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sess14 - 14 Reading Shu Vol II Ch 21 14.1 The equations of...

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Unformatted text preview: 14. Magnetohydrodynamics Reading: Shu, Vol. II, Ch. 21 14.1 The equations of magnetohydrodynamics In our preceding considerations we have treated gas independent of its state of ionization, yet we know that an ionized medium can carry and be influenced by electromagnetic fields, that should follow Maxwell’s equations. ~ ∇ · ~ E = 4 π ρ e ~ ∇ × ~ E =- 1 c ∂ ~ B ∂t (14 . 1- 2) ~ ∇ · ~ B = 0 ~ ∇ × ~ B = 4 π c ~ j e + 1 c ∂ ~ E ∂t (14 . 3- 4) where the charge density and current density are ρ e = Z e n i- e n e (14 . 5) ~ j e = Z e n i ~ V i- e n e ~ V e (14 . 6) Implicit to Maxwell’s equations is the charge conservation, for ∂ρ e ∂t = 1 4 π ~ ∇ · ∂ ~ E ∂t = c 4 π ~ ∇ · ( ~ ∇ × ~ B )- ~ ∇ · ~ j e ⇒ ∂ρ e ∂t + ~ ∇ · ~ j e = 0 (14 . 7) The effect of the electromagnetic fields is different depending on the spatial scale on which they arise. Small-scale perturbations of the fields typically lead to electromagnetic waves which we will discuss later.will discuss later....
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sess14 - 14 Reading Shu Vol II Ch 21 14.1 The equations of...

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