Download presentation

Presentation is loading. Please wait.

Published byKatharine Doherty Modified over 2 years ago

1
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

2
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.

3
Classical gyrokinetics: average out gyrophase Magnetized plasmas fast gyromotion. “Average-out" the fast gyromotion –Theoretically appealing –Algorithmically efficient Highly oscillatory characteristics Does not work

4
Modern gyrokinetics: all about gyro-symmetry Gyro-symmetry Decouple gyromotion

5
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

6
What is Poincare-Cartan-Einstein 1-form? On the 7D phase space

7
What is the phase space? 7D spacetime inverse of metric World-line

8
Symmetry is invaraint Noether’s Theorem (1918) Cartan’s formula

9
What is gyrosymmetry? Noether’s Theorem Gyrophase coordinate Amatucci, Pop 11, 2097 (2004).

10
Dynamics under Lie group of coordinate transformation Pullback Cartan’s formula Insignificant No need for Poisson bracket Taylor expansion

11
Lie perturbations Gyrocenter gauges

12
Perturbation techniques — quest of good coordinates Peanuts by Charles Schulz. Reprint permitted by UFS, Inc.

14
+ Freedoom Gyro-center gauges

15
Gyrocenter dynamics

16
Gyrocenter dynamics Banos drift Curvature drift Effective potentials

17
Gyrokinetic equations

18
Pullback of distribution function Particle distribution Gyrocenter distribution

19
Physics of pullback transformation — Spitzer paradox

20
Finally, gyrokinetic equations Gyrokinetic Maxwell’s equations

21
Gyrokinetic Poisson equation Polarization density

22
Physics of pullback transformation — polarization density

23
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

24
Gyrokinetic Poisson equation

25
1-form, 2-form, 3-form and all that … XX Inner product Pullback Push forward Vector field Any tensor Contra-variant base

26
Vector field and flow Lie symmetry group Phase Space Lie algebra is the Infinitesimal generator of Lie group

27
Lie perturbations Gyrocenter gauges Time dependent Pedestal dynamics Large Er shearing Orbit squeezing Micro turbulence ELM

28
Leading order gyrocenter coordinates Lab phase space coords Time-dependent Background EXB drift

31
Curvature drfit

32
Pullback of distribution function Needed for Maxwell’q eqs. Definition of pullback

Similar presentations

OK

Syed Ali Raza Supervisor: Dr. Pervez Hoodbhoy. A brief Overview of Quantum Hall Effect Spinning Disk Spinning Disk with magnetic Field Kubo’s Formula.

Syed Ali Raza Supervisor: Dr. Pervez Hoodbhoy. A brief Overview of Quantum Hall Effect Spinning Disk Spinning Disk with magnetic Field Kubo’s Formula.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google