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Uniform derivation of Coulomb collisional transport thanks to Debye shielding

Part of: Collisions in Collisionless Plasmas

Published online by Cambridge University Press:  25 July 2014

D. F. Escande ,
Yves Elskens  and
F. Doveil
D. F. Escande*
Affiliation:
Aix-Marseille Université and CNRS, UMR 7345 PIIM, case 321, campus Saint-Jérôme, FR-13013 Marseille, France
Yves Elskens*
Affiliation:
Aix-Marseille Université and CNRS, UMR 7345 PIIM, case 321, campus Saint-Jérôme, FR-13013 Marseille, France
F. Doveil*
Affiliation:
Aix-Marseille Université and CNRS, UMR 7345 PIIM, case 321, campus Saint-Jérôme, FR-13013 Marseille, France
*
†Email address for correspondence: [email protected]
[email protected]
[email protected]
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Abstract

The effective potential acting on particles in plasmas being essentially the Debye-shielded Coulomb potential, the particles collisional transport in thermal equilibrium is calculated for all impact parameters b, with a convergent expression reducing to Rutherford scattering for small b. No cutoff at the Debye length scale is needed, and the Coulomb logarithm is only slightly modified.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 1 , January 2015 , 305810101
Copyright
Copyright © Cambridge University Press 2015 

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References

REFERENCES

Balescu, R 1963 Statistical Mechanics of Charged Particles. London: Wiley–Interscience.Google Scholar
Balescu, R. 1997 Statistical Dynamics: Matter Out of Equilibrium. London: Imperial College Press.Google Scholar
Bénisti, D and Escande, D. F. 1997 Origin of diffusion in hamiltonian dynamics. Phys. Plasmas 4, 1576–1581.Google Scholar
Bénisti, D and Escande, D. F. 1998 Finite range of large perturbations in hamiltonian dynamics. J. Stat. Phys. 92, 909–972.Google Scholar
Besse, N., Elskens, Y., Escande, D. F. and Bertrand, P. 2011 Validity of quasilinear theory: refutations and new numerical confirmation. Plasma Phys. Control. Fusion 53, 025012 (36 pp).Google Scholar
Bodineau, Th., Gallagher, I. and Saint-Raymond, L. 2014 Limite de diffusion linéaire pour un système déterministe de sphères dures. C. R. Acad. Sci. – Math. 352, 411–419.CrossRefGoogle Scholar
Dewar, R. L. 2003 The screened field of a test particle. In: Celebration of K C Hines (eds. McKellar, B. H. J. and Amos, K.). Singapore: World Scientific, pp. 47–73.Google Scholar
Dewar, R. L. and Leykam, D. 2012 Dressed test particles, oscillation centres and pseudo-orbits. Plasma Phys. Control. Fusion 54, 014002 (8 pp).Google Scholar
Elskens, Y. 2012 Gaussian convergence for stochastic acceleration of N particles in the dense spectrum limit. J. Stat. Phys. 148, 591–605.CrossRefGoogle Scholar
Elskens, Y. and Escande, D. 2003 Microscopic Dynamics of Plasmas and Chaos. Bristol: IoP Publishing.Google Scholar
Elskens, Y., Escande, D. F. and Doveil, F. 2014 Vlasov equation and N-body dynamics: How central is particle dynamics to our understanding of plasmas? Eur. Phys. J. D at press.Google Scholar
Elskens, Y. and Pardoux, E. 2010 Diffusion limit for many particles in a periodic stochastic acceleration field. Ann. Appl. Prob. 20, 2022–2039.Google Scholar
Escande, D. F., Doveil, F. and Elskens, Y. 2013 New foundations and unification of basic plasma physics by means of classical mechanics. arXiv:1310.3096 [physics.plasm-ph].Google Scholar
Escande, D. F., Zekri, S. and Elskens, Y. 1996 Intuitive and rigorous microscopic description of spontaneous emission and Landau damping of Langmuir waves through classical mechanics. Phys. Plasmas 3, 3534–3539.CrossRefGoogle Scholar
Ferziger, J. H. and Kaper, H. G. 1972 Mathematical Theory of Transport Processes in Gases. Amsterdam: North-Holland.Google Scholar
Gallagher, I., Saint-Raymond, L. and Texier, B. 2014 From Newton to Boltzmann: Hard Spheres and Short-Range Potentials, Zurich Lect. Notes Adv. Math., vol. 18. Eur. math. soc. Zürich: Eur. math. soc. publishing house.Google Scholar
Gasiorowicz, S., Neuman, M. and Riddell, R. J. Jr. 1956 Dynamics of ionized media. Phys. Rev. 101, 922–934.Google Scholar
Hazeltine, R. D. and Waelbroeck, F. L. 2004 The Framework of Plasma Physics. Boulder: Westview Press.Google Scholar
Hubbard, J. 1961 The friction and diffusion coefficients of the Fokker-Planck equation in a plasma. II. Proc. Roy. Soc. (Lond.) A261, 371–387.Google Scholar
Kiessling, M. K.-H. 2014 The microscopic foundation of Vlasov theory for jellium-like newtonian N-body systems. J. Stat. Phys. 155, 1299–1328.Google Scholar
Lancellotti, C. 2010 From Vlasov fluctuations to the BGL kinetic equation. Nuovo Cim. 33 C, 111–119.Google Scholar
Rosenbluth, M. N., MacDonald, W. M. and Judd, D. L. 1957 Fokker-Planck equation for an inverse-square force. Phys. Rev. 107, 1–6.Google Scholar
Rostoker, N. 1964 Superposition of dressed test particles. Phys. Fluids 7, 479–490.Google Scholar
Rostoker, N. and Rosenbluth, M. N. 1960 Test particles in a completely ionized plasma. Phys. Fluids 3, 1–14.CrossRefGoogle Scholar
Spohn, H. 1991 Large Scale Dynamics of Interacting Particles. Berlin: Springer.Google Scholar