1. SMK – ITPA1 Stanley M. Kaye Wayne Solomon PPPL, Princeton University ITPA Naka, Japan October 2007 Rotation & Momentum Confinement Studies in NSTX Supported by

2. SMK – ITPA2 High Rotation (M ~0.5) and Rotational Shear Observed in NSTX Low B T (0.35-0.55 T) operation leads to values of  ExB up to the MHz range These ExB shear values can exceed ITG/TEM growth rates by factors of 5 to 10 Steady-state and perturbative momentum confinement studies on NSTX have started

3. SMK – ITPA3 Local Transport Studies Reveal Sources of Energy Confinement Trends Electrons primarily responsible for strong B T scaling in NSTX (  E ~B T 0.9 ) Electrons anomalousIons near neoclassical Variation in near-neoclassical ion transport primarily responsible for I p scaling (  E ~I p 0.4 ) Neoclassical Neoclassical levels determined from GTC-Neo: includes finite banana width effects (non-local)

4. SMK – ITPA4 Steady-State Momentum Transport Also Can Be Determined From These Scans No anomalous pinch necessary to explain rotation data

5. SMK – ITPA5 Core Momentum Diffusivities Up to An Order of Magnitude Lower Than Thermal Diffusivities Is momentum diffusivity tied more to electron diffusivity when ions are neoclassical?

6. SMK – ITPA6 Steady-State    Does Not Scale With  i As At Conventional Aspect Ratio Due to ITG suppresson? What is  , neo ? Steady-state: from momentum balance (TRANSP) assuming no explicit pinch

7. SMK – ITPA7 Momentum Diffusivity NOT Neoclassical Even Though Ion Thermal Diffusivity Is (~)  ,neo <<    , neo can be negative!

8. SMK – ITPA8 Inward Neoclassical Momentum Flux Driven By  T i Relation to source of intrinsic rotation?

9. SMK – ITPA9 Relation of   and   to  ,neo Independent of Ion Thermal Diffusivity and Its Relation to Neoclassical Extend analysis to  i >>  i,neo (L-mode)

10. SMK – ITPA10 Dedicated Perturbative Momentum Confinement Experiments Recently Carried Out Use non-resonant n=3 magnetic perturbations to damp plasma rotation –Previously been used to slow plasma rotation for ITER- relevant RWM stabilization experiments (Sabbagh et al.) Observed rotation damping consistent with neoclassical toroidal viscosity (NTV) theory Steady-state & transient application

11. SMK – ITPA11 Steady-State Application of n=3 NRMP Confirms Maximum Torque at R>~1.3 m Delay in start of v  decrease going inwards from ~1.38 m Beware: 10 ms time resolution V  at R=132 cm V   at center I RWM

12. SMK – ITPA12 Perturbative     Can be Obtained from Transient Application of nRMP No apparent delay in recovery of v  after nRMP braking removed R~1.15 m R~1.32 m

13. SMK – ITPA13 Momentum Confinement Time >>Energy Confinement Time in NSTX (Consistent with   <<  i ) Use dL/dt = T – L/   relation to determine instantaneous   Model spin-up to determine perturbative   using L(t) =   * [T – (T-L 0 /   ) * exp(-t/   )], where L = Angular momentum T = Torque (NB torque only) L 0 = Angular momentum at time of nRMP turn-off Steady-state  E ~ 50 ms

14. SMK – ITPA14 Perturbative Momentum Transport Studies Using Magnetic Braking Indicate Significant Inward Pinch Can determine v pinch only if ,  decoupled Assume   pert,  pinch pert constant in time Expt’l inward pinch generally scales with theoretical estimates based on low-k turbulence-driven pinch v Peeters =   /R [-4-R/L n ] (Coriolis drift) v Hahm =   /R [-3] (  B, curvature drifts) –Effect of off-diagonal terms (  T e,  n e )? –   s-s <   pert with inward pinch Important to consider when comparing   to  i

15. SMK – ITPA15 Reasonably Good Agreement Between Theory and Experiment in Limited Comparison Can comparisons with large variations in L n be used to discriminate between theories?

16. SMK – ITPA16 Varying Levels of Applied nRMP Can Probe Dynamics and Hysteresis of     Largest effect again seen for R>~1.3 m R~1.15 m R~1.32 m

17. SMK – ITPA17 Discussion Points Main conclusions –  f >>  E ;   pert >   s-s (inward pinch significant) –Inferred v pinch   , magnitude not inconsistent with theory predictions Will continue to run experiments over next couple of years to study steady-state and perturbative momentum transport – Long pulse plasmas to study   s-s itself and effect on energy transport –Multiple perturbations: use n=1 feedback, run at higher B T, lower  to suppress MHD –Apply additional torque in core: modulated beams (beam profile peaked) Need to understand decoupling of momentum and ion energy transport –Is this because ions are near neoclassical (i.e., ITG modes suppressed)? –Under what conditions would ITG be unstable? How low does ExB have to be? Will coupling re-emerge at this point? –Is   coupled to  e ? Need dedicated scans Is v pinch significant or necessary? –Significant within data uncertainties? –Is   pert & v pinch pert a better physics description than   s-s? Are theories for rotation damping (e.g., NTV) applicable to ITER, CTF? –Can they be used as a basis for prediction? –What do they predict?