### Abstract

The theory of weak turbulence of a plasma has been investigated in many papers [1-5]. It has been established that weak turbulence may be described by means of the kinetic wave equations. Here the collision term in the kinetic equation is the sum of two substantially different components. The first of these has the character of nonlinear wave damping and differs from zero in those cases where interaction between waves and particles is significant. It has a comparatively simple mathematical nature and can be analyzed. The second component is specifically a collision term, it depends closely on the form of the spectrum in the medium and describes the exchange of energy between different groups of waves. The case when the second component plays the principal role in the collision term has scarcely been studied. The present paper is devoted to a study of this case. The analysis is carried out for a simple isotropic model of a medium with an almost linear dispersion law, but with a positive second derivative; we shall call such a spectrum a decay spectrum. This model is much closer to reality than the model considered in [6]. The results obtained from this model are evidently fairly general in character and express substantially the regularity of behavior of weak turbulence in media with a weak decay spectrum. The basic result of the paper is as follows: apart from the Rayleigh-Jeans solution, there exists another solution which reduces the collision term to zero. This solution corresponds to a process which is substantially nonequilibrium, and may be realized in actual problems, where there are always wave sources or transfer terms playing the same part, only in cases where there is wave damping in the medium with a coefficient which increases fairly rapidly into the region of large k. Here the universal character, as it were, of the nonequilibrium process is realized.

Original language | English (US) |
---|---|

Pages (from-to) | 22-24 |

Number of pages | 3 |

Journal | Journal of Applied Mechanics and Technical Physics |

Volume | 6 |

Issue number | 4 |

DOIs | |

State | Published - 1967 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)
- Engineering(all)

### Cite this

**Weak turbulence in media with a decay spectrum.** / Zakharov, Vladimir E.

Research output: Contribution to journal › Article

*Journal of Applied Mechanics and Technical Physics*, vol. 6, no. 4, pp. 22-24. https://doi.org/10.1007/BF01565814

}

TY - JOUR

T1 - Weak turbulence in media with a decay spectrum

AU - Zakharov, Vladimir E

PY - 1967

Y1 - 1967

N2 - The theory of weak turbulence of a plasma has been investigated in many papers [1-5]. It has been established that weak turbulence may be described by means of the kinetic wave equations. Here the collision term in the kinetic equation is the sum of two substantially different components. The first of these has the character of nonlinear wave damping and differs from zero in those cases where interaction between waves and particles is significant. It has a comparatively simple mathematical nature and can be analyzed. The second component is specifically a collision term, it depends closely on the form of the spectrum in the medium and describes the exchange of energy between different groups of waves. The case when the second component plays the principal role in the collision term has scarcely been studied. The present paper is devoted to a study of this case. The analysis is carried out for a simple isotropic model of a medium with an almost linear dispersion law, but with a positive second derivative; we shall call such a spectrum a decay spectrum. This model is much closer to reality than the model considered in [6]. The results obtained from this model are evidently fairly general in character and express substantially the regularity of behavior of weak turbulence in media with a weak decay spectrum. The basic result of the paper is as follows: apart from the Rayleigh-Jeans solution, there exists another solution which reduces the collision term to zero. This solution corresponds to a process which is substantially nonequilibrium, and may be realized in actual problems, where there are always wave sources or transfer terms playing the same part, only in cases where there is wave damping in the medium with a coefficient which increases fairly rapidly into the region of large k. Here the universal character, as it were, of the nonequilibrium process is realized.

AB - The theory of weak turbulence of a plasma has been investigated in many papers [1-5]. It has been established that weak turbulence may be described by means of the kinetic wave equations. Here the collision term in the kinetic equation is the sum of two substantially different components. The first of these has the character of nonlinear wave damping and differs from zero in those cases where interaction between waves and particles is significant. It has a comparatively simple mathematical nature and can be analyzed. The second component is specifically a collision term, it depends closely on the form of the spectrum in the medium and describes the exchange of energy between different groups of waves. The case when the second component plays the principal role in the collision term has scarcely been studied. The present paper is devoted to a study of this case. The analysis is carried out for a simple isotropic model of a medium with an almost linear dispersion law, but with a positive second derivative; we shall call such a spectrum a decay spectrum. This model is much closer to reality than the model considered in [6]. The results obtained from this model are evidently fairly general in character and express substantially the regularity of behavior of weak turbulence in media with a weak decay spectrum. The basic result of the paper is as follows: apart from the Rayleigh-Jeans solution, there exists another solution which reduces the collision term to zero. This solution corresponds to a process which is substantially nonequilibrium, and may be realized in actual problems, where there are always wave sources or transfer terms playing the same part, only in cases where there is wave damping in the medium with a coefficient which increases fairly rapidly into the region of large k. Here the universal character, as it were, of the nonequilibrium process is realized.

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UR - http://www.scopus.com/inward/citedby.url?scp=34250510656&partnerID=8YFLogxK

U2 - 10.1007/BF01565814

DO - 10.1007/BF01565814

M3 - Article

AN - SCOPUS:34250510656

VL - 6

SP - 22

EP - 24

JO - Journal of Applied Mechanics and Technical Physics

JF - Journal of Applied Mechanics and Technical Physics

SN - 0021-8944

IS - 4

ER -