# Wave resonances and the partition of energy in ideal compressible magnetohydrodynamic fluids

## Abstract

Phase mixing and resonant absorption are two processes that have been under scrutiny for some time because of their role in wave damping and in providing a mechanism for heating space and laboratory plasmas. The accumulation or absorption of energy that develops within a resonant layer is usually attributed to a logarithmic singularity, but it will be shown that this build up of energy is inextricably tied to a discontinuity in the fluid displacement at the resonant point. This change in the dynamics of the problem will be examined by establishing a partition of energy that identifies and isolates the individual resonances within the fluid. The partition is based on a variational description of the Fourier transformed equations and is guided by an electrical model of the MHD system that not only illustrates the resonant structure threading the fluid but also exposes the mechanism driving the resonant absorption process. A simplified version of this model is then constructed to help determine the approximate rate of energy absorption.

- Authors:

- School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, Victoria 3000 (Australia)
- School of Mathematical Sciences, Monash University, Clayton, Victoria 3800 (Australia)

- Publication Date:

- OSTI Identifier:
- 22068870

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 19; Journal Issue: 11; Other Information: (c) 2012 American Institute of Physics; 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; APPROXIMATIONS; ENERGY ABSORPTION; FLUIDS; MAGNETOHYDRODYNAMICS; PARTITION; PLASMA; PLASMA HEATING; RESONANCE; SINGULARITY; VARIATIONAL METHODS

### Citation Formats

```
Zorzan, C., and Cally, P. S.
```*Wave resonances and the partition of energy in ideal compressible magnetohydrodynamic fluids*. United States: N. p., 2012.
Web. doi:10.1063/1.4764289.

```
Zorzan, C., & Cally, P. S.
```*Wave resonances and the partition of energy in ideal compressible magnetohydrodynamic fluids*. United States. doi:10.1063/1.4764289.

```
Zorzan, C., and Cally, P. S. Thu .
"Wave resonances and the partition of energy in ideal compressible magnetohydrodynamic fluids". United States. doi:10.1063/1.4764289.
```

```
@article{osti_22068870,
```

title = {Wave resonances and the partition of energy in ideal compressible magnetohydrodynamic fluids},

author = {Zorzan, C. and Cally, P. S.},

abstractNote = {Phase mixing and resonant absorption are two processes that have been under scrutiny for some time because of their role in wave damping and in providing a mechanism for heating space and laboratory plasmas. The accumulation or absorption of energy that develops within a resonant layer is usually attributed to a logarithmic singularity, but it will be shown that this build up of energy is inextricably tied to a discontinuity in the fluid displacement at the resonant point. This change in the dynamics of the problem will be examined by establishing a partition of energy that identifies and isolates the individual resonances within the fluid. The partition is based on a variational description of the Fourier transformed equations and is guided by an electrical model of the MHD system that not only illustrates the resonant structure threading the fluid but also exposes the mechanism driving the resonant absorption process. A simplified version of this model is then constructed to help determine the approximate rate of energy absorption.},

doi = {10.1063/1.4764289},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 11,

volume = 19,

place = {United States},

year = {2012},

month = {11}

}