V. Rozhansky St. Petersburg State Polytechnical University

1. V. Rozhansky St. Petersburg State Polytechnical University New version of B2SOLPS5.0 and simulations of H-regimes Coathors: E.Kaveeva, P. Molchanov, I. Veselova, S.Voskoboynikov, D.Coster

2. Problems with in B2SOLPS5.0 with driftsIn spite of many simulations performed for L-mode shots, the old version has following problems: • Small time step is required for L-mode. • Absence of convergence for H-mode. • 3. Big radial convective fluxes in the core and small transport coefficients results in artificial numerical transport, which might change profiles. Especially pronounced inside the transport barrier. • 4. The code should be rewritten to avoid big radial convective fluxes.

3. Transformation of the equation systemThe main idea is to replace large radial gradB driven convective fluxes by parallel fluxes with the same divergence both in particle and energy balance equations • Particle balance

4. New particle balance equation • Pfirsch-Schlueter flux:

5. Modifications of the energy balance equations • For electrons • is replaced by • and • is replaced by • 9-point stencil is used

6. Comparison of the simulation resultsL-mode

7. Comparison of the simulation resultsH-mode

8. Comparison of the simulation resultsH-mode

9. Comparison of the simulation resultsH-mode

10. Particle fluxes in the H-mode

11. Simulation of the H-mode shot #17151

12. Simulation of the H-mode shot #17151

13. Simulation of the H-mode shot #17151

14. Simulation of the H-mode shot #17151

15. Simulation of the H-mode shot #17151

16. Simulation of the H-mode shot #17151

17. Simulation of the H-mode shot #17151

18. Simulation of the H-mode shot #17151

19. Simulations were performed with time step • Drifts were switched on 100% from no drift case • Further tests of the new version are necessary

20. The potential outside the separatrix is determined by the parallel momentum balance for electrons . Electron temperature is decreasing with radius so the radial electric fields here is positive. For normal direction of the magnetic field drifts in SOL are directed from the inner to the outer divertor plate and in the private region from the outer to the inner plate.Poloidal drift velocity for the Ohmic discharge of AUG.Arrows represent full drifts in the xy plane and colors correspond to the values of the poloidal drifts.

21. Radial electric field in the core The radial electric field inside the separatrix is close to the neoclassical electric field for the wide set of plasma parameters. Radial profile of the toroidal velocity is governed by anomalous radial transport and hence the radial electric field profile cannot be predicted by standard neoclassical theory.

22. Radial electric field in the viscous layer The radial electric field is determined by the balance Neoclassical solution corresponds to e. g. Near the separatrix: Contains the radial scale:

23. Viscous layer width Components of the parallel momentum balance averaged over the flux surface. 1-anomalous perpendicular viscosity 2-classical viscosity Reversed magnetic field, no NBI, n=2·1019 m-3, Ti=42 eV point (r-a =-1cm). I=1 MA, B=2 T. neoclassical solution: average classical viscosity (curve 2) equals zero. Characteristic scale for the viscous layer:

24. Understanding of L-H transition threshold. Scaling for ExB drift shear TheExB drift shear: If the electric field is neoclassical: Neglecting small corrections and assuming where Neoclassical prediction: Scaling obtained in the simulations: (Ti in eV ,ins-1, in km/s) =5.4·103,=104, =105

25. Scaling for the L-H transition threshold The power, which is necessary to obtain the given ExB drift shear (ωs=3.5·105 s-1 at r-a = 1 см) B2SOLPS5.0 calculations L-H transition threshold for ASDEX-Upgrade as a function of ne and B Experiment

26. Andrew Y et al 2004 Plasma Phys. Control. Fusion 46 337 JET experiments demonstrated that edge Ti/B is a key parameter which determines the L-H transition threshold in accordance with simulation results!

27. 1. B2SOLPS5.0 is a fluid code and hence results of simulations are strictly valid for the collisional Pfirsch-Schlueter regime. 2. For low density cases plasma in the core region is at the edge of Pfirsch-Schlueter - plateau regime, or in the plateau regime, so the results of simulations could be outside of the applicability of the equation solved.. 3. To overcome this problem, the parallel viscosity has been modified to provide exact neoclassical solutions both for collisional and collisionless cases. 4.Four Ohmic shots of AUG with different collisionalities were chosen for simulations to investigate the collisionality dependence of the radial electric field.

28. Modification of B2SOLPS5.0 code • The parallel viscosity in the parallel momentum balance equation for the main ions is the sum of two contributions: -depends on parallel ion velocity -depends on parallel ion heat flux Modification :

29. For arbitrary collisionality • Collisionality-dependent coefficient • for collisional case • Corresponds to neoclassical electric field

30. Simulation results

31. Comparison with neoclasical electric field

32. Comparison with neoclasical electric field

33. Comparison with the turbulent phase velocity measurements (G.D. Conway et al Nucl. Fusion 46 (2006) S799)

34. Discussion • The coefficient kT (at the distance more than 3-4 cm from the separatrix) varied from 0.2 to 0.7. • One would not expect the strong dependence of the radial electric field at the core side on the collisionality (the toroidal rotation on the core side of the simulation region is the same for all shots, the contribution from change of density and temperature profiles is not larger than 40%). • To obtain in the simulations the measured core poloidal velocity in the shot 19055 its is necessary to assume the counter-current toroidal rotation at 2-4 cm inside the separatrix equal to 20km/s , which is unlikely for AUG

35. Conclusions • For all shots simulated radial electric field is close to the neoclassical electric field in the core region deeper than the viscous layer (of the order of 1cm inside the separatrix). • The simulation results do not reproduce the measured dependence of the poloidal velocity of the turbulence deep in the core. • The shape of the radial electric field in the separatrix vicinity both inside and outside the separatrix is consistent with the measured poloidal velocity of the turbulence. • The measured collisionality dependence might be connected with the phase velocity of the turbulence and not with ExB drift

36. More complicated issues are connected with the toroidal (parallel) rotation in the separatrix vicinity • Lower L-H transition power threshold for normal direction of the magnetic field (gradB drift directed towards X-point) • Dependence of the power threshold on the geometrical factors (LSN, USN or CDN case, shape, X-point height etc)

37. Scheme of the fluxes in the SOL Reversed magnetic field Normal magnetic field

38. Poloidal distribution for the parallel velocity for AUGParallel velocity is transported from the SOL through the separatrix!! Reversed magnetic field Normal magnetic field

39. Parallel (toroidal) velocity is transported from SOL to the core through the separatrix due to turbulent viscosity. Parallel velocity changes radial electric field in the viscous layer.

40. Radial electric field in the discharge with reversed toroidal magnetic field (AUG, B2SOLPS5.0) Electric field in the normal discharge with the same parameters

41. Radial electric field in ASDEX-Upgrade. Ohmic shots.Different magnetic configurations

42. Parallel (toroidal) velocity is transported to the core. Radial profiles of parallel velocity. MAST outer mid-plane inner mid-plane

43. Radial electric field at the outer mid-plane MAST

44. Radial electric field at the inner mid-planeSpike in electric field at HFS for CDN case is caused by different potential drops in two disconnected SOL’s MAST

45. The edge toroidal rotation might be controlled also by a change of a gas puff. Toroidal velocity at the outer mid-plane of MAST for shots №6467(outboard puff) and №6468 (inboard puff).

46. Scheme of the particle fluxes in the discharge with inboard gas puff

47. Parametric dependence of the edge toroidal rotation • Spontaneous generation of a toroidal rotation in the core of a tokamak in the absence of NBI is one of the most interesting findings of the recent years. There are some experimental indications, e.g. dependence of the central toroidal rotation on the divertor configuration (J. Rice et al 2005 Nucl. Fusion 45 251 ), that the edge toroidal rotation is the key parameter, which might determine the core rotation. Hence the study of the edge toroidal rotation and its parametric dependence is one of the main tasks now days.

48. Parametric dependence of the edge toroidal rotation Pfirsch-Schlueter velocity Velocity, compensating ExB drift Two contributions are associated with drifts. Both velocities are proportional to ion temperature, inversely proportional to poloidal magnetic field and are independent on density and toroidal magnetic field

49. Simulation results both for MAST and AUG are consistent with this parametric dependenceMAST AUG

50. Mach number at the equatorial mid-plane Similar parallel velocity was observed on MAST (S.Talents et al PSI- 17) AUG (H W Muller et al EPS32) TCV (R Pitts et al PSI-17) and other tokamaks AUG &MAST