Simple Core-SOL-Divertor Model To Investigate Plasma Operation Space Joint Meeting of US-Japan JIFT...

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Simple Core-SOL-Divertor Mo del To Investigate Plasma O peration Space Joint Meeting of US-Japan JIFT Workshop on Theory-Based Modeling and Integrated Simulation o f Burning Plasma and 21 COE Workshop on Plasma Theory Kyodai-Kaikan, Kyoto, 2003/12/15-17 . esearch Institute of Electric Power Industry (CRIEPI), Tokyo 201-85 i, K.Okano, Y.Asaoka f Science and Technology, Keio University, Yokohama 223-8511, Japan a, A.Hatayama, of Plasma Physics, Chinese Academy of Sciences, Hefei, P.R.China Institute for Fusion Science, Toki 509-5292, Japan

Transcript of Simple Core-SOL-Divertor Model To Investigate Plasma Operation Space Joint Meeting of US-Japan JIFT...

Simple Core-SOL-Divertor Model To Investigate Plasma Operation Space

Joint Meeting of US-Japan JIFT Workshop onTheory-Based Modeling and Integrated Simulation of Burning Plasma

and 21 COE Workshop on Plasma Theory

Kyodai-Kaikan, Kyoto, 2003/12/15-17

. Central Research Institute of Electric Power Industry (CRIEPI), Tokyo 201-8511, JapanR.Hiwatari, K.Okano, Y.Asaoka Faculty of Science and Technology, Keio University, Yokohama 223-8511, JapanY.Kuzuyama, A.Hatayama,Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, P.R.ChinaS.ZhuNational Institute for Fusion Science, Toki 509-5292, JapanY.Tomita

2003/12/16US-Japan JIFT Workshop

Motivation

A simple Core-SOL-Divertor model is useful to analyze the broad region of plasma parameter and the consistency between core and SOL-divertor.

Consistent ?One of the problem toward the fusion power plant

SOL-Divertor Plasma operationCore Plasma operationTemperature <T>, density <ne>H-mode, RS mode, ELM, etc.

Detached condition, He exhaustImpurity seed, MARFE, etc.

Consistent ?

Plasma performance required to generate net electric power with tokamak reactor[1]

R=7.5 mηe=30%

In case of 0.1nGWf•To generate Pnet=1000MW, <T> 20 keV is required≧(High <T> and Low <ne> operation)•Under <T> 16keV, P≦ net 500MW is impossible.≧•High <T> operation has a great impact on the divertor condition.

Divertor condition

Fig1.plasma performance required to generate net electric power

High <T> operation

required fnGW

2003/12/16US-Japan JIFT Workshop

To develop the core-SOL-divertor model (C-S-D model) to investigate core and SOL-divertor plasma operational space.

Concept of the C-S-D model[2]

SOL-Divertor PlasmaCore Plasma0D core plasma model ofITER physics guidelines[3]

Two-point model[4]

Output parameter Input parameter

•Heat flux across the separatrix:q⊥•Upstream SOL density:ns

•Heat flux across the separatrix:q⊥

•Particle flux across the separatrix:Γ⊥

Problem : How to derive the upstream SOL density ns ?

•To solve the particle balance for the SOL-divertor region (C-S-D model)

combine

Time dependent modelTransport time scale: sec order

Steady state modelTransport time scale: msec order

Because of the difference of transport time scale, the steady state SOL-divertor transport model is applicable to the time-dependent core transport model .

Objectives

2003/12/16US-Japan JIFT Workshop

Contents

• Physical model of C-S-D model

•Comparison with B2-EIRENE results

•Application to HT-7U and ITER

•Summary

2003/12/16US-Japan JIFT Workshop

0D plasma model based on ITER physics guidelines[3]

),( HeejSn

dt

dn

PPPPPW

dt

dW

jpj

jj

syncBradauxOHE

pp

Charge neutrality conditionScaling law of energy confinement timeParticle confinement time:τPj=CPjτE

Each definition from ITER physics guidelines

LH transition condition[5]

When the total input power within the separatrix (Pin) becomes larger than LH threshold power (P

thr), L to H transition occurs.When the total input power becomes smaller than the half of the LH threshold power, H to L transition occurs.

syncBradauxOHin

tthr

PPPPPPaRnBMP

76.023.177.020

92.0176.2

thrin PP thrin PP2

1

L to H transition case H to L transition case

Core Plasma Model

2003/12/16US-Japan JIFT Workshop

Two-point model[4]

dddssdivmom

divmom TnMTnfzTznzMf 22 1111

•momentum balance in SOL-divertor region

•global energy balance in SOL-divertor region

•radial energy transport in SOL region

•electron thermal transport along the field lines

•Constant temperature in SOL region•Include convection in the electron thermal transport

dddsddsimp TMhTCMnqLf 2'12

7

sssX

sss

dd LTC

MTn

T

TTqL

24

51

49

4

2

12/7

2/702

q

Tn ss2

5

Ls Ld

Mach number M(z)

temperature T(z)

density n(z)

SOL divertor

X-pointDivertor plate

ns

ndnX

TsTd

Md=1MX

Along the field line

Z0

0

0

Fig.2 The basic features of density, temperature, and Mach number in the SOL-divertor region.

SOL-Divertor Model

Relationship among the density and temperature of SOL and divertor regions

2003/12/16US-Japan JIFT Workshop

All neutral particle source rate at the edge region Nn including gas puff term Npuff

puffndsddn NRhTCMnN sin2

Core

SOL divertor

corenS

divnSSOL

nS

core

div||

exhaust

Neutral particle source rate at the divertor region is proportional to the particle flux to the divertor plate.

Fig.3 The model of steady state particle balance.

n

divion

SOLion

coren

ndivion

SOLion

SOLn

ndivion

divn

NffSNffS

NfS

111

With this simple neutral model, particle balance of divertor region is considered.

Neutral Transport Model[6]

sin1 expdiv d

ion divion

Lf

div nion

d

v

n v

•ionization rate in the divertor region

2003/12/16US-Japan JIFT Workshop

•Parallel particle flux:

•Cross section: A ndiv

iondivn

XXdivdiv NfSAA |||| zTCzMznz s||

Density nX and Mach number MX at X-point are required to solve divertor particle balance

Particle balance of Divertor Region

Density at X-point is estimated with the SOL upstream and divertor density.

2dsX nnn

Density at X-point

SOL

nplcores

Xddd

divmom

X

X SAe

mT

ATnM

f

M

M

22 1

1

1

Mach number at X-point is derived from the SOL particle balance and momentum balance

Mach number at X-point[7]

2003/12/16US-Japan JIFT Workshop

JT-60U simulation result for attached state [8]

•We focus on the inner divertor.•The fraction of the power entering inner SOL across the separatrix to the total power is Pin/Pall =0.34.•The percentage of the total radiation power to the input power fimp is about 30 %

Te

ne

Fig.4 Te and ne of B2-EIRENE

Comparison with B2-EIRENE

C-S-D model B2-EIRENE[5]

SOL density ns [m-3] 1.3×1019 ~1×1019

SOL Temp. Ts [eV] 62.5 ~55

Div density nd [m-3] 2.6×1019 ~3×1019

Div Temp. Td [eV] 15.9 ~16

2003/12/16US-Japan JIFT Workshop

HighRecycling

LowRecycling

Transition to High Recycling State

fion~1.0fion<<1.0

Transition from low recycling state to high recycling state is theoretically predicted[9] and also observed in the experiments[10]

This C-S-D model can reproduce the transition phenomena from low recycling to high recycling.

•Particle flux multiplication factor R=divX

•JT-60U plasma configuration•Total particle and energy flux into SOL region Pin and in

2003/12/16US-Japan JIFT Workshop

Case Fat-D

Shape Double-null

R/a (m) 1.97/0.5

κ 1.6

Divertor Outer&lower

τE (s) 0.15 (H-mode)

State High Recycling

Table 2: HT-7U parameter[7]

Application to HT-7U

•CSD model•Input parameters, Qin and in

•Divertor heat load is defined as ( ) sin sind B d d d sdq k T n M C

Divertor heat load for HT-7U

In the first phase of HT-7U project, current drive will be carried out by LH current drive and low density is preferable, but heat load to the divertor has to be decreased with high recycling state.

2003/12/16US-Japan JIFT Workshop

Application to HT-7U

*

*20

0.122

lne

p LHCD

T jI P

Rn p

3

2in e B e E oh LHCD ICRF

in e p p

Q n k T P P P

n V

E= fHEITER89

in=f(IP)Qin

LH current driving property for HT-7U

Preliminary result: heating power is restricted to ~3.5MW by LH heating

Linear relationship is obtained

Operation mode with other heating method andrelationship with LH transition condition are future work.

2003/12/16US-Japan JIFT Workshop

ne~6×1019

ne~2×1019

qd<3.5MW/m2

qd<5MW/m2

HT-7U Operational space for LH current driving

Fig.?: HT-7U Operational Space

Application ot HT-7U

There is operational space around 2x1019m-3

2003/12/16US-Japan JIFT Workshop

Time evolution of ITER plasma parameters

•Plasma parameters at t=250 sec are almost the same as the reference parameters of ITER inductive operation scenario for the fusion power Pfus=400 MW case.•At t=100 sec, plasma parameters are also similar to the reference parameters of ITER.•Density increases at t=95 sec.•Auxiliary heating is added at t=100 sec.•LH transition occurs at t=104 sec.

Fig8. reference scenario of ITER inductive operation[7].Fig.7 ITER LH transition phase by C-S-D model

Application to ITER LH Transition

2003/12/16US-Japan JIFT Workshop

Application to ITER LH Transition

•Divertor density oscillates around LH transition.•Is there any effect on the divertor operation ?•Good effect or bad effect ?

Is such divertor density oscillation observed at present ?

•Not yet install the detached plasma effect into two-point model•Calibrate particle confinement time to reproduce the design parameter of upstream SOL density at the steady state.

SOL-Divertor parameters

Calculation conditions

2003/12/16US-Japan JIFT Workshop

Time (sec)

Time (sec)

Time (sec)

Time (sec)

tJTth BnnP 5.0

1919

60 4.12.0

Application to JT-60U ConfigurationAccoding to H data, divertor density doesn’t oscillate[12]

Same calculation with JT-60U

•Plasma configuration. Bt=2.5 T, q95=4.0 Ip=1.2MA, k=1.5•LH threshold power is based on the experimental data[11] (parameter region: Ip = 0.9 ~ 2.4MA , B t= 1.5 ~ 4.0T)

Divertor density not oscillates but decreases.Consistent with experimental observation.

In the ITER, there is a possibility to observe nd oscillation.Further investigation is required.

2003/12/16US-Japan JIFT Workshop

Summary

•We developed a simple Core-SOL-Divertor (C-S-D) model

•The comparison with B2-EIRENE is carried out and the result

from CSD model looks good.

•We apply this C-S-D model to HT-7U operation space for LHC

D and found there is operational space around ne~2.0x1019 m-3

•We apply to ITER LH transition phase and found there is a possi

bility to oscillate the divertor density.

2003/12/16US-Japan JIFT Workshop

Reference[1]R.Hiwatari, et.al., Plasma Performance Required for a Tokamak Reactor to Generate Net Electric Power, J.Plasma Fusion Res. 78(2002)991, R.Hiwatari, et.al., To generate net electric power with a tokamak reactor under the foreseeable physical and engineering conditions, Nucl. Fusion, in press.

[2]R.Hiwatari et al., “Simple-Core-SOL-Divertor Model TO Imvestigate Plasma Operational Space”, Contrib. Submitted to Contrib. Plasma Phys.

[3]N.Uckan and ITER Physics Group, ITER Physics Design Guidelines:1989

[4] K.Borass, Nucl. Fusion 31(1991)1035, N.Hayashi, et al., J. Phys. Soc. Jpn. 66(1997)3815.

[5]ITER Physics Expert Groups, ITER Physics Basis Editors, Nucl. Fusion 39(1999)2175, T.Yamamoto, et al., Fusion Eng. Des. 39-40(1998)143

[6] M.Sugihara, et al., J.Nucl. Mater. 241-243(1997)299, N.Hayashi, et al., J. Phys. Soc. Jpn.66(1997)3815.

[7]K.Nagashima, et al., JAERI-RESEARCH-95-52 1995

[8] A.Hatayama, et al., Nucl. Fusion 40(2000)2009, J. Nucl. Mater. 290-293(2001)407

[9]M.Sugihara, et al., J.Nucl. Mater. 128-129(1984)114

[10]T.Takizuka, et al., JAERI-RESEARCH2003-010 2003

[11]K.Tuchiya, et al., Plasma Phys. Control. Fusion 38(1996)1295

[12] private communication with T.Takizuka (2003)