A single-fluid, self-consistent formulation of fluid dynamics and particle transport

L. L. Williams, J. R. Jokipii

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


We present the fluid equations for typical astrophysical plasmas, for the case of no average magnetic field and nonrelativistic flow speeds, in which particular acceleration occurs. When combined with the particle transport equation presented earlier by Williams, et al., one obtains a fully self-consistent description of particle transport and smooth fluid flow (length scales significantly larger than the mean free path). A presumed scattering law is taken for particles of all energies, and there is a single distribution function as well. This model of the interaction of particle transport, including acceleration, and fluid dynamics is in terms of four unknowns: the fluid velocity vector and the isotropic part of the particle distribution function. The four unknowns must satisfy a transport equation valid for all particles, and a vector momentum equation for the fluid, all correct to order λ/L. The fluid velocity is defined as the frame in which the scattering centers are at rest. We expect this approach to complement two-fluid models and Monte Carlo models used by previous authors to investigate the interaction between particle transport and fluid dynamics. The advantage of this approach over the two-fluid one is that there is no need to introduce arbitrary "closure parameters." Only the scattering law is assumed. The advantage over the Monte Carlo models is the computational efficiency gained by reducing the problem to a few coupled partial differential equations. Simple examples are presented which illustrate the concepts.

Original languageEnglish (US)
Pages (from-to)725-734
Number of pages10
JournalAstrophysical Journal
Issue number2
StatePublished - Nov 10 1993


  • Acceleration of particles
  • Cosmic rays
  • Hydrodynamics

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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