# Reduction of order in the geometric optics of plasmas

## Abstract

Small amplitude waves in plasmas are usually described by large systems of linearized Maxwell and kinetic equations. A procedure of elimination of components and reduction of the order of the system is discussed within the geometric optics approximation. In some cases characterized by Hermitian generalized dielectric tensors E-script describing the unreduced problem, the successive reduction procedure yields, at each step, energy conserving reduced systems that preserve the general form and first-order nature of the equations. The number of equations in the final reduced system is equal to the number of degenerate vanishing eigenvalues of E-script. The theory is applied in the case of transverse waves, propagating along the magnetic field in plasmas with plane parallel stratification. Both cold streaming plasma and kinetic problems are considered by using the same-order reduction procedure. The cold plasma case, at low densities, becomes doubly degenerate at cyclotron resonance, reflecting mode coupling between the vacuum electromagnetic and electron cyclotron modes. Mode conversion coefficients found from the solution of the reduced system of two first-order differential equations, characterizing this case, are in an excellent agreement with the results of the numerical solutions of the full unreduced system of equations. The kinetic case is approached by viewingmore »

- Authors:

- Publication Date:

- Research Org.:
- Yale University, P. O. Box 2159, New Haven, Connecticut 06520

- OSTI Identifier:
- 7242109

- Resource Type:
- Journal Article

- Journal Name:
- Phys. Fluids; (United States)

- Additional Journal Information:
- Journal Volume: 29:12

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; INHOMOGENEOUS PLASMA; PLASMA HEATING; WAVE PROPAGATION; AMPLITUDES; COLD PLASMA; CURRENT-DRIVE HEATING; ENERGY CONSERVATION; ENERGY CONVERSION; HERMITIAN OPERATORS; KINETIC EQUATIONS; MAXWELL EQUATIONS; OPTICS; TENSORS; CONVERSION; DIFFERENTIAL EQUATIONS; ELECTRIC HEATING; EQUATIONS; HEATING; JOULE HEATING; MATHEMATICAL OPERATORS; PARTIAL DIFFERENTIAL EQUATIONS; PLASMA; RESISTANCE HEATING; 700108* - Fusion Energy- Plasma Research- Wave Phenomena

### Citation Formats

```
Friedland, L, and Goldner, G.
```*Reduction of order in the geometric optics of plasmas*. United States: N. p., 1986.
Web. doi:10.1063/1.865750.

```
Friedland, L, & Goldner, G.
```*Reduction of order in the geometric optics of plasmas*. United States. https://doi.org/10.1063/1.865750

```
Friedland, L, and Goldner, G. 1986.
"Reduction of order in the geometric optics of plasmas". United States. https://doi.org/10.1063/1.865750.
```

```
@article{osti_7242109,
```

title = {Reduction of order in the geometric optics of plasmas},

author = {Friedland, L and Goldner, G},

abstractNote = {Small amplitude waves in plasmas are usually described by large systems of linearized Maxwell and kinetic equations. A procedure of elimination of components and reduction of the order of the system is discussed within the geometric optics approximation. In some cases characterized by Hermitian generalized dielectric tensors E-script describing the unreduced problem, the successive reduction procedure yields, at each step, energy conserving reduced systems that preserve the general form and first-order nature of the equations. The number of equations in the final reduced system is equal to the number of degenerate vanishing eigenvalues of E-script. The theory is applied in the case of transverse waves, propagating along the magnetic field in plasmas with plane parallel stratification. Both cold streaming plasma and kinetic problems are considered by using the same-order reduction procedure. The cold plasma case, at low densities, becomes doubly degenerate at cyclotron resonance, reflecting mode coupling between the vacuum electromagnetic and electron cyclotron modes. Mode conversion coefficients found from the solution of the reduced system of two first-order differential equations, characterizing this case, are in an excellent agreement with the results of the numerical solutions of the full unreduced system of equations. The kinetic case is approached by viewing the plasma as consisting of many beamlets each governed by the cold fluid approximation. The problem represents a multiply degenerate situation as many beamlets are in resonance at a time. Renormalized perturbation analysis of the partially reduced system in the low-density case predicts results similar to those found in the cold plasma, with possible broadening of the resonance region.},

doi = {10.1063/1.865750},

url = {https://www.osti.gov/biblio/7242109},
journal = {Phys. Fluids; (United States)},

number = ,

volume = 29:12,

place = {United States},

year = {1986},

month = {12}

}