 presentation. Okay, dear colleagues, this talk will be combined, will be mixed of two presentations. Okay, because one of the speakers was unable to come here, so I try to explain in details what all the work is about and it will be better to see a general picture of this phenomenon called ejecta. So, and before we begin, we can see what the term ejecta means. And so first it was found in shock compression experiments, so when the target with micrometo sized grooves was shocked there was found that ejecta particles, so in experiments it was seen that the particles appear near the free surface and so they were rather small and these particles and the phenomena was called ejecta, but the underlying physics were not understood at these times. But later it was found that this groove from these grooves appear spikes or jets which propagate with very big velocities from the free surface and involve material around them into the flow. And at the late stages these jets developed and experienced fragmentation into particles which are seen in the experiments. In the last decade, the theory of ejecta phenomena was based on the, became based on the Rakhmai Mishkov instability and why it is so, it is, it was considered as a special case of Rakhmai Mishkov instability in solids. For this particular case, the density of medium A is much bigger than density for medium B, so that the outward number is approximately minus one. And the researchers begin to use spike bubble terminology for the ejecta process and these jets are called spikes and there appear bubbles, so which is similar to the original Rakhmai Mishkov instability in liquid soil gases. But another special case for the Rakhmai Mishkov instability in ejecta is that interface grooves are micrometer sized and these spikes are very fast, they move with velocities of several kilometers per second. And in this talk I would like to answer several questions about how, what experimental techniques developed to measure ejecta properties and how to recover ejecta properties using optical measurements and what supporting information may be obtained with simulation for the ejecta phenomena. And first we begin with experiments. So initially, the first experiments were developed to measure the ejecta mass distribution. To obtain that distribution, James Cesse developed the following technique. So he used a sample with grooves which provides ejecta on the shock loading and the thin foil of, for example, aluminum or other materials which velocity were measured with interferometer. And so he obtained, when the ejecta heats the thin foil, it begins to accelerate and by gathering more and more ejecta, it accelerates more. And the velocity change is seen with the interferometer and provided the picture like that. So using simple equations from the velocity, from the acceleration of thin foil, we can recalculate it to the mass distribution as it arrives to this thin foil. But for some experiments, it was, a thin foil is very, so it can be distracted by the ejecta so that another technique was also developed by James Cesse later with the thick plate. So when ejecta heats this plate, the wave propagates to the free surface and also measured by interferometer. There appear more complex wave profile but it also can be recalculated to the mass distribution of ejecta. So it was first experiments which give the researchers the mass distribution for ejecta. And now it has done quite better with newer techniques. For example, piezo probes are used to measure the ejecta which gathered there. And also we can calibrate X-ray data to measure the density of ejecta cloud directly and there are results presented on these graphs. We can see that the piezo diagnostics and X-ray diagnostics provide very close mass distribution profiles. Next interesting property of ejecta is its velocity. To measure velocity in experiment, the photon or laser Doppler velocimetry is used. And there I show two experimental setups which first I call idealized because there are very precise grooves and the ejecta ejection is made into vacuum. So the obtained time velocity profiles with photon Doppler velocimetry can easily resolve the velocities of spikes or the top of the jets and the velocity of bubbles between jets. But more realistic experiments which are made by Föderhoff and Koleksen-Vniev. So first they use samples with imperfect grooves. So they are quite randomly distributed across the surface. And ejection is made into air. So first we can see that ejecta cloud has distribution in velocities and it is decelerated by the air so that at the late stages the ejected particles can be overtaken by the free surface. And to interpret these results our colleagues developed theory which will be discussed later. So another experimental setup is developed to measure fragment size distribution in a very precise way. So the technique is called ultraviolet holography. And in these experiments, authors Sorensen and his colleagues obtained a picture like that. So here we can see the dark dots which are ejected particles. And near to the free surface we can see that how the planar jet is distracted during the jets propagation. From these pictures they construct size distributions for the particles and the size distribution presented here. And the average diameter for these particles is about four, five micrometers. Another setup for the fragment size distribution measurement developed by another group of researchers and the setup is following. In the center of sample, there are periodic grooves. And after shock propagation the ejecta cloud appears and laser, so incident laser wave splits by the different angles according to me theory. And with the angle of scattered waves, so they can measure also the size distribution for particles. Both setups provide very close particle sizes, but these techniques are not useful for measuring ejecta in complex setup. So I mean air and surface with imperfect grooves. And to cope with that, the optical model is developed by our colleagues. So they started with the idea of understanding PDV in more detailed way. So they consider ejecta cloud as a set of particles and an incident wave scattered, experienced multiple scattering in this ejecta cloud. And the reflected wave consists of this reference wave and the sum of reflected waves and the interference of different waves. The resultant picture is, looks like that. And they ask, is it possible to extract fragment size distribution from that measurements? And to do that, they develop, first they develop ejecta cloud model. So they introduce some parameters of ejecta cloud. It's mass velocity distribution, which already discussed with experiments, transport optical thickness, transport scattering coefficient, which is connected closely to mass velocity distribution. And the relation between them are shown on this slide. So they use also some function to fit the experimental data for mass distribution. And they also use me theory to estimate transport optical thickness and recalculate these known parameters to transport scattering coefficient. After that, they use transport equation for intensity to calculate the scattered wave through the parameters of the ejecta cloud, which they introduce here. So they fit the parameters of their ejecta cloud model to describe this wave, this wave. And of course, it is rather difficult equation and they use some simplifications. And so, but at this slide, there are some results they achieve with their model. First is the influence of absorption. So if absorption is rather high in comparison to scattering, they find that the velocities which have, so omega s is the velocity of the free surface here. And so the particles with lower velocities for which lower frequencies correspond. With the high absorption, these small velocities cannot be, are not introduced in the scattered wave. So we cannot describe them with, if the ejecta cloud has very high absorption. And another is the optical thickness. So if the optical thickness is rather high, we cannot see the free surface position, free surface velocity behind the ejecta cloud. And they also provide two data recovery options from ejecta cloud. First is with the known size distribution and the PDV results, they can obtain mass distribution for the jet by fitting parameters for scattered waves. And another option is using also PDV image and mass distribution. They can reconstruct fragment size distribution. And this is what is done by more difficult experiments. So the first option is size to mass distribution is already obtained. So they take for example a window at the given time here by frequencies. And these are shown in details here on this picture, the wave distribution at different times. So they fit their model parameters to describe this field distribution. And so they recovered parameters for transport coefficient are given here. So we can see that at first earlier times ejected particles have bigger velocities. And with time, their velocities decreased. And the mass gathered near to the free surface. So which corresponds to the experimental data. So we can see even from this picture that particle velocities are decelerated. And the next option, so to use mass distribution for calculation of size distribution with that model, they asked us to provide this mass distribution from simulation. And so next I'll show how we do that. And at first we simulated experiments which I talked about earlier and said that it's idealized setup. So we use two methods for calculation. It's smooth particle hydrodynamics and molecular dynamics which are meshless and will correspond this problem. So for this particular test we obtained good agreement between experimental and calculated velocities. The problem for molecular dynamics is that on very rather small sizes which are close, which are about 100 nanometers, we can see that at the end of the jet a piece, a drop due to surface tension effects which slows the velocity of jet by moving towards free surface. So it can be seen on this picture that molecular dynamics velocities are smaller than smooth particle. So but in general the picture is quite similar for both methods of simulation. And using these methods we also try to construct mass distribution along the ejector cloud. But we can see from there that mass distribution along the jet has, at the end of the jet, there is a rim increase of mass at the tip of the spike. But if we consider experiments there is no rim. And so to demonstrate what the problem is that we try to simulate a surface which has not precise perturbation amplitude but it is, there is some randomness in the perturbation amplitude of grooves. And here is, I'm sorry, here is simulation of that surface which have randomness in grooves and we are clearly seen now that some jets have bigger velocities, some have smaller velocities. And to construct the mass, to realistic mass distribution, we have to account not a single jet but the ensemble of jets which appeared from different grooves. But this simulation is quite big and quite complex to provide for any kind of surface. So we develop a more simple approach. So we do, for example, three simulations at the different angles of groove, opening angles of groove. And first we have found that spike velocity grows linearly with the angle of groove. And next we obtain mass distributions for these jets and apply analytical fit for them. So after that we obtain the parameters for these analytical approximations and interpolate them between these angles. Next, so with that fit and parameters we can obtain any mass distribution for any jet in the, between the boundary angles. And when we apply for this ensemble of jets averaging using normal distribution, for example, we obtain that mass profile which already do not have rim at the end of the jet. And it looks closer to the experimental one. And so we came to conclusion. In this work the ejecta and its parameters I discussed the ejecta and the how to obtain its parameters I discussed in details. But we demonstrated that for some setup, I mean the complex setup when the surface has randomness in grooves and there is an error where the ejecta is moving. So for that the optical model developed to obtain mass distribution or particle size distribution directly from PDV diagnostics. And also using molecular dynamics and smooth particle hydrodynamics we demonstrated that jet velocities and mass distributions are obtained very close to experimental ones. And combining two methods together we can obtain particle size distribution of ejecta cloud using PDV measurements and simulations. But in simulations we have also introduced an approach of how to how to simulate realistic mass distribution for this surface which have randomness in grooves. And these results will be further used for the optical model to find particle size distribution. So thank you for your attention. Different lens because so there is some randomness in grooves so you can see that there is a smaller amplitude of groove and there is higher. So from that groove the spike moves with bigger velocity than from that groove and that is the reason. Yes there exist experiments which can measure temperature of ejecta cloud but we do not consider them here. But one experiment I know that it exists where they with infrared cameras they measure ejecta cloud temperature.