Kink Behavior of Central Open Flux Responsible for HelicityInjection Current Drive of the HIST Spheromak and ST Plasmas

M. Nagata, H. Hasegwa, K. Kawami, T. Takamiya, Y. KageiN. Fukumoto and T. Uyama

Department of Electrical Engineering, University of Hyogo

Contents• Background• Objectives• Hilights from relaxation studies on HIST (Comparison between Spk and ST, Formation and sustainment of flipped ST)

• Comparison with 3D MHD simulation results• Summary and future plan

# In collaboration with S. Masamune, Kyoto Inst. of Tech. and M. Katsurai, U of Tokyo

# The university name was changed from Himeji Inst. of Tech..

Ψbias

Flux ConserverCentral Conductor

Magnetized Coaxial Gun

Bias Flux Coil

Open Flux

Kinj=2ΨbiasVg

Ig

Coaxial helicity injection (CHI) technique was introduced to classical spheromaks andthen spherical tokamaks to sustain a plasma current in steady-state. The ability of CHI to drive acurrent has been examined in many spheromak/ST devices and also various kinds of MHDrelaxations and kink behavior have been interestingly observed.

Central open flux column

Closed flux

Magnetized coaxial plasma gun (MCPG)

To Study Helicity Injection Current Drive and theUnderlying Relaxation Physics

SSPXNSTX

HIT-IIHIST

Plasmoid ejection, Helical kink, Magnetic reconnection, Rotation

Solar flares

Close Analogy between Gun-Spheromak and AstrophysicalPlasmas

Robust kink behavior created by MCPG

Common self-organization phenomena are observed in both laboratory and space plasmas

「ようこう」ホームページより

Hsu and Bellan、PRLHIST

Laboratory experiments using the MCPG help us understand the solar andastrophysical relaxation phenomena (Flares, accretion disk and jet dynamics).

Objectives and Major Goals

• The present purpose of coaxial helicity injectionexperiments on HIST is to investigate self-organization problems in plasma physics, common tothe laboratory and space.

• Comprehensively understanding of the underlayingphysics in the helicity driven system allows one tocontrol dynamo activities (reduction in the relevantfluctuations), leading to the achievement of theefficient sustainment and better confinements ofspheromaks, RFP’s, and spherical tokamaks.

Increase in MHD activity, self-organized properties and large scale fluctuations

Increase in classical diffusion, stability and small scale fluctuations

TF coil current

Itf0

R0 /r

0

0.5

1

2

q

-0.5

-1

Spherical Tokamak(Normal/Flipped ST)

Spheromak

Spherical RFP

New Prediction: (see Dr. Kanki’s presentation) Formation of diamagnetic low-q ST with two fluid effect.

Diamagnetic Low q ST

FRC

Dynamics of driven spherical system

It is interesting to investigate whether ST plasmas collapseor survive after they pass through the rational barrier.

TF

VgIinj

time

time

1) Comparison study of kinkbehavior between SPK andST.

2) To see what happens to STby a rapid reversal of TF.

Understand Generic Properties of Self-Organization inHelicity-driven Spherical System; How to do it ?

Various Utilizations of TF coil current in the CHI scheme

Spheromak High-q STS-RFP

B. Future work

A. Present works

(d) Spherical RFP

λ>λc Ψt.e < 0

(c) Flipped ST

λ<λc Ψt.e <0

Bt.

(b) ST

λ<λc Ψt.e > 0

ItfΨt.e

Ψbias>0λ≅0 Ψt.e >0

(a) near a Vacuum Field

Magnetizedplasma Gun

Flux conserver

S T

F l i p p e d

R F P

F l i p p e d

S T

??

? ? ? ? ? ? E i g e n v a l u e ?

F l i p p e d S p hS p h

R F P

?

?

It f

> 0

It f

< 0

It f

= 0

Sequence of poloidal flux topologies of driven plasmas as λ is increased from zero to above the eigenvalue λc

Helicity-driven Relaxation Theory Predicts the Existence ofFlipped ST States in the Regime of TF < 0

Helicity-driven relaxed states basedon a single fluid MHD theory

∇×B = λB

Question: How are extensions ofthe helicity-driven relaxationtheory to two-fluid plasmas ?Then, how to approachexperimentally to that region ?

HIST and Diagnostics

Injection Current 20 kA,Injection Voltage < 600 VBias Flux < 5 mWbTF coil current < 0.3 MA

R = 0. 30 ma = 0.24 mA =1.25

Gas PuffValves (4)

InsulatorInnerElectrode

Vacuum Vessel

Outer ElectrodeCentralConductor

Toroidal Field Coil

Inner Bias Coil

VerticalField Coil

Outer Bias Coil FluxConserver

Itf

Sustainment Bank

Formation Bank

Iinj

100

80

60

40

20

02 41 3 50Time (ms)

2

4

6

0

#12672

(101

9m

- 3)

(kA

)I t

ne

Surface Magnetic Probe(Bt,Bp) Rogowski andFluxProbez=-74mm

MagneticProbe

1

26

19

8 12

15

5

22

17

10

(Br,Bφ,Bz)

MagnetizedCoaxialPlasmaGun

CentralConductor

ToroidalField Coil

Spherical FluxConserver

CO2 Laser Interferometer

z= 0mm

Toroidal modeprobe (8 chs)

It < 150 kAΔt = 4 - 8 msne = 2 - 8 x 1019 m-3

Comparison of Magnetic Fluctuations between Spk and ST

Intermittent generation of the toroidal current at the magnetic axis was observed inboth operations.

Spheromak Spherical Tokamak

n=1 mode and its rotation n=0 mode dominant

Toroidal current

Current density on the magnetic axis

n = 0

n = 1

Phase of n =1

Flux amplification/current generation in the spheromak case results from n=1MHD activity. In the other hand, that in the ST is associated with repetitivemerging of plasmoid injected from the gun which we proposed as a model ofcurrent drive so far.

Current generation on axis

Small scale fluctuations

Large scale fluctuations

Kruskal Shafranov limit

t=0.340 ms

t=0.365 ms

time

Kink mode is unstable

Evidence of Rotating Kink Behavior Driven by MCPG

12

0

22

>gc

tc

IRIR

λπ

VZ = 30 [km/s] , VR = 18 [km/s]

Exponential growth of the central openflux with the E×B toroidal rotation

Kinked central open flux

Velocity fluctuation produced by rotating kink motion.

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800 1000 1200 1400

I t

t (τA)

10-2

10-1

100

0 200 400 600 800 1000 1200 1400

n=0n=1

Wmag

[a.u.]

t (τA)

Dynamo Drive of Spheromak Exhibited by 3D MHD Simulation

Nonlinear kink behavior of the central flux/currentchannel.

This simulation result is in good agreement with the experimental observation.

Sustainment

Toroidal mode n=0, 1

Initial exponential growth of kink of the central column

Growth, nonlinear saturation and the following relaxationof the kinked flux column produces dynamo electric field,which includes flux conversion from toroidal to poloidal.

Resisitve decay

Closed flux surfaces are identified only as mean fields.

Edynamo = <ve×B>~ ~

0

2

4

6

0 200 400 600 800 1000 1200

Einj

t

[ 10-3 ]?~

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800 1000 1200

I t

t

10-5

10-4

10-3

10-2

10-1

100

0 200 400 600 800 1000 1200

n=0

n=1

n=2

n=3

n=4Wmag

t

Poincare plot of magnetic field atthe time when the magnetic energyin the n = 1 mode gets down to ~10-4

Multi-Pulse Helicity Drive iseffective for suppressing then = 1 fluctuation.

Decaying phase

Driven phase

Gun voltage on Gun voltage off

Improvement of confinementquality.

Multiple Pulse Operation for Improvement of SpheromakConfinement

Closed flux surfaces are produced during the decay phase.

Chaotic scattering of field lines

0.3mWb/l i ne

-0. 4 -0. 3

t=0. 385ms

-0. 4 -0. 3

t=0. 382ms

-0. 4 -0. 3

t=0. 383ms

t=0. 380ms

0.1

0. 15

0.

0. 25

t=0. 375ms

-0. 4 -0. 3

0. 1

0. 15

0.2

0. 25t=0. 381ms

t=0. 379 mst=0. 378ms(a) (b) (c) (d)

(e) (f ) (g) (h)

R(m)

R(m)

Z (m) Z(m) Z (m) Z(m)

Plasmoid ejection speed ~60km/s

Stabilization of kink instability by TF

Plasmoid ejection is axisymmetric and explosive.

Plasmoid Ejection from MCPG during the Formation of ST

Magnetic reconnection point

Application of a strong external TF decreases the magnetic reconnection rate so thatthe ratio of closed flux to the total flux in ST becomes smaller than that in SPK.

In constract with spheromak, it becomes more important in the ST case to understandsmall-scale fluctuations and local features of reconnections around the X(null)-point.

Current Sustainment by Repetitive Injection and Mergingof an Axisymmnetric Plasmoid from MCPG

2 VinjΨbias = 2VtΨt = K/τK

finj Ks = 2VtΨt = K/τK

Rsas

RST Itf

Ψt.s

Ψt

Ｉt

Ｉt.s

λs

λ

λ= ε λs

Ks

　

　Ks=μ2

0 λs as 4I2

tf/(8Rs )

　It.s= ItΨt.s/ (Ψt ε )　

　finj =16 ε RsVtΨ2t/ (μ3

0 a 4

s I2

tf It)

　For example, ST Reactor (Rs =1.65 m, as=0.25 m)

　 finj = 0.27ε[s-1] = 1.1 [s-1] （ε=30 [%]）

　It.s =1.1 [MA], Ψt.s =3.3 [Wb]Reference:　R.Farengo and T. Jarboe: Fusion Tech. Vol.20 407 (1991)

＜

M. Nagata et al. Phys. Rev. Lett. 90, 225001 (2003)

Self-reversal process

Observation of Self-reversal of Magnetic Fields by ReversingTF ; Relaxation from the ST toward the Flipped ST State.

Note that not only toroidal flux but alsopoloidal flux reverses the sign spontaneouslyduring the relaxation process.

0

0.2

0.4

0.6

0.81

nm

ode

(kG

)

n=0n=1n=2n=3

0.5 0.6 0.70.55 0.65 0.75

0.39

0 .00

-0.21

0.21

Time (ms)

(d)

R(m

)

0.105

0.173

0.241

0.309

0.377

0.445

J t(M

A/m

-2)

(c)

-0.4

-0.2

0

0.2

0.4

-70-50-30-1010305070

Bt.e

,<B

>(k

G)

t.co

re

I t( kA

)

Edge toroidal field

Core toroidal field

Toroidal current

(a)

Shot #4586

Flipped ST

Large growth of the n=1 kink mode

RFPST

Fast Camera Images Display Kink Behavior duringSelf-reversal Process

(g) (h)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-20

0204060

Time[ms]

I t[kA]

0.33 0.34 0.35 0.36 0.37 0.38-15

-10

-5

0

Time[ms]

I t[kA

]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-40-30-20-10

010

I g[kA

turn

]

(a) (b) (c) (d) (e) (f)

RF-ON#10152

0.340ms 0.345ms 0.350ms 0.355ms

0.360ms 0.365ms 0.370ms 0.375ms

(a) (b)

A B C

E FD

3D MHD Simulation of Self-organizing from ST to F-STConfigurations

Spontaneous reversal of not only poloidal but also toroidal flux

The system relaxes to a lower energy state by rearrangingcurrent distribution. The parallel current profile λ becomespeaked.Kink of the central open flux is essential to the self-reversal process.

0

2

4

6

8

10

12

0.2 0.4 0.6 0.8 1.0

λ

r

t=0

t=20

t=80

t=485

t=820

Mgnetic reconnection between the open and closed field.

Y. Kagei et al. PPCF, 45, L17 (2003)

Unique magnetic field lines geometry: Bt: opposite direction, Bp: same direction

Question; Can We Sustain the Flipped ST plasmas in Spite of No Central Open Flux ?

Non-flipped region Flipped region

F-ST is q>1.

q ~ Itf/It >1 Iinj > Itf > It.

No Magnetic Reconnection ?

But, the F-ST is isolated from the electrodes,so can we drive it by helicity injection?

Kink unstable condition: Iinj > Itf

The F-ST configuration is consisted of only closed flux surfaces so that it may have a better confinement quality ! ?

How to produce the dynamo activity ?

It is a key point to make the non-flipped field linesunstable for the kink mode.

Large injection current is required to sustain a large plasma current in the F-ST.

-1.0

-0.5

0.0

0.5

0.0 0.1 0.2 0.3 0.4 0.5

C

R[m]

[kG]

1.730[ms]

-1.0-0.50.00.51.0

0.0 0.1 0.2 0.3 0.4 0.5

B

R[m]

[kG]

1.705[ms]

-1.0

-0.5

0.0

0.5A

R[m]

[kG]

0.0 0.1 0.2 0.3 0.4 0.5

1.680[ms]

Radial Profile(z=74)

FlippedRegionNon-FlippedRegion

BtBzBrVacuumBt

-It

Bt

-It

Bp

Tim e [m s]1 .5 1.6 1.7 1.8 1.9 2.0

0.3

0.0

-0 .2

0.20.1

-0 .1

4020

0-20-40

Tim e [m s]

- 40

- 20

0

20

40# 4 3 0 9

Su stainm en t p haseQui esce nce phaseRe versal phase

S T formation ph ase

0 0 .5 1 .0 1 . 5 2 . 0 2. 5 3 . 0

Sustainment of F-ST Plasmas Driven by Kink Motion of Non-flipped Open Flux

Inboard

Outboard

Time (ms) Drive current

Non-reversed region

We have a plan to drive large flows by CT injection into ST plasmasto explore new helicity-driven two-fluid plasmas.

We have reviewed the MHD dynamo activities and self-organizationphenomena in various helicity-driven cases (ST, Spheromak, Flipped ST,and the transition process between them).

The common basic feature of the dynamo activities is the rotationalkink of the open flux column, which is essential to CHI current drivemechanism.

3D MHD simulation results are in good agreement with theexperimental results and also determined the role of the kink behaviorin dynamo drive.

Local features of reconnection at X-point play an important role in thesustainment of the ST which is in contrast with non-axisymmetric andglobal behavior in the spheromak case.

Summary and Future Plan

Plan: New Experimental Setup for Relaxation Studies of Two Fluid Plasmas

CT injector

High density: 1021-1022 m-3

High speed: 100 – 300 km/sLarge Hall parameter: he=ωceτe ~25

TFtime

Try to produce a diamagnetic low-qtokamak by injection a CT plasma withmagnetic helicity and a high speed ion flow.

Injection of a high energy CT plasma into thetoroidal vacuum chamber with TF coils