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A family of Vlasov–Maxwell equilibrium distribution functions describing a transition from the Harris sheet to the force-free Harris sheet

Part of: The Many Facets of the Vlasov Equation

Published online by Cambridge University Press:  19 June 2020

T. Neukirch Open the ORCID record for T. Neukirch [Opens in a new window] ,
F. Wilson Open the ORCID record for F. Wilson [Opens in a new window]  and
O. Allanson Open the ORCID record for O. Allanson [Opens in a new window]
T. Neukirch*
Affiliation:
School of Mathematics and Statistics, University of St Andrews, St AndrewsKY16 9SS, UK
F. Wilson
Affiliation:
School of Mathematics and Statistics, University of St Andrews, St AndrewsKY16 9SS, UK
O. Allanson
Affiliation:
Space and Atmospheric Electricity Group, Department of Meteorology, University of Reading, ReadingRG6 6BB, UK
*
†Email address for correspondence: tn3@st-andrews.ac.uk
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Abstract

We discuss a family of Vlasov–Maxwell equilibrium distribution functions for current sheet equilibria that are intermediate cases between the Harris sheet and the force-free (or modified) Harris sheet. These equilibrium distribution functions have potential applications to space and astrophysical plasmas. The existence of these distribution functions had been briefly discussed by Harrison & Neukirch (Phys. Rev. Lett., vol. 102, (2009a), 135003), but here it is shown that their approach runs into problems in the limit where the guide field goes to zero. The nature of this problem will be discussed and an alternative approach will be suggested that avoids the problem. This is achieved by considering a slight variation of the magnetic field profile, which allows a smooth transition between the Harris and force-free Harris sheet cases.

Keywords

astrophysical plasmasspace plasma physics
Type
Research Article
Information
Journal of Plasma Physics , Volume 86 , Issue 3 , June 2020 , 825860302
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

Abraham-Shrauner, B. 2013 Force-free Jacobian equilibria for Vlasov–Maxwell plasmas. Phys. Plasmas 20, 102117.CrossRefGoogle Scholar
Allanson, O., Neukirch, T., Troscheit, S. & Wilson, F. 2016 From one-dimensional fields to Vlasov equilibria: theory and application of Hermite polynomials. J. Plasma Phys. 82, 905820306.CrossRefGoogle Scholar
Allanson, O., Neukirch, T., Wilson, F. & Troscheit, S. 2015 An exact collisionless equilibrium for the force-free Harris sheet with low plasma beta. Phys. Plasmas 22, 102116.CrossRefGoogle Scholar
Alpers, W. 1969 Steady state charge neutral models of the magnetopause. Astrophys. Space Sci. 5, 425–437.CrossRefGoogle Scholar
Artemyev, A. V., Angelopoulos, V. & Vasko, I. Y. 2019a Kinetic properties of solar wind discontinuities at 1 AU observed by ARTEMIS. J. Geophys. Res. 124, 3858–3870.CrossRefGoogle Scholar
Artemyev, A. V., Angelopoulos, V., Vasko, I. Y., Runov, A., Avanov, L. A., Giles, B. L., Russell, C. T. & Strangeway, R. J. 2019b On the kinetic nature of solar wind discontinuities. Geophys. Res. Lett. 46, 1185–1194.CrossRefGoogle Scholar
Attico, N. & Pegoraro, F. 1999 Periodic equilibria of the Vlasov–Maxwell system. Phys. Plasmas 6, 767–770.CrossRefGoogle Scholar
Bobrova, N. A., Bulanov, S. V., Sakai, J. I. & Sugiyama, D. 2001 Force-free equilibria and reconnection of the magnetic field lines in collisionless plasma configurations. Phys. Plasmas 8, 759–768.CrossRefGoogle Scholar
Bowers, K. & Li, H. 2007 Spectral energy transfer and dissipation of magnetic energy from fluid to kinetic scales. Phys. Rev. Lett. 98, 035002.CrossRefGoogle ScholarPubMed
Channell, P. J. 1976 Exact Vlasov–Maxwell equilibria with sheared magnetic fields. Phys. Fluids 19, 1541–1545.CrossRefGoogle Scholar
Correa-Restrepo, D. & Pfirsch, D. 1993 Negative-energy waves in an inhomogeneous force-free Vlasov plasma with sheared magnetic field. Phys. Rev. E 47, 545–563.Google Scholar
Daughton, W. & Karimabadi, H. 2007 Collisionless magnetic reconnection in large-scale electron–positron plasmas. Phys. Plasmas 14, 072303.CrossRefGoogle Scholar
Daughton, W., Roytershteyn, V., Karimabadi, H., Yin, L., Albright, B. J., Bergen, B. & Bowers, K. J. 2011 Role of electron physics in the development of turbulent magnetic reconnection in collisionless plasmas. Nat. Phys. 7, 539–542.CrossRefGoogle Scholar
Dorville, N., Belmont, G., Aunai, N., Dargent, J. & Rezeau, L. 2015 Asymmetric kinetic equilibria: generalization of the BAS model for rotating magnetic profile and non-zero electric field. Phys. Plasmas 22, 092904.CrossRefGoogle Scholar
Fan, F., Huang, C., Lu, Q., Xie, J. & Wang, S. 2016 The structures of magnetic islands formed during collisionless magnetic reconnections in a force-free current sheet. Phys. Plasmas 23, 112106.CrossRefGoogle Scholar
Guo, F., Li, H., Daughton, W., Li, X. & Liu, Y.-H. 2016a Particle acceleration during magnetic reconnection in a low-beta pair plasma. Phys. Plasmas 23, 055708.CrossRefGoogle Scholar
Guo, F., Li, H., Daughton, W. & Liu, Y.-H. 2014 Formation of hard power laws in the energetic particle spectra resulting from relativistic magnetic reconnection. Phys. Rev. Lett. 113, 155005.CrossRefGoogle ScholarPubMed
Guo, F., Li, X., Li, H., Daughton, W., Zhang, B., Lloyd-Ronning, N., Liu, Y.-H., Zhang, H. & Deng, W. 2016b Efficient Production of high-energy nonthermal particles during magnetic reconnection in a magnetically dominated ion–electron plasma. Astrophys. J. Lett. 818, L9.Google Scholar
Guo, F., Liu, Y.-H., Daughton, W. & Li, H. 2015 Particle acceleration and plasma dynamics during magnetic reconnection in the magnetically dominated regime. Astrophys. J. 806, 167.CrossRefGoogle Scholar
Harris, E. G. 1962 On a plasma sheath separating regions of oppositely directed magnetic field. Nuovo Cimento 23, 115.CrossRefGoogle Scholar
Harrison, M. G. & Neukirch, T. 2009a One-dimensional Vlasov–Maxwell equilibrium for the force-free Harris sheet. Phys. Rev. Lett. 102, 135003.CrossRefGoogle Scholar
Harrison, M. G. & Neukirch, T. 2009b Some remarks on one-dimensional force-free Vlasov–Maxwell equilibria. Phys. Plasmas 16, 022106.CrossRefGoogle Scholar
Hesse, M. 2006 Dissipation in magnetic reconnection with a guide magnetic field. Phys. Plasmas 13, 122107.CrossRefGoogle Scholar
Hesse, M., Birn, J. & Kuznetsova, M. 2001 Collisionless magnetic reconnection: electron processes and transport modeling. J. Geophys. Res. 106, 3721–3736.CrossRefGoogle Scholar
Hesse, M., Kuznetsova, M. & Birn, J. 2004 The role of electron heat flux in guide-field magnetic reconnection. Phys. Plasmas 11, 5387–5397.CrossRefGoogle Scholar
Hesse, M., Kuznetsova, M., Schindler, K. & Birn, J. 2005 Three-dimensional modeling of electron quasiviscous dissipation in guide-field magnetic reconnection. Phys. Plasmas 12, 100704.CrossRefGoogle Scholar
Hesse, M., Neukirch, T., Schindler, K., Kuznetsova, M. & Zenitani, S. 2011 The diffusion region in collisionless magnetic reconnection. Space Sci. Rev. 160, 3–23.CrossRefGoogle Scholar
Hesse, M., Schindler, K., Birn, J. & Kuznetsova, M. 1999 The diffusion region in collisionless magnetic reconnection. Phys. Plasmas 6, 1781–1795.CrossRefGoogle Scholar
Huang, F., Xu, J., Yan, F., Zhang, M. & Yu, M. Y. 2017 Instabilities of current-sheet with a nonuniform guide field. Phys. Plasmas 24, 092104.CrossRefGoogle Scholar
Kocharovsky, V. V., Kocharovsky, V. V., Martyanov, V. Y. & Tarasov, S. V. 2016 Analytical theory of self-consistent current structures in a collisionless plasma. Phys. Uspekhi 59, 1165–1210.CrossRefGoogle Scholar
Kolotkov, D. Y., Vasko, I. Y. & Nakariakov, V. M. 2015 Kinetic model of force-free current sheets with non-uniform temperature. Phys. Plasmas 22, 112902.CrossRefGoogle Scholar
Kuznetsova, M. M., Hesse, M. & Winske, D. 1998 Kinetic quasi-viscous and bulk flow inertia effects in collisionless magnetotail reconnection. J. Geophys. Res. 103, 199–214.CrossRefGoogle Scholar
Kuznetsova, M. M., Hesse, M. & Winske, D. 2000 Toward a transport model of collisionless magnetic reconnection. J. Geophys. Res. 105, 7601–7616.CrossRefGoogle Scholar
Kuznetsova, M. M., Hesse, M. & Winske, D. 2001 Collisionless reconnection supported by nongyrotropic pressure effects in hybrid and particle simulations. J. Geophys. Res. 106, 3799–3810.CrossRefGoogle Scholar
Liu, Y.-H., Daughton, W., Karimabadi, H., Li, H. & Roytershteyn, V. 2013 Bifurcated structure of the electron diffusion region in three-dimensional magnetic reconnection. Phys. Rev. Lett. 110, 265004.CrossRefGoogle ScholarPubMed
Moratz, E. & Richter, E. W. 1966 Elektronen-Geschwindigkeitsverteilungsfunktionen für kraftfreie bzw. teilweise kraftfreie Magnetfelder. Z. Naturforsch. A 21, 1963.Google Scholar
Mottez, F. 2003 Exact nonlinear analytic Vlasov–Maxwell tangential equilibria with arbitrary density and temperature profiles. Phys. Plasmas 10, 2501–2508.CrossRefGoogle Scholar
Mynick, H. E., Sharp, W. M. & Kaufman, A. N. 1979 Realistic Vlasov slab equilibria with magnetic shear. Phys. Fluids 22, 1478–1484.CrossRefGoogle Scholar
Neukirch, T., Vasko, I. Y., Artemyev, A. V. & Allanson, O. 2020 Kinetic models of tangential discontinuities in the solar wind. Astrophys. J. 891, 86.CrossRefGoogle Scholar
Neukirch, T., Wilson, F. & Allanson, O. 2018 Collisionless current sheet equilibria. Plasma Phys. Control. Fusion 60, 014008.CrossRefGoogle Scholar
Neukirch, T., Wilson, F. & Harrison, M. G. 2009 A detailed investigation of the properties of a Vlasov–Maxwell equilibrium for the force-free Harris sheet. Phys. Plasmas 16, 122102.CrossRefGoogle Scholar
Nishimura, K., Gary, S. P., Li, H. & Colgate, S. A. 2003 Magnetic reconnection in a force-free plasma: simulations of micro- and macroinstabilities. Phys. Plasmas 10, 347–356.CrossRefGoogle Scholar
Panov, E. V., Artemyev, A. V., Nakamura, R. & Baumjohann, W. 2011 Two types of tangential magnetopause current sheets: cluster observations and theory. J. Geophys. Res. 116, A12204.CrossRefGoogle Scholar
Pritchett, P. L. 2001 Geospace environment modeling magnetic reconnection challenge: simulations with a full particle electromagnetic code. J. Geophys. Res. 106, 3783–3798.CrossRefGoogle Scholar
Pritchett, P. L. 2005 Onset and saturation of guide-field magnetic reconnection. Phys. Plasmas 12 (6), 062301.CrossRefGoogle Scholar
Pritchett, P. L. & Coroniti, F. V. 2004 Three-dimensional collisionless magnetic reconnection in the presence of a guide field. J. Geophys. Res. 109, 1220.CrossRefGoogle Scholar
Ricci, P., Brackbill, J. U., Daughton, W. & Lapenta, G. 2004 Collisionless magnetic reconnection in the presence of a guide field. Phys. Plasmas 11, 4102–4114.CrossRefGoogle Scholar
Rogers, B. N., Denton, R. E. & Drake, J. F. 2003 Signatures of collisionless magnetic reconnection. J. Geophys. Res. 108, 1111.CrossRefGoogle Scholar
Roth, M., de Keyser, J. & Kuznetsova, M. M. 1996 Vlasov theory of the equilibrium structure of tangential discontinuities in space plasmas. Space Sci. Rev. 76, 251–317.CrossRefGoogle Scholar
Schindler, K. 2007 Physics of Space Plasma Activity. Cambridge University Press.Google Scholar
Sestero, A. 1967 Self-consistent description of a warm stationary plasma in a uniformly sheared magnetic field. Phys. Fluids 10, 193–197.CrossRefGoogle Scholar
Shay, M. A., Drake, J. F., Denton, R. E. & Biskamp, D. 1998 Structure of the dissipation region during collisionless magnetic reconnection. J. Geophys. Res. 103, 9165–9176.CrossRefGoogle Scholar
Vasko, I. Y., Artemyev, A. V., Petrukovich, A. A. & Malova, H. V. 2014 Thin current sheets with strong bell-shape guide field: cluster observations and models with beams. Ann. Geophys. 32, 1349–1360.CrossRefGoogle Scholar
Wan, W., Lapenta, G., Delzanno, G. L. & Egedal, J. 2008 Electron acceleration during guide field magnetic reconnection. Phys. Plasmas 15, 032903.CrossRefGoogle Scholar
Wilson, F. & Neukirch, T. 2011 A family of one-dimensional Vlasov–Maxwell equilibria for the force-free Harris sheet. Phys. Plasmas 18, 082108.CrossRefGoogle Scholar
Wilson, F., Neukirch, T. & Allanson, O. 2017 Force-free collisionless current sheet models with non-uniform temperature and density profiles. Phys. Plasmas 24, 092105.CrossRefGoogle Scholar
Wilson, F., Neukirch, T. & Allanson, O. 2018 Collisionless distribution functions for force-free current sheets: using a pressure transformation to lower the plasma beta. J. Plasma Phys. 84, 905840309.CrossRefGoogle Scholar
Wilson, F., Neukirch, T., Hesse, M., Harrison, M. G. & Stark, C. R. 2016 Particle-in-cell simulations of collisionless magnetic reconnection with a non-uniform guide field. Phys. Plasmas 23, 032302.CrossRefGoogle Scholar
Zelenyi, L. M., Malova, H. V., Artemyev, A. V., Popov, V. Y. & Petrukovich, A. A. 2011 Thin current sheets in collisionless plasma: equilibrium structure, plasma instabilities, and particle acceleration. Plasma Phys. Rep. 37, 118–160.CrossRefGoogle Scholar
Zhou, F., Huang, C., Lu, Q., Xie, J. & Wang, S. 2015 The evolution of the ion diffusion region during collisionless magnetic reconnection in a force-free current sheet. Phys. Plasmas 22, 092110.CrossRefGoogle Scholar