High-speed fluid dynamicsin magnetic reconnection

in a low-beta plasma

Seiji ZENITANINational Astronomical Observatory of Japan

ST06-08-26-A010

• Magnetic reconnection expels a fast outflow jetat the upstream Alfvén speed

• How does the jet interact with an external medium?

• Key parameter

cA =B�4��

1��

�cA

cs

�2�

�V

cs

�2�M2

Motivation

outflow jet

? ?

� � pgas

pmag=

8�p

B2

Typical Mach number

Typical velocity

Sound speed

Branches of fluid dynamics

• Compressible fluid dynamics

• High-speed fluid dynamics• Adiabatic effects

• Shocks

• Shock-shock interaction

Mach 1887tenki.jp 2015

Conventionalfluid dynamics

Shock waves

• Incompressible fluids

Subsonic SupersonicTransonic

1

MHD simulation

+B0

-B0

SymmetryReconnection point

Density

Plasma sheet

β=0.2

Outflow velocity (Vx)

X

Z

z

x

1 23

45 7

6

8 910

Various shocks!

• Extensive analysison shock conditions (Minimum variance analysis; MVA-B)

Petschekslow shocks

Plasmoid (magnetic island)

vx

Normal shock: Analogy to airfoil

(b) t = 250

z

x

Transonic(0.8cs <V)

Subsonic(V << cs)

Supersonic(cs < V)

β=1.0

β=0.2

plasmoid

vx

• MHD slow shock

• Recovery/recompression shock

See also https://www.youtube.com/watch?v=8OIqfCTAZQo

vjet ~ cA

Shock diamond(b) t = 250

z

x Plasmoid frameSimulation frame

Plasma sheet

Plasma sheetOutflow jet

vx

vx

Plasmoid

• (a) Over-expanded flow

Supersonic nozzle problem

• (b) Under-expanded flow

pjet < pambient

pjet > pambient

cs < Vjet

cs < Vjet

Plasmoid frame Plasma sheet

Shapiro 1953

Shock Expansion wave

Expansion wave

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

PKS 0637-752 Godfrey+ 2012 ApJ

2x106 light years

Vz

Hidden shock-diamonds

• Under-expanded shock-diamonds at the shock crossing point

• Triple-point structure is even more complicated (Zenitani 2015 PoP)

• Contact discontinuity

• Slow expansion fan

β=0.1

X

Z

Petschekslow shocks

vx

Normal shock

A digital catalog of the plasmoid structure

1617

F

G

18

1��

�cA

cs

�2�

�V

cs

�2�M2

• In high Mach number, low-β regime, reconnection system is dominated by shocks

• This regime has long been unexplored!

• Simple, Scalable, and Shock-capturing MHD code• TVD Runge=Kutta method

• TVD MUSCL scheme + HLLD solver

• Hyperbolic divergence cleaning

• Parallel-IO

• Search “OpenMHD” without a space

OpenMHD code

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

Summary• We have investigated the shock structure of

a reconnection-plasmoid system

• In high Mach-number, low-β regime, several new structures are found:

• Recompression shock

• Over-expanded shock diamonds at the front

• Under-expanded shock diamonds inside the jet

• They are outcomes of high-speed (compressible) fluid effects :　

• Code publicly available• References:

• Zenitani, Phys. Plasmas 22, 032114 (2015)• Zenitani & Miyoshi, Phys. Plasmas 18, 022105 (2011)

M > 1

Thank you for your attention.Have a safe return trip!

BBC online http://www.bbc.com/future/story/20130701-flying-the-worlds-fastest-plane