Effect of plasma compression on plasma sheet stability
Plasma sheet stability to the ballooning mode is analyzed using several physical formulations: ideal MHD, stochastic theory, fast‐MHD, and the Kruskal‐Oberman formulation. It is shown that the major difference among them lies in the plasma compression expression. Explicit computations using the corr...
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Published in | Geophysical research letters Vol. 26; no. 17; pp. 2705 - 2708 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Washington, DC
Blackwell Publishing Ltd
01.09.1999
American Geophysical Union |
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Abstract | Plasma sheet stability to the ballooning mode is analyzed using several physical formulations: ideal MHD, stochastic theory, fast‐MHD, and the Kruskal‐Oberman formulation. It is shown that the major difference among them lies in the plasma compression expression. Explicit computations using the corresponding ballooning equations were performed for two different types of model field lines. For very high β field lines that are excessively stretched where the stochastic description is most appropriate, the ballooning mode is found to be stable or at best weakly unstable. For field lines that are not too much stretched but even rather round, the ballooning instability can be triggered, within both ideal MHD and the stochastic theory, when βe > βec: Here the threshold value of the equatorial beta, βec, is roughly less than unity and practically set by the ideal MHD limit. Also in contrast to a recent suggestion, the fast‐MHD description where the time scale of interest is too short to allow plasma parallel motion is shown to be more stable than ideal MHD. It indicates no instability in all the equilibria that were tested. The Kruskal‐Oberman description is even more stable than fast‐MHD. |
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AbstractList | Plasma sheet stability to the ballooning mode is analyzed using several physical formulations: ideal MHD, stochastic theory, fast-MHD, and the Kruskal-Oberman formulation. It is shown that the major difference among them lies in the plasma compression expression. Explicit computations using the corresponding ballooning equations were performed for two different types of model field lines. For very high beta field lines that are excessively stretched where the stochastic description is most appropriate, the ballooning mode is found to be stable or at best weakly unstable. For field lines that are not too much stretched but even rather round, the ballooning instability can be triggered, within both ideal MHD and the stochastic theory, when beta sub(e) > beta sub(e) super(c) : here the threshold value of the equatorial beta, beta sub(e) super(c) , is roughly less than unity and practically set by the ideal MHD limit. Also in contrast to a recent suggestion, the fast-MHD description where the time scale of interest is too short to allow plasma parallel motion is shown to be more stable than ideal MHD. It indicates no instability in all the equilibria that were tested. The Kruskal-Oberman description is even more stable than fast-MHD. Plasma sheet stability to the ballooning mode is analyzed using several physical formulations: ideal MHD, stochastic theory, fast‐MHD, and the Kruskal‐Oberman formulation. It is shown that the major difference among them lies in the plasma compression expression. Explicit computations using the corresponding ballooning equations were performed for two different types of model field lines. For very high β field lines that are excessively stretched where the stochastic description is most appropriate, the ballooning mode is found to be stable or at best weakly unstable. For field lines that are not too much stretched but even rather round, the ballooning instability can be triggered, within both ideal MHD and the stochastic theory, when β e > β e c : Here the threshold value of the equatorial beta, β e c , is roughly less than unity and practically set by the ideal MHD limit. Also in contrast to a recent suggestion, the fast‐MHD description where the time scale of interest is too short to allow plasma parallel motion is shown to be more stable than ideal MHD. It indicates no instability in all the equilibria that were tested. The Kruskal‐Oberman description is even more stable than fast‐MHD. Plasma sheet stability to the ballooning mode is analyzed using several physical formulations: ideal MHD, stochastic theory, fast‐MHD, and the Kruskal‐Oberman formulation. It is shown that the major difference among them lies in the plasma compression expression. Explicit computations using the corresponding ballooning equations were performed for two different types of model field lines. For very high β field lines that are excessively stretched where the stochastic description is most appropriate, the ballooning mode is found to be stable or at best weakly unstable. For field lines that are not too much stretched but even rather round, the ballooning instability can be triggered, within both ideal MHD and the stochastic theory, when βe > βec: Here the threshold value of the equatorial beta, βec, is roughly less than unity and practically set by the ideal MHD limit. Also in contrast to a recent suggestion, the fast‐MHD description where the time scale of interest is too short to allow plasma parallel motion is shown to be more stable than ideal MHD. It indicates no instability in all the equilibria that were tested. The Kruskal‐Oberman description is even more stable than fast‐MHD. |
Author | Lee, D.-Y. |
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Cites_doi | 10.1029/90JA02346 10.1029/98JA00589 10.1029/1998GL900105 10.1029/97JA01595 10.1029/93JA01746 10.1029/93GL03533 10.1063/1.1705885 10.1029/98GL00412 10.1029/1999JA900227 10.1029/91JA01106 10.1029/95JA01523 10.1029/96JA01314 10.1029/JA078i019p03773 10.1029/94JA00862 10.1029/92JA00875 10.1007/978-94-009-4722-1_17 10.1063/1.871099 |
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Keywords | Ballooning instability Plasma compression MHD model Two dimensional system Magnetospheric substorm Stochastic theory Theoretical study Plasma layer |
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References_xml | – volume: 2 start-page: 289 issue: 1 year: 1995 article-title: The stability of a stochastic plasma with respect to low frequency perturbations publication-title: Phys. Plasmas – volume: 101 start-page: 17347 year: 1996 article-title: On the possibility of the MHD‐ballooning instability in the magnetotail‐like field reversal publication-title: J. Geophys. Res. – volume: 98 start-page: 19369 year: 1993 article-title: Does the ballooning instability trigger substorms in the near‐earth magnetotail? publication-title: J. Geophys. Res. – volume: 1 start-page: 275 year: 1958 article-title: On the stability of plasma in static equilibrium publication-title: Phys. Fluids – volume: 100 start-page: 19421 year: 1995 article-title: A new approach to low‐frequency “MHD‐like” waves in magnetospheric plasmas publication-title: J. Geophys. Res. – volume: 96 start-page: 1503 year: 1991 article-title: Kinetic theory of geomagnetic pulsations, 1., Internal excitation by energetic particles publication-title: J. Geophys. Res. – volume: 78 start-page: 3773 year: 1973 article-title: On the structure of the magnetotail current sheet publication-title: J. Geophys. Res. – volume: 103 start-page: 11797 year: 1998 article-title: Hydromagnetic equilibrium and instabilities in the convectively driven near‐earth plasma sheet publication-title: J. Geophys. Res. – volume: 102 start-page: 19903 year: 1997 article-title: MHD ballooning stability of a sheared plasma sheet publication-title: J. Geophys. Res. – volume: 96 start-page: 17697 year: 1991 article-title: Plasma sheet instability related to the westward traveling surge publication-title: J. Geophys. Res. – volume: 97 start-page: 19251 year: 1992 article-title: Is the earth's magnetotail balloon unstable? publication-title: J. Geophys. Res. – volume: 25 start-page: 861 year: 1998 article-title: Ballooning instability of a thin current sheet in the high‐Lundquist‐number magnetotail publication-title: Geophys. Res. Lett. – volume: 99 start-page: 14863 year: 1994 article-title: Magnetotaildynamics under isobaric constraints publication-title: J. Geophys. Res. – start-page: 233 year: 1986 – volume: 21 start-page: 253 year: 1994 article-title: The kinetic response of a stochastic plasma to low frequency perturbations publication-title: Geophys. Res. Lett. – volume: 25 start-page: 4059 year: 1998 article-title: Ballooning instability in the tail plasma sheet publication-title: Geophys. Res. Lett. – year: 1999 article-title: Substorm trigger conditions publication-title: J. Geophys. Res. – ident: e_1_2_1_4_1 doi: 10.1029/90JA02346 – ident: e_1_2_1_18_1 doi: 10.1029/98JA00589 – ident: e_1_2_1_12_1 doi: 10.1029/1998GL900105 – ident: e_1_2_1_6_1 doi: 10.1029/97JA01595 – ident: e_1_2_1_15_1 doi: 10.1029/93JA01746 – ident: e_1_2_1_9_1 doi: 10.1029/93GL03533 – ident: e_1_2_1_11_1 doi: 10.1063/1.1705885 – ident: e_1_2_1_2_1 doi: 10.1029/98GL00412 – ident: e_1_2_1_5_1 doi: 10.1029/1999JA900227 – ident: e_1_2_1_16_1 doi: 10.1029/91JA01106 – ident: e_1_2_1_8_1 doi: 10.1029/95JA01523 – ident: e_1_2_1_13_1 doi: 10.1029/96JA01314 – ident: e_1_2_1_10_1 doi: 10.1029/JA078i019p03773 – ident: e_1_2_1_3_1 doi: 10.1029/94JA00862 – ident: e_1_2_1_14_1 doi: 10.1029/92JA00875 – ident: e_1_2_1_17_1 doi: 10.1007/978-94-009-4722-1_17 – ident: e_1_2_1_7_1 doi: 10.1063/1.871099 |
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Snippet | Plasma sheet stability to the ballooning mode is analyzed using several physical formulations: ideal MHD, stochastic theory, fast‐MHD, and the Kruskal‐Oberman... Plasma sheet stability to the ballooning mode is analyzed using several physical formulations: ideal MHD, stochastic theory, fast-MHD, and the Kruskal-Oberman... |
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SubjectTerms | Ballooning modes Earth, ocean, space Exact sciences and technology External geophysics Instability Magnetic storms, substorms Magnetohydrodynamics Mathematical models MHD Physics of the magnetosphere Plasma compression Stability Stochasticity |
Title | Effect of plasma compression on plasma sheet stability |
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