 Okay. Okay. Thank you very much. My presentation topic is effects of heat flux vector and go see on wave dissipation and instability in rotating anatropic plasmas as particular focus maybe for its application, maybe for solar corona. This is a portion of my publishing work. Maybe it is one section. The basic, basically the purpose of this topic was to deal on that of the instability. But here I am presenting some portion that is the application section for that one. Okay. A plasma is it is as you all know that plasma is it is a full set of matter, which is a quasi-neutral. Almost all of the observable matter in the universe is in a plasma state, which is around maybe 99%. It can be found naturally and it can be found also in the laboratory. Naturally, plasma is found at the core of the stars. Okay. Maybe we can suppose that here we have also like let's say solar corona, lightning discharges and solar winds and aurora burials. And we have a lot of stuff here. So my focus is on the solar corona. Solar corona, it has this kind of things. Let's say where there is wave dissipation is one of the mechanism that is solar corona that is heating. That dissipation means it is an order of motion of the waves are converted into this ordered motion of particles. And as you see here, there are loops, okay, there are corona loops. And this corona loops, it has also a filament and it is filled by a plasma. It's filled by a plasma. And when this one is filled by plasma and just it brushes out and like by forming a recognition and it can eject into internal medium. But as you see here, the corona, I mean, it has different kind of, it is the interior part and it's exterior part at the core of the corona. There is a hydrogen fusion reaction. And this produces some kind of let's say it just transformed from four hydrogen combined together and they form helium and the rest of the mass is converted into light. And that light is radiated that can pass through radiation, through the radiation zone. And then it goes to that of convective zone, that is by convection. And here, as you see the temperature is now it's increasing at the corona. Okay, this is corona basically, it is very here, tipped up. And here, there is a corona filament. And here you have a single corona loop, you can have this length L. And there's also that is some parameters. Several authors studied the solar corona heating mechanisms. That's Haluq, Haluq, et al. And also Ofman also just uses some kind of studies for the investigating the mechanisms of the corona heating. It's generally believed that the heating of the solar corona is coded by waves. It's okay, it's just waves originated in the photosphere and propagating into the corona where their energy is dissipated. The medium through which this wave propagates is in the general permitted by magnetic field complicating the behavior of the propagating waves. And this wave dissipates due to the supposed t rotation and the heat flux corrections. This one is let's say, it is set of equations for this set of equations. Here I use the momentum equation for let's say here we have a stress tensor and we have also a magnetic force and we have here some viscosity factors and we have also here is rotation for my purpose. For this only for this section, we will ignore the genus effects. And this one is a continuity equation. And here we have the induction equation. So this one is this the stress tensor pressure have linearized like this. The linearization of this pressure tensor can be calculated. Okay, I will show you this one later. So here the magnetic field has some kind of perturbation along that of the z direction. The divergence of perturbed viscosity also we just after some kind of like linearization by using Fourier space, we have the along the x-axis and along the y-axis and along the z-axis that is the Braggensky viscosity for let's say this is for compressional terms because there is full compressional I mean full coefficients of Braggensky. But here we use only the compressional parts one. And this is the induction equation. We can work this one like this. You can generate this one like this the induction equation and this one also that was the pressure tensor. It can be computed like this one. And this one is the closed set of equations which describe is the heat conducting plasmas. It can be written as Wang. And when we linearize this equation, let's say equation 12 up to the equation 15, we have the heat flux profiles. The heat flux profiles can be described by let's say for a parallel heat flux. We have this kind of expression and for a perpendicular heat flux we have this kind of these expressions. And similarly when you work for a parallel profile for a pressure profile, the pressure profile can be computed from the above set of heat flux equations. We have the parallel pressure and we have the perpendicular pressure how this kind this forms. Okay where this one is those are the coefficients those are the terms that are here and these are the data and alpha beta and this one are given here. On substituting the spatial and the time derivative of the above expressions into that of the momentum equations or that of set of equations and finally we can work that of the matrix in the matrix form one can write those set of equations into that of the equation of motion and what you can put finally in the matrix form and that's is equal to zero and we will obtain the dispersion relation of this one. Okay so having this dispersion relation we can analyze for different cases let's say for for a parallel and for perpendicular and for different kind of rotation like parallel to the magnetic field the axis is parallel to the magnetic field and the axis also perpendicular to the magnetic field. So here the above dispersion relation that is equation 20 represents the modified form of the dispersion relation that is of equation 14 of Ferrerae. Due to the presence of the heat flux corrections and plasma viscosity the reduced of the above dispersion relation in various limiting cases for example if we ignore that of the viscosity coefficients we exactly get the equation 20 of I mean that of Ram Prasid Prajapati's form and finally when we just work for the we did this for various kind of cases to investigate that of this and the stability for different cases but here I just took only the one section of my work that is just maybe to work on that of the solar corona because I was motivated from the work of Ofman Ital in 1998 he just he did this kind of approach for investigating the dissipations and like other waves. So since the effect of rotation in solar corona is significant to discuss the angular rotation in energetic solar wind PNM Charmital therefore the present dispersion relation may give rise to new dimensions for setting the combined effect of rotation heat flux and viscosity on the waves and the stability in the solar corona at hitting mechanisms or hitting problems. It's evident that the MHD wave plays a significant role in the transporting of energy and also momentum in astrophysical systems. For typical corona loops which is plasma beta P that's less than one percent corona loops are smaller than the gravitational scale heat and hence the effect of gravitational order of the genus effect you can remove the genus term to apply my set of more real equations for solar corona application. We have treats that is for smaller that is for a smaller scale and this one the genus term may be ignored and we have let's say for axis of rotation parallel to the magnetic field here I only took two cases of the dispersion relation that is the parallel and the perpendicular one one of the limitation of this kind of this kind of technique is it is it does give you a clear information for maybe for oblique propagation and other things that's for the let's say for that rotation parallel to magnetic fields that is omega x is zero so then that is the rotation axis is let's say maybe about that z so the dispersion relation equation 20 can be reduced this form okay I will use finally this one by then dimension analyzing this term and also for the case of that is parallel propagation case and for let's say rotation about x axis at zero and we have this expression and we ignore maybe that's the genus term finally so when we treats the out of the transversal propagation of that is equation this one okay equation this when we ignore the this genus term when we ignore this genus term for our case here that is the study of fast magnetic waves in solar corona loops is motivated by initial conditions given by ofman that's of my time that is 1998 taking the following parameters for magnetic field number density that is plasma density and also mass density and that is a fiven wave and that is a scale a and considering the plasma beta parameter that is a perpendicular that 0.04 for that estimating condition that is equation 23 can be written as this form that is so for for fast waves that is described by this expression and for fast wave and we consider that the initial conditions for velocity of that let's say vex that is we consider these things okay you consider these things and where that is this is the expression for that is tau it can be calculated from the result of dispersion relation for transverse mode with rotating perpendicular to the magnetic field and we obtain a result for perturbed magnetic fields that is with this scale and we have also the velocity along the x axis and we have also compute the alfieven waves alfieven waves for this condition is so here the effect of rotation on the solar corona parameters versus the alfieven time scales are set it let's say represents the density fluctuation and we have that's where velocities and you find also alfieven speeds let's say for omega alfieven speed that's omega for a zero that is black curve and you have that's a blue curve for the omega parameter just changes 0.5 and 1.5 and 4 that is the time t that is two times of the alfieven time the fluctuation in solar corona parameters get significantly increased due to an increase in the corona rotation the fluctuation gate disappears for that is 0.6 it is the fluctuation gate it appears after that is 0.6 and here showing the time scale for solar corona heating in its active regions the alfieven speed carries energy from the sun and it carries into outward and cascades from the large wavelength to shorter one and further shorter wavelength dissipates by heating solar corona and launching solar winds into the interstellar medium and this one the other one the alfieven speed that we calculate is it is maybe it's around which is 1250 kilometer per second in this time that is for time 1.6 this is a good result that we showed from another works which is done by which is this is a simulation result using the value of t equals two second for values of this and magnetic field this one and this density and the scale lengths and plasma magnetic field and plasma density respectively into the ideal that makes it equations of that is adaptive refined magnetic dynamics solver model that is used by this outer that is a wiper it tell as the alfieven speed has the value of it's around 1250 kilometer per second so as you see here in this results the alfieven speed that we how that we estimate is it is just around that is 1500 1250 kilometer per second so that for the slow mode wave now let's see for the case of for slow mode waves for slow mode waves I try to investigate or some kind let's say for like the heat flux effect the viscosity and rotation effect is that is for the slow mode which is just for a parallel propagation case for these conditions providing that this is the slow mode waves we have the this one for slow mode wave that is the acoustic speed it is yeah it is smaller than that of the magnetic one and here we have visited is it is a initial that is v0 sine of omega t minus kz where v0 is the amplitude and k is the wave number so that the density is it is given by this expression and using the fact that the linear oscillation oscillation is for visit is this v0 sine of pi that's z over l and that cosine of omega not t as exponential of this we can find that of from non-dimensionalizing okay by non-dimensionalizing of this equation okay by non-dimensionalizing of this equation we can compute by using some parameters we can compute the that is we can see that the effects of them is the viscosity scales that is let's say the effect of viscosity on the solar corona parameters versus alphaband timescales are studied and this figure eight represents the density fluctuation and b represents the velocity and shows the magnetic fluctuation and the alphaband the speed and for us for the constant parameters that is for a heat flux that is the non-dimensional form of that zeta and for that is omega at rotscher a that is this parameter the slow mode wave dissipates with due to the unincreasing the viscous parameters on the other hand the fast mode wave the alphaband wave gets increases with increasing the coronal rotation an application of the present world can be uh discussed in the solar convective zone of differential motion in the presence of plasma viscosity coronal rotation and pressure another entropy uh the convective zone uh at the high latitude its lags behind that of the uh the core and uh at the low latitude it is uh vice versa and this gives or this status a turbulence that is stress nature it serves as high viscous medium okay and this is uh the upper panel showed that is the alphaband uh alphaband speeds versus that of the uh that is that is uh scale of that is x over a that is um and here by varying the viscosity terms we saw that for slow mode and for fast mode okay for slow mode and for fast mode it is for slow mode and this one is also for fast mode by that's for different rotation parameters and for different that of uh discussed parameters and by using uh the magnetic field and uh that is uh this is an plasma density and we have also the temperature t and we have the scale a and magnetic field beta parameters for parallel perpendicular here the curve showed that due to the increase in the viscosity parameters there is a decrease in the slow mode waves in the bottom panel the sharp velocity gradient is observed for uh large rotation that is uh this one is there is large rotation so there is a sharp peak okay that is in the bottom panel the sharp velocity gradient is observed for a large rotation parameters and for uh alphaband time is much much less than that of uh uh colligional times that is uh for fast mode wave yeah already i'm complex yeah for fast mode wave alphaband wave increases with increasing the rotation parameters the fast mode are completely damped after uh 0.6 the effect of rotation parameter becomes negligible and to investigate the effect of viscosity and heat flux parameters on the solar condition is the normalized dispersion relation this one can be uh using this one to that of the uh dispersion relation for uh the case of uh parallel uh propagation uh we have uh the results that is uh the this is the non-dimensional form of uh that is uh a collisionless heat conducting and rotating anisotropic plasma and for plasma parameters chosen to be magnetic field that is chosen to be uh tangles and this is the number density and temperature and we have the magnetic field uh plasma beta parameters and this is the normalized wave phase speeds versus the normalized wave number the phase velocity decreases due to uh due to uh not only the increase in the wave number along the magnetic field but also due to the increase in the viscosity parameters uh here it's dividend that for slow mode wave determined as ratio that is acoustic to that of the magnetic uh uh ratio for the slow mode waves it's acoustic speed is much larger than that of the magnetic speed and for fast mode wave the magnetic speed is it's much greater than the sound speeds from the curve it is clear that the phase speed decreases rapidly for smaller value of the wave number and it becomes stable for large value of the wave numbers due to the an increase in the heat flux parameters the phase speeds increase while it decreases due to the increase in viscosity parameters okay thank you very much okay let me answer for a number one okay yeah uh from my from my discussion uh from my previous i mean from the my beginning of my discussion uh i explained for you that uh we ignore the genus effects okay i mean that is the self-graphed channel effects which which which one this one this is equation 23 it is uh it's correct it's correct but you see i ignore i ignore this grab channel term for the case of application of solar corona okay yeah i told you from the beginning from the beginning of my presentation uh i thought i just told you that the paper is it is fully deals on the instabilities it is this is one section okay the last section of my uh paper okay so i ignore i ignore for my application purpose i ignore the genus effect and i try to work only for that is for small scale okay so thank you again