Local Structures of Electron Temperature and Electrostatic Potential during ST

Merging Startup

*Boxin Gao, Akihiro KuwahataInomoto Lab

The University of TokyoSchool of Engineering

Department of Electrical Engineering and Information Systems 　

Outline

• Introduction– Plasma merging technique for economical fusion

reactor– Magnetic reconnection– Research purpose

• Experimental device and measurement– Plasma merging device– Measurement methods– Multi-channel Langmuir probes array

• Experiment result– 2D Electron Temperature– 2D Electrostatic Potential

• Summary and Future work

Plasma Merging Startup

• Spherical Tokomak (ST) is one of the promising concepts for magnetically confined fusion reactor because of its high beta and economic efficiency.

• To establish center-solenoid-free startup, various schemes such as RF, helicity injection and plasma merging, have been proposed.

Magnetic reconnection is considered as the main factor of plasma heating.

Magnetic reconnectionFig: 　 Plasma merging startup

Magnetic Reconnection

• Reconfigure magnetic field to a lower-energy state

• Release magnetic energy to surroundings– Heat plasma– Produce plasma flows

Magnetic field lines of opposite polarity are reconnected each other.

Fig: 　 Magnetic reconnection in space

Fig: 　 Magnetic reconnection

Research Purpose

• Examine the electron heating mechanism in ST merging start-up.

• Investigate the electron acceleration by in-plane electric field in high guide field.

Experiment observation on ion heating at reconnection outflow through fast shock[1]

Simulation on electron acceleration by parallel electric field at X point in high guide field[2]

Magnetic reconnection operates in company with high guide field during in ST merging start-up

Plasma merging device

Basic parameter R ~ 0.45 m 　 Bt ~ 0.10 T 　　 Br ~ 0.05 T 　　 Ti ~ 20eV　　 Te ~ 5-20eV 　 ne ~ 1x1019m-3

　　　 li-skin ~ 4cm ri-larmor ~ 2 mm

Fig: 　 Plasma merging device

Plasma merging process

Fig: 　 TS-4 device

Fig: 　 Plasma merging process

• Create 2 torus plasma• Reverse PF current

– make them emerge with each other

Reconnection point

Measurement Method

P1P2P3

Triple Probe

plasma

Fig: 　 quadruple probe

• Quadruple probe– Include a triple probe

which acquires Te and ne – Acquire plasma floating

potential

P4

𝑇 𝑒;𝑛𝑒Vf

Chamber

Fig: 　 5-channel quadruple probe

5mm / 10mm

Glass tubetungsten

2mm1mm

End View

One channel configuration :

Electron Temperature

t1 t2 t3 t4

Reconnection rate and magnetic flux

Electron temperature ：

• Electron heating both in current sheet and in outflow.• Maximum electron temperature at peak of reconnection rate.• Symmetric outflow electron heating at low reconnection rate but

the asymmetric heating at the peak of reconnection rate.

Electrostatic Potential

t1 t2 t3 t4

Reconnection rate

Floating potential and magnetic flux ：

• Quadruple distribution is observed at the peak of reconnection rate.• Great gradient of floating potential at the peak of reconnection rate.

Ep Distribution

• High in-plane electrostatic filed occurred during reconnection.

ExB Drift Motion

• Strong in-plane electric field is induced to keep the ExB drift motion.

• Particles’ motion will be strongly affected by this in-plane electric field.

Summary & Future work

• 2D profile of temperature was measured during magnetic reconnection with high guide field.

• 2D profile of the in-plane electric field was measured during magnetic reconnection with high guide field.

• Increase the 2D profile resolution of and .• Find the parameter dependence among , and

Thank you for your kind attentions!

14

Reference[1] Y. Ono and H. Tanabe: “Ion and Electron Heating Characteristics of Magnetic Reconnection in

Tokamak Plasma Merging Experiments”, Plasma Physics and Controlled Fusion, Vol.54, No.12, 124039 (2012)

[2] G. Lapenta and S. Markidis: “Scales of Guide Field Reconnection at the Hydrogen Mass Ratio”, Physics of Plasmas, Vol.17, No.8, 082106 (2010)

[3] P. L. Pritchett , Collisionless magnetic reconnection in a three-dimensional open system, Journal of geophysical research, Vol.106, Nov 1, 2001

[4] J. F. Drake, M. A. Shay, The Hall fields and fast magnetic reconnection, Physics of plasmas, 2008

[5] S. Chen, T. Sekiguchi, Instantaneous direct-display system of plasma parameters by means of triple probe, Journal of applied physics, Vol.36, No.8, Aug, 1965

[6] J. Yoo, M. Yamada, Observation of ion acceleration and heating during collisionless magnetic reconnection in a laboratory plasma, Vol. 110, 215007, 2013

[7] J. Egedal, W. Fox, Laboratory observations of spontaneous magnetic reconnection, Physical review letters, Vol. 98, 015003, 2007

[8] J. P. Eastwood, M. A.Shay, Asymmetry of the Ion Diffusion Region Hall Electric and Magnetic Fields during Guide Field Reconnection: Observations and Comparison with Simulations, Physical review letters, Vol. 104, May 21, 2010

[9] T. D. Tharp, M. Yamada, Study of the effects of guide field on Hall reconnection, Physics of Plasmas, Vol. 20, 055705, 2013

Reconnection in guide field• Bt (out-of-plane) appears as guide field

drift motion : 𝑉 𝑔𝑐=E×B

𝐵2

no guide field:( Bt = 0 )

𝐸𝑧=𝐸𝑟=0𝑉 𝑟=

𝐸𝑡𝐵𝑧−𝐵𝑡 𝐸𝑧

|𝐵|2

𝑉 𝑧=−𝐸𝑡𝐵𝑟+𝐸𝑟 𝐵𝑡

|𝐵|2

=0=0

under guide field:

𝑉 𝑟=𝐸𝑡𝐵𝑧−𝐵𝑡 𝐸𝑧

|𝐵|2=𝐸𝑡 𝐵𝑧

|𝐵|2−𝐵𝑡𝐸𝑧

|𝐵|2

𝑉 𝑧=−𝐸𝑡𝐵𝑟+𝐸𝑟 𝐵𝑡

|𝐵|2=−

𝐸 𝑡𝐵𝑟

|𝐵|2+𝐸𝑟𝐵𝑡

|𝐵|2

1st term 2nd term

Out-of-plane E component

In-plane E component

The same

Out-of-plane E component

only

Vf

ne

G. Lapenta and S. Markidis, Physics of Plasmas, Vol.17, No.8, 082106 (2010)

Vp　 [6]

ne• After probe compensation:

21

Nuclear fusion

Fig: 　 ITER 2020 ～Low cost is essential for

practical application of fusion power

• Large amounts of super-conducting coil to generate high toroidal magnetic field– Largest portion of construction cost

• Next generation of electric power plant– Less pollution – Low risk and radiation– Powerful and stable supply

• The international tokamak facility called ITER is now under construction

22

High β plasma

High beta plasma is expected

• Total Output fusion power is in proportion to value

– b : ratio of plasma thermal pressure to magnetic pressureVBP t42

02 2B

p

• b value is limited in tokamak plasma

– Aspect ratio A = R0/a

2max

1

AaB

I

t

pN

by Troyon’s law

The smaller Aspect ratio the higher beta

23

Spherical tokamak(ST)

• A promising candidate for fusion reactor core plasma– High b is achievable (up to

50%) [1]

– Better confinement property– Compact, low cost in

construction and operation

24

Problem in ST

Problem in ST : Little space

for Centre Solenoid (CS) coil

Plasma start-up method withoutCS coil is investigated

Fig: 　 CS coils used in tokamak

25

CS-less Plasma start-up method

• Waves injection startup– Electron cyclotron waves injection – Radio-frequency waves injection

• Plasma merging startup [2]

– Compact and economical– Achieve high b plasma– Heat plasma through magnetic reconnection process– Form a stable ST configuration efficiently

• Unnecessary of instability prevention process• Less usage of external heating instrument(such as NBI,RF…)

Fig: 　 Plasma merging startup

Magnetic reconnection

2-fluid Hall Effect

Fig: 　 Two-fluid dynamics in the reconnection layer

• Difference movement between ion fluid and electron fluid– Ion : big mass; less magnetized; big Larmor

radius– electron : few mass; strongly magnetized; small

Larmor radius

• Magnetic energy => kinetic energy and thermal energy– Ion and electron outflow are observed [3]

• Symmetry quad-pole distribution

Fig: 　 Hall reconnection simulation [9].

Fig: 　 Hall reconnection in experiment [9].

Hall Effect in guide field

Fig: 　 Hall reconnection configuration in guide field

Fig: 　 Hall reconnection simulation [9].

Fig: 　 Hall reconnection in experiment [9].

• Guide field always existed in ST• Asymmetry quad-pole distribution • Recent observation of hall effect in guide

field– Magnetic field distribution [9]– Magnetic fluctuation [10]– Ion temperature distribution [11]

• Undefined – Electron temperature distribution– Electrostatics potential distribution– Electrostatics fluctuation

Research purpose

• Invest the mechanism of energy transformation in collisionless magnetic reconnection with guide field– Find how electron is heated in reconnection region

• Measure electron temperature distribution

– Find whether electrostatic potential contribute to ion energy• Acquire electrostatic potential distribution

– Find whether electrostatic waves influence on plasma heating• Obtain electrostatic fluctuation

Measurement method

P1 P2 P3

I

Vd2 Vd

3

Probes

plasma

Fig: 　 Triple probe

• Triple probe– Low cost and easy alignment– Excellent in spatial resolutions– No voltage, frequency sweeps/switch– Acquire plasma parameter Te and ne …

simultaneously

A powerful diagnostic tool even for rapidly changing time-dependent plasma

Electron temperature and density

(fixed)

P1 P2 P3

I

Vd2 Vd

3

Probes

plasma

Fig: 　 Triple probe

1− exp (−𝜙𝑉 𝑑2)1− exp (−𝜙𝑉 𝑑3)

=12 (𝜙= 𝑒

𝑘𝑇 𝑒);

Measu

red

Plasma electron temperature () :

𝑇 𝑒

𝑛𝑒=( (𝑚𝑖 )12

𝑆𝐼 )∙ 𝑒𝑥𝑝 ( 12 )

𝑒 (𝑘𝑇𝑒 )12 [𝑒𝑥𝑝 (𝜙𝑉 𝑑2 )−1 ]′

Plasma electron density ( ) :𝑛𝑒

[5]

[5]

Quadruple probe array

Fig: 　 5-channel quadruple probe 2

Fig: 　 5-channel quadruple probe 1

5mm / 10mm

Glass tubetungsten

2mm1mm

End View

Probe End View

20mm

One channel configuration :

Probe array configuration:

Fig: 　 End view of 5-channel probe 1

32

3D Fluctuation probe

Fig: 　 3D fluctuation probe

End View :

4mm

0.5mm

1mm

2mm

0.5mm

1mm

2.5mm

2mmSide View :

Probe configuration :

Tungsten

Ceramic

Alignment

Fig: 　 Plasma merging device

5 channel probe 1

5 channel probe 2

Vf distribution of Hydrogen

• Quad-pole distribution of floating potential was observed– A typical evidence of hall effect in magnetic reconnection – About 10[eV] ion kinetic energy transformed from electrostatic energy are confirmed

Reconnection Rate

E ｘ B Drift Motion of Electron

drift motion : 𝑉 𝑔𝑐=E×B

𝐵2 --------------------------- [ プラズマ物理入門　 P20]

𝑉 𝑔𝑐=E×B𝐵2 =

(𝐸𝑡𝐵𝑧−𝐵 𝑡𝐸𝑧 ) ∙ r+ (𝐸𝑧𝐵𝑟−𝐸𝑟𝐵𝑧 ) ∙ t+ (𝐸𝑟 𝐵𝑡−𝐸𝑡 𝐵𝑟 ) ∙z  

(√𝐵𝑟2+𝐵𝑡

2+𝐵𝑧2 )2

𝑉 𝑟=𝐸 𝑡𝐵𝑧−𝐵𝑡𝐸𝑧

𝐵𝑟2+𝐵𝑡

2+𝐵𝑧2

𝑉 𝑡=𝐸𝑧𝐵𝑟−𝐸𝑟𝐵𝑧

𝐵𝑟2+𝐵𝑡

2+𝐵𝑧2

𝑉 𝑧=−𝐸𝑡𝐵𝑟+𝐸𝑟 𝐵𝑡

𝐵𝑟2+𝐵𝑡

2+𝐵𝑧2

Vf は t 方向に一様（軸対象性） ∆𝑉 𝑓=𝑉 𝑓|𝑡1→ 𝑡2

❑ =0

𝐸𝑡=0

𝑉 𝑟=−𝐵𝑡𝐸𝑧

𝐵𝑟2+𝐵𝑡

2+𝐵𝑧2

𝑉 𝑧=𝐸𝑟𝐵𝑡

𝐵𝑟2+𝐵𝑡

2+𝐵𝑧2

ExB Drift Motion

Inflow

Outflow

(Out-plane component)(In-plane component)

(total)

During reconnection After reconnection

• ExB Drift motion component by in-plane electric field is dominate over that by out-plane electric field .

Et Distribution

ExB Drift Motion (1st term )

• The Inflow and outflow is much similar to those in Sweet-Parker model.

ExB Drift Motion (2nd term)

• ExB drift motion caused by electrostatic field comes significant during reconnection period

• Electrostatic field greatly increases the speed of inflow and outflow in magnetic reconnection area

ExB Drift Motion

• ExB drift motion of electron in guide field is dominant by electrostatic field

ExB Drift Motion (1st term)

• Vp (Et only) --> (0.0000 1.0427) km/s• Vp (Ep only) --> (0.0191 35.6529) km/s• Vp (Et with Ep) --> (0.0331 35.4518) km/s

• Et (Et only) --> (-137.7242 56.7613) V/m• Ez (Ep only) --> (-1129.2 1755.9) V/m• Er (Et with Ep) --> (-1051.5 1146.9) V/m

ExB Drift Motion (1st t_noBt)

E ・ B Result

(E ・ B)/|B|^2 Result

(E ・ B)/|B|^2 Result

ExB Drift Motion

Electron Temperature

• Electron heating at outflow region is observed

During reconnection After reconnection

Te in mid-plane (z=0) :

Electron Density

• Electron density is greatly affected by plasma confinement in stead of magnetic reconnection

• Electron density is not obviously changed between outflow region

During reconnection After reconnection

ne in mid-plane (z=0) :

Before reconnection