Skip to main content
SpringerLink
Log in

Forces and Trapping of Dust Particles

  • Chapter
  • First Online:
Book cover Physics of Dusty Plasmas

Part of the book series: Lecture Notes in Physics ((LNP,volume 962))

  • 891 Accesses

Abstract

In this chapter we will discuss the main forces acting on dust particles in a plasma discharge. These forces are gravity, electric field force, ion drag force, thermophoresis and neutral drag. After the analysis of the forces under plasma conditions the trapping of large (micron-sized) dust particles in the laboratory and under microgravity as well as of small (submicron) particles in plasma processing devices will be described. We are then in a position to discuss vertical oscillations in the plasma sheath and to derive a first set of methods for the charge measurement in the sheath of a plasma.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 49.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    As an estimate: Taking ∇E ∼ E∕λ D with the Debye length λ D and E ∼ k B T e∕(eλ D) yields F dip ∼ F E(a∕λ D)2 ≪ F E for the typical situation a ≪ λ D.

  2. 2.

    In this case, the dipole moment is of the order of p ∼ (4πε 0 a)(k B T e∕e) a [3], hence, F dip ∼ F E(a∕λ D).

  3. 3.

    The different prefactor given here compared that in Ref. [9] is due to the different normalizations of the thermal velocity.

  4. 4.

    When defining the thermal velocity as \(\tilde {v}_{\mathrm {th,n}} = \sqrt { k_{\mathrm {B}} T_{\mathrm {n}}/m_{\mathrm {n}}}\), then \(\beta = \delta \sqrt {8/\pi }\, p /(a \rho _{\mathrm {d}} \tilde {v}_{\mathrm {th,n}})\).

  5. 5.

    When defining the thermal velocity as \(\tilde {v}_{\mathrm {th,n}} \,{=}\, \sqrt {k_{\mathrm {B}} T_{\mathrm {n}}/m_{\mathrm {n}}}\), then \(F_{\mathrm {th}} \,{=}\, -(16/15)\sqrt {\pi /2} a^2 k_{\mathrm {n}}/\tilde {v}_{\mathrm {th,n}} \nabla T_{\mathrm {n}}\).

  6. 6.

    For a 3 cm electrode gap this corresponds to a temperature difference of 6∘C, only.

  7. 7.

    Here, for convenience, we have dropped the index “d” for the dust charge and use Q(z) = |Q d(z)| as positive.

References

  1. S. Hamaguchi, R.T. Farouki, Phys. Rev. E 49, 4430 (1994)

    Article  ADS  Google Scholar 

  2. J.D. Jackson, Classical Electrodynamics (Wiley, New York, 1962)

    MATH  Google Scholar 

  3. I.H. Hutchinson, Plasma Phys. Control. Fusion 47, 71 (2005)

    Article  ADS  Google Scholar 

  4. S.A. Khrapak, A.V. Ivlev, V.V. Yaroshenko, G.E. Morfill, Phys. Rev. Lett. 102, 245004 (2009). https://link.aps.org/doi/10.1103/PhysRevLett.102.245004

    Article  ADS  Google Scholar 

  5. M.S. Barnes, J.H. Keller, J.C. Forster, J.A. O’Neill, D.K. Coultas, Phys. Rev. Lett. 68, 313 (1992)

    Article  ADS  Google Scholar 

  6. M.D. Kilgore, J.E. Daugherty, R.K. Porteous, D.B. Graves, J. Appl. Phys. 73, 7195 (1993)

    Article  ADS  Google Scholar 

  7. S. Khrapak, A.V. Ivlev, G. Morfill, H. Thomas, Phys. Rev. E 66, 046414 (2002)

    Article  ADS  Google Scholar 

  8. S.A. Khrapak, A.V. Ivlev, S.K. Zhdanov, G.E. Morfill, Phys. Plasmas 12, 042308 (2005)

    Article  ADS  Google Scholar 

  9. I.H. Hutchinson, Plasma Phys. Control. Fusion 48, 185 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  10. L. Patacchini, I.H. Hutchinson, Phys. Rev. Lett. 101, 025001 (2008)

    Article  ADS  Google Scholar 

  11. V.R. Ikkurthi, K. Matyash, A. Melzer, R. Schneider, Phys. Plasmas 16, 043703 (2009)

    Article  ADS  Google Scholar 

  12. I.H. Hutchinson, C.B. Haakonsen, Phys. Plasmas 20, 083701 (2013). https://doi.org/10.1063/1.4818144

    Article  ADS  Google Scholar 

  13. P.S. Epstein, Phys. Rev. 23, 710 (1924)

    Article  ADS  Google Scholar 

  14. B. Liu, J. Goree, V. Nosenko, L. Boufendi, Phys. Plasmas 10, 9 (2003)

    Article  ADS  Google Scholar 

  15. H. Jung, F. Greiner, O.H. Asnaz, J. Carstensen, A. Piel, Phys. Plasmas (1994-present) 22, 053702 (2015). http://dx.doi.org/10.1063/1.4920968

    Article  ADS  Google Scholar 

  16. H. Vestner, L. Waldmann, Physica 86A, 303 (1977)

    Article  ADS  Google Scholar 

  17. H. Rothermel, T. Hagl, G. Morfill, M. Thoma, H.M. Thomas, Phys. Rev. Lett. 89, 175001 (2002)

    Article  ADS  Google Scholar 

  18. C. Schmidt, O. Arp, A. Piel, Phys. Plasmas 18, 013704 (2011)

    Article  ADS  Google Scholar 

  19. O. Arp, D. Block, A. Piel, A. Melzer, Phys. Rev. Lett. 93, 165004 (2004)

    Article  ADS  Google Scholar 

  20. A. Ashkin, Phys. Rev. Lett. 24, 156 (1970)

    Article  ADS  Google Scholar 

  21. A. Melzer, Plasma Sources Sci. Technol. 10, 303 (2001)

    Article  ADS  Google Scholar 

  22. J. Schablinski, D. Block, A. Piel, A. Melzer, H. Thomsen, H. Kählert, M. Bonitz, Phys. Plasmas 19, 013705 (2012)

    Article  ADS  Google Scholar 

  23. H. Thomsen, H. Kählert, M. Bonitz, J. Schablinski, D. Block, A. Piel, A. Melzer, Phys. Plasmas 19, 023701 (2012)

    Article  ADS  Google Scholar 

  24. G.E. Morfill, H. Thomas, U. Konopka, H. Rothermel, M. Zuzic, A. Ivlev, J. Goree, Phys. Rev. Lett. 83, 1598 (1999)

    Article  ADS  Google Scholar 

  25. V.E. Fortov, O.S. Vaulina, O.F. Petrov, V.I. Molotkov, A.V. Chernyshev, A.M. Lipaev, G. Morfill, H. Thomas, H. Rothermel, S.A. Khrapak, Y.P. Semenov, A.I. Ivanov, S.K. Krikalev, Y.P. Gidzenko, JETP 96, 704 (2003)

    Article  ADS  Google Scholar 

  26. S. Khrapak, D. Samsonov, G. Morfill, H. Thomas, V. Yaroshenko, H. Rothermel, T. Hagl, V. Fortov, A. Nefedov, V. Molotkov, O. Petrov, A. Lipaev, A. Ivanov, Y. Baturin, Phys. Plasmas 10, 1 (2003)

    Article  ADS  Google Scholar 

  27. M.H. Thoma, H. Höfner, M. Kretschmer, S. Ratynskaia, G.E. Morfill, A. Usachev, A. Zobnin, O. Petrov, V. Fortov, Microgravity - Science and Technology 8(3), 47 (2006). http://dx.doi.org/10.1007/BF02870378

    Article  ADS  Google Scholar 

  28. M. Klindworth, A. Piel, A. Melzer, Phys. Rev. Lett. 93, 195002 (2004)

    Article  ADS  Google Scholar 

  29. M. Wolter, A. Melzer, O. Arp, M. Klindworth, A. Piel, Phys. Plasmas 14, 123707 (2007)

    Article  ADS  Google Scholar 

  30. M. Schwabe, S. Zhdanov, H. Thomas, A.V. Ivlev, M. Rubin-Zuzic, G.E. Morfill, V.I. Molotkov, A.M. Lipaev, V.E. Fortov, T. Reiter, New J. Phys. 10, 033037 (2008)

    Article  ADS  Google Scholar 

  31. B. Buttenschön, M. Himpel, A. Melzer, New J. Phys. 13, 023042 (2011)

    Article  ADS  Google Scholar 

  32. T. Bockwoldt, O. Arp, K.O. Menzel, A. Piel, Phys. Plasmas (1994-present) 21, 103703 (2014)

    Google Scholar 

  33. J.L. Dorier, C. Hollenstein, A. Howling, J. Vac. Sci. Technol. A 13, 918 (1995)

    Article  ADS  Google Scholar 

  34. J. Goree, G. Morfill, V. Tsytovich, S.V. Vladimirov, Phys. Rev. E 59, 7055 (1999)

    Article  ADS  Google Scholar 

  35. P. Belenguer, J.P. Blondeau, L. Boufendi, M. Toogood, A. Plain, A. Bouchoule, C. Laure, J.P. Boeuf, Phys. Rev. A 46, 7923 (1992)

    Article  ADS  Google Scholar 

  36. E. Tomme, D. Law, B.M. Annaratone, J. Allen, Phys. Rev. Lett. 85, 2518 (2000)

    Article  ADS  Google Scholar 

  37. A. Melzer, T. Trottenberg, A. Piel, Phys. Lett. A 191, 301 (1994)

    Article  ADS  Google Scholar 

  38. T. Trottenberg, A. Melzer, A. Piel, Plasma Sources Sci. Technol. 4, 450 (1995)

    Article  ADS  Google Scholar 

  39. A. Melzer, A. Homann, A. Piel, Phys. Rev. E 53, 2757 (1996)

    Article  ADS  Google Scholar 

  40. A. Homann, A. Melzer, A. Piel, Phys. Rev. E 59, 3835 (1999)

    Article  ADS  Google Scholar 

  41. S.A. Khrapak, S.V. Ratynskaia, A.V. Zobnin, A.D. Usachev, V.V. Yaroshenko, M.H. Thoma, M. Kretschmer, H. Höfner, G.E. Morfill, O.F. Petrov, V.E. Fortov, Phys. Rev. E 72, 016406 (2005)

    Article  ADS  Google Scholar 

  42. J. Carstensen, H. Jung, F. Greiner, A. Piel, Phys. Plasmas 18, 033701 (2011)

    Article  ADS  Google Scholar 

  43. J. Carstensen, F. Greiner, A. Piel, Phys. Rev. Lett. 109, 135001 (2012)

    Article  ADS  Google Scholar 

  44. H. Schollmeyer, A. Melzer, A. Homann, A. Piel, Phys. Plasmas 6, 2693 (1999)

    Article  ADS  Google Scholar 

  45. C. Zafiu, A. Melzer, A. Piel, Phys. Rev. E 63, 066403 (2001)

    Article  ADS  Google Scholar 

  46. A. Ivlev, U. Konopka, G. Morfill, Phys. Rev. E 62, 2739 (2000)

    Article  ADS  Google Scholar 

  47. J. Beckers, T. Ockenga, M. Wolter, W.W. Stoffels, J. van Dijk, H. Kersten, G.M.W. Kroesen, Phys. Rev. Lett. 106, 115002 (2011)

    Article  ADS  Google Scholar 

  48. S. Nunomura, T. Misawa, N. Ohno, S. Takamura, Phys. Rev. Lett. 83, 1970 (1999)

    Article  ADS  Google Scholar 

  49. S. Takamura, N. Ohno, S. Nunomura, T. Misawa, K. Asano, in Frontiers in Dusty Plasmas, ed. by Y. Nakamura, T. Yokota, P. Shukla (Elsevier Science B.V., Amsterdam, 2000), pp. 337–344. https://doi.org/10.1016/B978-044450398-5/50045-2. http://www.sciencedirect.com/science/article/pii/B9780444503985500452

    Chapter  Google Scholar 

  50. A.A. Sickafoose, J.E. Colwell, M. Horányi, S. Robertson, Phys. Rev. Lett. 84, 6034 (2000). http://link.aps.org/doi/10.1103/PhysRevLett.84.6034

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Physik, Universität Greifswald, Greifswald, Germany

    André Melzer

Authors
  1. André Melzer
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Melzer, A. (2019). Forces and Trapping of Dust Particles. In: Physics of Dusty Plasmas. Lecture Notes in Physics, vol 962. Springer, Cham. https://doi.org/10.1007/978-3-030-20260-6_3

Download citation

Publish with us

Policies and ethics

Search

Navigation