# On nonlinear evolution of low-frequency Alfvén waves in weakly-expanding solar wind plasmas

## Abstract

A multi-dimensional nonlinear evolution equation for Alfvén waves in weakly-expanding solar wind plasmas is derived by using the reductive perturbation method. The expansion of solar wind plasma parcels is modeled by an expanding box model, which includes the accelerating expansion. It is shown that the resultant equation agrees with the Wentzel-Kramers-Brillouin prediction of the low-frequency Alfvén waves in the linear limit. In the cold and one-dimensional limit, a modified derivative nonlinear Schrodinger equation is obtained. Direct numerical simulations are carried out to discuss the effect of the expansion on the modulational instability of monochromatic Alfvén waves and the propagation of Alfvén solitons. By using the instantaneous frequency, it is quantitatively shown that as far as the expansion rate is much smaller than wave frequencies, effects of the expansion are almost adiabatic. It is also confirmed that while shapes of Alfvén solitons temporally change due to the expansion, some of them can stably propagate after their collision in weakly-expanding plasmas.

- Authors:

- Faculty of Human Development, University of Toyama, 3190 Toyama City, Toyama 930-8555 (Japan)

- Publication Date:

- OSTI Identifier:
- 22408092

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 22; Journal Issue: 2; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ALFVEN WAVES; BOX MODELS; COLLISIONS; COMPUTERIZED SIMULATION; INSTABILITY; MATHEMATICAL EVOLUTION; MONOCHROMATIC RADIATION; NONLINEAR PROBLEMS; ONE-DIMENSIONAL CALCULATIONS; PERTURBATION THEORY; PLASMA; SCHROEDINGER EQUATION; SOLAR WIND; SOLITONS; WKB APPROXIMATION

### Citation Formats

```
Nariyuki, Y.
```*On nonlinear evolution of low-frequency Alfvén waves in weakly-expanding solar wind plasmas*. United States: N. p., 2015.
Web. doi:10.1063/1.4908544.

```
Nariyuki, Y.
```*On nonlinear evolution of low-frequency Alfvén waves in weakly-expanding solar wind plasmas*. United States. doi:10.1063/1.4908544.

```
Nariyuki, Y. Sun .
"On nonlinear evolution of low-frequency Alfvén waves in weakly-expanding solar wind plasmas". United States.
doi:10.1063/1.4908544.
```

```
@article{osti_22408092,
```

title = {On nonlinear evolution of low-frequency Alfvén waves in weakly-expanding solar wind plasmas},

author = {Nariyuki, Y.},

abstractNote = {A multi-dimensional nonlinear evolution equation for Alfvén waves in weakly-expanding solar wind plasmas is derived by using the reductive perturbation method. The expansion of solar wind plasma parcels is modeled by an expanding box model, which includes the accelerating expansion. It is shown that the resultant equation agrees with the Wentzel-Kramers-Brillouin prediction of the low-frequency Alfvén waves in the linear limit. In the cold and one-dimensional limit, a modified derivative nonlinear Schrodinger equation is obtained. Direct numerical simulations are carried out to discuss the effect of the expansion on the modulational instability of monochromatic Alfvén waves and the propagation of Alfvén solitons. By using the instantaneous frequency, it is quantitatively shown that as far as the expansion rate is much smaller than wave frequencies, effects of the expansion are almost adiabatic. It is also confirmed that while shapes of Alfvén solitons temporally change due to the expansion, some of them can stably propagate after their collision in weakly-expanding plasmas.},

doi = {10.1063/1.4908544},

journal = {Physics of Plasmas},

number = 2,

volume = 22,

place = {United States},

year = {Sun Feb 15 00:00:00 EST 2015},

month = {Sun Feb 15 00:00:00 EST 2015}

}