Particle transport in core and pedestal of Tokamak Plasmas R. Singh - PowerPoint PPT Presentation

1 Particle transport in core and pedestal of Tokamak Plasmas R. Singh WCI, NFRI, Daejeon, Republic of Korea Collaborators : H. Jhang and P. Diamond Acknowledgements: H. Nordman, P. Kaw and X. Garbet KSTAR Conference, Feb. 24 -26, 2014

2 High confinement (H-mode) discharges are identified: - Steep density and temperature profiles in edge region – form pedestal - Reduction in H  ( 1 H Plasma), D  (D-plasma) signals    E 1 H - H – factor:  L E Energy confinement time is defined by    3 (3/ 2) (T T ) n d x  e i E P input KSTAR Conference, Feb. 24 -26, 2014

3 Why Particle Transport? Power balance: 3 1 nT        2 ext ; P P P n v  H alfa alfa alfa 4 E - Thermonuclear Power 1           2 P n n v n v th D T 4  Particle and thermal Transport – they are correlated KSTAR Conference, Feb. 24 -26, 2014

4  Peaked density profile:  2 P n - yields high fusion power - th - stabilizes micro-instabilities (ITG, ETG) and reduces heat transport   - generates a large bootstrap fraction ( J ) required for b pol  continuous operation ( (1/ )(dP/ dr) ) J B b P - deep penetration of low Z , high Z impurities and H e ashes accumulation in reactor phase (disadvantages) KSTAR Conference, Feb. 24 -26, 2014

5  Variants of operating modes exit by density peaking   n - Improved Ohmic Confinement Mode (IOC) - E R. Aratari et al., ASDEX - 88 KSTAR Conference, Feb. 24 -26, 2014

6 - Super shot with solid deuterium pallets showed more peaked density profiles ( due to ITG turbulence suppression)- energy  achieved  20 3 confinement time was improved and ~10 n m s E - Radiative Improved moved: Energy transport reduced with impurities seeding (TEXTOR, Ongena et al 1995) KSTAR Conference, Feb. 24 -26, 2014

7 Particle versus thermal Transport  Particle transport is different from heat transport  Heat source is almost always located in the core  Distinction between pinch and diffusive terms difficult  Particle source is often located only in outer edge region, while showing peaked density profile  Distinction between pinch and diffusive terms easier KSTAR Conference, Feb. 24 -26, 2014

8  Traditional gradient and flux relation:         an neo ware ; D n V n V V V V  n V R  -> Peaked density parameter n D  Relation between gradient and flux is more complex  The vague form turbulent flux as          , , , D n T B KSTAR Conference, Feb. 24 -26, 2014

9  Gradient and Flux Matrix  General form of transport matrix         D D D V n Tn nV Dn         Q D D V T          nT T TV DT D F          J j V D D V          Vn VT DV                  KSTAR Conference, Feb. 24 -26, 2014

10  Outline  Neoclassical particle transport and limitations  Turbulent particle transport  Transport in pedestal: turbulent hyper-resistivity (  ) H || e  Summary and open issues KSTAR Conference, Feb. 24 -26, 2014

11  Neoclassical Transport and Limitations  Ware Pinch: conservation of canonical moment in the presence of induced toroidal electric field ( E  ), all trapped particles drift towards the magnetic axis  1/2 ware ~ 2.44 / V E B    Usually dominant in core at low power- Wagner 93  ITB (EDA H-mode) in Alcator C-Mod could be understood by ware pinch- Ernst 04 (??)  Peaked density is observed in no-inductive discharge i.e.,  ware 0 V KSTAR Conference, Feb. 24 -26, 2014

12  Some cases [high density H-mode in JET, ASDEX-UP] observed pinch found to be    neo ; V V D !! Sign of ETG Turbulence (discuss later) pinch e  Ware pinch cannot explain all experiments [L-mode in JET, D- IIID, TEXTOR, TCV, Tore-supra results] and no-inductive  ware 0 discharge (Tore-supra) i.e., V KSTAR Conference, Feb. 24 -26, 2014

13  NBI fuelling is not essential element for peaked density  Actions of toroidal rotation also of interest KSTAR Conference, Feb. 24 -26, 2014

14  Particle Turbulent transport  Quasi-linear particle flux results from linear phase shift   i   (1 ) n between density and potential perturbation -    micro-turbulence. Drift KE – Horton-83: transport by i    2           ( ) / ( / 1.5) / 2 / V kV R L E T R L R n k n e T Dk V k KSTAR Conference, Feb. 24 -26, 2014

15  TEP Theory (Yankov 94, Nycander-Rosenbluth 95, Naulin 98)        For ˆ  Compressible ˆ ( , ) / 0 v z B v B zB x y and ; E E     ; Here  ( / ) 0 n nv d n B n B is a Lagrangian invariant / t E t and equivalent to advection of n B /     Turbulence mixing  relaxation towards ln ln n B x x  ( ) n B x (equivalent to peaking factor) or canonical profile  Extension to toroidal momentum pinch (Hahm, Diamond--) - B  Turbulent mixing - relaxation 3 || / nV Lagrangian invariant    ln( ) 3 ln nV B towards || KSTAR Conference, Feb. 24 -26, 2014

16  Thermo-diffusion flux (Coppi 79, Waltz 89, Terry 89, Nordman 90----)  Term proportional to     ln - Thermo-diffusion flux R T             - Trapped particles ˆ ˆ , ( ), ( ), , ln RV D s s R T p nT rk d dtr eff k  Interaction between toroidal momentum and particle fluxes appears – step density with toroidal flows  D -Complex!! and depend on the characteristic of turbulence nT  ITG-TEM mode - CORE-region KSTAR Conference, Feb. 24 -26, 2014

17 KSTAR Conference, Feb. 24 -26, 2014

18  QL versus Non QL - Hot topic?  QL theory suggests a linear relation between gradient and flux and turbulent saturation - mixing length:       / 1/ n n n n k L x n          ˆ ( / ) / ( / )(1/ ) c B z e T k L , t e k x n T  Existence-multi-states: L-H, ITB, cold pulse expts. – suggests the relation between gradient and flux is quite intricate.  Multi-scales interaction between particle, thermal, and momentum fluxes, mean flows, zonal flows, zonal fields etc. – the hot topic  Meso-scale coherent structures and nonlocal diffusion is also vital (??) – complicated KSTAR Conference, Feb. 24 -26, 2014

19  Transport in H-mode pedestal (Singh et al PoP-13) KSTAR Conference, Feb. 24 -26, 2014

20 Questions:  What is the underlying physics of steep density formation though the particle source is absent? - Ion scales turbulence - ITG-TEM and DRBM, the main drivers  of transport channels, are suppressed due to E shear. B - Neo-classical diffusion is small to explain the rapid development of sharp profiles in H-mode transition. - Transition occurs in m-sec L- I - H - Pedestal Physics, not well understood. ITG, TEM, DRBM turbulence absent → Can it be ETG? KSTAR Conference, Feb. 24 -26, 2014

21  Propose: ETG mode may a possible candidate for particle pinch and electron thermal transports in.   Ped / n I - Confinement time - Ohkawa scaling E p  Streamers in local ETG simulations- Jenko 2000   Electron transport remains anomalous - unaffected from E B shear and MHz fluctuations are observed in: NSTX (Smith 09), FT-2 (Gusakov 06), Tore Supra (Hennequin09) KSTAR Conference, Feb. 24 -26, 2014

22  Toroidal ETG Mode - ETG is mirror image of ITG ITG ETG          ( / ); ( / ) n k V n k V  || e the i thi     ITG ETG ~ k ( / ); ~ k ( / ) V R L V RL   i thi n e the n   / ~ / m m i e i e       , OK in core |~ / L 1 - Condition for adiabatic ion k c   i s n    k   , | |~ k c 1 - Wave number and frequency ordering in pedestal:    i e - Both like Interchange mode- stabilize by Larmor radius - Interchange mode stabilize by Larmor radius KSTAR Conference, Feb. 24 -26, 2014

23  , ~ | | - For k c , ETG mode resonates with background ions, which results in  i I deviation of ions from Boltzmann condition. Non-adiabatic response can be determined by DKE,    f f f Ze       0 j j j 0. V E      t x m V J            ˆ ˆ 1/2 2 1 exp( ) ; n i   i i s   Electrostatic ETG eigenmode equation in ˆ geometry    2   C    2   0 A B   2 k   - Radial length of ETG mode  By balancing k      2 2 2 2 2 k (1 5 / 3) c Vorticity [i.e. ] ~ Parallel compression [i.e. ]  || e e KSTAR Conference, Feb. 24 -26, 2014