Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-19T02:50:02.826Z Has data issue: false hasContentIssue false
  • English
  • Français

Phase transition to blob-hole coherent structure in the Hasegawa–Mima model for plasmas

Part of: Hamiltonian Methods in Plasma Physics Focus on Fusion

Published online by Cambridge University Press:  01 December 2021

Chjan C. Lim Open the ORCID record for Chjan C. Lim [Opens in a new window]
Chjan C. Lim*
Affiliation:
Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY12180, USA
*
†Email address for correspondence: limchjan@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

An equilibrium statistical mechanics theory for the Hasegawa–Mima equations of toroidal plasmas, with canonical constraint on energy and microcanonical constraint on potential enstrophy, is solved exactly as a spherical model. The use of a canonical energy constraint instead of a fixed-energy microcanonical approach is justified by the preference for viewing real plasmas as an open system. A significant consequence of the results obtained from the partition function, free energy and critical temperature, is the condensation into a ground state exhibiting a blob-hole-like structure observed in real plasmas.

Keywords

plasmasturbulent flowsinstability
Type
Research Article
Information
Journal of Plasma Physics , Volume 87 , Issue 6 , December 2021 , 835870601
Check for updates
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Berlin, T.H. & Kac, M. 1952 The spherical model of a ferromagnet. Phys. Rev. 86, 821–835.10.1103/PhysRev.86.821CrossRefGoogle Scholar
Ding, X. & Lim, C.C. 2006 Monte-Carlo simulations of the spherical energy-relative enstrophy model for the coupled barotropic fluid – rotating sphere system. Physica A 374, 152–164.10.1016/j.physa.2006.08.036CrossRefGoogle Scholar
Ding, X. & Lim, C.C. 2009 First-order phase transitions high energy coherent spots in a shallow water model on a rapidly rotating sphere. Phys. Fluids 21 (4), 045102.10.1063/1.3103883CrossRefGoogle Scholar
D'Ippolito, D.A., Myra, J.R. & Zweben, S.J. 2011 Convective transport by intermittent blob-filaments: comparison of theory and experiment. Phys. Plasmas 18, 060501.10.1063/1.3594609CrossRefGoogle Scholar
Hasegawa, A. & Mima, K. 1978 Pseudo‐three‐dimensional turbulence in magnetized nonuniform plasma. Phys. Fluids 21, 85.10.1063/1.862083CrossRefGoogle Scholar
Kosuga, Y. & Diamond, P.H. 2013 Blob-Hole structures as non-axisymmetric equilibrium solutions for potential vorticity conserving fluids. Plasma Fusion Res.: Reg. Articles 8 (24030), 80.10.1585/pfr.8.2403080CrossRefGoogle Scholar
Kraichnan, R.H. 1975 Statistical dynamics of two-dimensional flows. J. Fluid Mech. 67, 155–175.10.1017/S0022112075000225CrossRefGoogle Scholar
Krasheninnikov, S.I. 2016 On the origin of plasma density blobs. Phys. Lett. A 380, 3905.10.1016/j.physleta.2016.09.046CrossRefGoogle Scholar
Lim, C.C. 2005 Energy maximizers and robust symmetry breaking in vortex dynamics on a non-rotating sphere. SIAM J. Appl. Maths 65, 2093–2106.10.1137/040605916CrossRefGoogle Scholar
Lim, C.C. 2007 a Energy extremals and nonlinear stability in an energy-relative enstrophy theory of the coupled barotropic fluid – rotating sphere system. J. Maths Phys. 48 (6), 065603.10.1063/1.2347900CrossRefGoogle Scholar
Lim, C.C. 2007 b Extremal free energy in a simple mean field theory for a coupled barotropic fluid – rotating sphere system. J. Discrete Continuous Dyn. Syst. 19 (2), 361–386.10.3934/dcds.2007.19.361CrossRefGoogle Scholar
Lim, C.C. 2012 Phase transition to super-rotating atmospheres in a simple planetary model for a nonrotating massive planet: exact solution. Phys. Rev. E 86 (6), 066304.10.1103/PhysRevE.86.066304CrossRefGoogle Scholar
Lim, C.C. & Assad, S.M. 2005 Self containment radius for rotating planar flows, single-signed vortex gas and electron plasma. Regul. Chaotic Dyn. 10 (3), 239–255.10.1070/RD2005v010n03ABEH000313CrossRefGoogle Scholar
Lim, C.C., Ding, X. & Nebus, J. 2009 Vortex Dynamics, Statistical Mechanics and Planetary Atmospheres. World Scientific.10.1142/7195CrossRefGoogle Scholar
Lim, C.C. & Mavi, R.S. 2007 Phase transitions for barotropic flows on a sphere – Bragg method. Physica A 380, 43–60.10.1016/j.physa.2007.02.099CrossRefGoogle Scholar
Lim, C.C. & Nebus, J. 2004 The spherical model of logarithmic potentials as examined by Monte Carlo methods. Phys. Fluids 16 (10), 4020–4027.10.1063/1.1790499CrossRefGoogle Scholar
Lim, C.C. & Nebus, J. 2006 Vorticity, Statistical Mechanics and Monte-Carlo Simulations. Springer-Verlag.Google Scholar
Lundgren, T.S. & Pointin, Y.B. 1977 Statistical mechanics of 2D vortices. J. Stat. Phys. 17, 323.10.1007/BF01014402CrossRefGoogle Scholar
Miller, J. 1990 Statistical mechanics of Euler equations in two dimensions. Phys. Rev. 65, 2137–2140.Google ScholarPubMed
Onsager, L. 1949 Statistical hydrodynamics. Nuovo Cimento 6, 279–289.10.1007/BF02780991CrossRefGoogle Scholar
Robert, R. & Sommeria, J. 1991 Statistical equilibrium states for two-dimensional flows. J. Fluid Mech. 229, 291–310.10.1017/S0022112091003038CrossRefGoogle Scholar
Zhang, Y. & Krasheninnikov, S.I. 2017 Blobs and drift wave dynamics. Phys. Plasmas 24, 092313. doi: 10.1063/1.4994833.CrossRefGoogle Scholar