# 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 »

- 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; 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}

}

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