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Degenerate continuous spectra producing localized secular instability – an example in a non-neutral plasma

Published online by Cambridge University Press:  09 September 2003

M. HIROTA
Affiliation:
Graduate School of Frontier Sciences, University of Tokyo, Tokyo 113-0033, Japan ([email protected])
T. TATSUNO
Affiliation:
Graduate School of Frontier Sciences, University of Tokyo, Tokyo 113-0033, Japan
Z. YOSHIDA
Affiliation:
Graduate School of Frontier Sciences, University of Tokyo, Tokyo 113-0033, Japan

Abstract

Fluctuations in ambient shear flow exhibit interesting transient phenomena. Shear flow produces not only Kelvin–Helmholtz modes (global exponential instabilities represented by point spectra) but also local algebraic instabilities associated with multiple continuous spectra. Since the generating operator is non-Hermitian, the orthogonality of eigenmodes is broken, and unresolvable mode couplings (resonances) bring about secular behavior (algebraic instability). We analyze electrostatic fluctuations in a magnetized non-neutral (single species) plasma where the electrostatic potential parallels the stream function. This secular behavior is reproduced by solving the initial value problem with a renormalization method.

Type
Papers
Copyright
© 2003 Cambridge University Press

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