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


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


Contents

• Physical model of C-S-D model

•Comparison with B2-EIRENE results

•Application to HT-7U and ITER

•Summary


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


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


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


•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]


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


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


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.


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.


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


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


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


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.


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.


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)

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

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