High-speed fluid dynamics in magnetic
reconnection in a low-β plasma

Seiji ZENITANI
National Astronomical Observatory of Japan[1] Zenitani & Miyoshi, Phys. Plasmas 18, 022105 (2011)[2] Zenitani, Phys. Plasmas 22, 032114 (2015)
http://sploid.gizmodo.com/rare-photos-of-the-sr-71-blackbird-show-its-amazing-his-1670184930

Magnetic reconnectionSun• Abrupt change of magnetic topology inspace and astrophysical plasmas• Magnetic reconnection interacts with anouter environment through an fast
outflow jet

Earth’s MagnetosphereJetJet

Previous MHD works• A lot of MHD simulations
since Ugai & Tsuda 1977
• A plasmoid (magnetic island)is formed in front of thereconnection outflow jet
Maezawa+ 1995 unpublished

Abe & Hoshino 2001 EPS

Plasma beta -- Mach number• The role of the plasma beta is not clear in MHD reconnection• The [upstream] plasma beta controls the sonic Mach number ofthe reconnection jet
outflow jet?
cA =?

B
4

Plasma β• Plasma beta

Alfvén speed

Typical velocity

pgas
8 p= 2pmag
BSound speed

Sonic Mach number

Branches of fluid dynamicsConventional
fluid phenomena

tenki.jp 2015

Subsonic• Incompressible fluids

Shock waves

Mach 1887

1TransonicV
Ms =csSupersonic• Compressible fluid dynamics• High-speed fluid dynamics•

Adiabatic effects•

Shocks•Shock-shock interaction

MHD code• Resistive MHD equations in a conservative form

• Second-order Godunov-type solver• Hybrid HLLC/HLLD solver is developed to fix a problem in thestandard HLLD solver

MHD simulation
Density+B0
Plasma sheet

Symmetry
Reconnection point

β=0.2-B0
Outflow velocity (Vx)ZX

Adiabatic acceleration(b) t = 250z

2Vx/CA0

1x

Cs/CA00020

4060xX

80

100• Super-Alfvénic outflow• A supersonic flow is adiabaticallyaccelerated when its cross section
increases (Shimizu & Ugai 2000, 2003)

120

Laval nozzle

Various shocks!
vx
5

7
64z

1

2

8
3

9

10

Petschekslow shocks

Plasmoid (magnetic island)x• Rankine-Hugoniot
analysis on shockconditions

Normal shock: Analogy to airfoil• MHD slow shock

Subsonic(V << cs)• Sometimes referred to as“recovery shock” or“recompression shock”
vjet ~ cAplasmoid (0.8 cA)

Transonic(0.8cs <V)(b) t = 250zSupersonic(cs < V)vxx

See also https://www.youtube.com/watch?v=8OIqfCTAZQoShock-shock interaction• Shock/discontinuity should
separate different fluids in thedownstream (Landau & Lifshitz)z(b) t = 250x(a) Forward SSSS

B

SS-2

Az

CDensity

SSC’

CDx

(b) Postplasmoid region
SSSSCDz

SS-1

A

BC’SSFSx

CDCFS

Shock diamond(b) tvx= 250
Plasmoid
Outflow jetz

Plasma sheetx
Simulation framevx• Bifurcated jets are supersonic• Diamond pattern inside theplasma sheet, due to multiple
reflection of oblique-shocks

Supersonic nozzle problem• (a) Over-expanded flow

cs < Vjet

pjet < pambient

Expansion
wave

Shock• (b) Under-expanded flow

cs < Vjet

pjet > pambient

Expansion
wave

Shapiro 1953

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

Shock diamonds in earlier simulations

Maezawa+ 1995 unpublishedHidden shock-diamonds• We expect shock-diamonds
wherever a supersonic jet
cross a sharp boundaryvx

β=0.1

NormalshockZ
cs < Vjet

pjet > pambient

XVz• Another shock-diamonds are
hidden inside the Petschek
outflow (Zenitani 2015)

Zenitani 2015

Kelvin-Helmholtz instability
inside the plasmoid• Plasma sheet is hit and reflected by thereconnection jet frontz(b) t = 250• KH instability due to the reflected flowxPlasmadensity& flowExtragalactic jet models• Physics of supersonic jets (Norman+ 1982...)• Similarities: cocoon, bow shock, contact/tangential discontinuities• Difference: reverse-shock vs oblique diffuser

Mizuta+ 2010 ApJ

Matsumoto+ 2012 ApJ

The plasmoid diagram (2011)• High-speed effects havenever seriously discussed
in reconnection industry• They result in complex
shock structure in a lowβ plasma

The plasmoid diagram (2016)
2016

8719C

A

14

15

E

13

9

1
B

18

114aD

104b175 612316

2
1. Petschek slow shock (Petschek 1964)
2. outer shell = slow shock (Ugai 1995)
3. intermediate shock (Abe & Hoshino 2001) or slow shock (Saito et al. 1995)
4a fast shock (Forbes & Priest 1983)
4b oblique shock & Mach disk (Takasao et al. 2015)
5. looptop front (Ugai 1987)
6. tangential discontinuity
7. post-plasmoid vertical slow shock (Zenitani et al. 2010)
8. outer vertical slow shock (Zenitani & Miyoshi 2011)
9. fast-mode wave front (Saito et al. 1995)
10.overexpanded shock-diamonds (Zenitani et al. 2010)
A. reconnection inflow
11.underexpanded shock-diamonds (Zenitani 2015)
B. outflow jet
12.slow expansion wavefront (Zenitani 2015)
C. post-plasmoid reverse flow
13.contact discontinuity (Zenitani & Miyoshi 2011, 2015)
D. internal flow
14.contact discontinuity (Zenitani 2015)
E. flapping jet (KH instability)
15.vortex-driven shocklets (Miura 1992, 1995)
16.contact discontinuity (Zenitani 2015)17.rotational discontinuity [in guide-field reconnection] (Petschek & Thorne 1967)
18.conduction front [with heat conduction] (Yokoyama & Shibata 1997)
19.forward head shock [in asymmetric reconnection] (Nitta et al. 2016)• High-speed effects havenever seriously discussed
in reconnection industry• They result in complex
shock structure in a lowβ plasma

OpenMHD code
• Simple, Scalable, and Shock-capturing MHD code•

TVD Runge=Kutta method•

MUSCL interpolation•

HLLC=HLLD hybrid solver•

Hyperbolic divergence cleaning• Reconnection problems are pre-configured

http://th.nao.ac.jp/MEMBER/zenitani/openmhd-e.html

Summary• MHD evolution of magnetic reconnectionin the low-β, high Mach-number regime• New features: Outcomes of high-speed fluid effects– Adiabatic acceleration– Normal shock– Shock-shock intersection– Overexpanded shock diamonds– Underexpanded shock diamonds– Kelvin-Helmholtz instability• The plasmoid diagram - It is still evolving• OpenMHD code - publicly available

Thank you for your attention.

(A Seattle style plasmoid)