Energetics of Reconnection: A Comparison of Steady and Transient Models in 1, 2 and 3 Dimensions Dana Longcope MSU Silvina Guidoni MSU Mark Linton NRL Thanks: Terry Forbes June 18, 2009 Boulder SPD 1
Classical Petschek Petschek 1964 Vasyliunas 1975 Soward & Priest 1982 • 2d steady model • CS separating perfectly anti-parallel field • Recon’n @ X-point * on CS (localization, E z imposed) Slow mode shocks (SMS): connect to X-point | B | significantly reduced at SMS Magnetic energy 40% thermal energy 60% bulk flow KE * line ⊥ to 2d plane June 18, 2009 Boulder SPD 2
Are reconnecting fields always anti-parallel? B reconnected field lines J 2001-08-11 TRACE MDI June 18, 2009 Boulder SPD 3 Longcope et al . 2005
Petschek & Thorne 1967 2.5D Petschek Soward 1982 y Skender et al. 2003 • CS between field @ Δθ (include “guide field” B z ) B z • steady model Δθ • Recon’n @ X-point * on CS z 2 shocks (co-planarity): • Intermediate shock (RD) v z • | B | unchanged Petschek & Thorne 1967 B z • KE in bulk flow & v z • Slow shock (SMS) • | B | reduced slightly • v z 0 ( ∴ KE ) • thermal energy * line ⊥ to 2d plane June 18, 2009 Boulder SPD 4
β << 1 ISs create converging flows SMSs stop convergence v z Δθ /2 v A,y c s small fraction of v z shortened field line slow shock angle ~ β 1/2 × IS angle June 18, 2009 Boulder SPD 5
In skewed ( Δθ < 120 o ) low β reconnection : • Magnetic field strength decreases only slightly Q: what is the source of energy? A: field lines are shortened (rather than weakened) • SMSs mostly stop converging flows (rather than weakening field, à la switch-off shock) ~ gas dynamic shocks (M ~ β -1/2 >> 1) • Heating occurs only in small central region Most released energy converted to KE � W M = B 2 1 dadl 8 � � � = d � B 1 dl 8 � June 18, 2009 * rather than weakening field Boulder SPD 6
Energetics Δθ /2 Q: what is the ratio, thermal to π /2 −Δθ /4 kinetic energy, from the ... Δθ /4 SS SS IS thermal IS specific energy no thermo- dynamic kinetic change @ IS ... all released energy: ... post-SS region: ratio of areas ratio of heights v Δθ /4 � � � � � � � � ~ � 1/2 tan 2 ~ tan 2 � � � � � � � � 4 4 June 18, 2009 Boulder SPD 7
SMS size (fraction) 3D transient (Longcope et al. 2009) 2.5D steady (Vrsnak & Skender 2005) 2D steady (Petschek 1964) 1D transient (Lin & Lee 1994) � Fraction of 10% released energy 110 o thermalized June 18, 2009 Boulder SPD 8 Δθ
Linton & Longcope 2006 3D transient Longope, Guidoni & Linton 2009 • CS between field @ Δθ (include “guide field” B z ) • Recon’n @ patch on CS • creates detached flux tubes • bend non-equilibrium Δθ • evolve as thin flux tubes z • “pull through” CS • | B | fixed by external layers - unchanged by reconnection IS IS GDS GDS • Riemann problem 2 shocks • Bends (IS) move @ v A • gas dynamic shocks (GDS) in straight section - movie disconnected from recon’n June 18, 2009 Boulder SPD 9
Temperature of “outflow” function of B & Δθ (little else*) T of = 20 MK B [G] Δθ [deg.] June 18, 2009 Boulder SPD 10 *indep’t of recon’n rate
Δθ =100 o Temps 3D* β =0.01 Δθ =180 o 2D β =0.03 SS Yokoyama & Shibata 1997 GDS conduction front IS June 18, 2009 Boulder SPD 11 * superposition of transient events
Summary Reconnecting field lines w/ Δθ < 180 o common to steady/transient 1D,2D,3D models: • Releases energy by shortening field lines (more than annihilating field) • Most properties: indep. of reconnection rate • Most energy kinetic energy of retracting flux • shortening flows converging at ~v A • Stopped in shocks (SMSs/GDS) which thermalize some kinetic energy (little | B |) • creates small (~ β 1/2 ) hot central region June 18, 2009 Boulder SPD 12
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