Statistics – Computation
Scientific paper
Oct 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000aipc..537...91v&link_type=abstract
WAVES IN DUSTY, SOLAR, AND SPACE PLASMAS. AIP Conference Proceedings, Volume 537, pp. 91-98 (2000).
Statistics
Computation
3
Dust Processes, Macroinstabilities
Scientific paper
Self-gravitating clouds have been shown by Jeans to be unstable to harmonic perturbations whose wavelength exceeds some critical value involving the mass density and some thermal velocity or equivalent information. Based upon the assumption that the unperturbed cloud is initially uniform, the Jeans instability is non-oscillatory and purely growing. However, Newtonian gravitation precludes strictly homogeneous equilibria, but a way out is offered, in theory, by considering local perturbations, small compared to the inhomogeneity scale lengths. While in itself plausible, this procedure can in most cases not be tested for internal consistency, because real knowledge about the equilibrium is lacking, and is therefore called the Jeans swindle. The severe limitations of such an approach lead to an unavoidable dichotomy, and an example of a plasma will be discussed where the computations can be done explicitly, both for the stationary as well as for the perturbed state, showing that the system is stable at all wavelengths compatible with the equilibrium inhomogeneity. Nevertheless, the present state of affairs does not allow self-consistent equilibria to be worked out in more complicated configurations, like in dusty plasmas with external magnetic fields. This typically leads to the Jeans swindle being used a little longer than desirable. .
Cadez Vladimir M.
Jacobs Gerald
Verheest Frank
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