Plasmoid-dominated turbulent reconnection
in a low-β plasma[Astrophys. J. Lett., 894, L7 (2020)]
Seiji ZENITANI (Kobe U)
Takahiro MIYOSHI (Hiroshima U)

MHD reconnection
Sweet-ParkerPetschek

plasmoid-dominatedSweet 1958, Parker 1957

Loureiro 2007, Bhattacharjee+ 2009
Uzdensky+ 2010, Huang+ 2010

Reconnection rate
Petschek

0.1

0.01

Sw

eet-Parker

Petschek 1964

Rate is expected tobe constant ~0.01
plasmoid-dominated

0.001
104

106
System length(Lundquist number: SL=L/η)Solar corona: β<<1Height
What are basic properties of plasmoidreconnection in a solar corona (β<<1)？
Earlier study (Ni+ 2012) reported
slower reconnection rate for lower β

Plasma beta
Gary 2001

pgas
⌘pmag

MHD simulation

MHD simulation
We control the background ββ0 = 0.2 ~ 5.0•

30,000 x 3,000 (x 2) grid points•

η = 1/1000, SL = 2.5 x 105 for Lcs = 250

Signatures for low-β: vertical slow shocks(b)•

Traveling in the left and right directions, even inside the plasmoids

Outflow speed (Vx)

vx(a)
(c)

(b) div V - Compression in red(d)vx(c)Similar to normal shocks on airfoil (see also SZ & Miyoshi 2011, SZ 2015)

Faster reconnection rate for lower-β
Faster for β=0.2

Rec.
rate

Conventional rate ~0.01
for β=5.0

Reconnected flux
Density variation

(a)

Rec.
rate

Faster rate forlower-β cases•

More compression for lower-β cases(b)Estimating the reconnection rate
Plasmoid-dominated layer

Mini Sweet-Parker (SP) layersof critical system size (SL ~104)

δL

Effective rate
＝ that of the central mini SP layer〜 SL-0.5 ＝ 0.01

Compressible Sweet-Parker theoryβinmini Sweet-Parker (SP) layer

δL•Compressible S-P theory (Hesse+ 2011) is necessary for βin <1•

Reconnection rate satisfies⇣ ⌘vinvin⇢out ⇣ ⌘R⌘⇡==rcA,invout⇢in LL<latexit sha1_base64="RVjMmEhWh20+LYoxeYseVY7iMEY=">AAAEFnichVLLbtNAFL2ueZTyaEo3SGws0kpFQtEYIbFC6mODEItCm7ZSHUXjyTQZ1S/GY5dq5B/gC/gFxD90h2DJhgWfwJoFGxZcjydS25BmLCfnnnvOvZ65E2aRyBUhP50599r1Gzfnby3cvnP33mJr6f5enhaS8S5Lo1QehDTnkUh4VwkV8YNMchqHEd8Pj7fq/H7JZS7SZFedZrwX02EijgSjCql+6yyIqRoxGum3lRfwd4UoveBIUqbLvg5k7ImkqjRr8MaTOvICmmUyff8fncVpoVD2wgoCOUrP8efiptqmGK6NpQMeKVrp1w39GGvIKwX9Vpt0iFneJPAtaINd2+mS40EAA0iBQQExcEhAIY6AQo7PIfhAIEOuBxo5iUiYPIcKFtBboIqjgiJ7jL9DjA4tm2Bc18yNm2GXCF+JTg9WyQ/yifwm38hn8ov8nVpLmxr1t5zif9h4edZf/PBg5w+6pvtC1FewivrQdB4gijGrYDSz21h3lV+aHXI4MTuLTS5BlcZciTxDd31+PcOMa4z3UUca2piv7ElOqzXEThRxZaL6TEMzn2rmVwxwVuWEr544MzNXMzpLq7noD8wdaOaKfrxz/uUbNgn2nnZ80vHfPGuvb9rbNw8P4RGs4Qk8h3V4CdvQBeasOK+cHWfX/eieuV/cr410zrGeZbiw3O//AGaL+T8=</latexit>
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sha1_base64="XaMqXEZXBwB9F9UGXSWnmd5OCcI=">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</latexit>
sha1_base64="yrHD49eqcKgOnpOciyCmbmX14co=">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</latexit>•If we fix the geometric factor (δ/L), we expect the acceleration factor

2 (1 + )R / r( , ) ⌘3(1) + 2<latexit sha1_base64="MlKpOubqBQ3yJjo6q+u1lhZnb8w=">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</latexit>•This is a function of plasma β and adiabatic index γ
Hesse, Birn, & SZ 2011

2-D parameter survey
Our prediction

2 (1 + )R / r( , ) ⌘3(1) + 2<latexit sha1_base64="MlKpOubqBQ3yJjo6q+u1lhZnb8w=">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</latexit>

Adiabatic index
Compressible
Compressible

= 0.2
0.5
Plasma β1.0
2.0
5.0

Incompressible= 1.33, 1.5, 1.67, 2.0

Incompressible

Simulation vs Theory•

Parameter survey in the 2-D parameter space of (β, γ)•Reconnection rate is proportional to the compression ratio (theory)•→ Plasma compression allows faster rate: R~0.02 in the β→0 limit

Outgoing energy flow
The ratio of (Bulk kineticenergy) : (enthalpy flux)

Rec. rate(Simulation)

SZ & Miyoshi 2020

Transient phase vs Quasisteady phase
Influenceof βInfluence ofthe initial currentsheet models(β=0.2)•Transient phase

Sensitive to the background β and the initial CS models•Quasisteady phase

Sensitive to the background β, but insensitive to the CS models•

We explored the quasisteady phase. Earlier study probably looked at the transient phase.

Our code: OpenMHD• Publicly available• Parallel F90 code for our works(SZ & Miyoshi 2011-2020)• Updates in 2020
• GPU code by CUDA Fortran• CUDA-aware MPI
https://sci.nao.ac.jp/MEMBER/zenitani/openmhd-e.html

GPU1000

x 40

750
500
2500

CPUi9-9900

CPUMPI x 4

GPU2080Ti

GPUGV100@NIFSfastSummary• Plasmoid-dominated reconnection for β << 1• Vertical slow shocks• Higher reconnection rate
• Plasma compression accelerates the rate to ~0.02 in the β→0 limit• Two-step evolution: Transient phase and quasisteady phase• OpenMHD• Publicly available, GPU-ready• Reference• Zenitani & Miyoshi, ApJL, 894, L7 (2020), https://doi.org/10.3847/2041-8213/ab8b5d•

https://sci.nao.ac.jp/MEMBER/zenitani/openmhd-e.html