The Boltzmann equation an d the one-fluid hydromagnetic equations in the absence of particle collisions

1956/07/10 by G. F. Chew, Geoffrey F. Chew, M. L. Goldberger +1 · 1,381 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Boltzmann equation #Classical mechanics #Collision #Convection–diffusion equation #Gas Dynamics and Kinetic Theory #Lorentz force #Lorentz transformation #Magnetic field #Magnetohydrodynamics #Mechanics #Physics #Plasma #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #Thermodynamics

paper · doi:10.1098/rspa.1956.0116

published in Proceedings of the Royal Society of London A Mathematical and Physical Sciences 236(1204), 112-118 (Royal Society)

openalex publication_date 1956/07/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29

Abstract

Abstract Starting from the Boltzmann equation for a completely ionized dilute gas with no interparticle collision term but a strong Lorentz force, an attempt is made to obtain one-fluid hydromagnetic equations by expanding in the ion mass to charge ratio. It is shown that the electron degrees of freedom can be replaced by a macroscopic current, but true hydrodynamics still does not result unless some special circumstance suppresses the transport of pressure along magnetic lines of force. If the longitudinal transport of pressure is ignored, a set of self-contained one-fluid hydromagnetic equations can be found even though the pressure is not a scalar.

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