from Part I - 1-D MHD in Ten Weeks
Published online by Cambridge University Press: 05 June 2025
This chapter introduces the magnetic induction, B̅, to fluid dynamics. After a brief introduction establishing the ubiquity of magnetism in the universe, the ideal induction equation is derived from the idea of electromagnetic force balance and Faraday’s law. By proposing and proving the flux theorem, Alfvén’s theorem is proven to show that in an ideal MHD fluid, magnetic flux is conserved and frozen-in to the fluid. It is further shown how the introduction of Bti introduces the Lorentz force density to the momentum equation and the Poynting power density to the energy equation. Two variations of the equations of MHD are assembled, both involving the conservative variables. Finally, the vector potential, magnetic helicity, and magnetic topology are introduced in an optional section where the link to solar coronal flux loops is made.
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