(10) |

(11) |

which is known as the induction equation. This states that a local change in the magnetic field is due to both convection and diffusion. The magnetic Reynolds number is the ratio of the convective to the diffusive term,

(14) |

(14) |

For large R_{m} (»1), as found in most astrophysical cases, the convective term dominates in Eqn. 12, and the field lines move as if they are frozen into the plasma (Alfvén, 1943) with typical timescale, t_{c} = *l*_{0}/v_{0}. For small R_{m} («1), typically found in laboratory plasmas, the diffusion term dominates and flux `leaks' with typical ohmic diffusion timescales then given by t_{d} = *l*_{0}^{2}/η. For typical solar photospheric values (v_{0} 10 m s^{-1},η~ 10^{3} m^{2} s^{-1}) R_{m} becomes less than unity (t_{d} ~ t_{c}) for *l*_{0} ~ 100m, ohmic dissipation becomes important, and magnetic reconnection may occur.

^{1} In fact η varies with both temperature and density, from ~ 10^{3} m^{2} s^{-1} in the photosphere to ~ 1 m^{2} s^{-1} in the corona (Priest 1982)

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