磁気リコネクションの二流体 MHD シミュレーション物理学会 2004 年秋期大会東大新領域, 核融合研沼田龍介, 吉田善章, 林隆也物理学会 13aXB-9 2004/ 9/13 – p.1/10 Introduction Processes at microscopic scales (associated with particle motion) plays an important role in obseved macroscopic dynamics. Magnetic reconnection is a good example. No known microprocess that causes dissipation can account for observed fast reconnection rate. In the Hall-magnetohydrodynamics (Hall-MHD), two disparate interacting scale structures will be self-organized. Mesoscopic model (structure of dissipation region) ✁ ✁ ✁ Importance of the Hall term is pointed out by many researchers. Birn et al., JGR (2001) Ion kinetic (inertia) effects become important at a small scale of the ion skin depth. Chaos-induced resistivity 物理学会 13aXB-9 2004/ 9/13 – p.2/10 Chaos-Induced Resistivity Chaotic motion of ions in an inhomogeneous magnetic field with magnetic nulls produces strong dissipation. (R. Numata & Z. Yoshida, Phys. Rev. Lett. 88, 045003 (2002)) field line orbit E chaotic orbit ✟ . i ci eff ✞ ☎ ✆ ✁ Effective resistivity is given by eff ✄ ✂ ✝ ✝ Effective resistivity is localized in the chaos region (size of the chaos region is i ) Outside the chaos region, particles describe regular motion. 物理学会 13aXB-9 2004/ 9/13 – p.3/10 Scale Hierarchy chaos region (∼δi) dissipation region mesoscopic macroscopic microscopic : chaos region 物理学会 13aXB-9 2004/ 9/13 – p.4/10 ✆ ✘ ✦ i system size . ✁ ✟ ★ ✝ ✩ ✧ ✟ ✝ ✂ ✚ ✒ , ✁ ✓ ✒ ✥ ✁ ✚ ✒ ✤ ✓ ✒ ✔ ✕ ✓ ✒ ✔ ✠ ✁ ✢ ✞✢ ✆ ✢ ✏✢ ✍✆ ✌ ✌ ✢ ✞✢ ✎✍✆ ✌ ✝ ✝ ✝ ✑ ✑ ✣ ✄ ☎ ☎ ✁ ✁ ✆ ☛✜ ✞ ✆ ✆ ☛ ✟ ✞ ✝ ☛ ✁ ✚ ✒ ✛ ✁ ✌ ✏ ✍✆ ✍ ✏ ✍✆ ✠ ✏ ☎ ☎ ✆ ✖ ✞ ✟ ✝ ✘ ✙ ✗ ✑ ✄ ☎ ✆ ✖ ✍✆ ✏ ✕ ✓ ✒ ✔ ✠ ✁ ✌ ✌ ✞ ✆ ✆ ✞ ✆ ✝ ✟ ✟ ✝ ✝ ✑ ✑ ✄ ☎ ☎ ✁ ✆ ✝ ✟ ✏ ✏ ✍ ✟ ✎✍✆ ✌ ☞☛✆ ✞ ✞ ✁ ✝ ✆ ✞ ✟ ✁ ✝ ✄ ✁ ✁ ✝ ✆ ✞ ✠✡✟ ☎ ✆ ✁ ✂ Simulation Model (1) (2) (3) (4) (5) : the Reynolds number and the Magnetic Reynolds number. describes an inhomogeneity of the resistivity. 物理学会 13aXB-9 2004/ 9/13 – p.5/10 Simulation Model b b. ✆ ☎ ✞ and ✆ ☎ ✝ ✄✂✆ ✁ ✞ drift inflow: ✆ ✍✖ Upstream boundary Uniform and constant ✏ Boundary Condition ✟ ☛ ☎ ☛ ☛✝ ✟ ☞✢ ☎✠ ✠ ✢ ✟ ✧ ✟ ☎ ✟ ✠ ✝ ☎ ✟ ✠ ✝ ✡ Downstream boundary Open boundary condition is imposed by considering the filter region, outside the simulation domain, where a friction term initial ( initial is the initial value, b is the friction factor) damps outgoing waves. ✏✎✍ ☎ ✒ ✟ ✝ ✟ ✑ (6) ✓ ☎ ✆ ✂ ✝ ✆ ☎ ✌ ✂ Initial Condition [ Harris Sheet Equilibrium ] ✟ ✝ ✁✌ ✖ ✓ ✘ ☎ ✆ ✁ ✔✕ ✒✗ ✟ ✂ ✝ ✁ ✝ ✂ d (7) ✙✟ ✂ ✝ ☎ ✆ ✁ ✟ ✂ ✝ ☛ d is the temperature, d is the width of the current sheet. ✓ ☎ ✙ where (8) 物理学会 13aXB-9 2004/ 9/13 – p.6/10 Simulation Model ✟ ✢ ✟ ✁ ✁ ✁ ✠ ✕ ✆ ✠ ✠ ✑ ✆ ✟ ✝ is ✁ ✁ ✁ ✆ ✠ ✠ ✑ c ✆ ✝ ☎ ☎ ✢ ✟ ✏ ★ ✝ ✢ ✟ ★ where is a constant (amplitude of the chaos-induced resistivity), the position of magnetic null points, ☎ ✝ ✘ ✝ ☎ (9) ☎★ ★ ✢ ✄ ✆ ✂ ✁ ✟ ✁ ✌ ✑ ✟ ★ ✝ ✩ ✝ ✝ ✑ Inhomogeneity of Resistivity is given by the following equation, (10) 物理学会 13aXB-9 2004/ 9/13 – p.7/10 Global Structures MHD Hall-MHD 物理学会 13aXB-9 2004/ 9/13 – p.8/10 Electric Field (Reconnection Rate) (b). Spatial scructure (a). Time evolution 0.005 0 Ey -0.005 -0.01 -0.015 Chaos Resistivity Hall MHD MHD -0.02 -0.025 0 10 20 30 40 time [τA] 50 60 0.005 0 -0.005 -0.01 -0.015 -0.02 -0.025 -0.03 -0.035 -0.04 -0.045 -0.05 -2 70 -1.5 -1 -0.5 0 x 0.5 1 1.5 2 Electric Field VxB term Hall term Resistivity 物理学会 13aXB-9 2004/ 9/13 – p.9/10 Summary We have studied the magnetic reconnection process by means of the Hall-MHD simulation including the inhomogeneous chaos-induced resisitivity. We have observed that the magnetic reconnection rate is strongly enhanced by the inhomogeneous resistivity. However, how the inhomogeneous resistivity works is still unclear. (Hall term is dominant). Further studies on parameter dependence and reconnection scaling. 3 dimensional structure 物理学会 13aXB-9 2004/ 9/13 – p.10/10