## Abstract

The existence of localized regions of intense lower hybrid waves in the auroral ionosphere recently observed by rocket and satellite experiments can be understood by the study of a non‐linear two‐timescale coupling process. Such type of wave‐wave interactions was first described by Musher and Sturman [1975]. In this Letter, we demonstrate that the leading non‐linear term in the standard Musher‐Sturman equation vanishes identically in strict two‐dimensions (normal to the magnetic field). Instead, the new two‐dimensional equation is characterized by a much weaker non‐linear term which arises from the ponderomotive force perpendicular to the magnetic field, particularly that due to the ions. The old and new equations are compared by means of time‐evolution calculations of wave fields. The results exhibit a remarkable difference in the evolution of the waves as governed by the two equations. Such dissimilar outcomes motivate our investigation of the limitation of Musher‐Sturman equation in quasi‐two‐dimensions. We show that the equation may be applicable only if κ_{∥}²/κ_{⟂}²≫ω²/Ω_{e}², where ω² ≲ ω_{A}² or Ω_{i}² In addition, assumptions of quasi‐steady slow‐mode responses by ions and electrons require ω²/κ²ν_{i}² and ω²/κ_{∥}²ν_{e}² ≪ 1 respectively. Only within all these limits can Musher‐Sturman equation adequately describe the collapse of lower hybrid waves.

Original language | English |
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Pages (from-to) | 1125-1128 |

Number of pages | 4 |

Journal | Geophysical Research Letters |

Volume | 22 |

Issue number | 9 |

DOIs | |

Publication status | Published - 1995 May 1 |

## All Science Journal Classification (ASJC) codes

- Geophysics
- General Earth and Planetary Sciences