Defining dissipation/diffusion regions
in collisionless magnetic reconnection
andHigh-speed fluid dynamics in magnetic
reconnection in a low-β plasma

Seiji ZENITANI
National Astronomical Observatory of Japan

Topic 1:
Defining dissipation/diffusion regions incollisionless magnetic reconnection[1] Zenitani, Hesse, Klimas, & Kuznetsova, Phys. Rev. Lett. 106, 195003 (2011)[2] Zenitani & Umeda, Phys. Plasmas, 21, 034503 (2014)

“Diffusion regions” of collisionless reconnection

electronElectron Diffusion Region
Electron Dissipation Region

ion

Ion Diffusion Region
Ion Dissipation Region• How to define “Dissipation” or “Diffusion” regions?

Many proposals ...
[electron]

Dissipation
region?
Diffusion
region?

• Plasma nonidealness

E + vsB=0• Maximum flow speed, ve,max(Daughton+ 2006, Fujimoto 2006...)• Electric current, J• Parallel electric field E = 0• Agyrotropy in velocity distribution function
and GCT parameters (Scudder & Daughton 2008)• Plasma inertial effect (Klimas+ 2010)• Energy transfer in the electron’s moving
frame (Zenitani+ 2011, Birn & Hesse 2005)• Diffusion of magnetic flux (Zenitani & Umeda 2014)• Electron energy gain, Je . E (Yamada+ Yesterday)

Dissipation
region?

= A place where
magnetic dissipation occurs.

Diffusion
region?

= A place where
magnetic diffusion occurs.

What is magnetic dissipation?

What is Dissipation?
• Irreversible process• Something that never comesback

Magnetic energy dissipation
Total energy transfer

irreversible in MHD

Work by Lorentz force (Ideal MHD)

Birn & Hesse 2005

Nonideal energy conversion

2D PIC simulations

Magnetic energy dissipation
Total energy
transfer
Electron-framedissipation
measureLorentz factor
Electric current in theelectron frame

Electric field in theelectron frame

Charge density

Zenitani+ 2011 PRL
irreversible in MHD

Work by Lorentz force (Ideal MHD)

Birn & Hesse 2005

Nonideal energy conversion

De in various reconnections

AntiparallelZ

Guide-field

Symmetric Rx

Z

Asymmetric Rx

Dissipation Region

XX

2D PIC simulations

Irreversible?
• De measure is a driving term to increase MHD entropy
MHD specific entropy

Rossi & Olbert 1970

LHS ( t=0)

• Note:Dmhd・qobs

DDt

0 at the X-line

What is magnetic diffusion?

Diffusion in a coffee• Let’s consider colorful sugar
elements

Coffee coordinatesDiffusion in a coffee• Let’s consider colorful sugar
elements• Sugar spreads through thediffusion process

Coffee coordinatesDiffusion in a coffee flow
• Coffee frame moves and expands• If sugar elements are fixed in thecoffee coordinates, we don’t
think they are diffusing.

Diffusion in a coffee flow
• Coffee frame moves and expands• We expect that sugar elements
spread (diffuse) in the coffee frame

Magnetic flux diffusion
BFrozen-in condition(Flux preservation)v

R=0
Newcomb 1958
Stern 1966

L=b·(Magnetic lossR)b

SZ & Umeda 2014(R)Plasma connectivity(Line preservation)

Newcomb 1958

Electron diffusion region
vs Dissipation region (De)2D PIC simulation (mi/me=100)• A compact region with[diffusive] magnetic loss

Le = b · (ReLe

2D Vlasov simulation (mi/me=25)

DeRe )
E + veB

Topic 1: Summary• Dissipation region (DR)– Electron-frame dissipation measure– Nonideal energy transfer– Likely irreversible: Driving term in the MHD entropy equation• Electron diffusion region (EDR)– Diffusive evolution of magnetic fluxin the electron flow frame• DR and EDR are similar
Dissipation
Region (DR)Ion Diffusion Region (IDR)

Leb·(Re )Electron Diffusion Region (EDR)

Nongyrotropic layers(Not presented in this talk)Topic 2:
High-speed fluid dynamics in magnetic
reconnection in a low-β plasma[3] Zenitani & Miyoshi, Phys. Plasmas 18, 022105 (2011)[4] Zenitani, Phys. Plasmas 22, 032114 (2015)

Motivation• Magnetic reconnection expels a fast outflow jetat the upstream Alfvén speed• How does the jet interact with an external medium?
outflow jet?

?

B
4cA =Plasma β• Key parameterpgas
8 p= 2pmag
B

Alfvén speed

1cA
cs2

Sound speed

Typical velocity

Vcs2

M2
Typical Mach number

Branches of fluid dynamics
Conventional
fluid phenomena

tenki.jp 2015

Subsonic• Incompressible fluids

Shock waves

Mach 1887

1TransonicSupersonic• Compressible fluid dynamics• High-speed fluid dynamics• Adiabatic effects• Shocks• Shock-shock interaction

MHD simulation
Density+B0
Plasma sheet

Symmetry
Reconnection point

β=0.2-B0Outflow velocity (Vx)

ZX

Various shocks!
vx
5764z

1283

910Petschek
slow shocks

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

Normal shock: Analogy to airfoil• MHD slow shock

Subsonic(V << cs)

• Recovery shock orrecompression shock
vjet ~ cA

plasmoid (0.8 cA)

Transonic(0.8cs <V)(b) t = 250z

Supersonic(cs < V)vx

x

See also https://www.youtube.com/watch?v=8OIqfCTAZQoShock diamond(b) tvx= 250
PlasmoidOutflow jetz

Plasma sheet

xSimulation 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

Hidden shock-diamonds• Another shock-diamonds
are hidden inside thePetschek outflow

Vz• Shock-crossing point
between the normal shock
and Petschek slow shock ishighly complicated(Zenitani 2015)

vx

Zenitani 2015

β=0.1

NormalshockZX

The plasmoid diagram
2015

87

G
20

C

1719

A

13
12

14

9

E

1
B

161115D
4a 4b18 5 6

10F
3

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.contact discontinuity (Zenitani & Miyoshi 2011, 2015)
C. post-plasmoid reverse flow
13.contact discontinuity (Zenitani 2015)
D. internal flow
14.contact discontinuity (Zenitani 2015)
E. flapping jet (KH instability)
15.slow expansion wave front (Zenitani 2015)
16.conduction front [with heat conduction] (Yokoyama & Shibata 1997)
17.fast forward shock [in asymmetric reconnection] (Nitta et al. 2015)• A lot more to come• If you find something
new, please send me
your references so that
I will update thediagram

OpenMHD code
• Simple, Scalable, and Shock-capturing MHD code
• TVD Runge=Kutta method• MUSCL interpolation• HLLD flux solver• Hyperbolic divergence cleaning• Reconnection problems are pre-configured

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

Topic 2: Summary• MHD evolution of magnetic reconnectionin the low-β, high Mach-number regime
1cA
cs2

V
cs

2

M2

M>1

• New shock structures= outcomes of high-speed fluid effects– Recompression shock– Overexpanded shock diamonds at the front– Underexpanded shock diamonds inside the outflow exhaust• The plasmoid diagram - your contributions are welcome• OpenMHD code - publicly available

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

BBC online

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