Dynamos by Ph. Cardin and L.F. Cugliandolo (Eds.)

Dynamos by Ph. Cardin and L.F. Cugliandolo (Eds.)

By Ph. Cardin and L.F. Cugliandolo (Eds.)

This ebook is a set of lectures given in July 2007 on the Les Houches summer time university on "Dynamos". . offers a pedagogical advent to themes in Dynamos . Addresses each one subject from the root to the newest advancements . Covers the lectures through internationally-renowned and major specialists

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29 30 8 13 Euler (1701–1783) He was a great mathematician from Switzerland and left contributions in many area of science, working mainly in St Petersburg and Berlin. Euler equations (published in Mémoires de l’académie des sciences de Berlin, 1757) are a general version of Newton’s second law to a continuous medium with no internal shear stress ρ∂u/∂t + ρ(u · ∇)u = −∇p. They result from taking into account the continuity equation, another discovery by Euler: ∂ρ/∂t + div(ρu) = 0. 21 22 6 7 Newton (1642–1727) He spent his life as an academic in Cambridge (UK).

A dimensional velocity VA = √ B0 / ρμ. 6. Skin effect/field expulsion 24 25 3 7 = 22 23 2 24 This effect can be understood in terms of the induction equation alone, hence it is not particular to MHD. Let us consider an electrically conducting solid submitted to an external alternating magnetic field of frequency f . The dimensional induction equation in a solid can be written: 1 2 ∂B = ∇ B. 11) The scaling analysis of√this “heat equation” tells us that the AC magnetic field enters a depth δ ∼ 1/ μσf into the solid conductor.

1. 1. 2. 2. tex; 22/05/2008; 17:25 4 1 2 3 4 5 6 7 8 9 p. 4 T. 1. 3. Stability of non-dissipative MHD References 8. 1. 2. 3. 4. 5. 6. tex; 22/05/2008; 17:25 p. 5 1 1 2 2 3 3 4 4 5 5 6 6 7 7 Introduction 8 9 10 11 12 13 14 15 16 17 18 19 20 8 Dynamo action takes its origin in the coupling between dynamics and electromagnetism. In most case it concerns the dynamics of fluids with a good electrical conductivity and the magneto-quasi-static limit of electromagnetism is used. e. the coupling between dynamics and electromagnetism in an electrically conducting fluid, can then be modelled by the coupling between the Navier–Stokes equation and the induction equation.

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