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 wellknown 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 rangethis 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 »
 Authors:
 Univ. of Texas, Austin, TX (United States). Inst. for Fusion Studies, Dept. of Physics
 Harvard Univ., Cambridge, MA (United States). Harvard John A. Paulson School of Engineering and Applied Sciences; HarvardSmithsonian 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) (SC24); 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:
 AC0209CH11466; FG0580ET53088; AGS1338944
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 New Journal of Physics
 Additional Journal Information:
 Journal Volume: 19; Journal Issue: 1; Journal ID: ISSN 13672630
 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; solarwind turbulence; collisionless magnetic reconnection; gammaray bursts; Hallmagnetohydrodynamics; 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:10.1088/13672630/aa55eb.
Miloshevich, George, Lingam, Manasvi, & Morrison, Philip J. On the structure and statistical theory of turbulence of extended magnetohydrodynamics. United States. doi:10.1088/13672630/aa55eb.
Miloshevich, George, Lingam, Manasvi, and Morrison, Philip J. Mon .
"On the structure and statistical theory of turbulence of extended magnetohydrodynamics". United States.
doi:10.1088/13672630/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 wellknown 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 rangethis 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 = {10.1088/13672630/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}
}
Web of Science

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 wellknown idealMHDinverse cascade of magnetic helicity. After amore »

On the structure and statistical theory of turbulence of extended magnetohydrodynamics
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 wellknown idealMHDinverse cascade of magnetic helicity. After amore »Cited by 2 
Quantumfield renormalization group in the theory of turbulence: magnetohydrodynamics
This paper generalizes the quantumfield approach in the theory of developed isotropic turbulence to magnetohydrodynamics. The field formulation and proof of renormalizability are examined. Renormalizationgroup 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 threedimensional gyrotropic fluid. 
Statistical properties of ideal threedimensional Hall magnetohydrodynamics: The spectral structure of the equilibrium ensemble
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 threedimensional 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 »