### Abstract

A statistical description is developed for a self-sustained subcritical turbulence in inhomogeneous plasmas. Interchange mode in the presence of inhomogeneous magnetic field, which reveals a submarginal strong turbulence, is considered. Nonlinear dispersion relation is extended to a Langevin equation for a dressed test mode, in which nonlinear interactions are kept as renormalized drag and random self noise. Based upon the assumption that the random noise has a faster time scale, the solutions are obtained for the fluctuation level, decorrelation rate, auto- and cross-correlation functions and spectrum. They are expressed as nonlinear functions of non-equilibrium parameters like gradient. Extended fluctuation-dissipation theorem (Einstein relation) is described as statistical relations. Then the Langevin equation is reformulated into a Fokker-Planck equation of the probability distribution function. The steady state probability function is solved. Imposing the constraint of the self-noise, the power-law distribution with respect to the fluctuation amplitude is obtained in the tail of the distribution function.

Original language | English |
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Pages (from-to) | 1891-1906 |

Number of pages | 16 |

Journal | journal of the physical society of japan |

Volume | 68 |

Issue number | 6 |

DOIs | |

Publication status | Published - Jan 1 1999 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

*journal of the physical society of japan*,

*68*(6), 1891-1906. https://doi.org/10.1143/JPSJ.68.1891

**Statistical theory of subcritically-excited strong turbulence in inhomogeneous plasmas. I.** / Itoh, Sanae; Itoh, Kimitaka.

Research output: Contribution to journal › Article

*journal of the physical society of japan*, vol. 68, no. 6, pp. 1891-1906. https://doi.org/10.1143/JPSJ.68.1891

}

TY - JOUR

T1 - Statistical theory of subcritically-excited strong turbulence in inhomogeneous plasmas. I

AU - Itoh, Sanae

AU - Itoh, Kimitaka

PY - 1999/1/1

Y1 - 1999/1/1

N2 - A statistical description is developed for a self-sustained subcritical turbulence in inhomogeneous plasmas. Interchange mode in the presence of inhomogeneous magnetic field, which reveals a submarginal strong turbulence, is considered. Nonlinear dispersion relation is extended to a Langevin equation for a dressed test mode, in which nonlinear interactions are kept as renormalized drag and random self noise. Based upon the assumption that the random noise has a faster time scale, the solutions are obtained for the fluctuation level, decorrelation rate, auto- and cross-correlation functions and spectrum. They are expressed as nonlinear functions of non-equilibrium parameters like gradient. Extended fluctuation-dissipation theorem (Einstein relation) is described as statistical relations. Then the Langevin equation is reformulated into a Fokker-Planck equation of the probability distribution function. The steady state probability function is solved. Imposing the constraint of the self-noise, the power-law distribution with respect to the fluctuation amplitude is obtained in the tail of the distribution function.

AB - A statistical description is developed for a self-sustained subcritical turbulence in inhomogeneous plasmas. Interchange mode in the presence of inhomogeneous magnetic field, which reveals a submarginal strong turbulence, is considered. Nonlinear dispersion relation is extended to a Langevin equation for a dressed test mode, in which nonlinear interactions are kept as renormalized drag and random self noise. Based upon the assumption that the random noise has a faster time scale, the solutions are obtained for the fluctuation level, decorrelation rate, auto- and cross-correlation functions and spectrum. They are expressed as nonlinear functions of non-equilibrium parameters like gradient. Extended fluctuation-dissipation theorem (Einstein relation) is described as statistical relations. Then the Langevin equation is reformulated into a Fokker-Planck equation of the probability distribution function. The steady state probability function is solved. Imposing the constraint of the self-noise, the power-law distribution with respect to the fluctuation amplitude is obtained in the tail of the distribution function.

UR - http://www.scopus.com/inward/record.url?scp=0033414894&partnerID=8YFLogxK

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U2 - 10.1143/JPSJ.68.1891

DO - 10.1143/JPSJ.68.1891

M3 - Article

AN - SCOPUS:0033414894

VL - 68

SP - 1891

EP - 1906

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 6

ER -