I open a parenthesis I just want to show you so this is also another image taken by Cassini, one of the clearest image actually taken off Cassini of the moon. This is Enceladus. It's a nice moon and mostly water. And with Cassini. So this is also a set of images taken from Cassini and you can see here the water jet emitted from the southern pole of the moon. And in the southern pole actually it is characterized by this kind of structures, which is known as the tiger stripes, actually, and the water is emitted from these tiger styles, and how these moons actually were how these water plumes was actually discovered. It was discovered in situ using from the magnetic field data. Actually the first flyby of Enceladus was in 2005 and Cassini flew about 1000 kilometers above the moon. And from the magnetic field data and we this water plume was discovered accidentally, because in this plot here you see these first three panels are the three different components of the magnetic fields. And this is the last panel is the magnitude of the magnetic field. And you can see, at this specific time, there is a sharp gradient for change in the different components of the magnetic field. And it's like, I mean, different kind of variations that we observe if we cross a comet, a tail of a comet or Yes, this is real. Yeah. And here the team, I mean the, the, the Mac team at in 2005, they said, Okay, there is something going on around this moon, we really need to get closer to this one to really see what is going on why do we have this change in the magnetic field. And here they talked to the project scientists of the mission and it was kind of very difficult, I mean, we cannot change the orbits of the mission like this. And they decided, Okay, let's make few flybys closer flybys of this month and look closely what is going on. And here during the second flyby Cassini flew about 175 kilometers closer to the moon and they discovered these impressive, I mean, water jets emitted. And also, I mean, I'm not showing it here but they also discovered from the iron mass spectrometer I will talk about how do we do measurements from the iron mass spectrometer. They also observed the presence of organic molecules. They also observed heating or some heat around these tiger stripes. So basically they found the conditions to potential conditions to have life actually in this region. So there is heat, potential energy, there is organic molecules and there is water. And now there are future missions actually NASA mission called Europa Clipper mission maybe you have heard about it. It will be launched in 2004 and the aim of this mission Europa Clipper is to flyby. So there are other icy moons in the solar system, basically as well around Jupiter. So there is Europa is an icy moon and Europa Clipper it aims to make it's an orbiter around Europa to actually study these kinds of the ocean that lies underneath the surface of the moon. And also there is another European mission is called juice for Jupiter icy moons explorer and also it will, one of the main objectives of this mission is to study the habitability of the icy moons of Jupiter and also the coupling. And the coupling between Jupiter, the gas giants and its icy moons around. Is it true that most of the exoplanets that one is discussing, they have much more water than others? I mean, I've read something. Yes, I mean, I don't really know. Yeah, yeah, yeah. That's pretty amazing. And actually, after this discovery of Inceladus, there was also many other discoveries of icy moons in our solar system where there is a notion. And actually here, why do we observe this, I mean, this ocean is a salty ocean as well there is salt in this ocean. So it's very, yes, it's very impressive. And I have to think of what to do tonight. Yes. Yeah. Yeah. So actually and Cassini is maybe one of the first missions that aims to answer these grand questions in the universe are we alone in the universe or is there any life on other planets or other objects in the solar system. And this is, I mean, I will close this parenthesis talking about Inceladus and seconds but this is just to show you the images as one of the remote sensing techniques. Another remote sensing this technique is spectroscopy. And with spectroscopy as you know we will measure the spectrum of the electromagnetic radiations, while including the visible light infrared UV x-ray than for one. And then we can actually see the radiations from the stars or the objects that we are measuring. And from the spectrum, we can actually know the ion composition, the chemical composition, the temperature or the density. And I will show you here an example of measurements actually done in December 2012 by the Hubble Space Telescope, who image for the first time, this is the Europa, I see moons around Jupiter. The first three panels are Europa in the visible light, and the other patterns panels are Europa in the UV light. The second panel here is the hydrogen limon alpha line so, and the second, the last one is oxygen. And from these spectroscopical measurements, you could see that near the southern pole of Europa, there is also kind of the presence of emissions from the oxygen lines and the hydrogen lines. These were the first evidences of water also vapor emitted from these moons. And it was first discovered using this spectroscopy technique. And as I said, the Europa flipper mission will perform many flybys around this moon actually to see if actually these water plumes still exist or there's no water anymore ejected from the subsurface of the moon. Okay. Also, another way to another measurement set we do remotely is the magnetic field. We can also do magnetic field measurements remotely and this is based on the Zeeman effect. So, as you may know the Zeeman effect so is the effect by of the splitting of the spectral lines into several components, actually in the presence of magnetic fields. And it was first observed by the touch physicist Peter Zeeman in 1896 while doing experimentally laboratory experiments. And so this is here just well an illustration of the splitting of these spectral lines in different components. So if we don't have a magnetic field, we don't have any well shift in the energy we don't have any split but in the presence of magnetic field. We observe a broadening of the spectrum or if the magnetic field is very strong we observe a splitting in the spectral line. And here, why does it, I mean, here is kind of the formula that expresses the, well, the shifted frequency as a function of the unshifted frequency, plus and minus a term that depends on the magnetic fields. And here Mu is what we call the Bohr magnet on which basically the magnetic moment of the electrons, which is caused by the spin or the orbital angular momentum. And yeah so since it depends on the magnetic field from these kind of measurements we can know the magnitude of the magnetic field but also the orientation of the magnetic field. So this is here an example actually of an image of a sun squat. In black you see the sunspot and the sunspots are regions on the sun, which are characterized by very strong magnetic field. Why it's black because the temperature of the sunspot is much lower than the rest of the surface of the sun and but it's still very high temperature. And if we take if we measure the spectral line along this line here that crosses the sunspot but other region around the sunspot. And if we look at the spectrum, you see that in this region that lies just inside the sunspots, we clearly see a broadening of the spectrum, and here very clear splitting different spectral lines. And that's because of the presence of this magnetic field. However, above this region and below we still have a magnetic field but the magnitude is much less. And we only observe just the broadening of the magnetic field. Now, from this kind of measurements. And actually that's how we can measure the magnetic field of other stars for instance for our exoplanets. Because we cannot measure them, we cannot go there yet and measure them in situ with magnetometers. Anomalous. Okay. Ah, yes. Okay. Yeah, yeah, yeah, also with the anomalous even effect we can observe. Yeah. Okay, I don't want to answer something wrong. But I'm sure that. Yeah, we can observe this as well with the anomalous effect. But how I mean what's the difference exactly about in the observations. They are not really. Above and below the splitting level. It just comes to my mind. Yes. Yeah. Okay, and then also I said we can know the magnitude of the magnetic field we can measure but also we can also get an idea about the polarization of the light and this depends on the orientation of the magnetic field with respect to the line of sight. If the magnetic field is perpendicular to the line of sight then the polarization of the light is linear. And if it's magnetic field is along the line of sight then the correlation will be circular. Okay, so now I will move to the in situ kind of observations. And here I will also talk about different kind of instruments. And before I do that. I just want to say that as you all know, plasma physics is a very special field or particular field because it, it couples different fields in physics, electromagnetism fluid mechanics and statistical physics. And to be able to really study plasma physics, we really need to be able to measure all these quantities the electric fields, the magnetic fields, also the particles moments, and the velocities, the position as well and the densities and so on, and the charge density and that's why we need to have in situ measurements they are necessary to be able to to to measure all these quantities and then use them in the equations and compare or to apply the theory actually that we know in the observations. The first instrument I would like to talk about is the linear probe. Now, the linear probe it helps. Well, it aims. It makes actually active measurements in the plasma by perturbing the plasma. So I was first invited in the 90s in the 1920 by even Langmuir that you see here, and to measure actually the electron plasma densities and the electron temperature and very cold low density laboratory plasma. And then eight years later the term plasma actually was kind of coined to describe this partially ionized gas. And I think as far as I know plasma it comes from a Greek word which I mean it doesn't. It has nothing to do with the blood but is is. Yes, it's more like a gelat like gelatine kind of. Yes, yes. So that's then why they use this word plasma. And then only actually in the beginning of the 50s where the Langmuir pros were said to be mounted on board lock rockets and satellites to measure the electron and the ion density is in the ionosphere offers but also in space, but how does it work. So here I'm showing you an example of this is Langmuir probe. It's a spherical probe, you can see here the probe diameter is about five centimeter. And this Langmuir probe was mounted on the Cassini spacecraft you see here this is an illustration. And I don't know if you can see but in this circle you see that the probes. are mounted on the spacecraft and we it's always mounted on a boom also we wanted to be away from the spacecraft. So it's not affected by any kind of interferences from the spacecraft. Actually the principle of working off the landing probe is pretty easy the landing probe will measure the total current as a function of the bias voltage that we apply to it if we apply a positive voltage. So the landing probe will collect the negative current so the election current. And if we apply negative voltage, then the landing probe will collect the iron current the positive charge current. And the characteristic characteristic curve actually, which we call the current voltage curve, we can get to the properties of the plasma the electron density is the iron mass the electron temperature and so on. So here here is represent the total current collected by the Langmuir pro by sweeping along different values of the voltage so from negative to positive values. So this is the total current as I said is a contribution of the electron current which increases as you can see here for the positive values of the potential, and also a contribution from the iron current, which is mainly dominant for the negative part of the potential. Yes. Yes. Yes. And Spherical. Approximately a constant cross section. So how does the cylindrical. Also we. Yes. No, I mean also for the spherical probe we have a constant cross section of and of the probe. And the angle from the side. But in the sphere, actually it becomes the radius. Yes. So, I just meant to ask, can we use the same to use for normal improvement if you use some extra approximation for this. Well, I'm not sure I understand really the question, but I think. Yeah, but we can I can discuss this later on. Yeah, and actually and also so we can demonstrate that the electron current it actually depends on the electron number density here a is the surface area off of the probe the spherical probe that we know, and also on the electron temperature is an exponential function actually as a function of the bias potential and what we call the floating potential, what is the floating potential the floating potential is where the potential of the probe it balances the potential of the ambient plasma. And this also the floating potential, we can see it in the measurements I will show you that. And then also the iron current also is as a function of parameters that we can measure or we can make assumption on them and so we know the different parameters inside for the iron current. I will show you this was just an illustration qualitative. illustration of what is the total current look like measured by from the language probe. I don't know it's very clear but this in this figure these are real measurements from the Cassini language probe, the first panel so it's the current. And all of them as a function of the bias potential negative values and positive values here. These are the current here in linear space the second panel is in logarithmic escape. So it's basically the same thing but it's in logarithmic escape. The last part here is the derivative of the current versus the bias potential it's interesting to do this because this will allow us to observe any kind of variations in the current if we do the derivative. So we focus on the iron current. So the iron current is given by this red curve here. How can we estimate for instance the iron densities and the iron mass from this iron current. So what we do well simply we can fit this line. Well, the iron current before that we can reduce its form as a linear function. So we have it depends on the bias potential be here is the slope of the line and plus M which is the intercept at the current access here. So this iron current from the slope of this line. We know be this be and be depends on the surface area, the iron charge, the iron number densities. Here is the just the charge of the electrons over the drift iron velocity and the iron mass. Then the intercept here is equal as well also depend on the surface area, the iron charge the iron number densities and the drift velocity. Now knowing the intercept, knowing the surface area of the probe, assuming a value, there's always assumptions, assuming the value of the drift velocity, we can estimate the iron velocity, the iron density, sorry. So from this estimation of the iron density, if we plug it into the slope value here, we can also get an estimate on the iron mass. And also, now I didn't talk about the electron parameters, but from this exponential increase here, and assuming in a Maxwellian distribution for the electrons, we can estimate the electron temperature and also the electron number densities. But in the beginning that it's very important to have. Well, usually we always have different kind of instruments that will make the same kind of measurements. So the lengthy probe will give us an estimation of the iron number densities of the electron number densities based on some assumptions that we do. But then we have other instruments such as iron analyzers or electron analyzers that we also give estimates of the electron number densities and the iron number density. And by comparing both observations, we can cross calibrate the instrument and we can actually validate the observations from the lengthy probe. So here just to, I mean, from this derivative of the iron versus the voltage, we can also know the value of the floating potential because afterwards this current saturates actually. So that was for the lengthy probe instruments and how we can identify or infer the iron number densities and other parameters. Now I would like to talk about iron mass spectrometers. The iron mass spectrometers are spectrometers that will basically and mainly give us the iron composition in the environment where we are making well the measurements. But how does this instrument work, how can we know the iron composition if we are measuring oxygen helium plus or aluminum or iron, basically by measuring the mass per charge ratio. And in addition to the mass per charge ratio, this instrument it give us the information related to the direction of the ions we know exactly the direction of the ions that we are measuring measuring and the energy of the science. Now to show you an example of an iron mass spectrometer. So once you hear the iron mass spectrometer on board the Bepi-Colombo mission, which I mean this instrument is called MSA for mass spectrum analyzer. So just few words about the Bepi-Colombo mission so this mission is a joint project between the European Space Agency ESA and the Japanese Space Agency JAXA and it aims to study in details I will come back to that to this late in the end of the talk today. So we need to study in details using two probes, two orbiters, the mercaries as a planet but also the magnetosphere, the environment around Mercury. And there is so one magnetospheric orbiter this is the Japanese contribution and a planetary orbiter which is the European contribution and the MSA the mass spectrum analyzer is on board the magnetospheric orbiter. So this is the instrument. So it's quite big actually is like 40 centimeters per 20 centimeters, and is mounted so this is the magnetospheric orbiter. And is mounted on one of the edges of this kind of octagon, actually. And here you see actually, I will detail this later on, but it consists mainly where we do the met where the instrument collects the measurements of two parts. The first part is this one here, which is an electrostatic analyzer. And the second part is the time of flight chamber so it's a cylindrical trem chamber in which the master charge will be identified. And here the black region here are actually so this is not empty it's filled by different windows there are 32 windows actually from which the positively charged ions will enter and will be collected. Yeah, so this is just another image of the same instrument mounted so on the magnetospheric orbiter but covered by ceramics to protect it from the heat from the sun. And also, the windows here are protected by what MLI what you call multi layer insulation, also to protect them from the heat. Yes, they will basically measure the energy per charge. Yes. I will, I will just talk about this. But before this is just an illustration here again. So this is mercury. This is just a view from beside of the magnetospheric orbiter. And this is the instrument here, and these are the different windows or different sectors, they are 32. And so, and each sector is about 11.25 degrees. So 32 times this value we have 3030 360 degrees so we cover all the space so we can measure the ions coming from the different regions around the space brown. So how does this instrument works. This is an illustration of of the instrument, and you can see the instrument from the inside actually. So the first part is the electrostatic analyzer. And then the second part, as I said, is what we call a time of light chamber. So what happens is that we apply actually varying potential here on this sphere from about minus 2.2 volts up to minus five, six kilo volts. And this will to measure actually the positively charged ions with different energies. So with this instrument, we can detect the ions from about few electron volt up to 40 KV. So the incident ions will, if we take an example of here, one window so the incident ions will enter through these different windows, they will enter the electrostatic analyzer with a specific energy per charge. It's actually why do you know why it is spherical. It's actually we one of the reasons we make it spherical like this. Yes. Yes, but also because we need. I mean it can enter just directly. It's the detector below in the bottom, but we wanted to have a spherical shape because we want. If they are photons actually that enters from the windows they will hit the different walls, and only the ions with the specific energy per charge will continue its path down to the detector below. So that's one of the reasons why the electrostatic analyzer, we have it like a spherical shape like this. So all the other like photons or other ions that enter if they don't have the correct energy they will just hit the wall and they will not be able to continue the path. At the exit of this electrostatic analyzer so the first plus it just to select the ions for specific energy per charge. At the exit here, we have an acceleration actually a potential that will accelerate the ions to words a carbon foil. So this is an image what is actually inside this region. So, for each window, there is a kind of square here, and inside the square there is a carbon foil, and the ions will hit this carbon foil. And after hitting this carbon point they will enter the time of flight chamber and that's where the time of flight of the ions will be measured and so we can estimate the mass per charge of the ions. Now when the positively charged ions hit this carbon foil, they will interact with this carbon foil. So the positively charged ions, they will either lose an electron, and they will be positively charged inside this time of flight chamber, or they will leave an electron, or so they will leave as negatively charged, or they will leave as a nutrients inside this time of flight chamber. And actually the particularity of this time of flight chamber is that you see here there are some different walls like different like cylinders actually. And we apply actually a quadratic distribution of the potential along these walls, and this will give a linear electric field. And this role of this linear electric field is very important. Because what will happen is that the positively charged ions will be reflected, they will feel this electric field and they will be accelerated upward and detected here. The negatively charged ions after they interact with the carbon foil, they will be accelerated downwards. And the neutrals, while they will not feel this electric field and they will be detected well they will go what you say straight through and also will be detected in the bottom. What we call micro channel plates. Now how we calculate the time of flight. So once the ions actually enters the time of flight chamber, there is our secondary electrons emitted. And these secondary electrons will be detected in this part of the instrument here and this will create a start pulse or start signal. And then once the ions will be detected upward in these mcps or in the bottom mcps then we have a stop signals. And from the coincidences between each start and stop we can calculate the time of flight. So it's a very complex actually how to say to to really measure the time of light of inside the time of flight chamber, but it works actually very well. Now how from the time of light, we estimate the mass per charge nanoseconds. It's really really quick so we so we can sweep the full range of energies within nanoseconds as well. So, so everything is really like. There are, there are other kinds of mass spectrometers that have magnetic field and magnetometer inside. That's the bending. Yes, but for this instrument we don't have any. So, and the ions are passing to the problem for it, so irrespective of what they become like charge negative or negative, they will always have an electron. Yes, yes, always. And that's how. If this is similar to how we say for every interaction with the carbon foil there's a secondary electron which is in the case. Okay, so how do we estimate the mass per charge is, I'm spending maybe a time on this because it's very important because when I was a student well, I wasn't when I was wondering actually how can we get the iron composition how can we measure the election densities. And I think it's very important to really understand how the instruments work because the instrument does not measure the iron composition like this or that doesn't measure just the election densities or the election temperature. And actually, it's, it's complex but the same time the physics behind is very easy. Let's talk about the particles that are detected in this bottom detector that we call the straight through. So these ions are either the neutral or the negatively charged iron. So these ions, they will enter with an energy is zero. And as I said, they will be accelerated here by potential. So in addition to this is zero, we have as well an electric potential force potential that we can add to it. And this will be equal to the kinetic energy of the ions or the neutrals inside the time of light chamber. So if we just write to this formula, if we divide by q, we get then the relation directly.