Abstract
In this chapter magnetohydrodynamical (MHD) equations are derived from the Boltzmann equation. First, we discuss under what conditions particle systems can be treated as magnetohydrodynamical systems. Next, the set of magnetohydrodynamical equations are derived from the Boltzmann equation by taking the moments of the equation. In this derivation of MHD equations, we examine ion and electron systems separately, because it is instructive to see the origin of electromagnetic force on fluid. Generalized Ohm’s is also derived. In this chapter gravitational force is neglected for simplicity.
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References
Thompson, W.B.: An Intoduction to Plasma Physics, Chap. 8. Pergamon Press, Oxford (1962)
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Kato, S., Fukue, J. (2020). Derivation of Magnetohydrodynamical Equations from Boltzmann Equation. In: Fundamentals of Astrophysical Fluid Dynamics. Astronomy and Astrophysics Library. Springer, Singapore. https://doi.org/10.1007/978-981-15-4174-2_10
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DOI: https://doi.org/10.1007/978-981-15-4174-2_10
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Publisher Name: Springer, Singapore
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Online ISBN: 978-981-15-4174-2
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