4月3日 Theory of mirror instability in high beta plasma 

报告题目：Theory of mirror instability in high beta plasma

报告时间：4月3日（星期四）上午9:00-12:00

报告地点：EAST控制大厅三楼会议室

报告人：Prof. Dr. Evgeny Alexandrovich Kuznetsov,

Academician of the Russian Academy of Sciences；Head of Mathematical Physics Laboratory, P.N. Lebedev Physical Institute of RAS.

主持人：刘海庆

报告人简介：

Academician E.A. Kuznetsov, a distinguished theoretical physicist, has notably influenced the progression of nonlinear physics. He specializes in the domain of nonlinear phenomena in physics and its practical applications. His ownership of several foundational achievements in plasma theory, hydrophysics, nonlinear optics, mathematical physics, and optical telecommunications has altered the comprehension of nonlinear dynamics and nonlinear coherent wave phenomena within plasma, gases, liquids, and solids.

PS: The Lebedev Physical Institute (LPI) of the Russian Academy of Sciences stands as the largest and most venerable research center in Russia. The endeavors of LPI personnel have significantly contributed to nearly every facet of contemporary physics. The LPI justifiably takes pride in the accomplishments of its Nobel laureate scientists, including I.E. Tamm, P.A. Cherenkov, I.M. Frank, N.G. Basov, A.M. Prokhorov, A.D. Sakharov, and V.L. Ginzburg.

报告摘要：

Mirror instability is an important microscopic instability in plasma physics and space physics, mainly occurring in anisotropic plasma, especially when the plasma is subjected to perpendicular pressure p⊥ larger than the parallel one p||. This instability can lead to magnetic field perturbation, forming mirror modes, which are regions of local magnetic field  enhancement and weakening, thereby  affecting the plasma confinement and dynamic behavior.

The mirror instability is commonly observed in planetary magneto sheaths close to the magnetopause, as well as in the solar wind. In magnetic confinement fusion devices, such as tokamaks, magnetic mirror devices, high-energy particles (such as alpha particles) may cause mirror instability, degrading the plasma confinement, and may trigger other instabilities (such as Alfven waves).

The mirror instability is a kinetic instability first predicted by Vedenov and Sagdeev in 1957. It has later on been extensively studied both analytically and numerically. As shown by Hasegawa the linear instability is arrested at large k by finite ion Larmor radius (FLR) effects.

In this presentation, we review a weakly nonlinear theory of the mirror instability [1, 2]. We discuss a theoretical approach based on a mixed hydrodynamic-kinetic description for the weakly nonlinear regime expected to establish near threshold. In this regime, the unstable modes have wavevectors almost perpendicular to the ambient magnetic field B0 (kz/k⊥ < 1) with k⊥ρi < 1, where ρi is the ion Larmor radius, so that the perturbations can be described using a long-wavelength asymptotic. The latter allows one to apply the drift kinetic equation to estimate the main nonlinear effects that correspond to a local shift of the instability threshold. All the other nonlinearities, associated for example with ion inertia, are relatively small. As a result, we obtain an asymptotic equation for the parallel magnetic field fluctuation, that displays a quadratic nonlinearity. It is worth noting that this model can also be derived directly from Vlasov- Maxwell equations by means of a multi-scale expansion method. Next, we analyze within this asymptotic model the nonlinear dynamics of mirror modes, assuming that the mean ion distribution function is bi-Maxwellian. The resulting asymptotic equation belongs to the generalized gradient type with a free energy or a Lyapunov functional, so that the system evolves to reach minima of the Lyapunov functional.

[1] E.A. Kuznetsov, T. Passot and P.L. Sulem, Dynamic model for nonlinear mirror modes near threshold, PRL, 98, 235003 (2007).

[2] E.A. Kuznetsov, T. Passot, V.P. Ruban and P.L. Sulem, Variational approach for static mirror structures, Phys. Plasmas, 22, 042114 (2015).