A new fluid scheme for weakly collisional plasmas: 1. General theory
We present a new approach to the study of two‐fluid hydrodynamics of weakly collisional plasma systems, such as those frequently encountered in the astrophysical context. Our starting point is the novel procedure developed in past years by Chen, Rao, and Spiegel (CRS) for the fluid description of se...
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| Published in | Journal of Geophysical Research: Space Physics Vol. 116; no. A4 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Washington
Blackwell Publishing Ltd
01.04.2011
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0148-0227 2169-9380 2156-2202 2169-9402 |
| DOI | 10.1029/2010JA016395 |
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| Abstract | We present a new approach to the study of two‐fluid hydrodynamics of weakly collisional plasma systems, such as those frequently encountered in the astrophysical context. Our starting point is the novel procedure developed in past years by Chen, Rao, and Spiegel (CRS) for the fluid description of semicollisional neutral monoatomic gases. The new system of fluid equations that include viscous and conductive effects has been successfully tested. However, the extension of such a procedure to plasmas is not a straightforward one. We have to deal with (at least) two components, with vastly different values of the masses, and the nature of collisions between charged particles is substantially different from the neutral particle case. We perform a preliminary careful examination of the basic requirements of the CRS method and identify the conditions under which an extension of such method is indeed possible. We then derive the system of fluid equations appropriate to the description of a weakly collisional two‐component plasma in the new scheme and discuss the differences with respect to the more familiar Navier‐Stokes approach. This paper is therefore of a general theoretical nature. However, we also point out that solar wind is a good testing ground for the newly derived system of fluid equations. This application will be the subject of a subsequent paper.
Key Points
New approach to two‐fluid hydrodynamics of weakly collisional plasmas |
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| AbstractList | New approach to two-fluid hydrodynamics of weakly collisional plasmas We present a new approach to the study of two-fluid hydrodynamics of weakly collisional plasma systems, such as those frequently encountered in the astrophysical context. Our starting point is the novel procedure developed in past years by Chen, Rao, and Spiegel (CRS) for the fluid description of semicollisional neutral monoatomic gases. The new system of fluid equations that include viscous and conductive effects has been successfully tested. However, the extension of such a procedure to plasmas is not a straightforward one. We have to deal with (at least) two components, with vastly different values of the masses, and the nature of collisions between charged particles is substantially different from the neutral particle case. We perform a preliminary careful examination of the basic requirements of the CRS method and identify the conditions under which an extension of such method is indeed possible. We then derive the system of fluid equations appropriate to the description of a weakly collisional two-component plasma in the new scheme and discuss the differences with respect to the more familiar Navier-Stokes approach. This paper is therefore of a general theoretical nature. However, we also point out that solar wind is a good testing ground for the newly derived system of fluid equations. This application will be the subject of a subsequent paper. We present a new approach to the study of two‐fluid hydrodynamics of weakly collisional plasma systems, such as those frequently encountered in the astrophysical context. Our starting point is the novel procedure developed in past years by Chen, Rao, and Spiegel (CRS) for the fluid description of semicollisional neutral monoatomic gases. The new system of fluid equations that include viscous and conductive effects has been successfully tested. However, the extension of such a procedure to plasmas is not a straightforward one. We have to deal with (at least) two components, with vastly different values of the masses, and the nature of collisions between charged particles is substantially different from the neutral particle case. We perform a preliminary careful examination of the basic requirements of the CRS method and identify the conditions under which an extension of such method is indeed possible. We then derive the system of fluid equations appropriate to the description of a weakly collisional two‐component plasma in the new scheme and discuss the differences with respect to the more familiar Navier‐Stokes approach. This paper is therefore of a general theoretical nature. However, we also point out that solar wind is a good testing ground for the newly derived system of fluid equations. This application will be the subject of a subsequent paper. Key Points New approach to two‐fluid hydrodynamics of weakly collisional plasmas |
| Author | Chiuderi, C. Torricelli-Ciamponi, G. Pietrini, P. |
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| References | Cercignani, C. (1988), The Boltzmann Equation and Its Applications, Springer, New York. Morse, T. F. (1964), Kinetic model equations for a gas mixture, Phys. Fluids, 7, 2012-2013, doi:10.1063/1.1711112. Jackson, J. D. (1975), Classical Electrodynamics, John Wiley, New York. Chen, X., H. Rao, and E. A. Spiegel (2001a), Continuum description of rarefied gas dynamics. I. Derivation from kinetic theory, Phys. Rev. E, 64, 046308, doi:10.1103/PhysRevE.64.04630. Spitzer, L. (1962), Physics of Fully Ionized Gases, Interscience, New York. Gross, E. P., and M. Krook (1956), Model for collision processes in gases: Small-amplitude oscillations of charged two-component systems, Phys. Rev., 102, 593-604, doi:10.1103/PhysRev.102.593. Agarwal, R. K., K.-Y. Yun, and R. Balakrishnan (2001), Beyond Navier-Stokes: Burnett equations for flows in the continuum-transition regime, Phys. Fluids, 13, 3061-3085, doi:10.1063/1.1397256. Spiegel, E. A., and J.-L. Thiffeault (2003a), Higher-order continuum approximation for rarefied gases, Phys. Fluids, 15, 3558-3567, doi:10.1063/1.161328. Boyd, T. J. M., and J. J. Sanderson (2003), The Physics of Plasmas, Cambridge Univ. Press, Cambridge, U. K. Goedbloed, J. P., and S. Poedts (2004), Principles of Magnetohydrodynamics, With Applications in Laboratory and Astrophysical Plasmas, Cambridge Univ. Press, Cambridge, U. K. Chen, X., E. A. Spiegel, and H. Rao (2002), Continuum description of rarefied gas dynamics. III. The structures of shock waves, Phys. Rev. E, 65, 036304, doi:10.1103/PhysRevE.65.036304. Chen, X., H. Rao, and E. A. Spiegel (2001b), Continuum description of rarefied gas dynamics. II. The propagation of ultrasound, Phys. Rev. E, 64, 046309, doi:10.1103/PhysRevE.64.046309. Shoub, E. C. (1987), Failure of the Fokker-Planck approximation to the Boltzmann integral for (1/r) potentials, Phys. Fluids, 30, 1340-1352, doi:10.1063/1.866508. Chapman, S., and T. G. Cowling (1991), The Mathematical Theory of Non-uniform Gases, Cambridge Univ. Press, Cambridge, U. K. Shoub, E. C. (1992), Close encounters in Coulomb and gravitational scattering. I. Relaxation of isotropic test-particle distributions by like-particle collisions, Astrophys. J., 389, 558-589, doi:10.1086/171231. Chen, X., H. Rao, and E. A. Spiegel (2000), Macroscopic equations for rarefied gas dynamics, Phys. Lett. A, 271, 87-91, doi:10.1016/S0375-9601(00)00362-5. Shu, F. H. (1992), The Physics of Astrophysics: Gas Dynamics, vol. 2, Univ. Sci., Mill Valley, Calif. Uhlenbeck, G. E., and G. W. Ford (1963), Lectures in Statistical Mechanics, Am. Math. Soc., Providence, R. I. Bhatnagar, P. L., E. P. Gross, and M. Krook (1954), A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems, Phys. Rev., 94, 511-525, doi:10.1103/PhysRev.94.511. Grad, H. (1963), Asymptotic theory of the Boltzmann equation, Phys. Fluids, 6, 147-181, doi:10.1063/1.1706716. Greene, J. M. (1973), Improved Bhatnagar-Gross-Krook model of electron-ion collisions, Phys. Fluids, 16, 2022-2023, doi:10.1063/1.1694254. 1954; 94 1987; 30 2000 1963; 6 1964; 7 2002; 65 1992; 389 1973; 16 2000; 271 1975 2003; 15 1963 1962 2004 2003 1991 2001; 13 1969 1992; 2 2001; 64 1988 1956; 102 |
| References_xml | – reference: Cercignani, C. (1988), The Boltzmann Equation and Its Applications, Springer, New York. – reference: Goedbloed, J. P., and S. Poedts (2004), Principles of Magnetohydrodynamics, With Applications in Laboratory and Astrophysical Plasmas, Cambridge Univ. Press, Cambridge, U. K. – reference: Bhatnagar, P. L., E. P. Gross, and M. Krook (1954), A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems, Phys. Rev., 94, 511-525, doi:10.1103/PhysRev.94.511. – reference: Jackson, J. D. (1975), Classical Electrodynamics, John Wiley, New York. – reference: Chapman, S., and T. G. Cowling (1991), The Mathematical Theory of Non-uniform Gases, Cambridge Univ. Press, Cambridge, U. K. – reference: Shoub, E. C. (1987), Failure of the Fokker-Planck approximation to the Boltzmann integral for (1/r) potentials, Phys. Fluids, 30, 1340-1352, doi:10.1063/1.866508. – reference: Greene, J. M. (1973), Improved Bhatnagar-Gross-Krook model of electron-ion collisions, Phys. Fluids, 16, 2022-2023, doi:10.1063/1.1694254. – reference: Chen, X., H. Rao, and E. A. Spiegel (2001b), Continuum description of rarefied gas dynamics. II. The propagation of ultrasound, Phys. Rev. E, 64, 046309, doi:10.1103/PhysRevE.64.046309. – reference: Shu, F. H. (1992), The Physics of Astrophysics: Gas Dynamics, vol. 2, Univ. Sci., Mill Valley, Calif. – reference: Grad, H. (1963), Asymptotic theory of the Boltzmann equation, Phys. Fluids, 6, 147-181, doi:10.1063/1.1706716. – reference: Shoub, E. C. (1992), Close encounters in Coulomb and gravitational scattering. I. Relaxation of isotropic test-particle distributions by like-particle collisions, Astrophys. J., 389, 558-589, doi:10.1086/171231. – reference: Spiegel, E. A., and J.-L. Thiffeault (2003a), Higher-order continuum approximation for rarefied gases, Phys. Fluids, 15, 3558-3567, doi:10.1063/1.161328. – reference: Chen, X., H. Rao, and E. A. Spiegel (2001a), Continuum description of rarefied gas dynamics. I. Derivation from kinetic theory, Phys. Rev. E, 64, 046308, doi:10.1103/PhysRevE.64.04630. – reference: Chen, X., E. A. Spiegel, and H. Rao (2002), Continuum description of rarefied gas dynamics. III. The structures of shock waves, Phys. Rev. E, 65, 036304, doi:10.1103/PhysRevE.65.036304. – reference: Gross, E. P., and M. Krook (1956), Model for collision processes in gases: Small-amplitude oscillations of charged two-component systems, Phys. Rev., 102, 593-604, doi:10.1103/PhysRev.102.593. – reference: Spitzer, L. (1962), Physics of Fully Ionized Gases, Interscience, New York. – reference: Morse, T. F. (1964), Kinetic model equations for a gas mixture, Phys. Fluids, 7, 2012-2013, doi:10.1063/1.1711112. – reference: Chen, X., H. Rao, and E. A. Spiegel (2000), Macroscopic equations for rarefied gas dynamics, Phys. Lett. A, 271, 87-91, doi:10.1016/S0375-9601(00)00362-5. – reference: Uhlenbeck, G. E., and G. W. Ford (1963), Lectures in Statistical Mechanics, Am. Math. Soc., Providence, R. I. – reference: Agarwal, R. K., K.-Y. Yun, and R. Balakrishnan (2001), Beyond Navier-Stokes: Burnett equations for flows in the continuum-transition regime, Phys. Fluids, 13, 3061-3085, doi:10.1063/1.1397256. – reference: Boyd, T. J. M., and J. J. Sanderson (2003), The Physics of Plasmas, Cambridge Univ. Press, Cambridge, U. K. – start-page: 142 year: 1969 end-page: 255 – year: 1963 – year: 1962 – volume: 94 start-page: 511 year: 1954 end-page: 525 article-title: A model for collision processes in gases. I. Small amplitude processes in charged and neutral one‐component systems publication-title: Phys. Rev. – volume: 389 start-page: 558 year: 1992 end-page: 589 article-title: Close encounters in Coulomb and gravitational scattering. I. Relaxation of isotropic test‐particle distributions by like‐particle collisions publication-title: Astrophys. J. – year: 1988 – volume: 65 year: 2002 article-title: Continuum description of rarefied gas dynamics. III. The structures of shock waves publication-title: Phys. Rev. E – volume: 64 year: 2001 article-title: Continuum description of rarefied gas dynamics. I. Derivation from kinetic theory publication-title: Phys. Rev. E – volume: 2 year: 1992 – year: 2003 – year: 2004 – year: 2000 – year: 1975 – volume: 30 start-page: 1340 year: 1987 end-page: 1352 article-title: Failure of the Fokker‐Planck approximation to the Boltzmann integral for (1/r) potentials publication-title: Phys. Fluids – volume: 6 start-page: 147 year: 1963 end-page: 181 article-title: Asymptotic theory of the Boltzmann equation publication-title: Phys. Fluids – volume: 102 start-page: 593 year: 1956 end-page: 604 article-title: Model for collision processes in gases: Small‐amplitude oscillations of charged two‐component systems publication-title: Phys. Rev. – start-page: 377 year: 2003 end-page: 391 – year: 1991 – volume: 15 start-page: 3558 year: 2003 end-page: 3567 article-title: Higher‐order continuum approximation for rarefied gases publication-title: Phys. Fluids – volume: 271 start-page: 87 year: 2000 end-page: 91 article-title: Macroscopic equations for rarefied gas dynamics publication-title: Phys. Lett. A – volume: 64 year: 2001 article-title: Continuum description of rarefied gas dynamics. II. The propagation of ultrasound publication-title: Phys. Rev. E – volume: 7 start-page: 2012 year: 1964 end-page: 2013 article-title: Kinetic model equations for a gas mixture publication-title: Phys. Fluids – volume: 13 start-page: 3061 year: 2001 end-page: 3085 article-title: Beyond Navier‐Stokes: Burnett equations for flows in the continuum‐transition regime publication-title: Phys. Fluids – volume: 16 start-page: 2022 year: 1973 end-page: 2023 article-title: Improved Bhatnagar‐Gross‐Krook model of electron‐ion collisions publication-title: Phys. Fluids |
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| Snippet | We present a new approach to the study of two‐fluid hydrodynamics of weakly collisional plasma systems, such as those frequently encountered in the... New approach to two-fluid hydrodynamics of weakly collisional plasmas We present a new approach to the study of two-fluid hydrodynamics of weakly collisional... |
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| Title | A new fluid scheme for weakly collisional plasmas: 1. General theory |
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