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 Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 1, Pages 137–151 (Mi zvmmf58)

Solution of the skin effect problem with an arbitrary coefficient of specular reflection

A. V. Latyshev, A. A. Yushkanov

Moscow State Regional University, ul. Radio 10a, Moscow, 105005, Russia

Abstract: An analytical solution of the skin effect problem in a metal with specular-diffuse boundary conditions is obtained. A new analytical method is developed that makes it possible to obtain a solution up to an arbitrary degree of accuracy. The method is based on the idea of representing not only the boundary condition on the field in the form of a source (which is conventional) but also the boundary condition on the distribution function. The solution is obtained in the form of a von Neumann series.

Key words: skin effect in metals, specular-diffuse boundary conditions, analytical method for solving the skin effect problem, Neumann series.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:1, 131–145

Bibliographic databases:

UDC: 519.634

Citation: A. V. Latyshev, A. A. Yushkanov, “Solution of the skin effect problem with an arbitrary coefficient of specular reflection”, Zh. Vychisl. Mat. Mat. Fiz., 49:1 (2009), 137–151; Comput. Math. Math. Phys., 49:1 (2009), 131–145

Citation in format AMSBIB
\Bibitem{LatYus09} \by A.~V.~Latyshev, A.~A.~Yushkanov \paper Solution of the skin effect problem with an arbitrary coefficient of specular reflection \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 2009 \vol 49 \issue 1 \pages 137--151 \mathnet{http://mi.mathnet.ru/zvmmf58} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2559752} \transl \jour Comput. Math. Math. Phys. \yr 2009 \vol 49 \issue 1 \pages 131--145 \crossref{https://doi.org/10.1134/S0965542509010102} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000263128900010} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-59849118013} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Kvashnin A.Yu., Latyshev A.V., Yushkanov A.A., “Isothermal Slip of a Fermi Gas with Speculare-Diffuse Reflection from the Boundary”, Russ. Phys. J., 52:12 (2009), 1251–1257
2. A. V. Latyshev, A. A. Yushkanov, “Temperature jump in degenerate quantum gases in the presence of a Bose–Einstein condensate”, Theoret. and Math. Phys., 162:1 (2010), 95–105
3. A. V. Latyshev, A. A. Yushkanov, “Temperature jump in degenerate quantum gases with the Bogoliubov excitation energy and in the presence of the Bose–Einstein condensate”, Theoret. and Math. Phys., 165:1 (2010), 1358–1370
4. Latyshev A.V., Yushkanov A.A., “Skin effect with arbitrary specularity in Maxwellian plasma”, J. Math. Phys., 51:11 (2010), 113505, 10 pp.
5. Latyshev A.V., Yushkanov A.A., “Effect of the dependence of the specular reflectance on the angle of incidence of electrons on the impedance”, Technical Physics, 55:9 (2010), 1233–1239
6. N. B. Engibaryan, A. Kh. Khachatryan, “Solvability of an integrodifferential equation arising in the nonlocal interaction of waves”, Comput. Math. Math. Phys., 54:5 (2014), 834–844
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