Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-13T01:13:09.026Z Has data issue: false hasContentIssue false
  • English
  • Français

Electrostatic shielding in plasmas and the physical meaning of the Debye length

Published online by Cambridge University Press:  20 January 2014

G. Livadiotis  and
D. J. McComas
G. Livadiotis*
Affiliation:
Southwest Research Institute, San Antonio, TX, USA
D. J. McComas
Affiliation:
Southwest Research Institute, San Antonio, TX, USA Department of Physics & Astronomy, University of Texas at San Antonio, San Antonio, TX, USA
*
†Email address for correspondence: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper examines the electrostatic shielding in plasmas, and resolves inconsistencies about what the Debye length really is. Two different interpretations of the Debye length are currently used: (1) The potential energy approximately equals the thermal energy, and (2) the ratio of the shielded to the unshielded potential drops to 1/e. We examine these two interpretations of the Debye length for equilibrium plasmas described by the Boltzmann distribution, and non-equilibrium plasmas (e.g. space plasmas) described by kappa distributions. We study three dimensionalities of the electrostatic potential: 1-D potential of linear symmetry for planar charge density, 2-D potential of cylindrical symmetry for linear charge density, and 3-D potential of spherical symmetry for a point charge. We resolve critical inconsistencies of the two interpretations, including: independence of the Debye length on the dimensionality; requirement for small charge perturbations that is equivalent to weakly coupled plasmas; correlations between ions and electrons; existence of temperature for non-equilibrium plasmas; and isotropic Debye shielding. We introduce a third Debye length interpretation that naturally emerges from the second statistical moment of the particle position distribution; this is analogous to the kinetic definition of temperature, which is the second statistical moment of the velocity distribution. Finally, we compare the three interpretations, identifying what information is required for theoretical/experimental plasma-physics research: Interpretation 1 applies only to kappa distributions; Interpretation 2 is not restricted to any specific form of the ion/electron distributions, but these forms have to be known; Interpretation 3 needs only the second statistical moment of the positional distribution.

Type
Papers
Information
Journal of Plasma Physics , Volume 80 , Issue 3 , June 2014 , pp. 341 - 378
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - SA
The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution licence http://creativecommons.org/licenses/by-nc-sa/3.0/
Copyright
Copyright © Cambridge University Press 2014

References

REFERENCES

Abe, S. 2001 General pseudoadditivity of composable entropy prescribed by the existence of equilibrium. Phys. Rev. E 63, 061105.Google Scholar
Bains, A. S., Tribeche, M. and Ng, C. S. 2013 Dust-acoustic wave modulation in the presence of q-nonextensive electrons and/or ions in dusty plasma. Astrophys. Space Sci. 343, 621–628.CrossRefGoogle Scholar
Baumjohann, W. and Treumann, R. A. 2012 Basic Space Plasma Physics, Revised and Extended. London: Imperial College Press.CrossRefGoogle Scholar
Bryant, D. A. 1996 Debye length in a kappa-distribution. J. Plasma Phys 56, 87–93.Google Scholar
Chen, F. F. 1974 Introduction to Plasma Physics. New York: Plenum.Google Scholar
Chotoo, K., et al. 2000 The suprathermal seed population for corotating interaction region ions at 1 AU deduced from composition and spectra of H+, He++, and He+ observed by wind. J. Geophys. Res. 105, 23107.CrossRefGoogle Scholar
Christon, S. P. 1987 A comparison of the Mercury and Earth magnetospheres: electron measurements and substorm time scales. Icarus 71, 448–471.Google Scholar
Collier, M. R. and Hamilton, D. C. 1995 The relationship between kappa and temperature in energetic ion spectra at Jupiter. Geophys. Res. Lett. 22, 303–306.CrossRefGoogle Scholar
Dash, S. K. and Khuntia, S. R. 2010 Fundamentals of Electromagnetic Theory. New Delhi: PHI Learning, pp. 123.Google Scholar
Decker, R. B. and Krimigis, S. M. 2003 Voyager observations of low energy ions during solar cycle 23. Adv. Space Res. 32, 597–602.Google Scholar
Decker, R. B., Krimigis, S. M., Roelof, E. C., Hill, M. E., Armstrong, T. P., Gloeckler, G., Hamilton, D. G. and Lanzerotti, L. J. 2005 Voyager 1 in the foreshock, termination shock, and heliosheath. Science 309, 2020–2024.Google Scholar
Dialynas, K., Krimigis, S. M., Mitchell, D. G., Hamilton, D. C., Krupp, N. and Brandt, P. C. 2009 Energetic ion spectral characteristics in the Saturnian magnetosphere using Cassini/MIMI measurements. J. Geophys. Res. 114, A01212.Google Scholar
Eslami, P., Mottaghizadeh, M. and Pakzad, H. R. 2011 Nonplanar dust acoustic solitary waves in dusty plasmas with ions and electrons following a q-nonextensive distribution. Phys. Plasmas 18, 102303.Google Scholar
Fahlen, J. E., Winjum, B. J., Grismayer, T. and Mori, W. B. 2011 Transverse plasma-wave localization in multiple dimensions. Phys. Rev. E 83, 045401.Google Scholar
Gougam, L. A. and Tribeche, M. 2011 Debye shielding in a nonextensive plasma. Phys. Plasmas 18, 062102.Google Scholar
Grabbe, C. 2000 Generation of broadband electrostatic waves in Earth's magnetotail. Phys. Rev. Lett. 84, 3614.Google Scholar
Heerikhuisen, J., Pogorelov, N. V., Florinski, V., Zank, G. P. and le Roux, J. A. 2008 The effects of a k-distribution in the heliosheath on the global heliosphere and ENA flux at 1 AU. Astrophys. J. 682, 679–689.CrossRefGoogle Scholar
Hellberg, M. A., Mace, R. L., Baluku, T. K., Kourakis, I. and Saini, N. S. 2009 Comment on ‘Mathematical and physical aspects of Kappa velocity distribution’ [Phys. Plasmas 14, 110702 (2007)]. Phys. Plasmas 16, 094701.Google Scholar
Kallenrode, M.-B. 2004, Space Physics: An Introduction to Plasmas and Particles in the Heliosphere and Magnetospheres. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Kourakis, I., Sultana, S. and Hellberg, M. A. 2012 Dynamical characteristics of solitary waves, shocks and envelope modes in kappa-distributed non-thermal plasmas: an overview. Plasma Phys. Control. Fusion 54, 124001.Google Scholar
Krall, N. A. and Trivelpiece, A. W. 1973 Principles of Plasma Physics, McGraw-Hill: Kogakusha, LTD.Google Scholar
Le Roux, J. A., Webb, G. M., Shalchi, A. and Zank, G. P. 2010 A generalized nonlinear guiding center theory for the collisionless anomalous perpendicular diffusion of cosmic rays. Astrophys. J. 716, 671–692.Google Scholar
Leubner, M. P. 2004 Fundamental issues on kappa-distributions in space plasmas and interplanetary proton distributions. Phys. Plasmas 11, 1306–1308.Google Scholar
Livadiotis, G. 2009 Approach on Tsallis statistical interpretation of hydrogen-atom by adopting the generalized radial distribution function. J. Math. Chem. 45, 930–939.CrossRefGoogle Scholar
Livadiotis, G. 2012 Expectation values and variance based on Lp-norms. Entropy 14, 2375.CrossRefGoogle Scholar
Livadiotis, G. and McComas, D. J. 2009 Beyond kappa distributions: exploiting Tsallis statistical mechanics in space plasmas. J. Geophys. Res. 114, A11105.Google Scholar
Livadiotis, G. and McComas, D. J. 2010a Exploring transitions of space plasmas out of equilibrium. Astrophys. J. 714, 971–987.Google Scholar
Livadiotis, G. and McComas, D. J. 2010b Measure of the departure of the q-metastable stationary states from equilibrium. Phys. Scr. 82, 035003.Google Scholar
Livadiotis, G. and McComas, D. J. 2010c Non-equilibrium stationary states in the heliosphere: the influence of pick-up ions. AIP Conf. Proc. 1302, 70–76.Google Scholar
Livadiotis, G. and McComas, D. J. 2011a The influence of pick-up ions on space plasma distributions. Astrophys. J. 738, 64.Google Scholar
Livadiotis, G. and McComas, D. J. 2011b Invariant kappa distribution in space plasmas out of equilibrium. Astrophys. J. 741, 88.Google Scholar
Livadiotis, G. and McComas, D. J. 2012 Non-equilibrium thermodynamic processes: space plasmas and the inner heliosheath. Astrophys. J. 749, 11.CrossRefGoogle Scholar
Livadiotis, G. and McComas, D. J. 2013a Evidence of large scale phase space quantization in plasmas. Entropy 15, 1116–1132.CrossRefGoogle Scholar
Livadiotis, G. and McComas, D. J. 2013b Understanding kappa distributions: a toolbox for space science and astrophysics. Space Sci. Res. 175, 183–214.Google Scholar
Livadiotis, G. and McComas, D. J. 2013c Fitting method based on correlation maximization: applications in space physics. J. Geophys. Res. A118, 2863–2875.CrossRefGoogle Scholar
Livadiotis, G. and McComas, D. J. 2013d Near-equilibrium heliosphere – far-equilibrium heliosheath. AIP Conf. Proc. 1539, 344–347.CrossRefGoogle Scholar
Livadiotis, G. and McComas, D. J. 2013e Large-scale quantization in space plasmas. Summary and applications. Proc. Astron. Soc. Pacific (In Press).CrossRefGoogle Scholar
Livadiotis, G., McComas, D. J., Dayeh, M. A., Funsten, H. O. and Schwadron, N. A. 2011 First sky map of the inner heliosheath temperature using IBEX spectra. Astrophys. J. 734, 1.Google Scholar
Livadiotis, G., McComas, D. J., Randol, B. M., Funsten, H. O., Moebius, E. S., Schwadron, N. A., Dayeh, M. A., Zank, G. P. and Frisch, P. C. 2012 Pick-up ion distributions and their influence on energetic neutral atom spectral curvature. Astrophys. J. 751, 64.Google Scholar
Livadiotis, G., McComas, D. J., Schwadron, N. A., Funsten, H. O. and Fuselier, S. A. 2013 Pressure of the proton plasma in the inner heliosheath. Astrophys. J. 762, 134.Google Scholar
Maksimovic, M., et al. 2005 Radial evolution of the electron distribution functions in the fast solar wind between 0.3 and 1.5 AU. J. Geophys. Res. 110, A09104.Google Scholar
Mann, G., Classen, H. T., Keppler, E. and Roelof, E. C. 2002 On electron acceleration at CIR related shock waves. Astron. Astrophys. 391, 749–756.Google Scholar
Mauk, B. H., Mitchell, D. G., McEntire, R. W., Paranicas, C. P., Roelof, E. C., Williams, D. J., Krimigis, S. M. and Lagg, A. 2004 Energetic ion characteristics and neutral gas interactions in Jupiter's magnetosphere. J. Geophys. Res. 109, A09S12.Google Scholar
Milovanov, A. V. and Zelenyi, L. M. 2000 Functional background of the Tsallis entropy: ‘coarse-grained’ systems and ‘kappa’ distribution functions. Nonlinear Process. Geophys. 7, 211–221.Google Scholar
Milovanov, A. V. and Zelenyi, L. M. 2001 ‘Strange’ Fermi processes and power-law nonthermal tails from a self-consistent fractional kinetic equation. Phys. Rev. E 64, 052101.Google Scholar
Montgomery, D. C. and Tidman, D. A. 1964 Plasma Kinetic Theory. New York: McGraw-Hill.Google Scholar
Ogasawara, K., Angelopoulos, V., Dayeh, M. A., Fuselier, S. A., Livadiotis, G., McComas, D. J. and McFadden, J. P. 2013 Diagnosing dayside magnetosheath using energetic neutral atoms: IBEX and THEMIS observations. J. Geophys. Res. A118, 3126–3137.Google Scholar
Pierrard, V. and Lazar, M. 2010 Kappa distributions: theory and applications in space plasmas. Sol. Phys. 267, 153–174.Google Scholar
Raadu, M. A. and Shafiq, M. 2007 Test charge response for a dusty plasma with both grain size distribution and dynamical charging. Phys. Plasmas 14, 012105.Google Scholar
Rubab, N. and Murtaza, G. 2006 Debye length in non-Maxwellian plasmas. Phys. Scr. 74, 145.Google Scholar
Saberian, E. and Esfandyari-Kalejahi, A. 2013 Langmuir oscillations in a nonextensive electron-positron plasma. Phys. Rev. E 87, 053112.Google Scholar
Saito, S., Forme, F. R. E., Buchert, S. C., Nozawa, S. and Fujii, R. 2000 Effects of a kappa distribution function of electrons on incoherent scatter spectra. Ann. Geophys. 18, 1216–1223.Google Scholar
Schippers, P., et al. 2008 Multi-instrument analysis of electron populations in Saturn's magnetosphere. J. Geophys. Res. 113, A07208.Google Scholar
Treumann, R. A. 1999 Generalized-Lorentzian thermodynamics. Phys. Scripta. 59, 204–214.Google Scholar
Treumann, R. A. and Jaroschek, C. H. 2008 Gibbsian theory of power-law distributions. Phys. Rev. Lett. 100, 155005.Google Scholar
Treumann, R. A., Jaroschek, C. H. and Scholer, M. 2004 Stationary plasma states far from equilibrium. Phys. Plasmas 11, 1317.Google Scholar
Tribeche, M., Mayout, S. and Amour, R. 2009 Effect of ion suprathermality on arbitrary amplitude dust acoustic waves in a charge varying dusty plasma. Phys. Plasmas 16, 043706.Google Scholar
Tsallis, C. 1988 Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys. 52, 479–487.Google Scholar
Tsallis, C. 2009 Introduction to Non-extensive Statistical Mechanics: Approaching a Complex World. New York: Springer.Google Scholar
Tsallis, C., Mendes, R. S. and Plastino, A. R. 1998 The role of constraints within generalized nonextensive statistics. Physica A 261, 534–554.CrossRefGoogle Scholar
Vasyliũnas, V. M. 1968 A survey of low-energy electrons in the evening sector of the magnetosphere with OGO 1 and OGO 3. J. Geophys. Res. 73, 2839–2884.CrossRefGoogle Scholar
Yoon, P. H. 2012 Electron kappa distribution and steady-state Langmuir turbulence. Plasma Phys. 19, 052301.Google Scholar
Yoon, P. H., Rhee, T. and Ryu, C. M. 2006 Self-consistent formation of electron κ distribution. J. Geophys. Res. 111, A09106.Google Scholar
Yoon, P. H., Ziebell, L. F., Gaelzer, R., Lin, R. P. and Wang, L. 2012 Langmuir turbulence and suprathermal electrons. Space Sci. Rev. 173, 459–489.Google Scholar
Zank, G. P., Heerikhuisen, J., Pogorelov, N. V., Burrows, R. and McComas, D. J. 2010 Microstructure of the heliospheric termination shock: implications for energetic neutral atom observations. Astrophys. J. 708, 1092.Google Scholar