SM13B-4163

Low-beta MHD reconnection
as a showcase ofhigh-speed fluid dynamics

Seiji ZENITANI
National Astronomical Observatory of Japan

Motivation• Magnetic reconnection expels a fast outflow jet• How does the jet interact with an external medium ina large-scale system?
outflow jet?

?

• MHD approximation is useful to explore large-scaleevolution of plasma systems

Previous works• Many works over several decades

Ugai 1995 PoP

Yokoyama & Shibata 1998 ApJ

Abe & Hoshino 2001 EPS

Plasma betapgas
8 p= 2pmag
B
upstream=Sound speed

2cscA

2csV

2

Typical velocity

βcoronaβ<1upstream• Likely parameter to control
coronal reconnection• A parameter for compressible
fluid effects

Gary 2001 Sol. Phys.

MHD code• Resistive MHD equations in a conservative form

• Second order HLL/HLLD Riemann solver• HLL solver for 2011 paper is attached to arXiv:1101.2255• We’d be happy to offer our HLLD solver for collaboration

Initial configuration• A Harris-sheet with anti-parallel fields• Domain: [0, 200] x [0, 150] (6000 x 4500 cells)• Low beta in the upstream: β = 2p/B2 = 0.2

Density+B0

Beta = 0.2
Plasma sheet

ZSymmetry-B0Z

X

Localized resistivity

Plasma density

Outflow velocity (Vx)

ZX

Various shocks!
vx
Postplasmoid
slow shock

5z

6

4
1

2

8
3

Forwardslow shock

7
9

Slow shock

10Petschek
slow shocks

Plasmoid (magnetic island)x• Extensive analysis
on shock conditions(Minimum varianceanalysis; MVA-B)

Normal shock (Recompression shock)• MHD slow shock• Analogy to airfoil
jetSubsonic(V << cs)leading edge
Transonic(0.8cs <V)

MA=1.1(b) t = 250

MA=2.4z

Supersonic(cs < V)vxx

Super-Alfvénic flow(b) t = 250

2zBz
Vx
P
ρ/51x

00204060

80

100120x• Two reasons• RH condition for the rarefied upstream region• Adiabatic acceleration in the deconfinement
region (Shimizu & Ugai 2000, 2003)• Supersonic regime

Laval nozzle

Shock diamond(b) tv=x 250
Outflow jetz

Plasma sheetx
Lab frame

Co-moving frame
Plasmasheetvx

Shock diamond• (a) Over-expanded flow (過膨張)cs < Vjet

pjet < pambient

Compression(shock)Expansion• (b) Under-expanded flow (不足膨張)

cs < Vjetpjet > pambient

Expansion

Shock diamonds in aeronautics

BBC online

http://www.bbc.com/future/story/20130701-flying-the-worlds-fastest-planeShock diamonds in video game

Microsoft Flight Simulator X

https://www.youtube.com/watch?v=S8QGaiE4yWc

Shock diamonds in astrophysics
2x106 light years

PKS 0637-752

Godfrey+ 2012 ApJ

Hidden shock-diamondsvx• Crossing point between
Petschek shocks andrecompression shocks• Sufficient condition:

β=0.1

NormalshockZPetschekslow shocksXVz
PB

PB > PAPAZJetX

Kelvin-Helmholtz instability
inside the plasmoid• Plasmas are hit and reflected by thereconnection jet frontz(b) t = 250• KH instability due to the reflected flowx

Plasma density & flowin the moving frame

Comparison with astrophysical jet model• Supersonic jets (Norman+ 1982)• Very similar except reverse shock
No reverse shock

Mizuta+ 2010 ApJ

Pseudo-shock (oblique diffuser)• (a) Over-expanded flow

• Shock-train decelerates the flowx• Similar to Fanno flow

pjet < pambient2density

BzVx
P
ρ/5z

1pPseudoshockVx

0pjet > pambient

020

Reverse shock

406080x(b) t = 250• (b) Under-expanded flow

100120A complete catalog of plasmoid structure (2011)87

A. reconnection inflow
B. outflow jet
C. post-plasmoid backward flow
D. internal flow
E. flapping jet (KH instability)

CE

A

9

D
10
14B

5 611

1. Petschek slow shock (Petschek 1964)
2. outer shell = slow shock (Ugai 1995 PoP)
3. intermediate shock (Abe & Hoshino 2001 EPS)
4. fast shock (Forbes & Priest 1983 SoP)
5. loop-top front (Ugai 1987 GRL)
6. tangential discontinuity
7. post-plasmoid vertical slow shock (Zenitani+ 2010 ApJ)
8. outer vertical slow shock (Zenitani & Miyoshi 2011 PoP)
9. fast-mode wave front (Saito et al. 1995 JGR)
10. shock-reflection (diamond chain) (Zenitani+ 2010 ApJ)
11. contact discontinuity (Zenitani & Miyoshi 2011 PoP)

32

Zenitani & Miyoshi 2011 PoP

A complete catalog of plasmoid structure (2015)
87C

1618

A. reconnection inflow
B. outflow jet
C. post-plasmoid backward flow
D. internal flow
E. flapping jet (KH instability)

AE

1412D
1013
1

94

B21155 61119203172
1. Petschek slow shock (Petschek 1964)
2. outer shell = slow shock (Ugai 1995 PoP)
3. intermediate shock (Abe & Hoshino 2001 EPS)
4. fast shock (Forbes & Priest 1983 SoP)
5. loop-top front (Ugai 1987 GRL)
6. tangential discontinuity
7. post-plasmoid vertical slow shock (Zenitani+ 2010 ApJ)
8. outer vertical slow shock (Zenitani & Miyoshi 2011 PoP)
9. fast-mode wave front (Saito et al. 1995 JGR)
10. overexpanded shock-diamond (Zenitani+ 2010 ApJ)
11. contact discontinuity (Zenitani & Miyoshi 2011 PoP)

12. underexpanded shock-diamond
13. Slow-mode expansion fan?
14. contact discontinuity
15. contact discontinuity
16. preshock
17. contact discontinuity
18. vortex-driven shock
19. inner shell
20. pseudo shock
21. odd-parity KH instability

Plasmoid-dominated reconnection
vx• Run with very high Lundquist number : S = 10**5.5• Increasingly turbulent, due to a spectrum of normal slow shocks• Wave-drag to the plasmoid motion• ⇒ Global dynamics can be affectedSummary• We have investigated the fine structure of
the reconnection-plasmoid system• New structures are better understood as
high-speed (compressible) fluid effects
in low-β regimes• Adiabatic acceleration• Recompression shock• Shock diamonds• Relevance to the jet physics• The catalog project is going on• There are still basic issues in MHD reconnection physics

References• Zenitani & Miyoshi, Phys. Plasmas 18, 022105 (2011)
Code available at arXiv:1101.2255• Zenitani, submitted (2015)Paper request
Your namee-mailUnknown “shocks” explained
β= 0.25β= 0.2

Abe & Hoshino 2001 EPS

Tanuma & Shibata 2007 PASJ

Keppens+ 2013 PoP

Karpen+ 2012 ApJ