### Abstract

The linearized incompressible magnetohydrodynamic equations that include a generalized Ohm's law are solved for tearing eigenmodes of a plasma sheet with a normal magnetic field (B_{n}). In contrast to the Harris sheet with the equilibrium magnetic field [B=B_{0} tanh(z/a)x̂], the two-dimensional plasma sheet with the field [B=B_{0} tanh(z/a)x̂+B_{n}ẑ], in which the B_{n} field lies in the plane of the B_{x} field, has no neutral line if B _{n}≠0. Such a geometry is intrinsically resilient to tearing because it cannot change topology by means of linear perturbations. This qualitative geometrical idea is supported by calculations of growth rates using a generalized Ohm's law that includes collisional resistivity and finite electron inertia as the mechanisms for breaking field lines. The presence of B _{n} reduces the resistive tearing mode growth rate by several orders of magnitude (assuming B_{n}/B_{0}∼0.1) compared with that in the Harris sheet model (B_{n}=0). The growth rate scaling with Lundquist number (S) has the typical S^{-3/5} (S^{-1/3}) dependence for large (small) wave numbers and very small values of B_{n}. For larger values of B_{n}, all modes behave diffusively, scaling as S ^{-1}. The collisionless electron tearing mode growth rate is found to be proportional to δ_{e} ^{2} in the presence of significant B_{n}(> 10^{-2}B_{0}) and large k _{x}(∼0.1a^{-1}-0.5a^{-1}), and becomes completely stable (γ<0) for B_{n}/B_{0}≥0.2. Implications for magnetospheric substorms are discussed.

Original language | English (US) |
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Pages (from-to) | 3857-3864 |

Number of pages | 8 |

Journal | Physics of Plasmas |

Volume | 2 |

Issue number | 10 |

DOIs | |

State | Published - Jan 1 1995 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics

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## Cite this

*Physics of Plasmas*,

*2*(10), 3857-3864. https://doi.org/10.1063/1.871085