# The wave energy flux of high frequency diffracting beams in complex geometrical optics

## Abstract

We consider the construction of asymptotic solutions of Maxwell's equations for a diffracting wave beam in the high frequency limit and address the description of the wave energy flux transported by the beam. With this aim, the complex eikonal method is applied. That is a generalization of the standard geometrical optics method in which the phase function is assumed to be complex valued, with the non-negative imaginary part accounting for the finite width of the beam cross section. In this framework, we propose an argument which simplifies significantly the analysis of the transport equation for the wave field amplitude and allows us to derive the wave energy flux. The theoretical analysis is illustrated numerically for the case of electron cyclotron beams in tokamak plasmas by using the GRAY code [D. Farina, Fusion Sci. Technol. 52, 154 (2007)], which is based upon the complex eikonal theory. The results are compared to those of the paraxial beam tracing code TORBEAM [E. Poli et al., Comput. Phys. Commun. 136, 90 (2001)], which provides an independent calculation of the energy flow.

- Authors:

- Max Planck Institute for Plasma Physics, EURATOM Association, Boltzmannstr. 2, 85748 Garching (Germany)
- Istituto di Fisica del Plasma 'P. Caldirola,' Consiglio Nazionale delle Ricerche, EURATOM-ENEA-CNR Association, via R. Cozzi 53, I-20125 Milano (Italy)
- (Italy)

- Publication Date:

- OSTI Identifier:
- 22130433

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 20; Journal Issue: 4; Other Information: (c) 2013 EURATOM; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; BEAMS; COMPARATIVE EVALUATIONS; CROSS SECTIONS; CYCLOTRONS; DIFFRACTION; EIKONAL APPROXIMATION; ELECTROMAGNETIC RADIATION; ELECTRONS; MAXWELL EQUATIONS; OPTICS; PLASMA; PLASMA CONFINEMENT; RF SYSTEMS; TOKAMAK DEVICES; TRANSPORT THEORY; WAVE PROPAGATION

### Citation Formats

```
Maj, Omar, Poli, Emanuele, Mariani, Alberto, Universita degli Studi di Milano, Dipartimento di Fisica, Via Celoria 16, 20133 Milano, and Farina, Daniela.
```*The wave energy flux of high frequency diffracting beams in complex geometrical optics*. United States: N. p., 2013.
Web. doi:10.1063/1.4802935.

```
Maj, Omar, Poli, Emanuele, Mariani, Alberto, Universita degli Studi di Milano, Dipartimento di Fisica, Via Celoria 16, 20133 Milano, & Farina, Daniela.
```*The wave energy flux of high frequency diffracting beams in complex geometrical optics*. United States. doi:10.1063/1.4802935.

```
Maj, Omar, Poli, Emanuele, Mariani, Alberto, Universita degli Studi di Milano, Dipartimento di Fisica, Via Celoria 16, 20133 Milano, and Farina, Daniela. Mon .
"The wave energy flux of high frequency diffracting beams in complex geometrical optics". United States. doi:10.1063/1.4802935.
```

```
@article{osti_22130433,
```

title = {The wave energy flux of high frequency diffracting beams in complex geometrical optics},

author = {Maj, Omar and Poli, Emanuele and Mariani, Alberto and Universita degli Studi di Milano, Dipartimento di Fisica, Via Celoria 16, 20133 Milano and Farina, Daniela},

abstractNote = {We consider the construction of asymptotic solutions of Maxwell's equations for a diffracting wave beam in the high frequency limit and address the description of the wave energy flux transported by the beam. With this aim, the complex eikonal method is applied. That is a generalization of the standard geometrical optics method in which the phase function is assumed to be complex valued, with the non-negative imaginary part accounting for the finite width of the beam cross section. In this framework, we propose an argument which simplifies significantly the analysis of the transport equation for the wave field amplitude and allows us to derive the wave energy flux. The theoretical analysis is illustrated numerically for the case of electron cyclotron beams in tokamak plasmas by using the GRAY code [D. Farina, Fusion Sci. Technol. 52, 154 (2007)], which is based upon the complex eikonal theory. The results are compared to those of the paraxial beam tracing code TORBEAM [E. Poli et al., Comput. Phys. Commun. 136, 90 (2001)], which provides an independent calculation of the energy flow.},

doi = {10.1063/1.4802935},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 4,

volume = 20,

place = {United States},

year = {2013},

month = {4}

}