 But it's my pleasure to introduce our first speaker, Dr. Asano from Osaka University who will be speaking about inter-facial magneto-hydrodynamic disabilities and laser plasmas. Please. Thank you. Good morning. I'm Takayoshi Asano from Osaka University. First, I'd like to thank the organizer for inviting me to the conference. And today, I'll talk about the inter-facial instability, especially this my mescal fin instability, including the effect of magnetic field. So the method, our method are energy simulations and laser experiment. So here is our collaborators for the theory side and the experimental side. The laser experiment is a collaboration with the French group. For the laser experiment, we use GECO laser in Osaka University. So this is basically the open facility. So anybody here can apply the proposal to use this facility. OK, so this is the outline of this talk. And first, I'll talk about the background of my research, why RMI, why magnetic field. And then I'll talk about the three effects of the magnetic field on the inter-facial instability. One is the separation of the instability by strong magnetic field. And the second one is the field amplification by turbulent motion. And the last one is the effect of the anisotropic thermal conductivity. So the background. So the RMI driven turbulence plays an important role in various plasma phenomena. One example is the astrophysical plasma. So astrophysical plasma is basically magnetized. And the interaction between the supernova shock and the inhomogeneous inter-facial medium, that is quite similar situation to this my mescal fin instability. And which can give an origin of the inter-facial turbulence. And also it could help the amplification of magnetic field of the inter-facial field. So another example is the inertial confinement fusion. So for the implosion process, the mediation of the mixing by inter-facial instability is quite crucial problem. So and also for control the implosion and the inclusion of the external magnetic field is seriously discussed now. So now it is very important to understand the least my mescal fin instability or inter-facial instability with magnetic field. So and also it is good timing for the magnetized laser plasma because the generation of kilo tesla, the strong field, magnetic field has been achieved by high power lasers. So the strong magnetic field is now available in laser experiment. So I listed here the several methods to generate the strong field actually done by using Gecko laser. And one example is a capacitor cord. So for this capacitor cord, the about kilo tesla or the magnetic field are generated for nanosecond time scale. So kilo tesla is about three order of magnitude larger than the permanent magnet. So now this kind of strong field is available in laser experiment. So in terms of the least my mescal fin instability, there are many beautiful results of the room temperature experiment like this. But instead the laser experiment can treat the high energy density plasma. The advantage of that is it could generate the high Mach number shock. And also it's a plasma flow so that we can examine the effect of the magnetic field. And for the laser plasma least my mescal fin instability, there are two kinds. One is the so-called up relative RM type instability and another is a classical type of RMI. So in this talk, I'll just focus on the classical type of least my mescal fin instability of the heavy to light configuration. And the key ingredient of the least my mescal fin instability is a shock wave and the corrugated contact discontinuity. So this is the minimum setup of the least my mescal fin instability. It's called the single mode analysis. When the incident shock hits the corrugated contact discontinuity, we can see the growth of the mushroom shape spike in density distribution. The driving engine of the instability is a ball testy deposited at the corrugated interface. This figure shows the images around the new contact discontinuity just after the interaction. So when the incident shock hits the corrugated interface, the reflected shock and transmitted shock start to travel from the interface. If the interface is corrugated, then the shock surface is also rippled. So because of the overriddenness of the shock, the tangential flow is generated by reflection motion at the overridden shock interface here. So that generates the tangential flow. And this is the origin of the ball testy at the interface and that drives the instability. So then the linear growth velocity is strongly coupled with this tangential velocity. So this is the characteristic of the instability. The least my mescal fin instability is linear growth with time, not exponential. And it occurs without gravity and it's unstable for both light to heavy or heavy to light configuration. So any kind of, any size of the other number could be unstable for the least my mescal instability. So there are some formula predicting the linear growth rate, a growth velocity of the instability. So in this talk, we adopt the Bolchak and Nishihara formula that is given by this equation. The first term is derived from the tangential velocity. And the second term is becomes important when the shock Mach number is very large. So this term includes the effect of the sound wave propagation in between the interface and shock surface. So compared with the simple formula, so like this, so those are typically given by the art of number and also the interface velocity. The Bolchak model gives a lower velocity compared to the simple model because of the compressive effect. So we use this formula in this analysis. So there are three important effects of magnetic field on the instability that is shown by the simulation and the experiment. The first one is the separation of the least my mescal instability growth by a strong magnetic field. And the second one is the amplification of magnetic field by turbulent motion. The third one is the energy confinement due to the anisotropic thermal conduction. So I'll talk about these three effects in this talk. Okay, so first one is the suppression of least my mescal instability. This is studied by many authors and I studied this by energy simulations. So this is the basic equation for the simulation. That is the standard ideal energy equation. And for the energy scheme, I use Goddard-style grid-based scheme with an approximate energy limit solver to capture the strong shock. So initial setup for RMI is characterized just by four parameters. So this is a single model analysis in 2D and which has four non-dimensional parameters. Those are Mach number of the incident shock and density jam and correlation amplitude at the interface. And the last one is magnetic field strength, which is given by plasma beta. So least my mescal growth can be reduced if the magnetic field is larger than the critical value. So this figure shows the energy simulation result. So the left one is unstable and the right one is stabilized by magnetic field. So in many cases, the energy phenomenon, the plasma beta gives a criterion. Then how about this case? Actually the unstable case is the initial beta is unity and the stable case is 10. So which means relatively stronger field is unstable for this specific case. So it seems not so simple. And actually the critical strength depends on the Mach number of the incident shock. So this figure shows the boundary between unstable model and stabilized model in the initial parameter space of Mach number and field strength. So the boundary is depending on the Mach number. So then what determines the critical value? So it turns out the key process is the extraction of the ball test from the interface. For the hydro case, the ball test deposited at the interface stays there and drives the instability. So during the growth of the least my mescal instability, the ball test is always associated with the contact surface for hydro case. However, so if the magnetic field exists, the ball test travels away from the interface by our fan wave. They cannot stay here, there. So this is a snapshot of the density distribution and the ball test distribution. So ball test sheet blue one here is not associated with the contact surface for this case. And also instead it associated with the kink of the feed line. So this ball test sheet is moving away from the interface with our fan wave. So for this model, we could not see any growth of the least my mescal instability. So we can say the stability criterion should be determined by the competition between the arm fan wave for the extraction of the ball test sheet and growth velocity. So to see this, we define the arm fan number or arm fan mach number for least my mescal instability, which is defined by the ratio between the growth velocity to the arm fan velocity. So here for the growth velocity, we use a ball jack model here. So this number is determined by the initial condition. So I plotted the nonlinear outcome of the energy simulation and as a function of this arm fan mach number, actually the inverse of the arm fan mach number, which is proportional to the b here. So then we can see the clear critical value for this number. It's about 10 for our fan number. So if magnetic field is larger than this boundary, the blue one is always suppressed by magnetic field. But the red one is unstable. We can see the unstable growth in the simulation. The interesting part is this boundary number 10 is independent of mach number and density ratio and the perturbation amplitude and also the field direction. So it looks very robust criteria. So this is an energy simulation result. And the same result, same conclusion can be obtained by the cantibiotic seat model, the seat model. So for this model, Matsuoka talked about this, yes this. So I don't touch in detail here, but in this model, it models said the arm fan number is key quantity to distinguish the unstable growth and stable oscillation as a surface arm fan wave. So this condition determines the nonlinear phase of the Li-Mai-Mesh-Coinitability in magnetic field. So the critical field strength for the separation in laser plasma is estimated as about 10 Th. So using this critical value, we can calculate the critical B where we assume the solid density 1 gram per c and the growth velocity for a few kilometers per second. This is the typical size. So that gives 10 Th. So 10 Th is now available in laser experiments. So this critical formula will be test experimentally in the future. So that will be very interesting topics. So this was the suppression. So let's move on to the second part. That is the amplification of magnetic field by turbulent motion. For this topic, first I will talk about the simulation result and then introduce the laser experiment to this motivation. So theoretically, so this is the simulation. So the ambient magnetic field can be amplified dramatically by Li-Mai-Mesh-Coinitability. This is the snapshot of the non-linear phase of the Li-Mai-Mesh-Coinitability for density here and field strength and field lines here. So in the field strength distribution, you can see the localized filamentary structure and strong magnetic field region. And the amplification factor is more than 100. So this instability amplifies the magnetic field very efficiently. So amplification is caused by the stretching term in induction equation. So this panel shows the time evolution of the maximum field strength in the computation domain. So this is a growing phase. And the growth rate here is identical to the stretching rate of the interface. So that shows the stretching is key process for the amplification of magnetic field in this situation. And field amplification is independent of the initial field direction. So this figure shows the time evolution of the maximum field strength for three different initial field direction cases. So the magnetic initial field is parallel to the interface and perpendicular to the interface. And the last one is the oblique case. For three cases, we can see the efficient amplification in the simulation. And also we found that the saturation level of magnetic field is independent of any parameters such as Mach number, density jump, and fluctuation amplitude. So then what determines the final size of the magnetic field? So the maximum magnetic field strength is limited by actually growth velocity of least my mesh principality. This figure shows the time evolution of the maximum magnetic field strength is the same one, but now it's normalized by the turbulent kinetic energy. So the upper limit of this figure is about unity. So which means the saturation level of the field strength is of the order of turbulent kinetic energy. Again, this result is consistent with the current vortex sheet model. So energy simulation and current vortex sheet model gives the same result for the saturation amplitude. So magnetic field amplification can be seen in also 3D. So I put the 3D perturbation, the simple model, just cosine times cosine here, then see the nonlinear evolution of the least my mesh principality. So this is a 3D picture of the density isocontour here. And this is the magnetic energy distribution. And this figure shows the time history of the maximum magnetic field in the simulation in 2D and 3D cases. So the solid line is a 3D and dotted lines are 2D cases. And simply speaking, for the 3D case, it is also amplified. The magnetic field is amplified by the unstable motion. And I haven't done many simulation for 3D, but for this particular case, the 3D gives a larger amplification factor compared to the 2D case. That would be because this kind of small structure can be seen in 3D. That's enhanced the stretching rate. So that would be the origin of this difference just by factor 3D of something. OK, so this is the theory part. Then to confirm this phenomena, we just started the laser experiment by using GECO laser. But it is still preliminary, so I just show the kinds of status of our attempt. So classical RMI experiment using the high power lasers has been carried out by many groups. So they are used in low power lasers, omega lasers, and Nike lasers. And most of the cases, the boundary contact surface are made between the metal and foam or CH and foam. And they usually use X-ray diagnostics to see the evolution of the perturbation. So compared to those experiments, our trial is like this. So I use the boundary between the CH and gas, so the large density jump case. And we include magnetic field as a seed field. And also we use the optical measurement like this to see the longer time evolution. So this is the setup of our experiment. So here is the target. So the interface is made by the corrugated CH target here and ambient N2 gas of 5 tau. So then the density jump is huge. It's 10 to the minus 5. And the perturbation, so the wavelength is about 150 micron. And the amplitude is about 7.5 micron, so the ratio is about 5% of the wavelength. So this is our interface. So then we add the magnetic field here by using the permanent magnet. So the size is just 0.2 tesla at the target. So this is too weak to affect the dynamics. So the motivation of this experiment is to see the amplification. So we just start very weak seed field. So then we let it, the laser here. So the shockwave is generated by direct drive. Direct laser drive here. So you use the gate core laser, and the perturbation is about 2.5. And at the beginning the shockwave formed inside of the CH, and it propagates toward the rear side. And it hit the rear side, it generates or excites the Ristma-Meshqvins-Ridi. So before the RMI experiment, we estimate the shock transmitted shock velocity and interface velocity by using a flat target. This is optical radiography. So by using the flat target, we can see the transmitted shock front and contact surface here. So then we can estimate or calculate, measure the velocity of these surfaces. And this graph shows the velocity as a function of the intensity of the laser. So we just use the power or heat, then it gives the power index is 0.56 to the intensity. I use this for the estimation of the growth velocity later. So the evolution of the Ristma-Meshqvins-Ridi observed successfully by optical measurement. So this is a snapshot taken before the laser shot. So here is the target. And this line corresponds to the 5500 micron. And our fluctuation amplitude is about 10 microns. So we couldn't resolve that, but here is the modulated surface. And after the 60 nanoseconds later, so then we can see the finger-like structure, which is caused by the Ristma-Meshqvins-Ridi or the Ristma-Ridi tear instability growth. So the wavelength is exactly the same as the initial perturbation wavelength. And the amplitude is now more than 100 microns, so which means initially it's just 10 microns. The amplification factor is huge. The gecko experiment used heavy to light configuration. So the phase reversal at the very beginning was observed the past gecko experiment with the same target configuration. So in our case, we couldn't observe, but the phase should be changed at the beginning. So then growth velocity of the surface fluctuation can be evaluated as a snapshot of the fingers. So we measured the length of the finger as a function of time and derived the growth velocity. This is the result of the growth velocity, which is ranging from 2 km to 6 km in our experiment. And then compare with the numerical models, the Bojac-Nishihara model, assuming the density jump is 10 to the minus 5 and Mach number is 5, then they give this formula as a growth velocity. So it requires interface velocity here. So I put this, put here with the experimentally observed interface velocity as a function of the intensity, and then we can have the growth velocity of this model. So this soil line is the Bojac-Nishihara's prediction, and red circles are our experimental data. So obviously the experimental data has much larger growth velocity than this model. Which is because the Rayleigh-Taylor growth. I roughly calculated, estimated the growth rate of the growth time scale of the Rayleigh-Taylor instability in this situation. It's about 10 nanoseconds. So the contamination of the Rayleigh-Taylor instability must be considered to this analysis. So there are the future works. So this experiment is motivated to the amplification of magnetic field. So the most important measurement should be the magnetic field size of the magnetic field. But so far we couldn't succeed the measurement of the amplified magnetic field. So this would be the most important future work. And also we have to consider both the Rayleigh-Taylor and the Ritz-Meier-Meshkopf effect in this analysis. So the last one, this is the last view graph. The last one is the anisotropic thermal conduction. So this is the result of the gecko experiment. It is published already. So I just say the only important conclusion, the anisotropic thermal conduction affects the flow dynamics even when the plasma beta is large. That is an important result of this paper. This is the summary of this talk. We are investigating the MHD evolution of Ritz-Meier-Meshkopf instability by using the simulations and the Rayleigh experiments. And there are three interesting features of MHD-RMI. And one is the strong magnetic field can reduce the growth of the instability. And there, the AFL number is very important. And the second one is the turbulent motion by the instability can amplify a magnetic field. And the last one is the anisotropic thermal conduction can affect the hydrodynamic flow even when the plasma beta is much larger than unity. That is, thank you very much.