### Abstract

We derive a weak turbulence formalism for incompressible magnetohydrodynamics. Three-wave interactions lead to a system of kinetic equations for the spectral densities of energy and helicity. The kinetic equations conserve energy in all wavevector planes normal to the applied magnetic field B_{0} qq_{∥}. Numerically and analytically, we find energy spectra E^{±} approx. k_{⊥}^{n±}, such that n_{+} + n_{-} = -4, where E^{±} are the spectra of the Elsasser variables z^{±} = v ± b in the two-dimensional case (k_{∥} = 0). The constants of the spectra are computed exactly and found to depend on the amount of correlation between the velocity and the magnetic field. Comparison with several numerical simulations and models is also made.

Original language | English (US) |
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Pages (from-to) | 447-488 |

Number of pages | 42 |

Journal | Journal of Plasma Physics |

Volume | 63 |

Issue number | 5 |

Publication status | Published - Jun 2000 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Journal of Plasma Physics*,

*63*(5), 447-488.