project1 - B v A = Modes If k and v A are...

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Magneto-acoustic Effects in Stellar Winds
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Introduction The flux of particles from stars is called stellar wind Global parameters are dM/dt and v terminal Different stellar models predict different values for the above parameters Radiation pressure of the star is considered as a main source of stellar wind Red giants problem
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Alfven model The wind is treated as a highly conductive fluid ) ( B c v E j × + = σ t B c E - = × 1 B c B v c B v t B 2 4 ) ( 4 ) ( + × × - × × = π η
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) ( B v t B × × = The “frozen” field concept ρ ) ( v dt d - = v B B dt d ) ( ) ( = v x x dt d ) ( ) ( = δ δ
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Magnetic field lines
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MHD equations ) ( ) ( 4 1 ) ( 0 ) ( B v t B B B p v v t v v t × × = × × - -∇ = + = + π ρ
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Linearization t i x k i e v t x v t x u t x t x t x B B t x B ϖ ρ - = = + = + = 1 1 1 0 1 0 ) , ( ) , ( ) , ( ) , ( ) , ( ) , ( 0 ] ) ( ) ( ) )[( ( ) )( ( 1 1 1 1 2 2 1 2 = - - + + + + - A A A A A v v k k v v v k v k v k v k v s v = p s 2 0 2 0 2 4 πρ
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Unformatted text preview: B v A = Modes If k and v A are perpendicular-longitudinal mode with u long 2 =s 2 +v A 2 If k and v A are parallel, there are two modes Longitudinal with u=s (pure acoustic wave) Transverse with u= v A (Alfven wave) Mass loss rate of red giants ] [ ) 10 ( 10 1 . 9 1 13 2 / 3 * 2 / 7 * 4 17 units yr M M R B dt dM Sun-- = Gauss B M M R R Sun Sun 1 1 300 * * = = = ] [ 10 8 1 7 units yr M dt dM Sun-- = References [1]Henry J.G.L.M. Lamers, Joseph P. Cassinelli Introduction to Stellar Winds,1999 [2]Peter A. Sturrock Plasma Physics,1994 [3]J.D.Jackson Classical Electrodynamics,1975...
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project1 - B v A = Modes If k and v A are...

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