Computer Science – Numerical Analysis
Scientific paper
Jan 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993apj...403..377g&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 403, no. 1, p. 377-384.
Computer Science
Numerical Analysis
20
Charged Particles, Transport Theory, Asymptotic Methods, Numerical Analysis, Partial Differential Equations, Transport Properties
Scientific paper
We present a new derivation of the telegraph equation which modifies its coefficients. First, an infinite order partial differential equation is obtained for the velocity space solid angle-averaged phase-space distribution of particles which underwent at least a few collisions. It is shown that, in the lowest order asymptotic expansion, this equation simplifies to the well-known diffusion equation. The second-order asymptotic expansion for isotropic small-angle scattering results in a modified telegraph equation with a signal propagation speed of v(5/11) exp 1/2 instead of the usual v/3 exp 1/2. Our derivation of a modified telegraph equation follows from an expansion of the Boltzmann equation in the relevant smallness parameters and not from a truncation of an eigenfunction expansion. This equation is consistent with causality. It is shown that, under steady state conditions in a convecting plasma, the telegraph equation may be regarded as a diffusion equation with a modified transport coefficient, which describes a combination of diffusion and cosmic-ray inertia.
Gombosi Tamas I.
Jokipii Randy J.
Kota József
Lorencz K.
Williams Lance Lee
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