Presentation on theme: "Geometric Gyrokinetic Theory 几何回旋动力论 Hong Qin 秦宏 Princeton Plasma Physics Laboratory, Princeton University Workshop on ITER Simulation May 15-19, 2006,"— Presentation transcript:
Geometric Gyrokinetic Theory 几何回旋动力论 Hong Qin 秦宏 Princeton Plasma Physics Laboratory, Princeton University Workshop on ITER Simulation May 15-19, 2006, Peking University, Beijing, China http://www.pppl.gov/~hongqin/Gyrokinetics.php
Acknowledgement Thank Prof. Ronald C. Davidson and Dr. Janardhan Manickam for their continuous support. Thank Drs. Peter J. Catto, Bruce I. Cohen, Andris Dimits, Alex Friedman, Gregory W. Hammet, W. Wei-li Lee, Lynda L. Lodestro, Thomas D. Rognlien, Philip B. Snyderfor, and William M. Tang for fruitful discussions. US DOE contract AC02-76CH03073. LLNL’s LDRD Project 04-SI-03, Kinetic Simulation of Boundary Plasma Turbulent Transport.
Classical gyrokinetics: average out gyrophase Magnetized plasmas fast gyromotion. “Average-out" the fast gyromotion –Theoretically appealing –Algorithmically efficient Highly oscillatory characteristics Does not work
Modern gyrokinetics: all about gyro-symmetry Gyro-symmetry Decouple gyromotion
What is symmetry? Coordinate dependent version: Geometric version: Lie derivative Symmetry vector field Poincare-Cartan-Einstein 1-form Symmetry group S. Lie (1890s) Disadvantage: it takes longer to explain. Symmetry is group
What is Poincare-Cartan-Einstein 1-form? On the 7D phase space
What is the phase space? 7D spacetime inverse of metric World-line
Symmetry is invaraint Noether’s Theorem (1918) Cartan’s formula
What is gyrosymmetry? Noether’s Theorem Gyrophase coordinate Amatucci, Pop 11, 2097 (2004).
Dynamics under Lie group of coordinate transformation Pullback Cartan’s formula Insignificant No need for Poisson bracket Taylor expansion
Gyrokinetic Poisson equation Polarization density
Physics of pullback transformation — polarization density
Conclusions Gyrokinetic theory is about gyro-symmetry. Decouple the gyro-phase, not "averaging out". Pullback transformation is indispensable. http://www.pppl.gov/~hongqin/Gyrokinetics.php Decouple. Not average. Pullback