Nonlinear resistivity for magnetohydrodynamical models
Abstract
A new formulation of the plasma resistivity that stems from the collisional momentumtransfer rate between electrons and ions is presented. The resistivity computed herein is shown to depend not only on the temperature and density but also on all other polynomial velocityspace moments of the distribution function, such as the pressure tensor and heat flux vector. The full expression for the collisional momentumtransfer rate is determined and is used to formulate the nonlinear anisotropic resistivity. The new formalism recovers the Spitzer resistivity, as well as the concept of thermal force if the heat flux is assumed to be proportional to a temperature gradient. Furthermore, if the pressure tensor is related to viscous stress, the latter enters the expression for the resistivity. The relative importance of the nonlinear term(s) with respect to the wellestablished electron inertia and Hall terms is also examined. Lastly, the subtle implications of the nonlinear resistivity, and its dependence on the fluid variables, are discussed in the context of magnetized plasma environments and phenomena such as magnetic reconnection.
 Authors:
 Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Harvard Univ., Cambridge, MA (United States). John A. Paulson School of Engineering and Applied Sciences; HarvardSmithsonian Center for Astrophysics, Cambridge, MA (United States)
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Princeton Univ., NJ (United States). Dept. of Astrophysical Sciences; Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Publication Date:
 Research Org.:
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC24); National Science Foundation (NSF)
 OSTI Identifier:
 1358667
 Grant/Contract Number:
 AC0209CH11466; AGS1338944; AGS1552142
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 24; Journal Issue: 4; Journal ID: ISSN 1070664X
 Publisher:
 American Institute of Physics (AIP)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; collisionless magnetic reconnection; dynamo; simulations; plasmas; electrical resistivity; anisotropy; viscosity; maxwell equations; tensor methods
Citation Formats
Lingam, M., Hirvijoki, E., Pfefferlé, D., Comisso, L., and Bhattacharjee, A. Nonlinear resistivity for magnetohydrodynamical models. United States: N. p., 2017.
Web. doi:10.1063/1.4980838.
Lingam, M., Hirvijoki, E., Pfefferlé, D., Comisso, L., & Bhattacharjee, A. Nonlinear resistivity for magnetohydrodynamical models. United States. doi:10.1063/1.4980838.
Lingam, M., Hirvijoki, E., Pfefferlé, D., Comisso, L., and Bhattacharjee, A. 2017.
"Nonlinear resistivity for magnetohydrodynamical models". United States.
doi:10.1063/1.4980838.
@article{osti_1358667,
title = {Nonlinear resistivity for magnetohydrodynamical models},
author = {Lingam, M. and Hirvijoki, E. and Pfefferlé, D. and Comisso, L. and Bhattacharjee, A.},
abstractNote = {A new formulation of the plasma resistivity that stems from the collisional momentumtransfer rate between electrons and ions is presented. The resistivity computed herein is shown to depend not only on the temperature and density but also on all other polynomial velocityspace moments of the distribution function, such as the pressure tensor and heat flux vector. The full expression for the collisional momentumtransfer rate is determined and is used to formulate the nonlinear anisotropic resistivity. The new formalism recovers the Spitzer resistivity, as well as the concept of thermal force if the heat flux is assumed to be proportional to a temperature gradient. Furthermore, if the pressure tensor is related to viscous stress, the latter enters the expression for the resistivity. The relative importance of the nonlinear term(s) with respect to the wellestablished electron inertia and Hall terms is also examined. Lastly, the subtle implications of the nonlinear resistivity, and its dependence on the fluid variables, are discussed in the context of magnetized plasma environments and phenomena such as magnetic reconnection.},
doi = {10.1063/1.4980838},
journal = {Physics of Plasmas},
number = 4,
volume = 24,
place = {United States},
year = 2017,
month = 4
}
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