Response function and Statistical approach

for particle circulation on QUEST

H. Zushi, A. Kuzmin, I. Takagi1), S.K. Sharma2), M. Hasegawa, M. Kobayashi3), T.

Mutoh3),Y. Hirooka3), K. Hanada, A. Fujisawa, H. Idei, K. Nakamura, Y. Nagashima,

T. Onchi, N. Yoshida, S. Kubo3), S. Ide4), N. Ohno5), A. Hatayama6)

Research Institute for Applied Mechanics, Kyushu University, Kasuga, 816-8580, Japan 1) Kyoto University, 2) IPR India, 3)National Institute for Fusion Science (NIFS), Gifu, Japan,4) Japan Atomic Energy Agency (JAEA), Ibaraki,5) Nagoya University, 6) Keio University

8th IAEA Technical Meeting on Steady State Operation of

Magnetic Fusion Devices,26-29 May 2015 Nara, Japan

Related presentations

1) Invited talk by Hanada(on 29 May)

2) Poster presentation by Kuzmin(on 27 May)

3) Poster presentation by Hasegawa (on 27 May)

Acknowledgements; S24226020,NIFS13KUTR085,NIFS14KOAR017

Gas balance Analysis in Plasma

2

wrelretwplasmagas

pump

TtqtqANtQP

dt

dP)()()(

a) Langmuir experiment

b) After EBT steady plasma

(104 sec)

DP

DP

c) Retention rate in JET

d) Release rate after termination

JNM2013

NF2013

JNM1981

JNM1980

P(t)

qret(t)

QUEST AFRC

1) PdCu Plasma driven

permeation probe

QUEST and New diagnostics for (qret,qrel)

3

2) He partial pressure

in H-plasma

Monitor the release process

Deduce the retention flux

+ TMAP7

(He shots one week ago)

slab PlasmaTokamak

w/ natural divertor

SUS316 + W coated one (100°C)

QUEST AFRC

8th IAEA TM on SSO

CONTENTS

1) Externally controlled perturbation

methods in ECR plasmas

• Time response function to Gas fueling

• Frequency response function to interaction

region

2) Statistical approach in SSTO plasma

3) Summary

4

1-1) Perturbation of source term

2) Pressure response function in ECR plasma

relHegasHe

retincgasinc

HgasH

plasmawrelretwgas

pump

qdtQtP

qdtQt

dtQtP

NTtqtqAtQP

dt

dP

;)()()(

;)()()(

)()()(

)()()(

22

Understanding of retention and release processes induced by inc and He5

1) Perturbation of Qgas(t) in vacuum

QUEST AFRC

sTHatomsQ

tnTUnTtUQtQgas

1.0sec,405;106.1~

)()()(

20

0

0

D

D

)(tQP

dt

dpgas

pump

Long tail

(release as t-1.1)

1-1-1)Time response function of PH2

In Plasma

In Vacuum

・PH2 in vacuum

・ PH2 in Plasma

Pumping

(2.3 sec)

6

5sec

10sec

40sec

20sec

5sec

10sec

40sec

20sec

QUEST AFRC

Additional Pumping

(4.3 sec)

•Faster decay and higher base pressure

8th IAEA TM on SSO

1-1-2)Gas balance eq. in ECR Plasma

7

RR,RD,DD + trappingmodels

JET & others

Release rate t-0.73

11

1

3432 .gas

pump t

%L

sec.

P)t(Q

sec).(

P

dt

dp

5.0)( tt1.1)( tt

5.1)( tt

QUEST AFRC

),0(),0(2

0

tCKHDtx Hru

x

inc

x

C

1-1-3) Direct measurement of Retention flux

8

QUEST AFRC

PDP Flux

Retention

Flux

fgas=25mHz

32~

D

inc

inc

%10~pdp

pdp

D

Details; Poster by Kuzmin

1-1-4)Response function for retention flux

)exp()(

)()()(

3

pump

t

gasinc

ttt

dQtt

9

T=5,10,20,40secD0.4 sec

11

1

3432 .gas

pump t

%L

sec.

P)t(Q

sec).(

P

dt

dp

~ 7sec

QUEST AFRC

8th IAEA TM on SSO 10

QUEST AFRC

1-1-5) Response function for He pressure

a)

b)

c)

11

1

3432 .gas

pump t

%L

sec.

P)t(Q

sec).(

P

dt

dp

Long Sustainement of He may

be consistent with a long tail

Observations at various fgas

mHzfmplatemR

AwallsideAplatesbottomtopACSA

NTtqtqAtQP

dt

dP

PWI

wwww

plasma

i

wi

reli

reti

wi

gas

pump

33at )8.02.0 (54.029.0

;....., ;, /;,;

)()()(

3210

D

1-2) Perturbation in Ai (interaction region)

2) ECR plasma - Plates interaction was perturbed by sweeping the resonance layer

11

1) Plasma effects include contributions from various PWI regions

QUEST AFRC

PH2 complicated modulation

Is(R,t)

vacuuminPfS

fSfHfS

fSfHfS

HQgasQgas

QgasQgasHeQgasHe

QgasQgasHQgasH

puff :)(

);()()(

);()()(

2

22

1-2-2) Perturbation in Ai (interaction region)1) Frequency response function in ECR plasma by sweeping the resonance layer

12

QUEST AFRC

• Both H(H2) and H(He) shows release components at fPWI=33mHz.

• LF(f<33 mHz) contibutes to a slow gradual rise in both PH2 and PHe

2) In tokamak plasma uncontrable growth

in PH2,PHe,pdp at constant fgas=0.3 Hz

13

1) Both H2 & He response function changes in time,which are affected by enhanced wall release process.2) Both release and retention are enhanced.3) Plasma parameters(SOL /near wall) fluctuate

Puff at every 3s

<PH2>

<PHe>

QUEST AFRC

t

t

)T(f)t(Q

stochastic:)t(

)t()t(P)t(Q)t(P

dt

)t(dP

ervalintgas

gas

pump

events

2-2) Variable Puff interval pattern indicates

"wall recycling state"

14

1) Puff time pattern relates with plasma self-perturbations

QUEST AFRC

Details; Poster by Hasegawa

No puff after 500sec

300 600 sec

Ha

PH2

PHe

2-3)Puff interval vs Release & recycling

Middle phase of discharge End phase of discharge

Although the same amount of H2 is injected, Ha and PH2 are progressed in discharge.He is immediately released from the walls, then decays. 15

QUEST AFRC

2-4 Probability function of Tinterval and

temporal evolution

16

)exp(2

exp)(

)(

/21

1

NCNN

F

dCNNf

tFNNgNddt

dN

Fg

a

0) Response function=> d(NL pumping),g(L release), Q(stochastic force)

1) Steady state pdf

2) Time dependent FP eq.

PDF for steady state FP eq.

QUEST AFRC

Summary• Under controlled perturvation in ECRDC plasmas

response functions are experimentally determined.

1) Fast decay after puff and higher base level in PH2 can

be interpreted by additional wall pumping(0.5xpumps)

and a long tail

2) Contribution of interaction regions to release process

can be decided by position scan

• In tokamak operation "puff interval pattern" is analysed

to study self-growing perturvations in recycling.

17

5/26/2015 8th IAEA TM on SSO

SSTO in QUEST

19

Retention flux

Ha

nl

Temp @ div. plate

PH2

AG below plate

Ptotal at TMPIp

Middle phase of discharge

End phase of discharge

Negative response function evolves

during the SSTO plasma

20

plasmaretrelHout

pump

HH

rr

HH

H

NtqtqtqqtP

dt

tdP

dtqtP

tnTUnTtUqtq

)()()()()(

)exp(,)exp()()(

)()()(

.

222

280

22

02

D

Net negative term

plasmaretrelHout

pump

HH

r

HH

H

NtqtqtqqtP

dt

tdP

dtqtP

tnTUnTtUqtq

)()()()()(

,)exp()()(

)()()(

222

2

022

02

D

2-2)Negative response function is required

to reproduce the H2 perturbations

under the retention dominant conditions

Net negative term21

T=3 sec, D=0.2sec

Response function For He release from walls

Time evolution of the response function

for released He in SSTO H-plasma

22

D

dtqtP

tnTUnTtUqtq

r

HHe

H

)exp()()(

)()()(

2

02

Response function is Characterized by Fast rise and quick decay

Transition from High to Low Recycling

in SSTO w/well conditioned walls H2

HeHa

Phe is used to monitor the release flux from the wallsThis behavior depends on the discharge history

Before the apparent wall saturation

23

4) Rotation sustainmentCo-current toroidal (20km/s)&

ion diamagnetic poloidal (1km/s)flows

Fully NI plasma sustained by FB control

of recycling flux

Two shots (for rotation measurements) are presented.

Puff width(amount of H2) is fixed, the repetition frequency is FB controlled

to keep Ha constant24

Global gas balance in SSTO

25

Transition from High to Low Recycling

in SSTO w/well conditioned walls

H2

He

Ha

Phe is used to monitor the release flux from the wallsThis behavior depends on the discharge history

Before the apparent wall saturation

26

Stochastic Differential EquationSDE

221

21

2

211

,

02

1),(

),()()(

xFFdt

dxVNLxLx

dt

dxM

fdt

dx

xf

dt

dx

xt

txf

txtxNLxLdt

tdx

n

n

(s)

s

,exp2

exp)( 11/2xxx

nF

NLCxxf

snFLst

27

Stationary pdf f(n): gamma distribution is a plausible pdf

Fd<; amplitude of stochasiticity

1) Quasi Steady ECR Plasmas

(release dominant)

28

Ha

nl

PH2

Is(Top plate)

PH2

Ha

nl

ECR plasma

Wall release dominant conditionPuff at every 40 sec

Wall retention dominant conditionPuff is controlled to keep Ha const.

Vacuum

QUEST AFRC

plasmaretrelHout

pump

HH

out

r

HH

H

NtqtqtqqtP

dt

tdP

constq

dtqtP

tnTUnTtUqtq

)()()()()(

.

,)exp()()(

)()()(

.

222

5122

02

1

D

29

Vacuum(p=2.3sec

Plasma

1-2) Response functions of H2 pressure

w/ and w/o ECR-plasma

(T=40sec, D0.7 sec)

(=2.3sec in vacuum0.57 sec in ECR plasma)

Vacuum

Net positive term

Plasma

QUEST AFRC

2) Response functions of H2 pressure

w/ and w/o SSTO-plasma

(Retention dominant condition)

Symbols: measured data pointsLines: calculations from response functions

Small response of H2 for the same puff as that in vacuum

H2 is severely retained into the walls under the well wall-conditioned SSTO plasma

Vacuum(p=2.3sec

30

31

2) Quasi Steady ECR Plasmas

(retention dominant condition) QUEST AFRC

Vacuum