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Potential bounds and estimation for the multiple water-bag plasma

Published online by Cambridge University Press:  13 March 2009

Lim Chee-Seng
Lim Chee-Seng
Affiliation:
Department of Mathematics, National University of Singapore, Singapore 0511, Republic of Singapore
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Abstract

Bounds are established for the permanent-state radiation-conditioned response to a vibrating charge in the MWB (‘multiple water-bag’) model of a warm Maxwellian plasma. Those bounds vary with the observation position beyond the charge and, along any radial direction, serve as boundary curves of potential bands containing the exact potential curves. They can therefore be employed for potential estimation. The bounds are actually Poisson potentials and are independent of (the degree of accuracy in) the MWB modelling when the charge frequency ω exceeds the electron plasma frequency ωp. In this case each potential band narrows to improve potential estimation as ω/ωp increases, and in fact a relative error in estimation can be uniformly predetermined to as small as one desires for all MWB models, charge distributions and observation points by setting ω beyond an appropriate level above ωp. The bounds are, however, model-dependent if ωp exceeds ω in magnitude, in which case, they are partially Poissonian; moreover, potential estimation based on them improves as ω/ωp decreases, and an error analysis is again performed. In either case, a sharper estimation is obtained by averaging the bounds to get an estimate; thus, for instance, the associated relative error cannot exceed 0·01, 0·02 and 0·05 when ω/ωp = (101)½, (51)½ and (21)½ respectively. Applications are described.

Type
Research Article
Information
Journal of Plasma Physics , Volume 44 , Issue 3 , December 1990 , pp. 377 - 392
Copyright
Copyright © Cambridge University Press 1990

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