skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: On the structure and statistical theory of turbulence of extended magnetohydrodynamics

Abstract

Recent progress regarding the noncanonical Hamiltonian formulation of extended magnetohydrodynamics (XMHD), a model with Hall drift and electron inertia, is summarized. The advantages of the Hamiltonian approach are invoked to study some general properties of XMHD turbulence, and to compare them against their ideal MHD counterparts. For instance, the helicity flux transfer rates for XMHD are computed, and Liouville's theorem for this model is also verified. The latter is used, in conjunction with the absolute equilibrium states, to arrive at the spectra for the invariants, and to determine the direction of the cascades, e.g., generalizations of the well-known ideal MHD inverse cascade of magnetic helicity. After a similar analysis is conducted for XMHD by inspecting second order structure functions and absolute equilibrium states, a couple of interesting results emerge. When cross helicity is taken to be ignorable, the inverse cascade of injected magnetic helicity also occurs in the Hall MHD range-this is shown to be consistent with previous results in the literature. In contrast, in the inertial MHD range, viz at scales smaller than the electron skin depth, all spectral quantities are expected to undergo direct cascading. Finally, the consequences and relevance of our results in space and astrophysical plasmasmore » are also briefly discussed.« less

Authors:
 [1]; ORCiD logo [2];  [1]
  1. Univ. of Texas, Austin, TX (United States). Inst. for Fusion Studies, Dept. of Physics
  2. Harvard Univ., Cambridge, MA (United States). Harvard John A. Paulson School of Engineering and Applied Sciences; Harvard-Smithsonian Center for Astrophysics, Cambridge, MA (United States). Inst. for Theory and Computation; Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences
Publication Date:
Research Org.:
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Princeton Univ., NJ (United States); Univ. of Tennessee, Knoxville, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24); National Science Foundation (NSF); USDOE Office of Fossil Energy (FE); USDOE National Energy Technology Laboratory (NETL)
OSTI Identifier:
1355659
Alternate Identifier(s):
OSTI ID: 1357807
Grant/Contract Number:
AC02-09CH11466; FG05-80ET53088; AGS-1338944
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
New Journal of Physics
Additional Journal Information:
Journal Volume: 19; Journal Issue: 1; Journal ID: ISSN 1367-2630
Publisher:
IOP Publishing
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; extended magnetohydrodynamic turbulence; absolute equilibrium; hall and electron inertia; Hamiltonian; solar-wind turbulence; collisionless magnetic reconnection; gamma-ray bursts; Hall-magnetohydrodynamics; inverse cascade; action principle; MHD turbulence; dynamo action; formulation; mechanics; extended magnetohydrodynamic turbulence, absolute equilibrium, hall and electron inertia, hamiltonian

Citation Formats

Miloshevich, George, Lingam, Manasvi, and Morrison, Philip J. On the structure and statistical theory of turbulence of extended magnetohydrodynamics. United States: N. p., 2017. Web. doi:10.1088/1367-2630/aa55eb.
Miloshevich, George, Lingam, Manasvi, & Morrison, Philip J. On the structure and statistical theory of turbulence of extended magnetohydrodynamics. United States. doi:10.1088/1367-2630/aa55eb.
Miloshevich, George, Lingam, Manasvi, and Morrison, Philip J. Mon . "On the structure and statistical theory of turbulence of extended magnetohydrodynamics". United States. doi:10.1088/1367-2630/aa55eb. https://www.osti.gov/servlets/purl/1355659.
@article{osti_1355659,
title = {On the structure and statistical theory of turbulence of extended magnetohydrodynamics},
author = {Miloshevich, George and Lingam, Manasvi and Morrison, Philip J.},
abstractNote = {Recent progress regarding the noncanonical Hamiltonian formulation of extended magnetohydrodynamics (XMHD), a model with Hall drift and electron inertia, is summarized. The advantages of the Hamiltonian approach are invoked to study some general properties of XMHD turbulence, and to compare them against their ideal MHD counterparts. For instance, the helicity flux transfer rates for XMHD are computed, and Liouville's theorem for this model is also verified. The latter is used, in conjunction with the absolute equilibrium states, to arrive at the spectra for the invariants, and to determine the direction of the cascades, e.g., generalizations of the well-known ideal MHD inverse cascade of magnetic helicity. After a similar analysis is conducted for XMHD by inspecting second order structure functions and absolute equilibrium states, a couple of interesting results emerge. When cross helicity is taken to be ignorable, the inverse cascade of injected magnetic helicity also occurs in the Hall MHD range-this is shown to be consistent with previous results in the literature. In contrast, in the inertial MHD range, viz at scales smaller than the electron skin depth, all spectral quantities are expected to undergo direct cascading. Finally, the consequences and relevance of our results in space and astrophysical plasmas are also briefly discussed.},
doi = {10.1088/1367-2630/aa55eb},
journal = {New Journal of Physics},
number = 1,
volume = 19,
place = {United States},
year = {Mon Jan 16 00:00:00 EST 2017},
month = {Mon Jan 16 00:00:00 EST 2017}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 2works
Citation information provided by
Web of Science

Save / Share:
  • Recent progress regarding the noncanonical Hamiltonian formulation of extended magnetohydrodynamics (XMHD), a model with Hall drift and electron inertia, is summarized. The advantages of the Hamiltonian approach are invoked to study some general properties ofXMHDturbulence, and to compare them against their idealMHDcounterparts. For instance, the helicity flux transfer rates for XMHDare computed, and Liouville’s theorem for this model is also verified. The latter is used, in conjunction with the absolute equilibrium states, to arrive at the spectra for the invariants, and to determine the direction of the cascades, e.g., generalizations of the well-known idealMHDinverse cascade of magnetic helicity. After amore » similar analysis is conducted forXMHDby inspecting second order structure functions and absolute equilibrium states, a couple of interesting results emerge. When cross helicity is taken to be ignorable, the inverse cascade of injected magnetic helicity also occurs in the HallMHDrange—this is shown to be consistent with previous results in the literature. In contrast, in the inertialMHDrange, viz at scales smaller than the electron skin depth, all spectral quantities are expected to undergo direct cascading. The consequences and relevance of our results in space and astrophysical plasmas are also briefly discussed.« less
  • Recent progress regarding the noncanonical Hamiltonian formulation of extended magnetohydrodynamics (XMHD), a model with Hall drift and electron inertia, is summarized. The advantages of the Hamiltonian approach are invoked to study some general properties ofXMHDturbulence, and to compare them against their idealMHDcounterparts. For instance, the helicity flux transfer rates for XMHDare computed, and Liouville’s theorem for this model is also verified. The latter is used, in conjunction with the absolute equilibrium states, to arrive at the spectra for the invariants, and to determine the direction of the cascades, e.g., generalizations of the well-known idealMHDinverse cascade of magnetic helicity. After amore » similar analysis is conducted forXMHDby inspecting second order structure functions and absolute equilibrium states, a couple of interesting results emerge. When cross helicity is taken to be ignorable, the inverse cascade of injected magnetic helicity also occurs in the HallMHDrange—this is shown to be consistent with previous results in the literature. In contrast, in the inertialMHDrange, viz at scales smaller than the electron skin depth, all spectral quantities are expected to undergo direct cascading. The consequences and relevance of our results in space and astrophysical plasmas are also briefly discussed.« less
  • Cited by 5
  • This paper generalizes the quantum-field approach in the theory of developed isotropic turbulence to magnetohydrodynamics. The field formulation and proof of renormalizability are examined. Renormalization-group equations are presented. The calculation in lowest order in 'g' is presented and dimension 3 is discussed. The authors examine the gyrotropic fluid, in particular, the possibility of generalizing the renormalization group technique to the case of a three-dimensional gyrotropic fluid.
  • The nonlinear dynamics of ideal, incompressible Hall magnetohydrodynamics (HMHD) is investigated through classical Gibbs ensemble methods applied to the finite Galerkin representation. The spectral structure of HMHD is derived in a three-dimensional periodic geometry and compared with the MHD case. This provides a general picture of spectral transfer and cascade by the assumption that ideal Galerkin HMHD follows equilibrium statistics as in the case of Euler [U. Frisch et al., J. Fluid Mech. 68, 769 (1975)] and MHD [T. Stribling and W. H. Matthaeus, Phys. Fluids B 2, 1979 (1990)] theories. In HMHD, the equilibrium ensemble is built on themore » conservation of three quadratic invariants: The total energy, the magnetic helicity, and the generalized helicity. The latter replaces the cross helicity in MHD. In HMHD equilibrium, several differences appear with respect to the MHD case: (i) The generalized helicity (and in a weaker way the energy and the magnetic helicity) tends to condense in the longest wavelength, as in MHD, but also admits the novel feature of spectral enhancement, not a true condensation, at the smallest scales; (ii) equipartition between kinetic and magnetic energy, typical of Alfvenic MHD turbulence, is broken; (iii) modal distributions of energy and helicities show minima due to the presence of the ion skin depth. Ensemble predictions are compared to numerical simulations with a low-order truncation Galerkin spectral code, and good agreement is seen. Implications for general turbulent states are discussed.« less