Energetics of Reconnection: A Comparison of Steady and Transient - - PowerPoint PPT Presentation

June 18, 2009 Boulder SPD 1

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 2

Classical Petschek

• 2d steady model
• CS separating perfectly

anti-parallel field

• Recon’n @ X-point* on CS

(localization, Ez 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

Petschek 1964 Vasyliunas 1975 Soward & Priest 1982

June 18, 2009 Boulder SPD 3

Are reconnecting fields always anti-parallel?

J B reconnected field lines 2001-08-11 TRACE MDI

Longcope et al. 2005

June 18, 2009 Boulder SPD 4

2.5D Petschek

Petschek & Thorne 1967

Petschek & Thorne 1967 Soward 1982 Skender et al. 2003

• CS between field @ Δθ

(include “guide field” Bz)

• steady model
• Recon’n @ X-point* on CS

 2 shocks (co-planarity):

• Intermediate shock (RD)
• |B| unchanged
•  KE in bulk flow & vz
• Slow shock (SMS)
• |B| reduced slightly
• vz  0 (∴ KE  )
•  thermal energy

y z Δθ

Bz Bz vz

* line ⊥ to 2d plane

June 18, 2009 Boulder SPD 5

Δθ/2 vz vz

ISs create converging flows SMSs stop convergence

small fraction of shortened field line

vA,y cs

β << 1

slow shock angle ~ β1/2 × IS angle

June 18, 2009 Boulder SPD 6

In skewed (Δθ < 120o) 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

WM =

1 8

B2

• dadl

=

1 8

d B

• dl

* rather than weakening field

June 18, 2009 Boulder SPD 7

Energetics

specific energy kinetic thermal IS SS SS IS ... post-SS region: ratio of heights

Δθ/2 π/2−Δθ/4 Δθ/4

~ tan2

• 4
• ... all released energy:

ratio of areas Q: what is the ratio, thermal to kinetic energy, from the ...

~ 1/2 tan2

• 4
• no thermo-

dynamic change @ IS Δθ/4

v

June 18, 2009 Boulder SPD 8

• Fraction of

released energy thermalized 10% 110o 3D transient (Longcope et al. 2009) 2.5D steady (Vrsnak & Skender 2005) 2D steady (Petschek 1964) 1D transient (Lin & Lee 1994) SMS size (fraction) Δθ

June 18, 2009 Boulder SPD 9

3D transient

z Δθ

Linton & Longcope 2006 Longope, Guidoni & Linton 2009

• CS between field @ Δθ

(include “guide field” Bz)

• Recon’n @ patch on CS
• creates detached flux tubes
• bend non-equilibrium
• evolve as thin flux tubes
• “pull through” CS
• |B| fixed by external layers -

unchanged by reconnection

• Riemann problem  2 shocks
• Bends (IS) move @ vA
• gas dynamic shocks (GDS) in

straight section - disconnected from recon’n IS IS

GDS GDS

movie

June 18, 2009 Boulder SPD 10

Temperature of “outflow”

function of B & Δθ (little else*) Δθ [deg.]

B [G] Tof = 20 MK

*indep’t of recon’n rate

June 18, 2009 Boulder SPD 11

Yokoyama & Shibata 1997

Temps

2D 3D* SS GDS IS

conduction front Δθ=100o β=0.01 Δθ=180o β=0.03 * superposition of transient events

June 18, 2009 Boulder SPD 12

Summary

Reconnecting field lines w/ Δθ < 180o 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 ~vA
• Stopped in shocks (SMSs/GDS) which thermalize

some kinetic energy (little |B|)

• creates small (~β1/2) hot central region