Stanley M. KayeWayne Solomon

PPPL, Princeton University

ITPANaka, JapanOctober 2007

Rotation & Momentum Confinement Studies in NSTX

Supported by

High Rotation (M ~0.5) and Rotational Shear Observed in NSTX

• Low BT (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

Local Transport Studies Reveal Sources of Energy Confinement Trends

Electrons primarily responsible forstrong BT scaling in NSTX (E~BT

0.9)

Electrons anomalous Ions near neoclassical

Variation in near-neoclassical ion transport primarily responsible for Ip scaling (E~Ip

0.4)

Neoclassical

Neoclassical levels determined from GTC-Neo: includes finite banana width effects (non-local)

Steady-State Momentum Transport Also Can Be Determined From These Scans

No anomalous pinch necessary to explain rotation data

Core Momentum Diffusivities Up to An Order of Magnitude Lower Than Thermal Diffusivities

Is momentum diffusivity tied more to electrondiffusivity when ions are neoclassical?

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

Momentum Diffusivity NOT Neoclassical Even Though Ion Thermal Diffusivity Is (~)

,neo <<

, neo can be negative!

Inward Neoclassical Momentum Flux Driven By Ti

Relation to source of intrinsic rotation?

Relation of and to ,neo Independent of Ion Thermal Diffusivity and Its Relation to Neoclassical

Extend analysis to i>>i,neo (L-mode)

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

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

Vat center

IRWM

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

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-L0/) * exp(-t/)], whereL = Angular momentumT = Torque (NB torque only)

L0 = Angular momentum at time of nRMP turn-off

Steady-state

E ~ 50 ms

Perturbative Momentum Transport Studies Using Magnetic Braking Indicate Significant Inward Pinch

• Can determine vpinch 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

vPeeters= /R [-4-R/Ln](Coriolis drift)

vHahm= /R [-3](B, curvature drifts)

– Effect of off-diagonal terms (Te, ne)?

– s-s <

pert with inward pinchImportant to consider when

comparing to i

Reasonably Good Agreement Between Theory and Experiment in Limited Comparison

Can comparisons with large variations in Ln be used to discriminate between theories?

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

Discussion Points

• Main conclusions– f >>E;

pert>s-s (inward pinch significant)

– Inferred vpinch , 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 BT, 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 vpinch significant or necessary?

– Significant within data uncertainties?– Is

pert & vpinchpert 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?