# Fokker-Planck 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 Fokker-Planck 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 j-j{sub cd}={sigma}E. Here it is proposed to obtain at every time step a self-consistent approximation to the plasma resistivity from the Fokker-Planck 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 Fokker-Planck calculations including a self-consistent 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:

- FOM-Institute for Plasma Physics Rijnhuizen, Association EURATOM-FOM, 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; FOKKER-PLANCK EQUATION; NONLINEAR PROBLEMS; OHM LAW; PLASMA; PLASMA DENSITY; PLASMA SIMULATION; RF SYSTEMS

### Citation Formats

```
Merkulov, A., Westerhof, E., and Schueller, F. C..
```*Fokker-Planck 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..
```*Fokker-Planck 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 .
"Fokker-Planck modeling of current penetration during electron cyclotron current drive". United States.
doi:10.1063/1.2727479.
```

```
@article{osti_20974989,
```

title = {Fokker-Planck 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 Fokker-Planck 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 j-j{sub cd}={sigma}E. Here it is proposed to obtain at every time step a self-consistent approximation to the plasma resistivity from the Fokker-Planck 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 Fokker-Planck calculations including a self-consistent 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 Fokker-Planck 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}

}