Simple Core-SOL-Divertor Model To Investigate Plasma Operation Space Joint Meeting of US-Japan JIFT Workshop on Theory-Based Modeling and Integrated Simulation of Burning Plasma and 21 COE Workshop on Plasma Theory Kyodai-Kaikan, Kyoto, 2003/12/ Central Research Institute of Electric Power Industry (CRIEPI), Tokyo , Japan R.Hiwatari, K.Okano, Y.Asaoka Faculty of Science and Technology, Keio University, Yokohama , Japan Y.Kuzuyama, A.Hatayama, Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, P.R.China S.Zhu National Institute for Fusion Science, Toki , Japan Y.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 operation Core Plasma operation Temperature, density H-mode, RS mode, ELM, etc. Detached condition, He exhaust Impurity seed, MARFE, etc. Consistent ? Plasma performance required to generate net electric power with tokamak reactor[1] R=7.5 m η e =30% In case of To generate P net =1000MW, ≧ 20 keV is required (High and Low operation) Under ≦ 16keV, P net ≧ 500MW is impossible. High operation has a great impact on the divertor condition. Divertor condition Fig1.plasma performance required to generate net electric power High operation required fn GW

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 Plasma Core Plasma 0D core plasma model of ITER physics guidelines[3] Two-point model[4] Output parameter Input parameter Heat flux across the separatrix:q ⊥ Upstream SOL density:n s Heat flux across the separatrix:q ⊥ Particle flux across the separatrix:Γ ⊥ Problem : How to derive the upstream SOL density n s ? To solve the particle balance for the SOL-divertor region (C-S-D model) combine Time dependent model Transport time scale: sec order Steady state model Transport 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] Charge neutrality condition Scaling law of energy confinement time Particle confinement time:τ Pj =C Pj τ E Each definition from ITER physics guidelines LH transition condition[5] When the total input power within the separatrix (P in ) 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. L to H transition case H to L transition case Core Plasma Model

2003/12/16US-Japan JIFT Workshop Two-point model[4] 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 LsLs LdLd Mach number M(z) temperature T(z) density n(z) SOL divertor X-point Divertor plate nsns ndnd nXnX TsTs TdTd M d =1 MXMX Along the field line Z 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 N n including gas puff term N puff Core SOL divertor 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. With this simple neutral model, particle balance of divertor region is considered. Neutral Transport Model [6] ionization rate in the divertor region

2003/12/16US-Japan JIFT Workshop Parallel particle flux: Cross section: A Density n X and Mach number M X 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. Density at X-point 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 P in /P all =0.34. The percentage of the total radiation power to the input power f imp is about 30 % Te nene Fig.4 T e and n e of B2-EIRENE Comparison with B2-EIRENE C-S-D modelB2-EIRENE[5] SOL density n s [m -3 ]1.3×10 19 ~1×10 19 SOL Temp. T s [eV]62.5~55 Div density n d [m -3 ]2.6×10 19 ~3×10 19 Div Temp. T d [eV]15.9~16

2003/12/16US-Japan JIFT Workshop High Recycling Low Recycling Transition to High Recycling State f ion ~1.0 f ion <<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=  div  X JT-60U plasma configuration Total particle and energy flux into SOL region P in and  in

2003/12/16US-Japan JIFT Workshop CaseFat-D ShapeDouble-null R/a (m)1.97/0.5 κ1.6 DivertorOuter&lower τ E (s)0.15 (H-mode) StateHigh Recycling Table 2: HT-7U parameter[7] Application to HT-7U CSD model Input parameters, Q in and  in Divertor heat load is defined as 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  E = f H  E ITER89  in =f(I P )Q in 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 and relationship with LH transition condition are future work.

2003/12/16US-Japan JIFT Workshop n e ~6×10 19 n e ~2×10 19 q d <3.5MW/m 2 q d <5MW/m 2 HT-7U Operational space for LH current driving Fig.?: HT-7U Operational Space Application ot HT-7U There is operational space around 2x10 19 m -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 P fus =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) Application to JT-60U Configuration Accoding 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 n d 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 LHCD and found there is operational space around n e ~2.0x10 19 m -3 We apply to ITER LH transition phase and found there is a possibility 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 (1998)143 [6] M.Sugihara, et al., J.Nucl. Mater (1997)299, N.Hayashi, et al., J. Phys. Soc. Jpn.66(1997)3815. [7]K.Nagashima, et al., JAERI-RESEARCH [8] A.Hatayama, et al., Nucl. Fusion 40(2000)2009, J. Nucl. Mater (2001)407 [9]M.Sugihara, et al., J.Nucl. Mater (1984)114 [10]T.Takizuka, et al., JAERI-RESEARCH [11]K.Tuchiya, et al., Plasma Phys. Control. Fusion 38(1996)1295 [12] private communication with T.Takizuka (2003)