亚阿尔芬剪切流对撕裂模不稳定性的影响
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摘要
磁场重联伴随着磁场拓扑结构的改变,是磁能转化为等离子体动能和热能的重要方式,它被用来解释自然界中很多能量的突然释放现象。剪切流不论在空间等离子体还是实验室等离子体中都广泛存在,所以有必要去研究等离子体中剪切流对撕裂模等不稳定性的影响。
本文研究了亚Alfven速度的剪切流对撕裂模不稳定性的影响。我们应用数值模拟的方法在可压缩电阻磁流体力学模型和可压缩Hall磁流体力学模型下重点讨论了加入亚Alfven速度的剪切流之后等离子体比压值β和Hall效应对重联率的影响。
我们在固定剪切流的渐进速度而改变剪切流的半宽度时发现剪切流对撕裂模既可以致稳也可以解稳。在等离子体比压值较大(β=5.0,β=2.0)的情况下,当剪切流的半宽度超过一个阈值时,剪切流对撕裂模有明显的促进作用,即重联率的峰值远高于没有剪切流时的重联率峰值,这与不可压磁流体模型得到的结果完全吻合；在等离子体比压值较小(β=0.5,β=0.2)的情况下,剪切流虽然也可以使撕裂模解稳,但是促进作用基本消失,即持续增大剪切流半宽度时,重联率的峰值仍然和没有剪切流的情况接近,这与上下入流区域出现一对不连续的结构有关。我们认为剪切流对重联率的影响可以通过垂直模拟平面的扰动涡旋的分布和强度的变化来解释。在引入Hall效应后,剪切流同样对撕裂模的发展同样既有促进作用也有抑制作用,但离子惯性长度d,较大即Hall效应较强时,由于无剪切流时重联率已经较大,所以这种促进作用会变弱。
Magnetic reconnection associated with the change of magnetic field topology plays an important role on which magnetic energy can be transferred into plasma kinetic energy and plasma thermal energy.Magnetic reconnection has been used to explain many natural phenomena of the sudden release of magnetic energy.Since plasma shear flow is ubiquitous in both space and laboratory plasmas,it is worth investigating an impact of the plasma shear flow in some instabilities such as the tearing mode instability.
In this paper,we adopt the numerical simulation to study the sub-Alfvenic shear flow influence on tearing mode stability.Based on compressible resistive MHD model and compressible Hall MHD model,we investigate the plasma beta and Hall effects on the reconnection rate in the presence of sub-Alfvenic shear flow.
We fix the asymptotic velocity of shear flow and vary the half width of shear flow.We find that the shear flow can either stabilize or destabilize the tearing mode instability.In the cases of high plasma beta(β=5.0,β=2.0),when the half width of shear flow exceeds a threshold value,the shear flow can boost the tearing mode instability,that is,the peak reconnection rate is much higher than the case in the absence of shear flow,which is in a good agreement with the results from incompressible simulation;in the cases of low plasma beta(β=0.5,β=0.2),though the shear flow can destabilize the tearing mode,the boosting effect nearly disappears,that is,when increasing the half width of shear flow,the peak reconnection rate is still close to the case without shear flow,which is associated with the presence of a pair of discontinuities in the upper and lower inflow region.We believe that the shear flow influence on reconnection rate can be explained by studying the distribution and strength of perturbed vortex at the Y direction.With the inclusion of the Hall effect,shear flow can still either stabilize or destabilize magnetic reconnection,but when the ion inertial length d is large,in other words,the Hall effect is strong,the boosting effect becomes weak since the reconnection rate is already large without considering shear flow.
本文研究了亚Alfven速度的剪切流对撕裂模不稳定性的影响。我们应用数值模拟的方法在可压缩电阻磁流体力学模型和可压缩Hall磁流体力学模型下重点讨论了加入亚Alfven速度的剪切流之后等离子体比压值β和Hall效应对重联率的影响。
我们在固定剪切流的渐进速度而改变剪切流的半宽度时发现剪切流对撕裂模既可以致稳也可以解稳。在等离子体比压值较大(β=5.0,β=2.0)的情况下,当剪切流的半宽度超过一个阈值时,剪切流对撕裂模有明显的促进作用,即重联率的峰值远高于没有剪切流时的重联率峰值,这与不可压磁流体模型得到的结果完全吻合；在等离子体比压值较小(β=0.5,β=0.2)的情况下,剪切流虽然也可以使撕裂模解稳,但是促进作用基本消失,即持续增大剪切流半宽度时,重联率的峰值仍然和没有剪切流的情况接近,这与上下入流区域出现一对不连续的结构有关。我们认为剪切流对重联率的影响可以通过垂直模拟平面的扰动涡旋的分布和强度的变化来解释。在引入Hall效应后,剪切流同样对撕裂模的发展同样既有促进作用也有抑制作用,但离子惯性长度d,较大即Hall效应较强时,由于无剪切流时重联率已经较大,所以这种促进作用会变弱。
Magnetic reconnection associated with the change of magnetic field topology plays an important role on which magnetic energy can be transferred into plasma kinetic energy and plasma thermal energy.Magnetic reconnection has been used to explain many natural phenomena of the sudden release of magnetic energy.Since plasma shear flow is ubiquitous in both space and laboratory plasmas,it is worth investigating an impact of the plasma shear flow in some instabilities such as the tearing mode instability.
In this paper,we adopt the numerical simulation to study the sub-Alfvenic shear flow influence on tearing mode stability.Based on compressible resistive MHD model and compressible Hall MHD model,we investigate the plasma beta and Hall effects on the reconnection rate in the presence of sub-Alfvenic shear flow.
We fix the asymptotic velocity of shear flow and vary the half width of shear flow.We find that the shear flow can either stabilize or destabilize the tearing mode instability.In the cases of high plasma beta(β=5.0,β=2.0),when the half width of shear flow exceeds a threshold value,the shear flow can boost the tearing mode instability,that is,the peak reconnection rate is much higher than the case in the absence of shear flow,which is in a good agreement with the results from incompressible simulation;in the cases of low plasma beta(β=0.5,β=0.2),though the shear flow can destabilize the tearing mode,the boosting effect nearly disappears,that is,when increasing the half width of shear flow,the peak reconnection rate is still close to the case without shear flow,which is associated with the presence of a pair of discontinuities in the upper and lower inflow region.We believe that the shear flow influence on reconnection rate can be explained by studying the distribution and strength of perturbed vortex at the Y direction.With the inclusion of the Hall effect,shear flow can still either stabilize or destabilize magnetic reconnection,but when the ion inertial length d is large,in other words,the Hall effect is strong,the boosting effect becomes weak since the reconnection rate is already large without considering shear flow.
引文
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[9]Huang, J., Z. W. Ma, and D. Li, Debye-length scaled structure of perpendicular electric field in collisionless magnetic reconnection, Geophys. Res. Lett.2008,35, L10105, doi: 10.1029/2008GL033751
[10]Shay. M. A and J. F. Drake, The role of electron dissipation on the rate of collisionless magnetic reconnection, Geophys. Res. Lett.1998,25,20,3759:3762
[11]Hesse, M., K. Schindler, J. Birn, M. Kuznetsova, The diffusion region in collisionless magnetic reconnection, Phys. Plasmas 1999,6,5,1781:1795
[12]Zeiler, A. and D. Biskamp, J. F. Drake, B. N. Rogers, and M. A. Shay, M. Scholer, Three-dimensional particle simulations of collisionless magnetic reconnection J. Geophys. Res.2002,107 (A9),6-1:6-9
[13]Daughton, W and J. Scudder, Fully kinetic simulations of undriven magnetic reconnection with open boundary conditions, Phys. Plasmas 2006,13,072101,1:12
[14]Klimas, A, M. Hesse, and S. Zenitani, Particle-in-cell simulation of collisionless reconnection with open outflow boundaries, Phys. Plasmas 2008,15,082102,1:9
[15]Villasenor, J. and O. Buneman, Rigorous charge conservation for local electromagnetic field solvers, Comput. Phys. Commun.1992,69,306:316
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[19]Drake, J. F. and Y. C. Lee, Kinetic theory of tearing instabilities, Phys. Fluids 1977,20,8, 1341:1353
[20]Wang, X. G, A. Bhattacharjee and Z. W. Ma, Scaling of collisionless forced reconnection, Phys. Rev. Lett.2001,87(26),265003-1:265003-4
[21]Cassak, P. A., M. A. Shay and J. F. Drake, Scaling of Sweet-Parker reconnection with secondary islands, Phys. Plasmas 2009,16,120702,1:4
[22]Birn, J., J. E. Borovsky, M. Hesse and K. Schindler, Scaling of asymmetric reconnection in compressible plasmas, Phys. Plasmas 2010,17,052108,1:4
[23]Cassak, P. A. and M. A. Shay, Scaling of asymmetric magnetic reconnection:General theory and collisional simulations, Phys. Plasmas 2007,14,102114,1:11
[24]Fitzpatricka, R, Scaling of forced magnetic reconnection in the Hall-magnetohydrodynamical Taylor problem, Phys. Plasmas 2004,11(3),937:946
[25]Fitzpatricka, R, Scaling of forced magnetic reconnection in the Hall-magnetohydrodynamical Taylor problem with arbitrary guide field, Phys. Plasmas 2004,11(8),3961:3968
[26]Wang, X. G., H. A. Yang and S. P, Jin, Scalings of steady state Hall magnetobydrodynamic reconnection in high-beta plasmas, Phys. Plasmas 2006,13,060702,1:4
[27]Huang, Y. M. and A. Bhattacharjee, Scaling laws of resistive magnetohydrodynamic reconnection in the high-Lundquist-number, plasmoid-unstable regime, Phys. Plasmas 2010, 17,0602104,1:8
[28]Shay, M. A., J. F. Drake, M. Swisdak and B. N. Rogers, The scaling of embedded collisionless reconnection, Phys. Plasmas 2004,11(5),2199:2213
[29]Shay, M. A., J. F Drake, B. N. Rogers, and R. E. Denton, The scaling of collisionless magnetic reconnection for large systems, Geophys. Res. Lett.1999,26(14),2163:2166
[30]Ma, Z. W. and A. Bhattacharjee Hall magnetohydrodynamic reconnection:The Geospace Environment Modeling challenge, J. Geophys. Res.,2001,106(A3),3773:3782
[31]Ma, Z. W., Sudden disruption of the cross-tail current in the magnetotail, Phys. Plasmas 2008, 15,032906,1:4
[32]Pritchett, P. L., Geospace Environment Modeling magnetic reconnection challenge: Simulations with a full particle electromagnetic code, J. Geophys. Res.,2001,106(A3),3783: 3798
[33]Otto, A., Geospace Environment Modeling (GEM) magnetic reconnection challenge:MHD and Hall MHD-constant and current dependent resistivity models, J. Geophys. Res.,2001, 106(A3),3751:3757
[34]Birn, J. and M. Hesse, Geospace Environment Modeling (GEM) magnetic reconnection challenge:Resistive tearing, anisotropic pressure and Hall effects, J. Geophys. Res.,2001, 106(A3),3737:3750
[35]Hesse, M., J. Birn and M. Kuznetsova, Collisionless magnetic reconnection:Electron processes and transport modeling, J. Geophys. Res.,2001,106(A3),3721:3735
[36]Shay, M. A., J. F Drake, B. N. Rogers, and R. E. Denton, Alfvenic collisionless magnetic reconnection and the Hall term, J. Geophys. Res.,2001,106(A3),3759:3772
[37]Huba, J. D. and L. I. Rudakov, Hall magnetic reconnection rate, Phys. Rev. Lett.2004,93(17), 175003-1:175003-4
[38]Biskamp, D. E. Schwarz and J. F. Drake, Two-fluid theory of collisioniess magnetic reconnection, Phys. Plasmas 1997,4(4),1002:1009
[39]Wang, X. G., A. Bhattacharjee and Z. W. Ma, Collisionless reconnection:Effects of Hall current and electron pressure gradient, J. Geophys. Res.,2000,105(A12),27633:27648
[40]傅德薰,马延文,计算流体力学,北京：高等教育出版社,2002
[41]Paris, R. B. and W. N-C. Sy, Influence of equilibrium shear flow along the magnetic field on the resistive tearing instability, Phys. Fluids 1983,26(10),2966:2975
[42]Chen, X. L. and P. J. Morrison, Resistive instability with equilibrium shear flow, Phys. Fluids 1990a, B 2(3),495:507
[43]Chen, X. L. and P. J. Morrison, The effect of viscosity on the resistive tearing mode with the presence of shear flow, Phys. Fluids B 1990b,2(11),2575:2580
[44]Shen, C. and Z. X. Liu, Tearing mode with strong flow shear in the viscosity-dominated limit, Phys. Plasma 1996,3(12),4301:4303
[45]Einaudi, G. and F. Rubini, Resistive instabilities in a flowing plasma:I. Inviscid case, Phys. Fluids 1986,29(8),2563:2568
[46]Einaudi, G. and F. Rubini, Resistive instabilities in a flowing plasma:Ⅱ. Effects of viscosity, Phys. Fluids B 1989,1,2224:2228
[47]Ofman, L., X. L. Chen, P. J. Morrison and R.S. Steinolfson, Resistive tearing mode instability with shear flow and viscosity, Phys. Fluids B 1991,3(6),1364:1373
[48]Ofman, L., P. J. Morrison, and R. S. Steinolfson, Nonlinear evolution of resistive tearing mode instability with shear flow and viscosity, Phys. Fluids B 1993,5,376:387
[49]Li, J. H. and Z. W. Ma, Nonlinear evolution of resistive tearing mode with sub-Alfvenic shear flow, J. Geophys. Res.,2010,115, A09216, doi:10.1029/2010JA015315.
[50]Chen, Q., A. Otto, and L. C. Lee, Tearing instability, Kelvin-Helmholtz instability, and magnetic reconnection, J. Geophys. Res.1997,102,151:161
[51]Shen, C. and Z. X. Liu, The coupling mode between Kelvin-Helmholtz and resistive instabilities in compressible plasma, Phys. Plasma 1999,6(7),2883:2886
[52]L. Chacon, D. A. Knoll, J. M. Finn, Hall MHD effects on the 2D Kelvin-Helmholtz/tearing instability. Phys. Lett. A 2003,308,187:197
[53]Knoll, D. A, and L. Chacon, Magnetic reconnection in the two-dimensional Kelvin-Helmholtz instability, Phys. Rev. Lett.2002,88(21),215003-1:215003-4
[54]Scurry, L. and C. T. Russell, J. T. Gosling, Geomagnetic activity and the beta dependence of the dayside reconnection rate, J. Geophys. Res 1994,99 (A8),14811:14814
[55]Biskamp, D., Magnetic Reconnection in Plasmas, Cambridge UK:Cambridge University Press,2000
[2]Furth, H. P., J. Killeen, and M. N. Rosenbluth, Finite-resistivity instabilities of a sheet pinch, Phys. Fluids 1963,6,459:484
[3]李定,陈银华,马锦绣,杨维紘,等离子体物理学,北京：高等教育出版社,2006
[4]王水,李罗权,磁场重联,安徽：安徽教育出版社,1999
[5]Ma, Z. W. and A. Bhattacharjee, Fast impulsive reconnection and current sheet intensification due to electron pressure gradients in semi-collisional plasmas, Geophys. Res. Lett.1996,23, 13,1673:1676
[6]Birn, J., J. F. Drake, M. A. Shay, B. N. Rogers, R. E. Denton, M. Hesse, M. Kuznetsova, Z. W. Ma, A. Bhattacharjee, A. Otto and P. L. Pritchett, Geospace Environment modeling (GEM) reconnection challenge, J. Geophys. Res.2001,106 (A3),3715:3810
[7]Cai, H. J., L. C. Lee, The generalized Ohm's law in collisionless magnetic reconnection, Phys. Plasmas 1997,4(3),509:520
[8]Cai, H. J. and L. C. Lee, Magnetic flux generation near an O-line in collisionless reconnection-A new dynamo process, Phys. Plasmas 1995,2(10),3852:3856
[9]Huang, J., Z. W. Ma, and D. Li, Debye-length scaled structure of perpendicular electric field in collisionless magnetic reconnection, Geophys. Res. Lett.2008,35, L10105, doi: 10.1029/2008GL033751
[10]Shay. M. A and J. F. Drake, The role of electron dissipation on the rate of collisionless magnetic reconnection, Geophys. Res. Lett.1998,25,20,3759:3762
[11]Hesse, M., K. Schindler, J. Birn, M. Kuznetsova, The diffusion region in collisionless magnetic reconnection, Phys. Plasmas 1999,6,5,1781:1795
[12]Zeiler, A. and D. Biskamp, J. F. Drake, B. N. Rogers, and M. A. Shay, M. Scholer, Three-dimensional particle simulations of collisionless magnetic reconnection J. Geophys. Res.2002,107 (A9),6-1:6-9
[13]Daughton, W and J. Scudder, Fully kinetic simulations of undriven magnetic reconnection with open boundary conditions, Phys. Plasmas 2006,13,072101,1:12
[14]Klimas, A, M. Hesse, and S. Zenitani, Particle-in-cell simulation of collisionless reconnection with open outflow boundaries, Phys. Plasmas 2008,15,082102,1:9
[15]Villasenor, J. and O. Buneman, Rigorous charge conservation for local electromagnetic field solvers, Comput. Phys. Commun.1992,69,306:316
[16]Langdon, A. B., and B. F. Lasinski, Electromagnetic and relativistic simulation models, in Methods in Computational Physics 1976, vol.16, edited by B. Alder et al., p.327, Academic, San Diego, Calif
[17]Ara, G. B., B. Basu, B. Coppi, G. Laval, M. N. Rosenbluth and B. V. Waddell, Magnetic reconnection and m=l oscillation in current carrying plasma, Ann. Phys.1978,112,443:476
[18]胡希伟,等离子体理论基础,北京：北京大学出版社,2006
[19]Drake, J. F. and Y. C. Lee, Kinetic theory of tearing instabilities, Phys. Fluids 1977,20,8, 1341:1353
[20]Wang, X. G, A. Bhattacharjee and Z. W. Ma, Scaling of collisionless forced reconnection, Phys. Rev. Lett.2001,87(26),265003-1:265003-4
[21]Cassak, P. A., M. A. Shay and J. F. Drake, Scaling of Sweet-Parker reconnection with secondary islands, Phys. Plasmas 2009,16,120702,1:4
[22]Birn, J., J. E. Borovsky, M. Hesse and K. Schindler, Scaling of asymmetric reconnection in compressible plasmas, Phys. Plasmas 2010,17,052108,1:4
[23]Cassak, P. A. and M. A. Shay, Scaling of asymmetric magnetic reconnection:General theory and collisional simulations, Phys. Plasmas 2007,14,102114,1:11
[24]Fitzpatricka, R, Scaling of forced magnetic reconnection in the Hall-magnetohydrodynamical Taylor problem, Phys. Plasmas 2004,11(3),937:946
[25]Fitzpatricka, R, Scaling of forced magnetic reconnection in the Hall-magnetohydrodynamical Taylor problem with arbitrary guide field, Phys. Plasmas 2004,11(8),3961:3968
[26]Wang, X. G., H. A. Yang and S. P, Jin, Scalings of steady state Hall magnetobydrodynamic reconnection in high-beta plasmas, Phys. Plasmas 2006,13,060702,1:4
[27]Huang, Y. M. and A. Bhattacharjee, Scaling laws of resistive magnetohydrodynamic reconnection in the high-Lundquist-number, plasmoid-unstable regime, Phys. Plasmas 2010, 17,0602104,1:8
[28]Shay, M. A., J. F. Drake, M. Swisdak and B. N. Rogers, The scaling of embedded collisionless reconnection, Phys. Plasmas 2004,11(5),2199:2213
[29]Shay, M. A., J. F Drake, B. N. Rogers, and R. E. Denton, The scaling of collisionless magnetic reconnection for large systems, Geophys. Res. Lett.1999,26(14),2163:2166
[30]Ma, Z. W. and A. Bhattacharjee Hall magnetohydrodynamic reconnection:The Geospace Environment Modeling challenge, J. Geophys. Res.,2001,106(A3),3773:3782
[31]Ma, Z. W., Sudden disruption of the cross-tail current in the magnetotail, Phys. Plasmas 2008, 15,032906,1:4
[32]Pritchett, P. L., Geospace Environment Modeling magnetic reconnection challenge: Simulations with a full particle electromagnetic code, J. Geophys. Res.,2001,106(A3),3783: 3798
[33]Otto, A., Geospace Environment Modeling (GEM) magnetic reconnection challenge:MHD and Hall MHD-constant and current dependent resistivity models, J. Geophys. Res.,2001, 106(A3),3751:3757
[34]Birn, J. and M. Hesse, Geospace Environment Modeling (GEM) magnetic reconnection challenge:Resistive tearing, anisotropic pressure and Hall effects, J. Geophys. Res.,2001, 106(A3),3737:3750
[35]Hesse, M., J. Birn and M. Kuznetsova, Collisionless magnetic reconnection:Electron processes and transport modeling, J. Geophys. Res.,2001,106(A3),3721:3735
[36]Shay, M. A., J. F Drake, B. N. Rogers, and R. E. Denton, Alfvenic collisionless magnetic reconnection and the Hall term, J. Geophys. Res.,2001,106(A3),3759:3772
[37]Huba, J. D. and L. I. Rudakov, Hall magnetic reconnection rate, Phys. Rev. Lett.2004,93(17), 175003-1:175003-4
[38]Biskamp, D. E. Schwarz and J. F. Drake, Two-fluid theory of collisioniess magnetic reconnection, Phys. Plasmas 1997,4(4),1002:1009
[39]Wang, X. G., A. Bhattacharjee and Z. W. Ma, Collisionless reconnection:Effects of Hall current and electron pressure gradient, J. Geophys. Res.,2000,105(A12),27633:27648
[40]傅德薰,马延文,计算流体力学,北京：高等教育出版社,2002
[41]Paris, R. B. and W. N-C. Sy, Influence of equilibrium shear flow along the magnetic field on the resistive tearing instability, Phys. Fluids 1983,26(10),2966:2975
[42]Chen, X. L. and P. J. Morrison, Resistive instability with equilibrium shear flow, Phys. Fluids 1990a, B 2(3),495:507
[43]Chen, X. L. and P. J. Morrison, The effect of viscosity on the resistive tearing mode with the presence of shear flow, Phys. Fluids B 1990b,2(11),2575:2580
[44]Shen, C. and Z. X. Liu, Tearing mode with strong flow shear in the viscosity-dominated limit, Phys. Plasma 1996,3(12),4301:4303
[45]Einaudi, G. and F. Rubini, Resistive instabilities in a flowing plasma:I. Inviscid case, Phys. Fluids 1986,29(8),2563:2568
[46]Einaudi, G. and F. Rubini, Resistive instabilities in a flowing plasma:Ⅱ. Effects of viscosity, Phys. Fluids B 1989,1,2224:2228
[47]Ofman, L., X. L. Chen, P. J. Morrison and R.S. Steinolfson, Resistive tearing mode instability with shear flow and viscosity, Phys. Fluids B 1991,3(6),1364:1373
[48]Ofman, L., P. J. Morrison, and R. S. Steinolfson, Nonlinear evolution of resistive tearing mode instability with shear flow and viscosity, Phys. Fluids B 1993,5,376:387
[49]Li, J. H. and Z. W. Ma, Nonlinear evolution of resistive tearing mode with sub-Alfvenic shear flow, J. Geophys. Res.,2010,115, A09216, doi:10.1029/2010JA015315.
[50]Chen, Q., A. Otto, and L. C. Lee, Tearing instability, Kelvin-Helmholtz instability, and magnetic reconnection, J. Geophys. Res.1997,102,151:161
[51]Shen, C. and Z. X. Liu, The coupling mode between Kelvin-Helmholtz and resistive instabilities in compressible plasma, Phys. Plasma 1999,6(7),2883:2886
[52]L. Chacon, D. A. Knoll, J. M. Finn, Hall MHD effects on the 2D Kelvin-Helmholtz/tearing instability. Phys. Lett. A 2003,308,187:197
[53]Knoll, D. A, and L. Chacon, Magnetic reconnection in the two-dimensional Kelvin-Helmholtz instability, Phys. Rev. Lett.2002,88(21),215003-1:215003-4
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