Effect of velocity dependence of Coulomb logarithm on the solution of the Fokker-Planck equation

Cooper, G.E.

doi:10.1063/1.1694156

Cited by 11 publications

(4 citation statements)

References 3 publications

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“…is different from the 8™ act used above. This representation permits a discussion of the influence of the velocity dependence of the Coulomb logarithm (Cooper & Herman 1973), since one can, in contrast to 8£> act , use the approximations of 8 -4 1 and a velocity-independent logarithm independently from each other.…”

Section: Discussionmentioning

confidence: 99%

Transfer integrals for fully ionized gases

1996

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The general transfer integrals describing the collisional exchange of momentum and energy between the constituents of multicoimponent gases are evaluated for different plasma scenarios characterized by Maxwellian as well as non-Maxwellian distribution functions of the plasma species. Following a brief presentation of the standard approximation frequently employed in the literature, a comparison of numerical evaluations of the transfer integrals for various distribution functions reveals significant differences in the corresponding collisional momentum and energy exchange rates, which are shown to depend mainly on the core structure of the distributions. We demonstrate the inadequacy of the standard approximation and hence the importance of an accurate evaluation of the transfer integrals with an application to the electron proton as well as the helium proton interaction in the solar wind plasma.

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Section: Discussionmentioning

confidence: 99%

Transfer integrals for fully ionized gases

1996

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“…ROSEN-BLUTH, MACDONALD, and JUDD pointed out that such treatment is made mainly because no better way could be found [8] . Some authors have noted the defect [12] ; however, no sound justification has ever been given for this treatment.…”

Section: Introductionmentioning

confidence: 99%

The Modified Friction and Diffusion Coefficients of Fokker–Planck Equation and Relaxation Rates for Non-Maxwellian Scattering

Xiang

Ding

Huishan

2008

Plasma Sci. Technol.

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In this paper, a new method to derive the Fokker-Planck coefficients defined by a non-Maxwellian velocity distribution function for the field particles is presented. The threefold integral and the new Debye cutoff parameter, which were introduced by CHANG and LI, are applied. Therefore, divergence difficulties and the customary replacement of relative velocity g by thermal velocity υ th are naturally avoided. The probability function P (v, Δv) for non-Maxwellian scattering is derived by the method of choosing velocity transfer Δv, which is a true measure of collision intensity, as an independent variable. The method enables the difference between small-angle scattering and small-momentum-transfer collisions of the inverse-square force to be well clarified. With the help of the probability function, the Fokker-Planck coefficients are obtained by a normal original Fokker-Planck approach. The friction and diffusion coefficients of the Fokker-Planck equation are modified for non-Maxwellian scattering and are used to investigate the relaxation processes for the weakly coupled plasma. The profiles of the relaxation rates show that the slowing down and deflection processes are weakened in the conditions of non-Maxwellian scattering.

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“…A more general approach to calculate these coefficients has been established by Rosenbluth and collaborators' 4 ', which seems to be perfect except an unevaluated approximation about the velocity dependence of the Coulomb logarithm' 4,5 ]. It is also believed' 6 ' 7 ] that Chandrasekhar's expression for (Au^) is not valid when vl/vj t > In A (v pt is the thermal velocity of the field particle).…”

Section: Introductionmentioning

confidence: 99%

The Friction and Diffusion Coefficients with Maxwellian Scatters

Chang¹,

Yuping²,

Liu³

1993

Commun. Theor. Phys.

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The Fokker-Planck coefficients for Coulomb interaction, or the friction coefficient (the average change in velocity) and the diffusion coefficient , are evaluated by an appropriate variable change technique. This approach reduces the five-fold integral expressions of the Fokker-Planck coefficients to one-fold integral without meeting the divergence difficulties. A new Debye cutoff parameter , instead of the customary cutoff avoids the error incurred through the customary neglecting of velocity dependence of the Coulomb logarithm. The dominant terms of the new results are similar to Chandrasekhar's results. A non-dominant term, which can exceed the dominant one in the case of is added for .

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Effect of velocity dependence of Coulomb logarithm on the solution of the Fokker-Planck equation

Cited by 11 publications

References 3 publications

Transfer integrals for fully ionized gases

Transfer integrals for fully ionized gases

The Modified Friction and Diffusion Coefficients of Fokker–Planck Equation and Relaxation Rates for Non-Maxwellian Scattering

The Friction and Diffusion Coefficients with Maxwellian Scatters

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