# Vortices in hot plasma, not in real space, but in phase-space.

by maxime.lesur
Tags: nonlinear, plasma, real, simulation, space, turbulence, vortex, vortices
 P: 8 Let me give you a glimpse at my research. I uploaded a video of my latest simulation on youtube, https://www.youtube.com/watch?v=tUfvYgXxRwY. You can see the formation and evolution of vortices in hot plasma such as fusion plasma. The subtlety is that these vortices do not live in the real, everyday-life 3D space, but in an imaginary, mathematical 6D space. They do impact 3D space though. To be more precise, this video shows the nonlinear growth, evolution and interaction of self-coherent phase-space structures in a numerical simulation of ion-acoustic turbulence (actually 1D with periodic boundary conditions, or 2D in phase-space). The turbulence grows in contradiction with linear theory, which predicts that all waves are stable in this system. In other words, this is a subcritical instability. Up-left and up-center: perturbed distribution function of ions and electrons. Bottom-left: spatially-averaged velocity distribution. Bottom-center, spatially-averaged perturbed velocity distribution. Bottom-right: electric field spectrum. Top-right: time-evolution of the field energy, with an horizontal line to indicate the instant of each frame. During this simulation, several vortices form spontaneously and interact with each others. This process is associated with a significant redistribution of the electrons, anomalous resistivity and turbulent heating. Please ask me any question or clarification. It's a very good exercise for me explain my research to laypeople.
 P: 787 What is the source of free energy here? Did you use a realistic value for m_i/m_e? I'm wondering since the lower left plot shows the initial width of the electron distribution to be only slightly bigger than the width of the ion distribution, suggesting T_e << T_i. You show the electron distribution flattening out... or is it just getting much hotter? The wings of the electron distribution are cut off by the graph. Do they go out a lot farther?
P: 8
 Quote by Khashishi What is the source of free energy here? Did you use a realistic value for m_i/m_e? I'm wondering since the lower left plot shows the initial width of the electron distribution to be only slightly bigger than the width of the ion distribution, suggesting T_e << T_i. You show the electron distribution flattening out... or is it just getting much hotter? The wings of the electron distribution are cut off by the graph. Do they go out a lot farther?
Thank you for your interest. You guessed correctly, that the mass ratio is unrealistic, m_i/m_e = 4. I use this value for pedagogical reasons, because the evolution of structures becomes much clearer than for m_i/m_e = 1836. However, I get similar results for m_i/m_e = 1836, except that the effects of vortices on the ion distribution are negligible. I will try to produce a video for real mass ratio. Here T_e = T_i. In the wings that are cut off, the redistribution is negligible.

The source of free energy is the initial velocity drift. The electron distribution is flattening out indeed, you could say that it's getting hotter but since the distribution becomes strongly non-Gaussian, the temperature doesn't make much sense. It's less confusing to say that the mean thermal energy is increasing. Actually, the mean thermal energy is doubling due to the phase-space activity.

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