### 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 |
---|---|

Pages (from-to) | 1125-1128 |

Number of pages | 4 |

Journal | Geophysical Research Letters |

Volume | 22 |

Issue number | 9 |

DOIs | |

Publication status | Published - 1995 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Geophysics
- Earth and Planetary Sciences(all)

### Cite this

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*Geophysical Research Letters*, vol. 22, no. 9, pp. 1125-1128. https://doi.org/10.1029/95GL01063

**The limitation and applicability of Musher‐Sturman Equation to two‐dimensional lower hybrid wave collapse.** / Tam, Sunny Wing-Yee; Chang, Tom.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The limitation and applicability of Musher‐Sturman Equation to two‐dimensional lower hybrid wave collapse

AU - Tam, Sunny Wing-Yee

AU - Chang, Tom

PY - 1995/1/1

Y1 - 1995/1/1

N2 - 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/Ωe², where ω² ≲ ωA² or Ωi² In addition, assumptions of quasi‐steady slow‐mode responses by ions and electrons require ω²/κ²νi² and ω²/κ∥²νe² ≪ 1 respectively. Only within all these limits can Musher‐Sturman equation adequately describe the collapse of lower hybrid waves.

AB - 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/Ωe², where ω² ≲ ωA² or Ωi² In addition, assumptions of quasi‐steady slow‐mode responses by ions and electrons require ω²/κ²νi² and ω²/κ∥²νe² ≪ 1 respectively. Only within all these limits can Musher‐Sturman equation adequately describe the collapse of lower hybrid waves.

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U2 - 10.1029/95GL01063

DO - 10.1029/95GL01063

M3 - Article

AN - SCOPUS:84984455237

VL - 22

SP - 1125

EP - 1128

JO - Geophysical Research Letters

JF - Geophysical Research Letters

SN - 0094-8276

IS - 9

ER -