Federici, G.

Gribov, Y.

Horton, L.

Loarte, A.

Polevoi, A.

Portone, A.

Shimada, M.

Tanga, A.

Zolotukhin, O.

English

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Simulations of ITER Plasma Limiter Start-Up Conditions

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Simulations of ITER Plasma Limiter Start-Up Conditions O. Zolotukhin1, G. Federici1, A. Tanga1, A. Loarte2, L. Horton3, A. Portone2, Y. Gribov4, A. Polevoi4, M. Shimada4 1 ITER Garching JWS, Boltzmannstraße 2, 85748 Garching, Germany 2 EFDA-CSU Garching, Boltzmannstr. 2, D-85748 Garching, Germany 3 Max-Planck-Institut für Plasmaphysik, Boltzmannstraße 2, 85748 Garching, Germany 4 ITER JWS Naka Co-centre, 801-1 Mukouyama,Naka-machi,Naka-gun,Ibaraki-ken,Japan 1. Introduction. Analysis of the current ramp-up phase of plasma discharges in ITER is an important part of the design. Among other things, good accuracy is required to determine the fraction of power flowing to the plasma boundary and intercepted by the start-up limiter(s), and the resulting heat flux distribution, throughout the limiter phase of the discharge, for all anticipated limiter start-up scenarios. This paper summarizes the results of a recent modeling effort conducted with the plasma transport code ASTRA to simulate typical limiter start-up sequences proposed for ITER. 2. Transport model. This study was conducted by using the plasma transport code ASTRA [1] which is a 1.5-dimensional time dependent simulation code that comprises of a system of 1-D diffusion equations for densities and temperatures of ions and electrons, a 2-D equilibrium equation, and, a variety of other modules to describe additional heating, current drive and other non-diffusive processes in tokamak plasmas. The heat transport of electrons and ions is evaluated assuming that the properties of the plasma confinement during the current ramp-up are close to those during the steady state ohmic discharges. Several calibration runs were performed by using either one of the Ohmic ( )( )22][][1.1 ][,, 63.0114.0 GextorGexmmTtorOhmicE nnkBnnkaRB ⋅+⋅⋅⋅⋅⋅=τ  or L-mode 5.0][5.02.0][1.0]10[5.03.0][2.1][85.0][,89, 320048.0−⋅⋅⋅⋅⋅⋅⋅⋅=− MWiTmxmmMApLE PABnkaRIτ  energy confinement scalings [2] or a combination of them according to the formulation recommended by Shimomura-Odajima [3] in cases with additional heating. In these models, the electron heat flux and the ion heat flux depend only on their own respective temperature gradients. The values of the heat conductivities have been derived from the knowledge of the plasma cross section. The ion transport is assumed to be purely neoclassical. The particle transport is governed by the Ware pinch and by a diffusion coefficient proportional to the ion and electron heat transport coefficients with ( )ieD χχ +⋅= 2.0 . For simulation of ITER ramp-up, gas puffing was adjusted to keep a volume-averaged electron density at the level a Greenwald limit fraction Ge nn . 33rd EPS Conference on Plasma Phys. Rome, 19 - 23 June 2006 ECA Vol.30I, P-1.120  (2006)It is supposed that the main ions are deuterium and tritium ions ( TD nn = ) and the impurity concentration (in our case, ions of beryllium and carbon) is proportional to the plasma density, i.e., the fraction of impurity species k in the plasma, ekk nnf =  was assumed to be a constant. For the calculations discussed here, the concentration of impurities has been fitted to provide the experimentally measured effective charge effZ  in the range 2-3.The radiated power profile is calculated in a coronal approximation. The effect of the finite residence time of impurities on the radiation in the plasma, which enhances radiation compared to the corona model, was taken in account by using of a normalization factor to provide the global value in agreement with the empirical scaling described in Refs. [4,5], which gives a reasonable match (within a factor of 2.5) of the experimental  results of JET and ASDEX Upgrade. The total radiation losses are described in the form synchrbremsscoronaradcoronaradradnoncorrad PPPPPCP ++⋅⋅= /exp, , where parameter noncorC  variation from noncorC  = 2.5 for low densities n ~ 1019 m-3 to noncorC  = 1 for moderate densities n ~ 2.5 1019 m-3 is required to fit the experimental data Prad,exp by experimental scaling dependence ( )110 23exp, −⋅⋅⋅= − effeplrad ZnAP . Here plA  is plasma surface area in m2, en  is line-averaged electron density in 1019m-3. As one can see a range of uncertainty in the applied model is determined by the numerical coefficient 1-2.5 (Figure 2). 3. A validation of the model against experimental data. The model has been first calibrated against two well diagnosed standard ohmic limiter discharges in existing tokamaks (i.e., JET: shot  # 27884 with 7 MA, and ASDEX Upgrade: shot # 11492 with ~1 MA).  Details of these simulations are discussed elsewhere [7, 8]. Here, we show only some selected results for the JET case (Figs 1 and 2). In the Fig.1a-d radial profiles of electron and ion temperatures as well as electron density are presented for the JET case at t=45s and t=49s .  Fig.2 shows time evolution of the ohmic power ΩP , average electron temperature eT  and radiation power RADP  in comparison with the experiment. Although, preliminary results for global parameters at the final phase of the current ramp-up look satisfactorily, the applied model need to be developed further to include effects of radial impurity distribution on plasma density and radiation profiles and provide betted fit to the low density range. It is also necessary to validate the model vs the JET data with radiative catastrophic behavior.  33rd EPS 2006; O.Zolotukhin et al. : Simulations of ITER Plasma Limiter Start-Up Conditions 2 of 40123450 0,4 0,8 1,2a, mT, keV a) 0123450 0,4 0,8 1,2a, mT, keV b) 012340 0,4 0,8 1,2a, mne, 1019 m-3 c) 012340 0,4 0,8 1,2a, mne, 1019 m-3 d) Fig.1. Electron (red) and ion temperature (blue) and electron density radial profiles (solid curves) for the JET case in comparison with experimental results (×) for t=45 s (a, c)and t=49 s (b, d). Transport model here is based on L-89 scaling. 02468P OH, MW a) 0246T e, keV b) 01242 44 46 48 50Time, sP rad, MW c) Fig.2. Comparison of time histories of experimental (red ×’s) and calculated values (solid) for ohmic power (a), average electron temperature (b), radiated power (c). Transport model here is based on L-89 scaling.  4. ITER limiter star-up simulations. The transport model has been applied to simulate limiter start-up in ITER for the reference start-up scenario 2 (15 MA inductive scenario, fusion power 500 MW and Q=10) [6]. It was found that for the ramp-up at relatively low plasma density (e.g., Gnn ~0.2, i.e., <1x1019 m-3, which is about a factor of 2 lower than in current experiments), the power to the limiter is moderate (ø3 MW). Operating at this very low density causes problems in present experiments (e.g., onset of slideway / runaway effects, lock-modes, runaway erosion effects), but it is not completely clear what are the risks 33rd EPS 2006; O.Zolotukhin et al. : Simulations of ITER Plasma Limiter Start-Up Conditions 3 of 4arising for ITER. A sensitivity study with respect to density, impurity concentration and the level of auxiliary heating to study the physics trade-off issues and explore possible ranges of parameters and window of operation has been carried out. In all simulations the most optimistic value noncorC  = 1 is suggested. The results of these runs are compared in Table, where maximal values of ΩP , RADP , total power to the limiter LP  are presented for both L-89 and ohmic scaling transport model (L89/ohmic) to show reliable “error bars” for the applied model. It is seen that the predictions are close, however, ohmic scaling gives somewhat lower confinement. Supplementary heating early during the limited discharge is required to avoid radiation collapse, which is predicted by our modeling at higher densities (e.g., 0.4-0.5Gn ) due to the strong contribution of ( )110 23exp, −⋅⋅⋅= − effeplrad ZnAP  term. The power to the limiter for the cases analyzed could increase up to <4 MW. Taking into account the observed difference of the model predictions we assume a factor of 2.5 uncertainty in the present estimates. In this case the upper bound of LP should be about 6 MW. ne/nG Zeff Paux,MW PΩ,max,MW Prad,mx,MW PL,max,MW trun, s 0.2 2 0 3.1/3.3 0.5/0.5 2.4/2.6 >tramp-up 0.2 3 0 3.6/3.9 0.9/0.9 2.5/2.8 >tramp-up 0.3 2 0 4.1/4.3 1.1/1.1 2.9/3.1 >tramp-upp 0.3 3 0 4.8/5.0 1.9/1.9 2.6/2.9 >tramp-up 0.4 2 0 4.9/5.2 1.8/1.9 2.8/3.1 ø50/tramp-up 0.4 3 0 5.6/6.0 3.3/3.3 2.1/2.5 ø30/50 0.4 2 ø10 4.8/- 1.8/- 2.9/- >tramp-up 0.4 3 ø10 5.2/5.6 3.2/3.4 2.5/2.8 >tramp-up 0.5 2 0 4.3/5.3 2.4/2.6 1.4/2.5 ø20/27 0.5 3 0 3.7/4.7 2.4/3.2 1.1/1.3 ø15/20 0.5 2 ø10 4.5/5.8 3.3/3.3 3.3/2.9 >tramp-up 0.5 3 ø10 4.1/4.9 4.5/3.8 1.5/1.4 ø17/23 References. 1. G.V.Pereverzev, P.N.Yushmanov, IPP Report, IPP 5/98, February 2002 2. G.Bracco, K.Thomsen, Nucl.Fusion 37 (1997), p.759. 3. Y.Shimomura, K.Odajima, Comm.Plasma Phys.Contr.Fusion,10,No.5(1987), p.207. 4. S.K.Erents, et al., Nucl.Fusion 28 7 (1988), p.1209. 5. K.Behringer, et al., in Plasma Phys. and Contr.Nucl.Fusion Res.1986,vol.1,IAEA,Vienna(1987),p.197. 6. CSD, Appendix B, N 19 RI 14 R0.1, Aug.2004. 7. G.Federici, et al., 17th PSI Conf., Hefei (2006) 8. G. Federici, et al., Simulations of ITER start-up for limiter power load assessment, ITER document ITER_D_2229DE v1, Jan. 2006, to be submitted to Plasma Phys. and Contr. Fus. 33rd EPS 2006; O.Zolotukhin et al. : Simulations of ITER Plasma Limiter Start-Up Conditions 4 of 4

Simulations of ITER Plasma Limiter Start-Up Conditions

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