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The limitation and applicability of Musher‐Sturman Equation to two‐dimensional lower hybrid wave collapse
Author(s) -
Tam Sunny W. Y.,
Chang Tom
Publication year - 1995
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/95gl01063
Subject(s) - physics , wave equation , electron , field (mathematics) , ponderomotive force , quantum electrodynamics , computational physics , classical mechanics , quantum mechanics , mathematics , pure mathematics
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.