Experimental test of the neoclassical theory of poloidal rotation

Experimental test of the neoclassical theory of poloidal rotation Presented by Wayne Solomon with contributions from K.H. Burrell, R. Andre, L.R. Baylor, R. Budny, P. Gohil, R.J. Groebner, C.T. Holcomb, W.A. Houlberg, and M.R. Wade Presented at the 47th APS-DPP Meeting Denver, Colorado October 24 28, 2005

Testing neoclassical theory of poloidal rotation is required to obtain predictive knowledge of rotation Momentum transport remains poorly understood, despite critical role of rotation in high performance plasma operation If neoclassical theory of poloidal rotation were experimentally validated, it would provide predictive knowledge that is sought Neoclassical theory has been successful in predicting the magnitude of bootstrap current and associated neoclassical resistivity in experiments Calculation of bootstrap current comes from same order in neoclassical theory as poloidal rotation Complexity in properly interpreting charge exchange recombination (CER) rotation measurements makes comparison with theory difficult Continued improvements in DIII-D CER system now make it feasible to test neoclassical theory of poloidal rotation

Key Results Persistent disagreement between measured and neoclassically predicted poloidal rotation profiles Magnitude and direction! Radial electric field measurements are consistent with non-neoclassical poloidal rotation

Outline Analysis techniques including atomic physics corrections to rotation measurements Verification of analysis results Comparisons of poloidal rotation profiles with neoclassical theory Radial electric field considerations Discussion

CER rotation measurements need to be corrected for the energy-dependent cross-section Rotation obtained by measuring line shift of spectrum of ion having undergone charge exchange with a beam neutral

CER rotation measurements need to be corrected for the energy-dependent cross-section Emission intensity from CX process: I n b n σ i CX r r r r ( V Vb ) V Vb

CER rotation measurements need to be corrected for the energy-dependent cross-section Emission intensity from CX process: I n b n σ i CX r r r r ( V Vb ) V Vb CX cross-section is energy dependent creates apparent rotation Effect scales with ion temperature

Presence of excited beam neutrals can dramatically alter cross-section curve 0 6+ + 5+ D ( n D ) + C D + C ( ) n * The n D =2 cross-section 100x larger than n D =1 cross-section at low energies [Isler et al Phys Rev A 1988, Hoekstra et al PPCF 1998] Tiny fraction of excited beam neutrals distorts effective cross-section n D =2 population varies across radius Effective cross-section varies spatially Need to include n D =2 beam neutrals if want accurate rotation measurements

An apparent poloidal velocity is also generated from the energy-dependent cross-section Gyro motion of ion + finite lifetime of excited state gives apparent poloidal velocity For lifetime τ, ions travel ω c τ around gyro-orbit before radiating conversion of apparent radial velocity to apparent poloidal velocity Effect was huge on TFTR [Bell & Synakowski AIP Conf. Proc. 2000] ω c τ ~ 0.1 0.25 B T i ~ 20 30 kev V θ app, gyro ~ 10 40 km/s Same order of magnitude as measured velocity In DIII-D, even with reduced B and T i, the effect is still important Neoclassical prediction is ~ 1-2 km/s

Both tangential and vertical CER system have complete profile coverage 27 tangential chords 25 vertical chords 1 radial chord θ^ φ^

Toroidal and poloidal rotation profiles are obtained using all measured velocities simultaneously The plasma rotation is represented by r v V = kb + RΩˆφ where φˆ is the unit toroidal vector, and k(ρ) and Ω(ρ) are flux surface quantities. from MHD level of equations, including incompressibility constraint Profiles of k and Ω are represented by cubic splines Plasma rotation can be re-projected back into line-of-sight (LOS) apparent velocities using actual geometry and atomic physics corrections Use least squares fit to find k, Ω and τ consistent with measured LOS velocities

Near axis vertical chords key in obtaining poloidal rotation measurements across plasma radius Vertical chords near magnetic axis measure predominantly atomic physics corrections No poloidal rotation on axis Such chords provide rigid constraints on combined effect of corrections

Use radial chord to validate cross-section Chord viewing along major radius measures only atomic physics No real radial plasma velocity!

Apparent radial velocity measurement validates cross-sections used in analysis Chord viewing along major radius measures only atomic physics No real radial plasma velocity! Using only n D =1 cross-section, expected apparent velocity too large Including n D =2 population of beam ions accurately reproduces measured apparent radial velocity

Further evidence of effect of cross-section correction on velocity measurements Interspersed views from different directions do not lie on smooth curve as expected

Chords from different views agree after inclusion of cross-section corrections Interspersed views from different directions do not lie on smooth curve as expected Corrected rotation values now form one smooth curve

Chords from different views agree after inclusion of cross-section corrections over whole time history Generate expected value Spatially interpolated for view #1 from view #2 Uncorrected measurements do not agree with expectation value Corrected measurements show good agreement with expectation

QH-mode and ELM suppressed H-mode plasmas provide interesting candidates for rotation studies These plasmas interesting because Good performance w/o ELMs Long steady phase allows multiple time slices to be analyzed High ion temperature makes atomic physics corrections significant

Neoclassical prediction for carbon poloidal velocity too small and in wrong direction in QH-mode Measurement confirmed using repeat shot looking at different carbon transitions Different atomic physics Measured plasma profiles input into NCLASS T e, n e, T i, n C, (corrected) V φ EFIT reconstruction data

Poloidal rotation does not respond to changes in neutral beam input as suggested by theory In high power phase, see typical disagreement between experiment and theory Later in discharge, power is stepped down T i and V φ change all systematic offsets change Poloidal rotation remains unchanged after corrections Neoclassical prediction for rotation is smaller, owing to changes in profiles

In ELM-suppressed H-modes, discrepancy with neoclassical prediction even more severe ELMs suppressed by resonant magnetic perturbation using internal non-axisymmetric coil [T.E. Evans, Tuesday morning] Close to factor of 10 difference in poloidal rotation in some radial regions General disagreement with direction of rotation Can magnetic perturbation be a source of extra anomaly?

Atomic physics corrections critical for determination of radial electric field E r determined from radial force balance E = P Zen + V B V B r i / i φ θ θ φ Significant difference seen between E r obtained from corrected or uncorrected rotation profile E r determined from MSE agrees better with corrected data

E r determined from different impurities agree as expected when using corrected poloidal rotation Individual terms differ appreciably for carbon and neon Major contribution to E r from V φ However, V θ contribution not negligible Precise cancellation from V θ and P terms give net E r agreement

E r agreement excellent across profile over extended time period Scatter plot constructed by taking all E r points for carbon and neon between 0 < ρ < 0.9, and 3000 < t (ms) < 4000

Assumption of neoclassical poloidal rotation violates toroidal rotation measurements also Write expected neon toroidal rotation in terms of carbon V φ V φ, Ne = V φ, C B B φ θ 1 + B θ ( V V ) θ, C PC ZCen θ, Ne C PNe Z en Ne Ne If assume neoclassical V θ, then conclude neon and carbon rotate at approx same rate

Neon cross-section produces correct apparent radial velocity Again, including n D =2 population of beam ions accurately reproduces measured apparent radial velocity If we modify cross-section to bring neon and carbon toroidal rotation into agreement, then apparent radial velocity is off a factor of 2 Agreement shows difference in carbon and neon toroidal rotation is real

Experimental poloidal velocity difference between C and Ne from two independent methods is consistent Δ V θ = Vθ, C Vθ, Ne Determine in separate ways Directly from V θ measurement Indirectly from V φ measurements using radial force balance ΔV θ = B B θ φ 1 PC PNe ( V ) + φ, C Vφ, Ne Bφ ZCenC ZNeenNe From NCLASS Both experimental approaches consistent Both experimental results differ markedly from neoclassical prediction

Need to identify drive for additional poloidal rotation Poloidal rotation is heavily damped due to variations in magnetic field around flux surface in neoclassical theory Possibilities include Fast ions Neutral beam injection capable of driving parallel flow, through friction between fast ions and the thermal population. Would change with beam power it doesn t! Would expect sign of anomaly depends on I p direction it doesn t! Turbulence-driven Turbulent Reynolds stress theoretically predicted and demonstrated experimentally as mechanism for generating poloidal flow Difficult to make required measurement in core of plasma

Future work will add new views of counter beam for improved determination of cross-section correction Comparing views of co vs. counter beams sensitive to cross-section 100 s of km/s difference Measure over greater spatial region Additional test of cross-section Multiple spatial locations New views can improve both toroidal and poloidal rotation measurements Validated cross-section critical for interpreting ITER data

Summary Velocities after atomic physics corrections pass various consistency checks Measured carbon poloidal rotation shows significant discrepancy with neoclassical prediction Radial electric field for different impurities consistent with non-neoclassical poloidal rotation Measured toroidal rotation difference of carbon and neon confirms that poloidal rotation is not neoclassical Difference in carbon and neon poloidal rotation confirmed by two different experimental techniques.

Supplementary slides

Poloidal rotation relatively insensitive to uncertainties in geometry and cross-section model As an example, lens location of vertical chords are shifted 1 degree toroidally to affect toroidal pickup All individual contributions to LOS measurement change significantly However, net change of all effects is small Consequence of constraint imposed by near axis vertical chords

Poloidal rotation makes a small contribution to the overall vertical LOS velocity Multiple physics considerations explain overall vertical LOS velocity measurement: poloidal rotation only + toroidal rotation pickup + cross-section correction + gyro-correction measurement More than half of measurement is atomic physics related

Effective lifetimes are consistent across all discharges studied Tau generally found to be between 1.8 to 2.5 ns. Substantially higher than found in TFTR results Can easily be explained by error in any of the potential corrections to vertical LOS measurements Even still, poloidal rotation is reliable

E r corrections less severe in usual forward I p discharges Here, at least effects of toroidal and poloidal rotation corrections are in opposite sense on E r Overall magnitude less severely affected, although still residual effect including modification to profile shape