On the Vlasov-Poisson system of equations for an inhomogeneous cylindrical plasma

Diaz, C. J.

doi:10.1088/0032-1028/23/5/007

Cited by 11 publications

(5 citation statements)

References 12 publications

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“…The tapered lens tube is designed so that: (i) If all electrodes are biased at the same high voltage except the outer grounded ones, then the plasma surface will follow a flux tube. In this case the plasma dispersion relation (Diaz 1981) for a cylindrical column of axially uniform plasma can apply, i.e. the wave-vector k does not depend on z .…”

Section: Methodsmentioning

confidence: 99%

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Density distribution of an electron plasma column in a Penning discharge

Xi¹

1986

J. Phys. D: Appl. Phys.

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A technique of determining the density distribution of an electron plasma column confined by non-uniform magnetic fields is presented. The non-uniform confining fields cause the electron density distribution to be non-uniform not only radially, but also axially. Calculations of the plasma shapes show that for a stable plasma mode the plasma surface follows a flux tube in some range of the z axis and gradually shrinks towards the ends. For the plasma whose surface follows a flux tube, the central density profile can be deduced from the measured axially projected density profile. Analysis of the l=0 plasma wave dispersion relation further supports the diagnostics in the electron density distribution.

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Section: Methodsmentioning

confidence: 99%

“…The resonance condition of the longitudinal plasma wave is a means to further support the previous diagnostics in the electron-density distribution. For an inhomogeneous cylindrical plasma, the dispersion relations of the plasma waves have been given in detail by Diaz (1981).…”

Section: Resonance Conditionmentioning

confidence: 99%

Density distribution of an electron plasma column in a Penning discharge

Xi¹

1986

J. Phys. D: Appl. Phys.

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“…where χ φ ψ = − . Any well behaved function of r z t , , , ( ) ψ can be expanded in terms of orthogonal functions as [11]: The orthonormal set Y r z , ,…”

Section: Dielectric Tensor Of Inhomogeneous Plasmamentioning

confidence: 99%

“…The effects of an arbitrary size density gradient were considered by Vranjes and Poedts [10], and the corresponding equation for the spatially dependent wave amplitude was solved analytically. The formal solution of the linearized Vlasov-Poisson equations for an inhomogeneous strongly magnetized plasma column was carried out by Diaz [11]. He used the Fourier-Bessel transformation to obtain the dispersion relation.…”

Section: Introductionmentioning

confidence: 99%

Radially inhomogeneous bounded plasmas

Zakeri-Khatir

Aghamir

2016

Plasma Phys. Control. Fusion

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On the basis of kinetic theory along with self-consistent field equations, the expressions for dielectric tensor of radially inhomogeneous magnetized plasma columns are obtained. The study of dielectric tensor characteristics allows the accurate analysis of the inhomogeneous properties, beyond limitations that exist in the conventional method. Through the Bessel-Fourier transformation, the localized form of material equations in a radially inhomogeneous medium are obtained. In order to verify the integrity of the model and reveal the effect of inhomogeneity, a special case of a cylindrical plasma waveguide completely filled with inhomogeneous magnetized cold plasma was considered. The dispersion relation curves for four families of electromagnetic (EH and HE) and electrostatic (SC and C) modes are obtained and compared with the findings of the conventional model. The numerical analysis indicates that the inhomogeneity effect leads to coupling of electromagnetic and electrostatic modes each having different radial eigen numbers. The study also reveals that the electrostatic modes are more sensitive to inhomogeneous effects than the electromagnetic modes.

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“…Therefore, we use the Fourier-Bessel transformation and differential Fourier-Bessel transformation to localize these equations. [41,42] The localization of the material equation in Fourier-Bessel space is expressed as In addition, the components of this tensor are obtained through the Vlasov equation in the localized space by Bessel-Fourier expansion. Without loss of generality, from the dielectric tensor of the magnetized inhomogeneous warm plasma, [42] one can find the dielectric tensor of the plasma without density gradient for cyclotron harmonic numbers n = −1, 0, 1 as…”

Section: Wave Equationsmentioning

confidence: 99%