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

Sunny W.Y. Tam, Tom Chang

研究成果: Article

6 引文 (Scopus)

摘要

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 κ²/κ²≫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/κ²νe² ≪ 1 respectively. Only within all these limits can Musher‐Sturman equation adequately describe the collapse of lower hybrid waves.

原文English
頁(從 - 到)1125-1128
頁數4
期刊Geophysical Research Letters
22
發行號9
DOIs
出版狀態Published - 1995 五月 1

指紋

magnetic field
ponderomotive forces
ion
wave field
rockets
magnetic fields
ionospheres
ionosphere
ions
electron
electrons
experiment
interactions
calculation

All Science Journal Classification (ASJC) codes

  • Geophysics
  • Earth and Planetary Sciences(all)

引用此文

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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/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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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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