### Abstract

The statistical behavior of magnetic lines in a sheared magnetic configuration with reference surface x=0 is investigated within the framework of the kinetic theory. A Liouville equation is associated with the equations of motion of the stochastic magnetic lines. After averaging over an ensemble of realizations, it yields a convection-diffusion equation within the quasilinear approximation. The diffusion coefficients are space dependent and peaked around the reference surface x=0. Due to the shear, die diffusion of lines away from the reference surface is slowed down. The behavior of the lines is asymptotically strongly noo-Gaussian The reference surface acts like an attractor around which the magnetic lines spread with an effective subdiffusive behavior. Comparison is also made with more usual treatments based on the study of die first two moments equations. For sheared systems, it is explicitly shown that the Corrsin approximation assumed in the latter approach is no longer valid. It is also concluded dial the diffusion coefficients cannot be derived from the mean square displacement of the magnetic lines in an inhomogeneous medium.

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

Pages (from-to) | 815-823 |

Number of pages | 9 |

Journal | Physics of Plasmas |

Volume | 3 |

Issue number | 3 |

State | Published - Mar 1996 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Physics of Plasmas*,

*3*(3), 815-823.

**Strongly anomalous diffusion in sheared magnetic configurations.** / Vanden Eijnden, E.; Balescu, R.

Research output: Contribution to journal › Article

*Physics of Plasmas*, vol. 3, no. 3, pp. 815-823.

}

TY - JOUR

T1 - Strongly anomalous diffusion in sheared magnetic configurations

AU - Vanden Eijnden, E.

AU - Balescu, R.

PY - 1996/3

Y1 - 1996/3

N2 - The statistical behavior of magnetic lines in a sheared magnetic configuration with reference surface x=0 is investigated within the framework of the kinetic theory. A Liouville equation is associated with the equations of motion of the stochastic magnetic lines. After averaging over an ensemble of realizations, it yields a convection-diffusion equation within the quasilinear approximation. The diffusion coefficients are space dependent and peaked around the reference surface x=0. Due to the shear, die diffusion of lines away from the reference surface is slowed down. The behavior of the lines is asymptotically strongly noo-Gaussian The reference surface acts like an attractor around which the magnetic lines spread with an effective subdiffusive behavior. Comparison is also made with more usual treatments based on the study of die first two moments equations. For sheared systems, it is explicitly shown that the Corrsin approximation assumed in the latter approach is no longer valid. It is also concluded dial the diffusion coefficients cannot be derived from the mean square displacement of the magnetic lines in an inhomogeneous medium.

AB - The statistical behavior of magnetic lines in a sheared magnetic configuration with reference surface x=0 is investigated within the framework of the kinetic theory. A Liouville equation is associated with the equations of motion of the stochastic magnetic lines. After averaging over an ensemble of realizations, it yields a convection-diffusion equation within the quasilinear approximation. The diffusion coefficients are space dependent and peaked around the reference surface x=0. Due to the shear, die diffusion of lines away from the reference surface is slowed down. The behavior of the lines is asymptotically strongly noo-Gaussian The reference surface acts like an attractor around which the magnetic lines spread with an effective subdiffusive behavior. Comparison is also made with more usual treatments based on the study of die first two moments equations. For sheared systems, it is explicitly shown that the Corrsin approximation assumed in the latter approach is no longer valid. It is also concluded dial the diffusion coefficients cannot be derived from the mean square displacement of the magnetic lines in an inhomogeneous medium.

UR - http://www.scopus.com/inward/record.url?scp=5244238697&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=5244238697&partnerID=8YFLogxK

M3 - Article

VL - 3

SP - 815

EP - 823

JO - Physics of Plasmas

JF - Physics of Plasmas

SN - 1070-664X

IS - 3

ER -