Physics – Plasma Physics
Scientific paper
Oct 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994jgr....9919301s&link_type=abstract
Journal of Geophysical Research (ISSN 0148-0227), vol. 99, no. A10, p. 19,301-19,323
Physics
Plasma Physics
1
Boltzmann Transport Equation, Distribution Functions, Eigenvectors, Particle Diffusion, Plasmas (Physics), Scattering, Transport Theory, Velocity, Angles (Geometry), Differential Equations, Integrals, Magnetic Fields, Pitch (Inclination), Plasma Physics, Theorems
Scientific paper
Gombosi et al. (1993) recently derived a modified telegrapher's equation for charged particle transport under the influence of isotropic scattering. This equation obeys causality and disallows upstream diffusion for particles with random velocities smaller than the bulk flow velocity. The acausal diffusion equation was obtained to lowest order in the expansion of smallness prameters. The paper by Gombosi et al. (1993) prompted responses from Pauls et al. (1993) and Earl (1993). This paper is written to explain the differences between the methods, assumptions, and results of Gombosi et al. (1993), Pauls et al. (1993), and Earl (1993) and presents a new method of obtaining approximate solutions. It is shown that the assumptions used by Gombosi et al. (1993) and Pauls et al. (1993) are physically equivalent. In our solution method, the solution of the modified telegrapher's equation is obtained as the casual limit of solutions accurate to second order in the smallness parameter expansion. In order to investigate the coherent velocity, we have also developed `wavenumber eigenfunctions' which account for all the pitch angle dependence in our Boltzmann equation. Using truncation, Earl (1993) obtains approximations for the wavenumber dependence of the lowest two frequency modes, which correspond to two of the wavenumber eigenmodes. We find that a consequence of including only two wavenumber eigenmodes is that one obtains solutions which disobey causality at sufficiently short times. Furthermore, the coherent velocity of the two eigenmodes is strongly dependent on wavenumber and approaches the particle velocity in the limit of large wavenumber for both isotropic and anisotropic scattering processes.
Gombosi Tamas I.
Schwadron Nathan A.
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