Convective growth of parametrically unstable modes in inhomogeneous media

Journal Article · Sat Jun 01 04:00:00 EDT 1991 · Physics of Fluids B; (USA)

DOI:https://doi.org/10.1063/1.859719· OSTI ID:5673855

Williams, E A ^[1]

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1. Lawrence Livermore National Laboratory, L472, Box 5508, Livermore, California 94550 (US)

By a suitable definition of an amplification coefficient, a convenient analytic criterion for convective instability of damped parametrically coupled unstable modes in an inhomogeneous medium is obtained. The net growth factor {ital F}{sub 3} on propagation through the resonant interaction region is found to be given by {ital F}{sub 3} = exp(({pi}{gamma}{sup 2}{sub 0}/{kappa}{prime}{ital v}{sub 1}{ital v2}){ital F}({radical}{nu}{sub 1}{nu}{sub 2}/{gamma}{sub 0})), where the reduction factor {ital F}({ital x}) = (2/{pi})(acos({ital x}) {minus} {ital x}{radical}1{minus}{ital x}{sup 2}). This can readily be seen to reduce to the usual inhomogeneous gain formula when damping is negligible and {ital F}=1, and to manifest the homogeneous convective threshold, {gamma}{sup 2}{sub 0} {gt} {nu}{sub 1}{nu}{sub 2}. This result should find useful application in laser fusion plasmas, where damping and spatial inhomogeneity are frequently suppression mechanisms of comparable importance for laser-driven parametric instabilities.

• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 5673855
• Journal Information: Physics of Fluids B; (USA), Journal Name: Physics of Fluids B; (USA) Vol. 3:6; ISSN PFBPE; ISSN 0899-8221
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700107* -- Fusion Energy-- Plasma Research-- Instabilities
700108 -- Fusion Energy-- Plasma Research-- Wave Phenomena
700208 -- Fusion Power Plant Technology-- Inertial Confinement Technology
AMPLIFICATION
ANALYTICAL SOLUTION
CONVECTIVE INSTABILITIES
COUPLING
DAMPING
ENERGY
INHOMOGENEOUS PLASMA
INSTABILITY
INSTABILITY GROWTH RATES
LASER-PRODUCED PLASMA
PARAMETRIC INSTABILITIES
PLASMA
PLASMA INSTABILITY
PLASMA MACROINSTABILITIES
RESONANCE
THRESHOLD ENERGY
WKB APPROXIMATION