Electromagnetic nonlinear gyrokinetics with polarization drift
Abstract
A set of new nonlinear electromagnetic gyrokinetic Vlasov equation with polarization drift and gyrokinetic Maxwell equations is systematically derived by using the Lietransform perturbation method in toroidal geometry. For the first time, we recover the driftkinetic expression for parallel acceleration [R. M. Kulsrud, in Basic Plasma Physics, edited by A. A. Galeev and R. N. Sudan (NorthHolland, Amsterdam, 1983)] from the nonlinear gyrokinetic equations, thereby bridging a gap between the two formulations. This formalism should be useful in addressing nonlinear ion Compton scattering of intermediatemodenumber toroidal Alfvén eigenmodes for which the polarization current nonlinearity [T. S. Hahm and L. Chen, Phys. Rev. Lett. 74, 266 (1995)] and the usual finite Larmor radius effects should compete.
 Authors:
 SNU Division of Graduate Education for Sustainabilization of Foundation Energy, Seoul National University, Gwanakro 1, Gwanakgu, 151744 Seoul (Korea, Republic of)
 Department of Nuclear Engineering, Seoul National University, Gwanakro 1, Gwanakgu, 151744 Seoul (Korea, Republic of)
 College of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074 (China)
 Publication Date:
 OSTI Identifier:
 22303765
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physics of Plasmas; Journal Volume: 21; Journal Issue: 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ACCELERATION; BOLTZMANNVLASOV EQUATION; COMPTON EFFECT; CURRENTS; LARMOR RADIUS; MAXWELL EQUATIONS; NONLINEAR PROBLEMS; PERTURBATION THEORY; PLASMA; POLARIZATION
Citation Formats
Duthoit, F.X., Hahm, T. S., Email: tshahm@snu.ac.kr, and Wang, Lu. Electromagnetic nonlinear gyrokinetics with polarization drift. United States: N. p., 2014.
Web. doi:10.1063/1.4891435.
Duthoit, F.X., Hahm, T. S., Email: tshahm@snu.ac.kr, & Wang, Lu. Electromagnetic nonlinear gyrokinetics with polarization drift. United States. doi:10.1063/1.4891435.
Duthoit, F.X., Hahm, T. S., Email: tshahm@snu.ac.kr, and Wang, Lu. 2014.
"Electromagnetic nonlinear gyrokinetics with polarization drift". United States.
doi:10.1063/1.4891435.
@article{osti_22303765,
title = {Electromagnetic nonlinear gyrokinetics with polarization drift},
author = {Duthoit, F.X. and Hahm, T. S., Email: tshahm@snu.ac.kr and Wang, Lu},
abstractNote = {A set of new nonlinear electromagnetic gyrokinetic Vlasov equation with polarization drift and gyrokinetic Maxwell equations is systematically derived by using the Lietransform perturbation method in toroidal geometry. For the first time, we recover the driftkinetic expression for parallel acceleration [R. M. Kulsrud, in Basic Plasma Physics, edited by A. A. Galeev and R. N. Sudan (NorthHolland, Amsterdam, 1983)] from the nonlinear gyrokinetic equations, thereby bridging a gap between the two formulations. This formalism should be useful in addressing nonlinear ion Compton scattering of intermediatemodenumber toroidal Alfvén eigenmodes for which the polarization current nonlinearity [T. S. Hahm and L. Chen, Phys. Rev. Lett. 74, 266 (1995)] and the usual finite Larmor radius effects should compete.},
doi = {10.1063/1.4891435},
journal = {Physics of Plasmas},
number = 8,
volume = 21,
place = {United States},
year = 2014,
month = 8
}

A set of the electrostatic toroidal gyrokinetic Vlasov equation and the Poisson equation, which explicitly includes the polarization drift, is derived systematically by using Lietransform perturbation method. The polarization drift is introduced in the gyrocenter equations of motion, and the corresponding polarization density is derived. Contrary to the widespread expectation, the inclusion of the polarization drift in the gyrocenter equations of motion does not affect the expression for the polarization density significantly. This is due to modification of the gyrocenter phasespace volume caused by the electrostatic potential [T. S. Hahm, Phys. Plasmas 3, 4658 (1996)].

Comment on 'Nonlinear gyrokinetic theory with polarization drift' [Phys. Plasmas 17, 082304 (2010)]
In this comment, we show that by using the discrete particle distribution function the changes of the phasespace volume of gyrocenter coordinates due to the fluctuating ExB velocity do not explicitly appear in the Poisson equation and the [Sosenko et al., Phys. Scr. 64, 264 (2001)] result is recovered. It is demonstrated that there is no contradiction between the work presented by Sosenko et al. and the work presented by [Wang et al., Phys. Plasmas 17, 082304 (2010)]. 
Response to 'Comment on 'Nonlinear gyrokinetic theory with polarization drift'' [Phys. Plasmas 17, 124701 (2010)]
We agree that there is no contradiction between Wang and Hahm [Phys. Plasmas 17, 082304 (2010)] and Sosenko et al. [Phys. Scr. 64, 264 (2001)]. However, by explicitly evaluating the change in phasevolume due to the electrostatic potential [T. S. Hahm, Phys. Plasmas 3, 4658 (1996)], Wang and Hahm [Phys. Plasmas 17, 082304 (2010)] has demonstrated that the polarization density remains the same even when the polarization drift explicitly appears in the gyrocenter equations of motion, and has derived an energy invariant in general toroidal geometry. 
Nonlinear instability of electromagnetic drift waves
A pair of electromagnetic drift waves is shown to be excited simultaneously by an induced Cerenkov emission by electrons. The instability is shown to be explosive. However, its property is different from the ordinary explosive instability involving three wave interactions with a negative energy wave pump. The instability here is excited by the inverted population of electrons (inverse Landau damping) and is less sensitive to the frequency mismatch or dissipation. The nonlinear growth rate is shown to exceed the linear growth rate at a reasonably small level of wave amplitude. A magnetic field perturbation is essential for this process.