Normal Modes of a Nonuniform Plasma

Leavens, W. M.

doi:10.1063/1.1692024

Cited by 5 publications

(1 citation statement)

References 7 publications

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“…The relation FAOH in herderite and hydroxylherderite were also studied in different ways. In a systematic optical and chemical characterization, Leavens et al [20] have described the dependence of the refractive index with the F/OH ratios and have established the increase of refractive index to the decrease of F content.…”

Section: Introductionmentioning

confidence: 99%

Raman, infrared and near-infrared spectroscopic characterization of the herderite–hydroxylherderite mineral series

Frost

Scholz

López

et al. 2014

Spectrochimica Acta Part A: Molecular and Biomolecular Spectros

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Natural single-crystal specimens of the herderite-hydroxylherderite series from Brazil, with general formula CaBePO4(F,OH), were investigated by electron microprobe, Raman, infrared and near-infrared spectroscopies. The minerals occur as secondary products in granitic pegmatites. Herderite and hydroxylherderite minerals show extensive solid solution formation. The Raman spectra of hydroxylherderite are characterized by bands at around 985 and 998 cm(-1), assigned to ν1 symmetric stretching mode of the HOPO3(3-) and PO4(3-) units. Raman bands at around 1085, 1128 and 1138 cm(-1) are attributed to both the HOP and PO antisymmetric stretching vibrations. The set of Raman bands observed at 563, 568, 577, 598, 616 and 633 cm(-1) are assigned to the ν4 out of plane bending modes of the PO4 and H2PO4 units. The OH Raman stretching vibrations of hydroxylherderite were observed ranging from 3626 cm(-1) to 3609 cm(-1). The infrared stretching vibrations of hydroxylherderites were observed between 3606 cm(-1) and 3599 cm(-1). By using a Libowitzky type function, hydrogen bond distances based upon the OH stretching bands were calculated. Characteristic NIR bands at around 6961 and 7054 cm(-1) were assigned to the first overtone of the fundamental, whilst NIR bands at 10,194 and 10,329 cm(-1) are assigned to the second overtone of the fundamental OH stretching vibration. Insight into the structure of the herderite-hydroxylherderite series is assessed by vibrational spectroscopy.

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Section: Introductionmentioning

confidence: 99%

Raman, infrared and near-infrared spectroscopic characterization of the herderite–hydroxylherderite mineral series

Frost

Scholz

López

et al. 2014

Spectrochimica Acta Part A: Molecular and Biomolecular Spectros

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Kinetic Model of Tonks-Dattner Resonances in Plasma Columns

Baldwin

1969

The Physics of Fluids

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The linearized Vlasov equation is used to describe the coupling to plasma waves in bounded plasmas of externally driven quasistatic electric fields of frequency ω, treating as an example a cylindrically symmetric equilibrium. The coupling takes place at the plasma resonance, where ω equals the local plasma frequency. It is described by an asymptotic theory based upon the small parameter νT/ωL < < 1, whereνT, where is the electron thermal velocity and L the equilibrium scale length. A previously suggested mechanism based on a WKB solution of the Vlasov equation is then developed to provide trapping of the plasma waves between the plasma resonance and the wall sheath, including the effects of Landau damping. The effect of these internal resonances on the external admittance of the plasma is shown, and a numerical example containing typical experimental parameters is given. A comparision is made with previous theories which utilized a fluid model of the plasma.

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Normal Mode Representation of the High-Frequency Properties of an Inhomogeneous Plasma

Leavens

Love²

1969

The Physics of Fluids

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Analysis of “exact” numerical solutions of the Vlasov equation for longitudinal perturbations of a realistic inhomogeneous plasma shows that the response Ep(x)eiwt to an externally supplied driving field Ed(x)eiwt is well described by a normal mode representation Ep(x) = ∑ n=1N En(x)ω2 − ωn2 ∫ 0L En(x′) dx′. The free oscillation frequencies ωn and the normal modes En(x) are determined from solutions of the Vlasov equation for a δ-function driving field. The normal mode representation is then used to obtain the solution of the Vlasov equation for a uniform driving field, and the results compare well with “exact” solutions.

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Normal Modes of a Nonuniform Plasma

Abstract: The spectrum of undriven electron plasma oscillations of a realistic, nonuniform, collisionless plasma with a sheath is determined. The spectrum is found to be discrete.

Cited by 5 publications

References 7 publications

Raman, infrared and near-infrared spectroscopic characterization of the herderite–hydroxylherderite mineral series

Raman, infrared and near-infrared spectroscopic characterization of the herderite–hydroxylherderite mineral series

Kinetic Model of Tonks-Dattner Resonances in Plasma Columns

Normal Mode Representation of the High-Frequency Properties of an Inhomogeneous Plasma

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