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- W588481694 abstract "1 Modeling acoustic modes and zonal flows in the framework of MHD As in Ref. [1] small electrostatic perturbations about a static MHD equilibrium are studied. In this work the notation of Refs. [2] is used. For electrostatic perturbations ∂~B/∂ t = 0, so that from Faraday’s law the perturbed electric field E1 is the gradient of a potential Φ1. Therefore, Ohm’s law for the perturbation electric field may be written as E1 = −∇Φ1 = B0 × ∂tξ , where ~ξ is the MHD displacement vector. Three scalar perturbation functions related to ~ξ are used: the normal displacement ξ s = ~ξ ·∇s, and the two components varying in the magnetic surface s = const, η = −F ′ t ~ξ · (∇θ − ι∇φ), and μ = √gF ′ t ~ξ · (∇φ + ι∇θ). Because of B0 ·∇Φ1 = 0, the potential of the perturbed electric field is a surface function, i.e. Φ1 = Φ1(s). Equating the component of E1 along ∇s×~B0 shows that 0 = ∇s×~B0 ·∇Φ1 = (∇s×~B0) · (∂tξ ×~B0) = B0 ∂tξ s, i.e. ξ s ≡ 0. With this result, taking the component of E1 along ∇s shows that Φ1,s = −η . Since Φ1 is a surface function, η must also be a surface function, η = η(s), with the assumptions made here, i.e. for electrostatic perturbations. With a time dependence exp(iω t), the MHD equation of motion reduces to −ρ0ω ~ξ = −∇p1, and the pressure equation to p1 = −γ p0 ∇ ·~ξ . Taking the component of the equation of motion along B0, a magnetic DE is obtained for ∇ ·~ξ , −ρ0ω √ g ~ξ ·~B0 = γ p0 √ gB0 ·∇(∇ ·~ξ ). Its integrability condition is √ g ~ξ ·~B0 〉" @default.
- W588481694 created "2016-06-24" @default.
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- W588481694 date "2006-01-01" @default.
- W588481694 modified "2023-09-23" @default.
- W588481694 title "3-d linear MHD for acoustic modes and zonal flows" @default.
- W588481694 hasPublicationYear "2006" @default.
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