MRX
Laboratorystudiesofmagne5creconnec5on:
HowcantheybeappliedtoCTresearch?
Masaaki Yamada*
August 23, 2016
US-JapanCTWorkshop
Incollabora5onwithJongsooYoo
Mo5va5onandContents
•  Magne5creconnec5onisknownforefficient
conversionofmagne5ctopar5cleenergy.
•  Iden5fica5onofmechanismsfortheenergyconversion
hasnotbeenmadewhileithasbeenacentralproblem.
•  Isthereafundamentalprincipleforenergy
par55oninginaproto-typicalreconnec5onlayer?
•  HowcantheresultsbeappliedtoCTResearch?
NatureComms,5,4774(2014)
Phys.Plasmas,23,055402(2016)
EnergyConversionintheSweet-ParkerModel
IncomingPoyn5ngflux;S=ExB
Negligibleflowenergy
AlfvénicouXlow
Hotplasma
NegligiblePoyn5ngflux
S=(ExB)out~0
Ohmichea5ng ηj2
2-D, resistive MHD model
•  Plasma heating occurs slowly on Ohmic dissipation inside
the diffusion region.
Bin 2
ρ
→ Wp + Vs2
µ0
2
Experimental Setup and Formation of Current Sheet on MRX
Experimentally measured flux evolution
ne= 1-10 x1013 cm-3,
Te~5-15 eV,
B~100-500 G,
How is magnetic energy converted to plasma?
Experimental set-up [Yoo et al, 2013]
Magnetic Probe Array
Equilibrium
Field Coil
Magnetic
Field Lines
37.5cm
Flux Core
R Current Sheet
Y Z
•  Helium discharge
•  IDSP to measure Ti
•  λmfp,e≥ c/ωpi > δCS (~2cm)
Twofluidregime
MeasurementofenergyinventoryinMRX
IncomingFluxes
Changesinenergy
enclosedinthe
volume
45
R (cm)
40
OutgoingFluxes
35
30
0
5
Z (cm)
10
15
•  Energytransportequa5on:
)
,
 ρ 2%
"3
"5
∂ ) B2
ρ 2 %,
+ ∑ $ nsTs + Vs '. + ∇ ⋅ +S + ∑ $ nsTsVs + Vs Vs ' + qs . = 0
+
&
∂t * 2µ 0 s=e,i # 2
2 &2
* s=e,i # 2
-
BirnandHesse,2005
6
InventoryofEnergy
Magnetic energy inflow rate!
1.0±0.1!
Magnetic energy
outflow rate!
0.49±0.05!
Energy deposition
rate to electrons!
0.18±0.04!
Energy deposition
rate to ions!
0.37±0.07!
MHD component!
0.22±0.02!
0.22±0.02!
Change of
thermal energy!
0.14±0.05!
0.14±0.05!
Change of flow
energy!
0.07±0.02!
0.07±0.02!
Hall-field
Hall-field
component!
component!
0.27±0.03!
0.27±0.03!
Energy
Energy loss
loss rate
rate
(Conduction,
(Conduction,
radiation)
radiation)
0.08±0.04!
0.08±0.04!
Change
Change of
of
thermal
energy!
thermal energy!
0.17±0.05!
0.17±0.05!
Energy
Energy loss
loss rate
rate
(Conduction,
(Conduction,
neutrals)
neutrals)
≤
≤ 0.16!
0.16!
Yamadaetal,NatureCommunica5ons(2014)
Particle dynamics of the two-fluid reconnection layer
Generalized Ohm’s law: Normalized with
Erec + Vin × Brec = 0
Ve × Brec ≈ Erec ≈
dΨ
dt
Electron inertia
term
Hall term
B
Y
44
(G)
Ion Flow
42
40
40
R (cm)
Electron
pressure term
Electron Flow
Separatrix
20
Magnetic Field
Line
38
0
36
−20
34
32
−9
Electron
Diffusion Region
Ion Diffusion
Region
−40
−6
−3
0
Z (cm)
3
6
9
8
Electron dynamics and electron heating in MRX
R (cm)
R (cm)
A
A
Magnetic Field Lines and Electron Flow Vectors
44 Magnetic Field Lines and Electron Flow Vectors
44
42
42
40
40
B
B
3−D View of Fig.a
3−D View of Fig.a
Z (cm)
5 Z (cm)
10
15
5
10
15
0
0
38
38
40
40 R (cm)
R (cm)
36
36
35
35
34
34
32
32
0
0
5
5Z (cm)
Z (cm)
10
10
T (eV)
Te (eV)
e
12
12
2−D Electron Temperature Profile
2−D Electron Temperature Profile
42
42
D
D
10
10
38
38
9
9
36
36
8
8
34
34
7
7
32
32
0
0
5
5
Z (cm)
10
10
15
15
6
6
30
−5
30
0
−5
0
Y (cm)
Y (cm)
Electron gain energy by Ey
3
j ⋅E Profile
je E Profile
(W/cm )
(W/cm3)
e
42
42
11
11
40
40
5
5
10
10
15
15
150
150
40
40
RR(cm)
(cm)
C
C
RR(cm)
(cm)
j=CurlB,Ve=je/ne
45
45
100
100
38
38
36
36
50
50
34
34
0
0
- Energy deposition occurs very near
the X-point.
- The electron heating seen in wider
region through heat conduction
j ⊥ E⊥ >> j // E//
32
32
0
0
5
5
Z (cm)
10
10
15
15
Thephysicsofthehighenergydeposi5onrateisnotyetresolsved.
9
4seconds
ofdata
Alargein-planeelectricHallfieldverifiedintheMRX
reconnec5onlayerduetotwo-fluideffects.
Φf (V)
30
42
20
R (cm)
40
10
38
0
36
−10
34
−20
32
0
5
Z (cm)
L-J.Chenetal,2008
10
15
−30
J. Yoo et al, 2013
40
p
Wygantetal,2005
Hoshinoetal,1998
Drakeetal,2009
Φ (V)
60
20
0
−5
45
0
40
5
10
15 30
35 R (cm)
11
Ionaccelera5onandhea5nginthereconnec5onlayer
Ionhea5ngisajributedtore-magne5za5onofacceleratedions
Sizeofpoten5aldropcanbeanaly5callyes5mated
Yamadaetal,
PoP(2016)
Bsh
Bz
ER ≈ Vey BZ −
1 ∂pe
ene ∂R
(1)
Equation of motion for electrons
(2)
After integrating (1) w.r.t. R
•  Isthereafundamentalprincipleforenergy
par55oninginaproto-typicalreconnec5on
layer?
EnergyConversioninTwo-fluidReconnec5on:
Ionsgainsenergyprimarilyontheseparatrices
Out-of-plane
Magnetic Field
Ion Flow
Electron Flow
Separatrix
Magnetic Field
Line
Electron
Diffusion Region
Ion Diffusion
Region
2
Bsh
Wion~LiVin nee<δΦ> ∼ LiVin
2µ 0
2
B
WM ~ LiVin sh
µ0
Wion/WM ~ 1/2
Aslargeas50%ofincomingmagne5cenergyisconvertedtopar5cleenergyofions
EnergyConversioninTwo-fluidReconnec5on:
Energydeposi5ontoelectronsonlyoccurs
atthee-diffusionregion
Out-of-plane
Magnetic Field
Ion Flow
Electron Flow
Separatrix
Magnetic Field
Line
Electron
Diffusion Region
Ion Diffusion
Region
WeuseSweet-Parkermodelforelectronhea5ng/bulkaccelera5on
2
B
We ∼ LeVin sh
µ0
2
B
sh
WM ~ LiVin
µ0
=>
We
L
1
~ e ~
WM
Li
4
Onlyafrac5onofincomingmagne5cenergyisconvertedtopar5cleenergyofelectrons
2DPICsimula5ononenerge5cs;
byJ.JaraAlmonteandW.Daughton
a)
0
1 b)
Open Boundary Simulation
MRX
Theenergypar55oningdoesnotstronglydependon
thesizeofmonitoringboundary
MRX data is compared with simulations and space data
Magnetic
energy
Inflow
Magnetic
Energy
outflow rate
Energy
Energy
deposition deposition
to ions
to electrons
MRX Data
1.0
0. 45
0.35
0.20
Numerical
simulation
1.0
0. 42
0.34
0.22
0.4
0.39
0.18
Magnetotail
1.0
data
(Eastwood)
•
•
Enthalpy flux dominates in the down flow region
Magnetic energy outflow substantial
Energy deposition to ions is generally larger than to electrons.
With the electrons’ heat transport loss is larger than that of ions’,
⇒  Ti >> Te
Very important for reconnection in CT plasmas
Strongionhea5ngisobservedduringsawtoothreconnec5oninRFP
Reconnec5onEvent
Time(ms)
(rela5vetoreconnec5onevent)
SpheromakMergingExperimentsinMRX
(ToroidalEnergy=>PlasmaKine5cEnergy)
Plasma Initiation
(1)
Speromak Merging
Spheromak Formation
-
+
Final CT
(1)
SpheromakMergingExperimentsinU.Tokyo
(ToroidalEnergy=>PlasmaKine5cEnergy)
TS-3; Yamada et al PRL (1990)
Ono et al PRL(1996)
Norman’s 70 year Symposium (1995)
FLARE(FacilityforLaboratoryReconnec5onExperiment)
Ji(PI)etal
Summary
•  Energy partitioning are quantitatively analyzed in the MRX reconnection layer
•  This result is consistent with theory for the dynamics of two-fluid
reconnection layer with a single X-line geometry
-Energydeposi5ontoelectronsoccursneartheX-pointthrough j ⊥e E⊥
-Energydeposi5ontoionsoccursneartheseparatricesthrough j ⊥i E⊥
•  Based on the MRX data and analytical consideration, we conclude a
fundamental principle for energypar55oninginaproto-typicalreconnec5onlayer.
- Substantial component of outgoing magnetic energy (~ 50%) in the Hall
reconnection
- ~ 50 % of incoming magnetic energy can go to plasma particles
•  TheresultshaveanimportantmessagetoCTresearch
Duringtwo-fluidmagne5creconnec5on,asignificantamountofEfieldis
generatedandmagne5cenergyisconvertedtoionskine5cenergy.