自発的高速磁気リコネクションモデルとフレアの三次 元構造 鵜飼（愛媛大学） （太陽フレア現象の物理機構？） Question: What is the physical mechanism responsible for large dissipative events observed in space plasmas (solar flares, substorms)? 1. First phase: magnetic energy is stored in a large-scale region (current sheet) 2. Second phase: critically stored magnetic energy is explosively released Observations ⇒ magnetic reconnection is essential for flares 「 In space plasmas, the most powerful magnetic energy converter is provided by slow shocks (Petschek, 1964) ⇒ the fast reconnection mechanism involving standing slow shocks is most responsible for flares 」 Question: How can the fast reconnection mechanism be realized as an eventual solution of an initial problem and be sustained steadily in the system?

(two plasma processes be simultaneously explained) 1. Magnetic energy storage 「 magnetic reconnection should not occur effectively until magnetic energy is critically stored; i.e., any effective dissipation mechanism may not exist in the usual current-sheet system in static equilibrium 」 *in usual circumstances in space (collisionless) plasmas, R m >>1; no effective dissipation mechanism ⇒ no effective magnetic reconnection (reconnection electric field is readily short-circuited) 2. Explosive magnetic energy release 「 fast magnetic reconnection is suddenly triggered when magnetic energy is critically stored in the large-scale current-sheet system 」 *storage of magnetic energy is associated with enhancement of currents; hence, enhanced currents ⇒ key to triggering of fast reconnection *the resulting fast reconnection mechanism involving slow shocks should be sustained steadily ⇒ explosive system collapse

＜ Spontaneous Fast Reconnection Model (SFRM) ＞ (Basic idea; flare scenario) (i) critically enhanced currents in the system (during storage of magnetic energy) ⇒ current-driven anomalous resistivity (as a possible dissipation mechanism) (ii) positive feedback between the (macroscopic) reconnection flow and (microscopic) current-driven anomalous resistivity ⇒ evolution of the fast reconnection mechanism as an eventual solution (iii) the resulting fast reconnection mechanism sustained steadily ⇒ explosive magnetic energy release, drastic collapse of the field system A new-type nonlinear instability due to coupling between micro- and macro- plasma processes: different from the conventional externally driven model (Petschek, Priest and Forbes, Sato….)

> ( Assumption ) *current-driven anomalous resistivity model (experiments, Ono; Yamada ) [η(r,t) is assumed to increase with V d as a function of macroscopic quantities when V d >Vc (η determined by the feedback from macroscopic reconnection flows)] I. 2D simulations: different parameters in various situations 「 fast magnetic reconnection builds up by the positive feedback between the plasma flow and the anomalous resistivity, which simultaneously grow explosively 」 「 resulting fast reconnection mechanism (slow shocks) is sustained steadily and extends outwards with time ⇒ drastic collapse of the overall current sheet system 」 (1). localized diffusion region with locally enhanced anomalous resistivity (2). standing slow shocks extending outwards with time; fast reconnection jet (3). large-scale plasmoid swelling and propagating outwards (Nitta, Ap.J, 2004)

「 Fast reconnection mechanism involving standing slow shocks can be realized as an eventual solution of 2D MHD equations 」 「 Resulting fast reconnection (slow shock) configuration is consistent with the one suggested by theoretical studies based on conservation laws of MHD quantities 」 * new discoveries: never recognized by previous theoretical studies on the fast reconnection mechanism (Petschek, 1964; Vasyliunas, 1975; Priest and Forbes, 1986 ； in particular, different from Petschek Model ) (i) Spontaneous evolution as a nonlinear instability ( 外部条件の影響も考慮可能； emerging flux ） (ii) Large-scale plasmoid at the end of the (supersonic) fast reconnection jet (in a free space) (iii) Large-scale magnetic loop (in a closed system); fast shock at the loop top

II. Spontaneous Fast Reconnection Model in Three Dimensions *no analytical study on the 3D fast reconnection mechanism; only a few 3D simulations 「 basic 3D fast reconnection configuration has little been understood 」 「 Key points to be clarified 」 *Whether or not the fast reconnection mechanism involving standing slow shocks can be realized as an eventual solution in three dimensions? *How the positive feedback between 3D reconnection flow and current-driven anomalous resistivity works as a nonlinear instability? (Ugai and Shimizu, Phys. Plasmas, 1996) 「 when a current-driven anomalous resistivity (diffusion region) appears in a region of sufficiently large extent in the z direction, the 3D fast reconnection mechanism can be realized 」 (Ugai et al, Phys. Plasmas, 2004) 「 so long as η increases with V d with a sufficiently large threshold, the fast reconnection mechanism can explosively evolve by the positive feedback even in 3D situations 」 Question: What is the 3D fast reconnection configuration that can be sustained steadily?

*3D simulation model: direct extension of the precise 2D simulation to the z direction [Evolution of the 3D fast reconnection mechanism] * temporal behaviors of E and the anomalous resistivity η measured at the origin r=0 (for different plasma β) 「 explosive buildup by the positive feedback 」 「 establishment of fast reconnection mechanism 」 「 more powerful for the smaller β 」 「 E 0 does not mean that the fast reconnection is suddenly terminated 」 (3D diffusion region; unstable against tearing instability; bifurcated into a pair of 3D diffusion regions; moving away from each other) β=0.3, 0.5, 1.0, 2.0   

t=50.6 [Resulting 3D fast reconnection configurations] *magnetic field in the (x,y) plane and isosurface of large plasma pressure (3D plasmoid) before and after the tearing -- *plasma flow vectors *isosurface of the resulting anomalous resistivity; resistive tearing in the diffusion region; 3D diffusion region where the anomalous resistivity is locally enhanced moves in the x direction t=50.6 O O

[ Slow shock profiles ] *profiles of quantities in the y direction at different x on the x axis 「 standing switch-off shock structure– in good agreement with the one of the well-known 2D fast reconnection mechanism 」 *fast reconnection jet u x for different plasma β along the x axis 「 reconnection jet u x : accelerated exactly to the Alfven velocity （ consistent with the 2D fast reconnection theory) 」 β=0.15, 0.3, 0.5, 1, 2

「 fast reconnection mechanism involving slow shocks is sustained steadily to be confined in a finite extent in the z direction 」 「 the fast reconnection mechanism is extending outwards with time so that the overall magnetic field system explosively collapses 」 *isosurface of high current density viewed from different angles ； 3D slow shock structure t=50.6

*isosurface of large current density: slow shock and diffusion region 「 3D slow shock extends in the positive x direction 」 (the isosurface does not exactly indicate the slow shock) *3D structure of the standing slow shock (z-extent)? t=38.5 t=44

*magnetic field in the xy plane and the isosurface of plasma pressure P of large value (identified with a large-scale plasmoid; its cross section) [growth of the plasmoid in accordance with the proceeding of the spontaneous fast reconnection process]

*isosurface of plasma density; cross section [strong plasma rarefaction in the fast reconnection region and distinct plasma compression in the plasmoid]

O *temporal behaviors of virtual (magnetized) particles placed at y=1.5 [the ambient magnetized plasma is sucked into the fast reconnection region and is strongly accelerated by standing slow shocks, leading to drastic collapse of overall magnetic field system in accordance with the proceeding of the spontaneous fast reconnection] O t=22 t=44

t=33 t=38.5 t=44 t= ４９．５ *temporal behaviors of plasma flow vectors; growth of the fast reconnection jet with time

(in a long current sheet system with free boundaries: Ugai et al, 2005) *Basic idea: 「 magnetic energy storage →critically enhanced currents → dissipation mechanism (anomalous resistivity)→fast magnetic reconnection →flares 」 (Assumption : current-driven anomalous resistivity model with a (large) threshold, consistent with laboratory experiments: Ono, Yamada,..) 1. 「 Only when a current-driven anomalous resistivity is caused in a sufficiently large extent in the z direction, the fast reconnection mechanism involving standing slow shocks can be realized as an eventual solution and sustained in three dimensions 」 2. 「 Central 3D diffusion region is unstable against resistive tearing and is bifurcated into a pair of diffusion regions; 3D slow shocks extend outwards, and, attached to the fast reconnection jet, a large-scale 3D plasmoid swells and propagates 」 3. 「 Resulting fast reconnection mechanism remains to be confined in a finite extent in the z direction; its basic configuration is, both qualitatively and quantitatively, in good agreement with the well-known 2D one 」

*closed system: symmetry boundary conditions on (y,z) plane, across which plasma cannot flow (Masuda et al, 1994) NP t=36 t=42t=48 t=36

Temporal dynamics of ３ D slow and fast shocks *Green: Slow shock; Blue: Fast Shock

*temporal behavior of the slow and fast shocks *Green: Slow shock Blue: Fast Shock

* Slow and fast shocks viewed from different angles *Green: Slow shock Blue: Fast Shock