A perturbative correction for electron-inertia in magnetized sheath structures

  • Munmi Gohain
  • Pralay K. Karmakar
Regular Article


We propose a hydrodynamic model to study the equilibrium properties of planar plasma sheaths in two-component quasi-neutral magnetized plasmas. It includes weak but finite electron-inertia incorporated via a regular perturbation of the electronic fluid dynamics only relative to a new smallness parameter, δ, assessing the weak inertial-to-electromagnetic strengths. The zeroth-order perturbation around δ leads to the usual Boltzmann distribution law, which describes inertialess thermalized electrons. The forthwith next higher-order yields the modified Boltzmann law describing the putative lowest-order electron-inertial correction, which is applied meticulously to derive the local Bohm criterion for sheath formation. It is found to be influenced jointly by electron-inertial corrective effects, magnetic field and field orientation relative to the bulk plasma flow. We establish that the mutualistic action of electron-inertia amid gyro-kinetic effects slightly enhances the ion-flow Mach threshold value (typically, M i0 ⩾ 1.140), against the normal value of unity, confrontationally towards the sheath entrance. A numerical illustrative scheme is methodically constructed to see the parametric dependence of the new sheath properties on diverse problem arguments. The merits and demerits are highlighted in the light of the existing results conjointly with clear indication to future ameliorations.

Graphical abstract


Plasma Physics 


  1. 1.
    D. Bohm, The Characteristics of Electrical Discharges in Magnetic Fields, edited by A. Guthrie, R. Wakerling (McGraw-Hill, New York, 1949)Google Scholar
  2. 2.
    P.C. Stangeby, The Plasma Boundary of Magnetic Fusion Devices (IOP Publishing Ltd., Bristol and Philadelphia, 2000)Google Scholar
  3. 3.
    K.U. Riemann, J. Phys. D 24, 493 (1991)ADSCrossRefGoogle Scholar
  4. 4.
    P.K. Karmakar, U. Deka, C.B. Dwivedi, Phys. Plasmas 12, 032105 (2005)ADSCrossRefGoogle Scholar
  5. 5.
    P.K. Karmakar, C.B. Dwivedi, J. Math. Phys. 47, 032901 (2006)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    P.K. Karmakar, U. Deka, C.B. Dwivedi, Phys. Plasmas 13, 104702 (2006)ADSCrossRefGoogle Scholar
  7. 7.
    U. Deka, A. Sarma, R. Prakash, P.K. Karmakar, C.B. Dwivedi, Phys. Scr. 69, 303 (2004)ADSCrossRefGoogle Scholar
  8. 8.
    U. Deka, C.B. Dwivedi, Braz. J. Phys. 40, 333 (2010)CrossRefGoogle Scholar
  9. 9.
    M. Gohain, P.K. Karmakar, Europhys. Lett. 112, 45002 (2015)ADSCrossRefGoogle Scholar
  10. 10.
    R. Chalise, R. Khanal, J. Mater. Sci. Eng. A 5, 41 (2015)Google Scholar
  11. 11.
    X. Zou, J.Y. Liu, Y. Gong, Z.X. Wang, Y. Liu, X.G. Wang, Vacuum 73, 681 (2004)CrossRefGoogle Scholar
  12. 12.
    X. Zou, M. Qiu, H. Liu, L. Zhang, J. Liu, Y. Gong, Vacuum 83, 205 (2009)ADSCrossRefGoogle Scholar
  13. 13.
    J. Ou, J. Yang, Phys. Plasmas 19, 113504 (2012)ADSCrossRefGoogle Scholar
  14. 14.
    J.E. Allen, Contrib. Plasma Phys. 48, 400 (2008)ADSCrossRefGoogle Scholar
  15. 15.
    M.M. Hatami, B. Shokri, A.R. Niknam, Phys. Plasmas 15, 123501 (2008)ADSCrossRefGoogle Scholar
  16. 16.
    H. Liu, X. Zou, M. Qiu, Plasma Sci. Technol. 16, 633 (2014)ADSCrossRefGoogle Scholar
  17. 17.
    U.L. Rohde, G.C. Jain, A.K. Poddar, A.K. Ghosh, Introduction to Integral Calculus (Wiley, New Jersey, 2012)Google Scholar
  18. 18.
    M. Khoramabadi, H.R. Ghomi, M. Ghoranneviss, J. Plasma Fusion Res. 8, 1399 (2009)Google Scholar
  19. 19.
    J.C. Butcher, Appl. Num. Math. 24, 331 (1997)MathSciNetCrossRefGoogle Scholar
  20. 20.
    S. Kuhn, K.U. Riemann, N. Jelic, D.D. Tskhakaya Sr., D. Tskhakaya Jr., M. Stanojevic, Phys. Plasmas 13, 013503 (2006)ADSCrossRefGoogle Scholar
  21. 21.
    S.F. Masoudi, Zh. Ebrahiminejad, Eur. Phys. J. D 59, 421 (2010)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of PhysicsTezpur UniversityTezpurIndia

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