FokkerPlanck modeling of current penetration during electron cyclotron current drive
Abstract
The current penetration during electron cyclotron current drive (ECCD) on the resistive time scale is studied with a FokkerPlanck simulation, which includes a model for the magnetic diffusion that determines the parallel electric field evolution. The existence of the synergy between the inductive electric field and EC driven current complicates the process of the current penetration and invalidates the standard method of calculation in which Ohm's law is simply approximated by jj{sub cd}={sigma}E. Here it is proposed to obtain at every time step a selfconsistent approximation to the plasma resistivity from the FokkerPlanck code, which is then used in a concurrent calculation of the magnetic diffusion equation in order to obtain the inductive electric field at the next time step. A series of FokkerPlanck calculations including a selfconsistent evolution of the inductive electric field has been performed. Both the ECCD power and the electron density have been varied, thus varying the well known nonlinearity parameter for ECCD P{sub rf}[MW/m{sup 3}]/n{sub e}{sup 2}[10{sup 19} m{sup 3}] [R. W. Harvey et al., Phys. Rev. Lett 62, 426 (1989)]. This parameter turns out also to be a good predictor of the synergetic effects. The results are then compared with the standard method ofmore »
 Authors:
 FOMInstitute for Plasma Physics Rijnhuizen, Association EURATOMFOM, Trilateral Euregio Cluster (Netherlands)
 Publication Date:
 OSTI Identifier:
 20974989
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 5; Other Information: DOI: 10.1063/1.2727479; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; APPROXIMATIONS; CURRENTS; DIFFUSION; DIFFUSION EQUATIONS; ECR CURRENT DRIVE; EFFICIENCY; ELECTRIC CONDUCTIVITY; ELECTRIC FIELDS; ELECTRON DENSITY; ELECTRONS; FOKKERPLANCK EQUATION; NONLINEAR PROBLEMS; OHM LAW; PLASMA; PLASMA DENSITY; PLASMA SIMULATION; RF SYSTEMS
Citation Formats
Merkulov, A., Westerhof, E., and Schueller, F. C. FokkerPlanck modeling of current penetration during electron cyclotron current drive. United States: N. p., 2007.
Web. doi:10.1063/1.2727479.
Merkulov, A., Westerhof, E., & Schueller, F. C. FokkerPlanck modeling of current penetration during electron cyclotron current drive. United States. doi:10.1063/1.2727479.
Merkulov, A., Westerhof, E., and Schueller, F. C. Tue .
"FokkerPlanck modeling of current penetration during electron cyclotron current drive". United States.
doi:10.1063/1.2727479.
@article{osti_20974989,
title = {FokkerPlanck modeling of current penetration during electron cyclotron current drive},
author = {Merkulov, A. and Westerhof, E. and Schueller, F. C.},
abstractNote = {The current penetration during electron cyclotron current drive (ECCD) on the resistive time scale is studied with a FokkerPlanck simulation, which includes a model for the magnetic diffusion that determines the parallel electric field evolution. The existence of the synergy between the inductive electric field and EC driven current complicates the process of the current penetration and invalidates the standard method of calculation in which Ohm's law is simply approximated by jj{sub cd}={sigma}E. Here it is proposed to obtain at every time step a selfconsistent approximation to the plasma resistivity from the FokkerPlanck code, which is then used in a concurrent calculation of the magnetic diffusion equation in order to obtain the inductive electric field at the next time step. A series of FokkerPlanck calculations including a selfconsistent evolution of the inductive electric field has been performed. Both the ECCD power and the electron density have been varied, thus varying the well known nonlinearity parameter for ECCD P{sub rf}[MW/m{sup 3}]/n{sub e}{sup 2}[10{sup 19} m{sup 3}] [R. W. Harvey et al., Phys. Rev. Lett 62, 426 (1989)]. This parameter turns out also to be a good predictor of the synergetic effects. The results are then compared with the standard method of calculations of the current penetration using a transport code. At low values of the Harvey parameter, the standard method is in quantitative agreement with FokkerPlanck calculations. However, at high values of the Harvey parameter, synergy between ECCD and E{sub parallel} is found. In the case of cocurrent drive, this synergy leads to the generation of large amounts of nonthermal electrons and a concomitant increase of the electrical conductivity and current penetration time. In the case of countercurrent drive, the ECCD efficiency is suppressed by the synergy with E{sub parallel} while only a small amount of nonthermal electrons is produced.},
doi = {10.1063/1.2727479},
journal = {Physics of Plasmas},
number = 5,
volume = 14,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}

A new threedimensional relativistic FokkerPlanck code (poloidal angle and two dimensions in momentum space) has been developed for the analysis of electron cyclotron current drive (ECCD) in tokamak plasmas. This numerical code takes into consideration trapped electron effects without using the bounceaverage approximation. Simulations have been carried out using the code, and the results were compared with those of a bounceaveraged FokkerPlanck code. There are differences in the current drive efficiencies calculated by the two codes, and this difference is shown to be caused by a change in electron velocity parallel to the magnetic field due to the inhomogeneous magneticmore »

Comments on {open_quote}{open_quote}Analysis of electron cyclotron current drive using neoclassical Fokker{endash}Planck code without bounceaverage approximation{close_quote}{close_quote} [Phys. Plasmas {bold 2}, 4570 (1995)]
The conclusion reached in ref. 1 that the 3D FokkerPlanck code verses the 2D bounceaveraged code does not yield the correct current density is prove to be wrong. It is aruged that the results for the 3D code are very close to those of the 2D code that employs a bounceaverage procedure.(AIP) {copyright} {ital 1996 American Institute of Physics.} 
On selfconsistent raytracing and FokkerPlanck modeling of the hard xray emission during lowerhybrid current drive in tokamaks
A detailed investigation is presented on the ability of combined raytracing and FokkerPlanck calculations to predict the hard xray (HXR) emission during lowerhybrid (LH) current drive in tokamaks when toroidally induced ray stochasticity is important. A large number of rays is used and the electron distribution function is obtained by selfconsistently iterating the appropriate power deposition and FokkerPlanck calculations. It is shown that effects due to radial diffusion of suprathermal electrons and to radiation scattering by the inner wall can be significant. The experimentally observed features of the HXR emission are fairly well predicted, thus confirming that combined raytracing andmore » 
Gaussian shorttime propagators and electron kinetics: Numerical evaluation of pathsum solutions to Fokker{endash}Planck equations for rf heating and current drive
Knowing that shorttime propagators for Fokker{endash}Planck equations are Gaussian, and based on a pathsum formulation, an efficient and simple numerical method is presented to solve the initialvalue problem for electron kinetics during rf heating and current drive. The formulation is thoroughly presented and discussed, its advantages are stressed, and general, practical criteria for its implementation are derived regarding the time step and grid spacing. The new approach is illustrated and validated by solving the onedimensional model for lowerhybrid current drive, which has a wellknown steadystate analytical solution. {copyright} {ital 1997 American Institute of Physics.} 
3D bounce averaged FokkerPlanck calculation of electron cyclotron current drive efficiency
Electron cyclotron current drive heating efficiency in tokamak is calculated using 3D bounce averaged FokkerPlanck equation. A computer code has been assembled which predicts the profiles of heating and current drive. (AIP)