Physics 777 Plasma Physics and Magnetohydrodynamics MHD Instructor

Physics 777 Plasma Physics and Magnetohydrodynamics (MHD) Instructor: Gregory Fleishman Lecture 8. Weak Turbulence and Magnetic Reconnection 21 October 2008

Plan of the Lecture • MHD turbulence, general ideas and approaches • Plasma Nonlinearity and Wave-Wave Interactions • Spectral Description of the Turbulence; Random Phase Approximation, • Magnetic Reconnection in the Plasma

Section 1. MHD turbulence, general ideas and approaches What is the turbulence? (V 2/L) / (n. V/L 2) • Reynolds number: Re=VL/n =- + V 2/L n. V/L 2 • When Re << Recritical, flow = laminar When Re >> Recritical, flow = turbulent l b Credit: J. Cho

Example: wake behind a sphere critical Re = 40~50 Re~15, 000 Credit: J. Cho

Example: cylinder in water nwater ~ 0. 01 (cgs) If v=10 cm/sec & D=1 cm, Re~1000. ==> turbulence! Credit: J. Cho

Interstellar gas Orion nebula Astrophysical fluids are turbulent and magnetized Credit: J. Cho (Re > 1010)

Spectra: Cho & Vishniac (2000) |B| B 0 See also Muller & Biskamp (2000); Maron & Goldreich (2001) Credit: J. Cho

Anisotropy B Credit: J. M. Stone Smaller eddies are more elongated ÞRelation between parallel size an perp size? Þ Critically balanced turbulence l|| ~l^2/3 Credit: J. Cho

Section 2. Plasma Nonlinearity and Wave-Wave Interactions Credit: E. Kontar

Section 3. Spectral Description of the Turbulence • • • Structural functions of the turbulence Spectral description Random phase approximation Statistically uniform turbulence Isotropic and anisotropic turbulence

Section 4. Magnetic Reconnection in the Plasma

Section 7. Homework • See the web page