<i>Plasma Kinetic Theory</i>

Montgomery, David; Tidman, D. A.; Chang, Howard H. C.

doi:10.1063/1.3047452

Cited by 34 publications

(59 citation statements)

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“…An alternative and very frequently used interpretation of the Debye length (e.g. Montgomery and Tidman 1964;Chen 1974) involves the distance where the exponential factor, which is included in the spatial function of the electric potential, falls to ∼1/e of its unshielded value. For the 1-D case, the spatial dependence of the potential is given only by the exponential factor, i.e.…”

Section: R(x)mentioning

confidence: 99%

“…Kallenrode 2004;Baumjohann and Treumann 2012), and (2) the distance at which the potential energy from a charge perturbation has fallen to 1/e of its unshielded value (e.g. Montgomery and Tidman 1964;Chen 1974). Interpretation 1 is a physical property of Debye shielding; it involves the distance where a sort of equilibrium is established between the 'source' of the shielding that is the restoring electric potential, and the 'sink' of the shielding that is the disturbing thermal energy.…”

Section: Introductionmentioning

confidence: 99%

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Electrostatic shielding in plasmas and the physical meaning of the Debye length

Livadiotis

McComas

2014

J. Plasma Phys.

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This paper examines the electrostatic shielding in plasmas, and resolves inconsistencies about what the Debye length really is. Two different interpretations of the Debye length are currently used: (1) The potential energy approximately equals the thermal energy, and (2) the ratio of the shielded to the unshielded potential drops to 1/e. We examine these two interpretations of the Debye length for equilibrium plasmas described by the Boltzmann distribution, and non-equilibrium plasmas (e.g. space plasmas) described by kappa distributions. We study three dimensionalities of the electrostatic potential: 1-D potential of linear symmetry for planar charge density, 2-D potential of cylindrical symmetry for linear charge density, and 3-D potential of spherical symmetry for a point charge. We resolve critical inconsistencies of the two interpretations, including: independence of the Debye length on the dimensionality; requirement for small charge perturbations that is equivalent to weakly coupled plasmas; correlations between ions and electrons; existence of temperature for nonequilibrium plasmas; and isotropic Debye shielding. We introduce a third Debye length interpretation that naturally emerges from the second statistical moment of the particle position distribution; this is analogous to the kinetic definition of temperature, which is the second statistical moment of the velocity distribution. Finally, we compare the three interpretations, identifying what information is required for theoretical/experimental plasma-physics research: Interpretation 1 applies only to kappa distributions; Interpretation 2 is not restricted to any specific form of the ion/electron distributions, but these forms have to be known; Interpretation 3 needs only the second statistical moment of the positional distribution.

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Section: R(x)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Electrostatic shielding in plasmas and the physical meaning of the Debye length

Livadiotis

McComas

2014

J. Plasma Phys.

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“…The BBGKY kinetic theory was suggested (Rostoker and Rosenbluth 1960;Frieman and Book 1963;Montgomery and Tidman 1964;Liboff 1969) as an alternative approach to overcome the difficulty. It was further realized that the correlation contribution could be modeled in terms of a distributed field (Liboff 1969) and corresponds to the Vlasov term (LHS) of the kinetic equation describing the time evolution of the one particle distribution function.…”

Section: Discussionmentioning

confidence: 99%

“…According to BBGKY theory (Montgomery and Tidman 1964;Liboff 1969) f 2 can only be accepted as satisfactory provided that:…”

Section: The Basic Distribution Functionmentioning

confidence: 99%

“…Its importance has been stressed in the last four decades (Frieman and Book 1963;Montgomery and Tidman 1964;Liboff 1969;Chapman and Cowling 1970;van Beyeren and Ernst 1979;Klimontovich 1982;Zubarev et al 1991;Xing 1998) and is estimated by either of the ratios τ = t c /t m , χ= σ/l m where t c is the time spent within the field effect of the target, σ is the radius of the cross section for interaction, l m and t m the mean free path and mean collision time. When τ Ӷ 1 and χ Ӷ 1, the Boltzmann collision term is valid; otherwise, correlation aspects must be considered.…”

Section: Introductionmentioning

confidence: 99%

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A collision term valid from rarefied to dense gases and plasmas

Zamlutti

2004

J. Plasma Phys.

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Abstract. The Boltzmann collision integral for binary encounters is restricted to rarefied gases and plasmas by the constraint that the mean free path be much larger than the range of interaction. For dense media the two lengths become comparable and a proper account of the mutual influence exerted by one particle on the other during a collision must be taken. There are also other situations involving chargedcharged long-range interactions for which this condition is met even in rarefied plasmas. The matter is considered in this work with the solution of the BBGKY (Born, Bogoliubov, Kirkwood, (H. S.) Green, Yvon) equation to determine the joint distribution function for the encountering particles. It is shown, in particular, that for dense gases the results replace the traditional Enskog χ factor, whereas for plasmas oscillatory phenomena can be driven. The proposed theory constitutes an improvement over the revised Enskog theory (RET) to the extent that it is not restricted to the soft sphere encounters, but valid for any sort of field interaction between colliding particles. Moreover the correlation term replaces the unsuitable restitution coefficient of the RET approach, which is restricted to impact theory. The present material is important for studies in solar and terrestrial physics, which require the sole knowledge of the one particle distribution function, namely gas dynamics and Coulomb plasma research.

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Higher Harmonics and Transport Coefficients of Plasmas in Circulary Polarized Magnetic Fields and Additional Electromagnetic Fields

Kirsten

Vojta²

1972

Contrib Plasma Phys

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With the methods of kinetic theory on the basis of the Boltzmann and Fokker-Planck kinetic equations the behaviour of a Lorentz plasma in a circularly polarized (rotating) magnetic field (rotation frequencyw), a n alternating electric field (frequency 0') and additional constant electromagnetic fields is inveatigated. By means of a generalized Fourier expansion it is shown that the above fields create in the plasma currenta of the frequencies 0, w', w-w', w, w+w', 2w-w', 20, and 2w+w'. Tramport, coefficients are calculated explicitly and the validity of Onsager reciprocity relations and that of Kronig-liramers relations is discussed. The special c&98 of the electric field induced by the rotating magnetic field is treated separately. Finally, problems of plasma containment are discussed.

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Plasma Kinetic Theory

Cited by 34 publications

References 0 publications

Electrostatic shielding in plasmas and the physical meaning of the Debye length

Electrostatic shielding in plasmas and the physical meaning of the Debye length

A collision term valid from rarefied to dense gases and plasmas

Higher Harmonics and Transport Coefficients of Plasmas in Circulary Polarized Magnetic Fields and Additional Electromagnetic Fields

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