1. 1 SIMULATION OF ANOMALOUS PINCH EFFECT ON IMPURITY ACCUMULATION IN ITER

2. 2 Introduction Description of the model Influence of anomalous pinch of the bulk plasma (effect of the bulk plasma density profile peaking) Effect of the anomalous impurity pinch Conclusions RUSSIAN RESEARCH CENTRE «KURCHATOV INSTITUTE» NUCLEAR FUSION INSTITUTE 9th ITPA CDB&M TG Meeting 3-6 Oct.2005, St.Perersburg, Russia (V. Leonov, V.Zhogolev )

3. 3 As it has been shown in the paper [1], using of only neoclassical pinch of the bulk plasma and impurities together with anomalous diffusion gives flat profiles of the impurities. [1] V.Leonov, V.Zhogolev: Simulation of high-Z impurity behavior for ITER operational scenarios using the ZIMPUR impurity code” PPCF 47 (2005) 903. RUSSIAN RESEARCH CENTRE «KURCHATOV INSTITUTE» NUCLEAR FUSION INSTITUTE anomalous Ar diffusionneoclassical + anomalous Neoclassical thermodiffusion at flat bulk density profile helps to prevent impurities accumulation in the plasma core 9th ITPA CDB&M TG Meeting 3-6 Oct.2005, St.Perersburg, Russia (V. Leonov, V.Zhogolev )

4. 4 RUSSIAN RESEARCH CENTRE «KURCHATOV INSTITUTE» NUCLEAR FUSION INSTITUTE 9th ITPA CDB&M TG Meeting 3-6 Oct.2005, St.Perersburg, Russia (V. Leonov, V.Zhogolev )

5. 5 RUSSIAN RESEARCH CENTRE «KURCHATOV INSTITUTE» NUCLEAR FUSION INSTITUTE 9th ITPA CDB&M TG Meeting 3-6 Oct.2005, St.Perersburg, Russia (V. Leonov, V.Zhogolev ) Transport model: 1.5D ASTRA transport code for the description of the bulk plasma (2D equilibrium + 1D transport) ZIMPUR code for the modeling of transport and radiation of impurities (considers all impurity ions) NCLASS code for simulation of the neoclassical impurity fluxes (for arbitrary aspect ratio and collisionality) 

6. 6 RUSSIAN RESEARCH CENTRE «KURCHATOV INSTITUTE» NUCLEAR FUSION INSTITUTE 9th ITPA CDB&M TG Meeting 3-6 Oct.2005, St.Perersburg, Russia (V. Leonov, V.Zhogolev ) In simulations we use artificial transport coefficients with parabolic radial dependence  i,e = D e =  i,e,o. (1 + 3.  n 2 ). F H-mode +  i neo,  io = 2  eo, D eo =  eo In the region of the H-mode external transport barrier (  n > 0.92) transport coefficients of the main plasma have been reduced to the ion neoclassical heat diffusivity level (F H-mode = 0). The normalization coefficient  eo was fitted to obtain  E =   scaling H-98(y2) As the boundary conditions for the bulk plasma we use approximations on the basis of B2-Eirine results. Bulk plasma density is controlled by the gas puff (kinetic approach). Thermalized helium pumping speed on the boundary was fitted to produce   He /  E = 3.

7. 7 RUSSIAN RESEARCH CENTRE «KURCHATOV INSTITUTE» NUCLEAR FUSION INSTITUTE 9th ITPA CDB&M TG Meeting 3-6 Oct.2005, St.Perersburg, Russia (V. Leonov, V.Zhogolev ) Radial components of impurity ion fluxes was written as:  s k = - D an  n k /   - V p an n k +  k nc The relation between impurity ion fluxes  k x and ion densities n k x was used as the boundary condition:  k x = V  n k x (at  n =  max = 1) The value V  is equal to the velocity of the bulk plasma electrons. The impurity source was defined as the impurity neutral flux on the plasma boundary, which was fitted to produce the desirable impurity concentration in plasma (for example: which gives the necessary level of the total radiated power).

8. 8 RUSSIAN RESEARCH CENTRE «KURCHATOV INSTITUTE» NUCLEAR FUSION INSTITUTE The bulk plasma ion concentration was determined from a quasi-neutrality condition taking into account the densities of electrons, of all impurity ions and helium. For the description of anomalous pinch velocity we use the relation: V p an = k p. D an. (  /a 2 ) and we can scan it by changing the normalization coefficient k p For the description of density profiles shape we use the profile picking factor: f n = n(0) / ; - volume averaged density 9th ITPA CDB&M TG Meeting 3-6 Oct.2005, St.Perersburg, Russia (V. Leonov, V.Zhogolev )

9. 9 RUSSIAN RESEARCH CENTRE «KURCHATOV INSTITUTE» NUCLEAR FUSION INSTITUTE 9th ITPA CDB&M TG Meeting 3-6 Oct.2005, St.Perersburg, Russia (V. Leonov, V.Zhogolev ) Investigations have been done for the basic inductive ITER scenario with plasma current I p = 15 MA, average plasma density n e  10.1. 10 19 m -3 and fusion power P fus  400 MW. We consider two tasks: 1) To test the transformation of radial profiles of different impurities (Ar, Be, He) and bulk plasma density profiles at the variation of the anomalous pinch velocity value. 2) To test possibility to keep the main characteristics of this regime inside the operational limits close to the nominal values, or select the maximum value of anomalous pinch when it is possible.

10. 10 RUSSIAN RESEARCH CENTRE «KURCHATOV INSTITUTE» NUCLEAR FUSION INSTITUTE 9th ITPA CDB&M TG Meeting 3-6 Oct.2005, St.Perersburg, Russia (V. Leonov, V.Zhogolev ) The main discharge characteristics which was keeping in these scans : 1) constant fusion power P fus  MW by selection of average plasma density (changing the neutrals flux to the plasma boundary). 2) constant level of the total plasma radiation P rad  47 MW (what at the constant P fus and P aux gives the constant power flux through the separatrix P loss in the steady-state conditions) by selection of Ar impurity seeding on the plasma boundary. 3) boundary conditions for Be and He was fixed in all considered cases as in the reference regime.

11. 11 RUSSIAN RESEARCH CENTRE «KURCHATOV INSTITUTE» NUCLEAR FUSION INSTITUTE 9th ITPA CDB&M TG Meeting 3-6 Oct.2005, St.Perersburg, Russia (V. Leonov, V.Zhogolev ) 3 scans: 1) Addition of anomalous pinch in the electron density equation only. (to test the effect of the bulk plasma density profiles picking on the impurities accumulation). 2) Addition of the identical anomalous pinch in all plasma components (in the bulk plasma and impurities). 3) Adition of the anomalous pinch which is proportional to (Z k / Z eff ) into all plasma components (in the bulk plasma and impurities).

12. 12 RUSSIAN RESEARCH CENTRE «KURCHATOV INSTITUTE» NUCLEAR FUSION INSTITUTE 9th ITPA CDB&M TG Meeting 3-6 Oct.2005, St.Perersburg, Russia (V. Leonov, V.Zhogolev ) 1) Addition of anomalous pinch in the electron density equation only. (to test the effect of the bulk plasma density profiles picking on an impurities accumulation).

13. 13 RUSSIAN RESEARCH CENTRE «KURCHATOV INSTITUTE» NUCLEAR FUSION INSTITUTE Change of He density profile is small Increase of the bulk plasma density profile peaking doesn’t result in the impurities accumulation (impurity density profiles stay flat). (The reason of this is the prevailing of anomalous impurity diffusion under the neoclassical impurity pinch). 9th ITPA CDB&M TG Meeting 3-6 Oct.2005, St.Perersburg, Russia (V. Leonov, V.Zhogolev )

14. 14 RUSSIAN RESEARCH CENTRE «KURCHATOV INSTITUTE» NUCLEAR FUSION INSTITUTE V pinch- Z = 0 variation of V pinch- e No impurity accumulation decrease of and increase of the Ar flux into the plasma for the discharge quality keeping. It results in increase of value when Z eff (  ) profile peaking factor decreases. 9th ITPA CDB&M TG Meeting 3-6 Oct.2005, St.Perersburg, Russia (V. Leonov, V.Zhogolev )

15. 15 RUSSIAN RESEARCH CENTRE «KURCHATOV INSTITUTE» NUCLEAR FUSION INSTITUTE 9th ITPA CDB&M TG Meeting 3-6 Oct.2005, St.Perersburg, Russia (V. Leonov, V.Zhogolev ) 2) Addition of the identical anomalous pinch for all plasma components (for the bulk plasma and impurities).

16. 16 RUSSIAN RESEARCH CENTRE «KURCHATOV INSTITUTE» NUCLEAR FUSION INSTITUTE V pinch -Z = V pinch -e Change of He density profile is small Impurity density profiles are similar to the bulk plasma density profiles. 9th ITPA CDB&M TG Meeting 3-6 Oct.2005, St.Perersburg, Russia (V. Leonov, V.Zhogolev )

17. 17 RUSSIAN RESEARCH CENTRE «KURCHATOV INSTITUTE» NUCLEAR FUSION INSTITUTE V pinch -Z = V pinch -e Increased accumulation of impurities is absent. Peaking factors of the bulk plasma density profiles and impurities density profiles are similar profile of Z eff stay flat · He contamination increases. 9th ITPA CDB&M TG Meeting 3-6 Oct.2005, St.Perersburg, Russia (V. Leonov, V.Zhogolev )

18. 18 RUSSIAN RESEARCH CENTRE «KURCHATOV INSTITUTE» NUCLEAR FUSION INSTITUTE 9th ITPA CDB&M TG Meeting 3-6 Oct.2005, St.Perersburg, Russia (V. Leonov, V.Zhogolev ) 3) Addition of the anomalous pinch, which is proportional to (Z k / Z eff ), for all plasma components (for the bulk plasma and impurities).

19. 19 RUSSIAN RESEARCH CENTRE «KURCHATOV INSTITUTE» NUCLEAR FUSION INSTITUTE V pinch ~ Z k Change of He density profile is small Impurities profiles sharpening increases with impurity charge 9th ITPA CDB&M TG Meeting 3-6 Oct.2005, St.Perersburg, Russia (V. Leonov, V.Zhogolev )

20. 20 RUSSIAN RESEARCH CENTRE «KURCHATOV INSTITUTE» NUCLEAR FUSION INSTITUTE V pinch ~ Z k impurities accumulation increases with impurity charge and Be and He percentage increase some sharpening of Z eff profile and increase of. Discharge quality can be keeping by some increase of and control of Ar seeding into the plasma. 9th ITPA CDB&M TG Meeting 3-6 Oct.2005, St.Perersburg, Russia (V. Leonov, V.Zhogolev )

21. 21 RUSSIAN RESEARCH CENTRE «KURCHATOV INSTITUTE» NUCLEAR FUSION INSTITUTE CONCLUSIONS The modeling of the parametric dependencies of impurity accumulation versus the value of anomalous pinch showed that:  Increase of the bulk plasma density profile peaking (without the anomalous pinch of impurities increase) doesn’t result in the impurities accumulation (impurity density profiles stay flat). The reason of this is the prevailing of anomalous impurity diffusion under the neoclassical impurity pinch. In this case discharge quality can be keeping by some decrease of and increase of the Ar flux into the plasma. 9th ITPA CDB&M TG Meeting 3-6 Oct.2005, St.Perersburg, Russia (V. Leonov, V.Zhogolev )

22. 22 RUSSIAN RESEARCH CENTRE «KURCHATOV INSTITUTE» NUCLEAR FUSION INSTITUTE  In the case of equil anomal pinch velocities of the bulk plasma and impurities, impurity density profiles are similar to the bulk density profiles and profile of Z eff stay flat (increased accumulation of impurities is absent). To keep the total radiation power in this case it is necessary to increase the Ar seeding into the plasma.  If anomalous pinch velocity proportional to the ion charge one indicates impurities accumulation which increases with impurity charge (It results in some sharpening of Z eff (  ) profile). Change of He density profile is small Some increase of and control of the Ar seeding into the plasma help to keep the discharge qality. 9th ITPA CDB&M TG Meeting 3-6 Oct.2005, St.Perersburg, Russia (V. Leonov, V.Zhogolev )