# 3-D Ray-tracing and 2-D Fokker-Planck simulations of radiofrequency application to tokamak plasmas

## Abstract

A state of the art numerical tool has been developed to simulate the propagation and the absorption of coexisting different types of waves in a tokamak geometry. The code includes a numerical solution of the three-dimensional (R, Z, {phi}) toroidal wave equation for the electric field of the different waves in the WKBJ approximation. At each step of integration, the two-dimensional (v{sub (parallel} {sub sign)}, v{sub (perpendicular} {sub sign)}) Fokker-Planck equation is solved in the presence of quasilinear diffusion coefficients. The electron Landau damping of the waves is modeled taking into account the interaction of the wave electric fields with the quasilinearly modified distribution function. Consistently, the code calculates the radial profiles of non-inductively generated current densities, the transmitted power traces and the total power damping curves. Synergistic effects among the different type of waves (e.g., lower hybrid and ion Bernstein waves) are studied through the separation of the contributions of the single wave from the effects due to their coexistence. (c) 1999 American Institute of Physics.

- Authors:

- Columbia University, New York, New York (United States)
- Associazione Euratom-ENEA sulla Fusione, Frascati, Rome, (Italy)
- Plasma Physics Laboratory, Princeton, New Jersey (United States)

- Publication Date:

- OSTI Identifier:
- 20216699

- Resource Type:
- Journal Article

- Journal Name:
- AIP Conference Proceedings

- Additional Journal Information:
- Journal Volume: 485; Journal Issue: 1; Other Information: PBD: 20 Sep 1999; Journal ID: ISSN 0094-243X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; HIGH-FREQUENCY HEATING; TOKAMAK TYPE REACTORS; WKB APPROXIMATION; ELECTRON DENSITY; BOLTZMANN EQUATION; PLASMA SIMULATION; THEORETICAL DATA

### Citation Formats

```
Paoletti, F., Cardinali, A., and Bernabei, S.
```*3-D Ray-tracing and 2-D Fokker-Planck simulations of radiofrequency application to tokamak plasmas*. United States: N. p., 1999.
Web. doi:10.1063/1.59681.

```
Paoletti, F., Cardinali, A., & Bernabei, S.
```*3-D Ray-tracing and 2-D Fokker-Planck simulations of radiofrequency application to tokamak plasmas*. United States. doi:10.1063/1.59681.

```
Paoletti, F., Cardinali, A., and Bernabei, S. Mon .
"3-D Ray-tracing and 2-D Fokker-Planck simulations of radiofrequency application to tokamak plasmas". United States. doi:10.1063/1.59681.
```

```
@article{osti_20216699,
```

title = {3-D Ray-tracing and 2-D Fokker-Planck simulations of radiofrequency application to tokamak plasmas},

author = {Paoletti, F. and Cardinali, A. and Bernabei, S.},

abstractNote = {A state of the art numerical tool has been developed to simulate the propagation and the absorption of coexisting different types of waves in a tokamak geometry. The code includes a numerical solution of the three-dimensional (R, Z, {phi}) toroidal wave equation for the electric field of the different waves in the WKBJ approximation. At each step of integration, the two-dimensional (v{sub (parallel} {sub sign)}, v{sub (perpendicular} {sub sign)}) Fokker-Planck equation is solved in the presence of quasilinear diffusion coefficients. The electron Landau damping of the waves is modeled taking into account the interaction of the wave electric fields with the quasilinearly modified distribution function. Consistently, the code calculates the radial profiles of non-inductively generated current densities, the transmitted power traces and the total power damping curves. Synergistic effects among the different type of waves (e.g., lower hybrid and ion Bernstein waves) are studied through the separation of the contributions of the single wave from the effects due to their coexistence. (c) 1999 American Institute of Physics.},

doi = {10.1063/1.59681},

journal = {AIP Conference Proceedings},

issn = {0094-243X},

number = 1,

volume = 485,

place = {United States},

year = {1999},

month = {9}

}