Predicting the Rotation Profile in ITER

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1 Predicting the Rotation Profile in ITER by C. Chrystal1 in collaboration with B. A. Grierson2, S. R. Haskey2, A. C. Sontag3, M. W. Shafer3, F. M. Poli2, and J. S. degrassie1 1General Atomics 2Princeton Plasma Physics Laboratory 3Oak Ridge National Laboratory Presented at the 27th IAEA Fusion Energy Conference Ghandinagar, Gujarat, India October 22-27, 18!1

2 Rotation Is Important for Determining Stability and Performance in Tokamaks, Affects Predictions of ITER Performance Rotation is important for determining ExB shear, MHD stability, transport of high-z particles All key for determining fusion power output Also key for ITER is affect of pedestal rotation on access to ELM free H-mode via QH-mode 1 and RMP ELM suppression 2 Scaling arguments offer favorable prospect of RMP ELM suppression (krad/s) ω ITER ITER modeling has shown a doubling of fusion power when taking rotation into account due to ExB shear suppression of turbulence 8! [1] Garofalo, Nucl. Fusion 51, 8318 (11) [2] Moyer, Phys. Plasmas 24, 1251 (17)

3 Determining Rotation in ITER Is Difficult Due to the Presence of Many Similar Size Momentum Sources Momentum source in many current tokamaks dominated by NBI ITER s larger moment of inertia means non-nbi sources need to be well understood because NBI torque will not be dominant 8 DIII-D Intrinsic rotation profiles display features caused by many physical effects that may be present in ITER Deuterium V ϕ (km/s) 6 4 H-mode Intrinsic Rotation Examples!

4 Determining Rotation in ITER Is Difficult Due to the Presence of Many Similar Size Momentum Sources Momentum source in many current tokamaks dominated by NBI ITER s larger moment of inertia means non-nbi sources need to be well understood because NBI torque will not be dominant Co-current LCFS feature: -Orbit loss 8 DIII-D -Co/counter current transport -Residual stress -Neutral particles -Fast-ion loss -Field ripple/ntv Deuterium V ϕ (km/s) 6 4 H-mode Intrinsic Rotation Examples!

5 Determining Rotation in ITER Is Difficult Due to the Presence of Many Similar Size Momentum Sources Momentum source in many current tokamaks dominated by NBI ITER s larger moment of inertia means non-nbi sources need to be well understood because NBI torque will not be dominant Co-current LCFS feature: -Orbit loss -Co/counter current Core gradient: caused by many physical effects that transport -Residual stress may be present in ITER -Residual stress -Beam torque -Neutral particles -MHD/NTV Intrinsic rotation profiles display features -Fast-ion loss -Field ripple/ntv Deuterium V ϕ (km/s) DIII-D H-mode Intrinsic Rotation Examples!

6 Determining Rotation in ITER Is Difficult Due to the Presence of Many Similar Size Momentum Sources Momentum source in many current tokamaks dominated by NBI ITER s larger moment of inertia means non-nbi sources need to be well understood because NBI torque will not be dominant Co-current LCFS feature: -Orbit loss -Co/counter current Core gradient: caused by many physical effects that transport -Residual stress may be present in ITER -Residual stress -Beam torque -Neutral particles -MHD/NTV -Fast-ion loss -Field ripple/ntv Intrinsic rotation profiles display features Evaluating 3D field torques requires Deuterium V ϕ (km/s) DIII-D!6 rotation profile, subject of future work after initial condition is laid down H-mode Intrinsic Rotation Examples

7 Outline DIII-D investigation of LCFS co-current feature in intrinsic rotation plasmas Fast-ion effects on scaling Neutral particle effects on intrinsic momentum transport ITER prediction based on co-current feature and core NBI Implications for RMP ELM suppression and conclusion!7

8 Scaling of Intrinsic Co-current Rotation Feature Is Key for Predicting ITER Rotation Boundary Condition Low operating regime of ITER cannot be achieved in current tokamaks Robust co-current rotation near LCFS is a boundary condition, investigated by: empirical scaling 1,2, dimensionless parameters scans 3, reduced physics models 4,5 DIII-D Pedestal Top (krad/s) Counter-Ip QH-mode 25 5 Low Torque: Intrinsic, QH, High Co-Ip Torque IBS, etc. ITER [2] [5] [3] [4]!8 Similar predictions: 4-1 krad/s, but discrepancy exists between databases (M~ 1 ) and dimensionless parameter scan (M~ -1 ) Databases vary more widely, dimensionless parameter scan varies alone BUT had significant fast-ion population Dimensionless parameter scan (intrinsic torque) results need to be verified in intrinsic rotation conditions [1] Rice, Nucl. Fusion 47, 1618 (7) [2] degrassie, Phys. Plasmas 23, 8251 (16) [3] Chrystal, Phys. Plasmas 24, 4251 (17) [4] Rice, Nucl. Fusion 57, 1164 (17) [5] Ashourvan, Phys. Plasmas 25, (18)

9 Measured Scaling of Intrinsic Rotation in ECH H-modes Has Smaller Discrepancy and Increases Confidence in ITER Prediction No significant scaling of intrinsic Mach number measured with in dimensionless parameter scan, defying both possible expectations Fundamentally different from observing variation with Mach number in a database Expectation was M~ -1±.9, new result not quite within error bar, perhaps edge plasma factors or Zeff changes are the cause of variation in results Other dimensionless parameters matched Adjust previous intrinsic torque based ITER prediction of ~1 krad/s: result is 3 krad/s, very near the previous Mach Number (=.8).1 1 predictions (4-1 krad/s) 1 1 1!9

10 Measured Scaling of Intrinsic Rotation in ECH H-modes Has Smaller Discrepancy and Increases Confidence in ITER Prediction No significant scaling of intrinsic Mach number measured with in dimensionless parameter scan, defying both possible expectations Fundamentally different from observing variation with Mach number in a database Expectation was M~ -1±.9, new result not quite within error bar, perhaps edge plasma factors or Zeff changes are the cause of variation in results Other dimensionless parameters matched Adjust previous intrinsic torque based ITER prediction of ~1 krad/s: result is 3 krad/s, very near the previous Mach Number (=.8) predictions (4-1 krad/s) 1 1 1!1

11 Measured Scaling of Intrinsic Rotation in ECH H-modes Has Smaller Discrepancy and Increases Confidence in ITER Prediction No significant scaling of intrinsic Mach number measured with in dimensionless parameter scan, defying both possible expectations Fundamentally different from observing variation with Mach number in a database Expectation was M~ -1±.9, new result not quite within error bar, perhaps edge plasma factors or Zeff changes are the cause of variation in results Other dimensionless parameters matched Adjust previous intrinsic torque based ITER prediction of ~1 krad/s: result is 3 krad/s, very near the previous Intrinsic rotation predictions are consistent enough for ITER prediction Mach Number (=.8) Are there boundary.1 effects 1 influencing attempts to measure the scaling? -1 predictions (4-1 krad/s) 1 1 1!11

12 <latexit sha1_base64="rnf1usclqy25ler7u6uhqgc2ljo=">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</latexit> <latexit sha1_base64="rnf1usclqy25ler7u6uhqgc2ljo=">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</latexit> <latexit sha1_base64="rnf1usclqy25ler7u6uhqgc2ljo=">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</latexit> <latexit sha1_base64="rnf1usclqy25ler7u6uhqgc2ljo=">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</latexit> Momentum Transport from Neutrals in Pedestal Is a Hidden Variable that May Affect Current Tokamaks Much More than ITER Neutral particles in pedestal are a hidden variable for most current experiments because they are rarely measured, may be corrupting ITER predictions Experiment in DIII-D made proxy investigation: change neutrals particles significantly through SOL conditions, observe intrinsic rotation M ped f nnuet n e, n neut arn neut Basic idea: neutrals affect rotation via charge exchange and ionization, effect is much reduced in ITER due to decreased neutral penetration into plasma ASDEX-U Inward Outward Integrated Momentum Flux!12 Omotani, Nucl. Fusion 57, 6648 (17)

13 Proxy Investigation Uses Divertor Closure to Change Neutral Trapping, Effect Shown by SOLPS Modeling 1.5 Closed Open Mirrored Open.5 DIII-D upper divertor can be made significantly more closed than lower divertor Create similar intrinsic rotation discharges (ECH H-modes) in 1..5 Gas Puff n e (1 /m 3 ) (b)!13 these two configurations Measure main-ion rotation from core to LCFS with main-ion CER z (m) B B B B Gas Puff (a) R (m) T i (kev) V ϕ (km/s) 6 4 (c) (d)

14 Proxy Investigation Uses Divertor Closure to Change Neutral Trapping, Effect Shown by SOLPS Modeling DIII-D upper divertor can be made significantly more 1e18 closed than lower divertor Create similar intrinsic rotation discharges (ECH H-modes) in these two configurations Measure main-ion rotation from core to LCFS with main-ion CER SOLPS modeling shows neutrals in open configuration more easily reach and penetrate LCFS, increasing z (m) Closed Open 1e17 1e16 1e15 1e14 1e13 Hydrogenic Atom Density (m -3 ) neutral density R (m) R (m)!14

15 Proxy Investigation Uses Divertor Closure to Change Neutral Trapping, Effect Shown by SOLPS Modeling DIII-D upper divertor can be made significantly more closed than lower divertor Create similar intrinsic rotation discharges (ECH H-modes) in these two configurations Measure main-ion rotation from core to LCFS with main-ion CER SOLPS modeling shows neutrals in open configuration more easily reach and penetrate LCFS, increasing z (m) Closed Open 1e24 1e23 1e22 1e21 1e 1e19 Recycling Particle Source (s -1 m -3 ) neutral density and particle source in pedestal region R (m) R (m)!15

16 Across Database of Open/Closed Plasmas, Pedestal Top Rotation Constant While Midplane Neutral Emission Changes Pedestal top intrinsic rotation (carbon) gives basic indication of changes in edge/ pedestal rotation For the parameters varied in these discharges, main trend is expected to be with Ti LFS Midplane D α (1 14 ph/sr/s/cm 2 ) Closed Open R-R sep ω (krad/s) Closed Open T (kev) i Neutrals appear to have little effect because rotation data sets essentially the same while midplane neutral emission clearly increase for open cases!16

17 DIII-D Intrinsic Rotation in Open/Closed Divertors Do Not Change Significantly with Changes in Pedestal Fueling Divertor closure affects amount of neutral fueling near LCFS as seen by SOLPS modeling and density profile results, even when other parameters are the same Density profiles changes are significant given the same Ip, β, etc. Main-ion intrinsic rotation is largely unaffected compared to normal experimental variation Edge neutrals have no significant effect on intrinsic rotation z (m) Closed Open Mirrored Open B B B B Gas Puff Gas Puff (a) R (m) n e (1 /m 3 ) T i (kev) V ϕ (km/s) (b) (c) (d) s s !17

18 DIII-D Intrinsic Rotation in Open/Closed Divertors Do Not Change Significantly with Changes in Pedestal Fueling Divertor closure affects amount of neutral fueling near LCFS as seen by SOLPS modeling and density profile results, even when other parameters are the same Density profiles changes are significant given the same Ip, β, etc. Main-ion intrinsic rotation is largely unaffected compared to normal experimental variation Edge neutrals have no significant effect on intrinsic rotation z (m) Closed Open Mirrored Open B B B B Gas Puff Intrinsic rotation predictions are consistent enough for ITER prediction No significant contamination of Gas Puff (a) R (m) n e (1 /m 3 ) T i (kev) intrinsic rotation experiment from neutral particles With increased confidence in boundary condition for ITER, we proceed with prediction V ϕ (km/s) (b) (c) (d) s s !18

19 Initial ITER Modeling Done Without Rotation Is Baseline for Evaluating Effect of Rotation Predictive TRANSP determines sources ITER baseline scenario (15 MA), EPED pedestal 35 N m and 33 MW NBI, 1 MW ICRF, 6 MW ECCD (at q=3/2, 2 surfaces) Core solution with TGYRO with TGLF+NEO transport Next, use edge rotation boundary condition and also solve transport in momentum channel with NBI TGLF momentum transport worked well in DIII-D 1 at lower collisionality and q ω (krad/s) (kev) Te Rotation Set Uniformly to (kev) ne (1 19 /m 3 ) Ti ! [1] Chrystal, Phys. Plasmas 24, (17)

20 Core Rotation Shear in ITER Is Predicted to Significantly Improve Fusion Performance! Rotation boundary condition of 4 krad/s is used, relatively modest value within 3-1 krad/s range of predictions Core rotation determined from TGLF momentum flux and 35 N m source Deuterium Mach numbers are modest: Mcore~.2, Mped~4 Significant for heavy impurity transport Qfus approximately doubles due to density peaking and increased temperatures caused by rotation shear Grains of salt: Q values are idiosyncratic to the impurities and radiated power, there are nonlinearities and initial condition is important, residual stress not included in core (see Grierson EX/P6-3 this afternoon) (krad/s) ω (kev) Te No Rotation With Rotation (kev) ne (1 19 /m 3 ) Ti

21 Performance Improvement From Rotation Shear Is Due to Reduction of Low-k Turbulence and Increase in Density Peaking In simulation with rotation, low-k turbulence => outward particle flux, intermediate-k => inward particle flux Without ExB shear, total flux would be outward, force TGYRO to flatten density profile ExB shear suppresses low-k turbulence more strongly, so flux Γ/ΓGB V E B.25 V E B.5 V E B.75 V E B 1. V E B is balanced even with a peaked density profile k θ V Increased Te due to reduced transport further destabilizes intermediate-k turbulence, increasing inward particle flux, as seen in similar studies 1 [1] Grierson, Phys. Plasmas 25, 2259 (18)!21

22 Performance Improvement From Rotation Shear Is Due to Reduction of Low-k Turbulence and Increase in Density Peaking In simulation with rotation, low-k turbulence => outward particle flux, 6 intermediate-k => inward particle flux Without ExB shear, total flux would be outward, force TGYRO to flatten density profile Γ/ΓGB 4 2 Total Flux: +45 V E B.25 V E B.5 V E B.75 V E B 1. V E B ExB shear suppresses low-k turbulence more strongly, so flux is balanced even with a peaked density profile k θ V Increased Te due to reduced transport further destabilizes intermediate-k turbulence, increasing inward particle flux, as seen in similar studies 1 [1] Grierson, Phys. Plasmas 25, 2259 (18)!22

23 Performance Improvement From Rotation Shear Is Due to Reduction of Low-k Turbulence and Increase in Density Peaking In simulation with rotation, low-k turbulence => outward particle flux, intermediate-k => inward particle flux Without ExB shear, total flux would be outward, force TGYRO to flatten density profile ExB shear suppresses low-k turbulence more strongly, so flux Γ/ΓGB Total Flux: +45 V E B.25 V E B.5 V E B.75 V E B 1. V E B Total Flux: -1 is balanced even with a peaked density profile k θ V Increased Te due to reduced transport further destabilizes intermediate-k turbulence, increasing inward particle flux, as seen in similar studies 1 [1] Grierson, Phys. Plasmas 25, 2259 (18)!23

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sha1_base64="fzoicufux2slrxu9ocyyvdv672k=">aaaccxicbzdlssnafiyn9vbrlerszwarujcsdkplggguk9glncfmpqftekyzeyeelp146u4cagiw9/anw/jtm1cw38y+pjpozw5fyg4u9pxvq3s2vrg5lz5u7kzu7d/yb8edvsssgptmvbe9kkiglmy2pppdjhguqhh244uz7vuw8gfuvie5j8cmyitmquaknfdi45g2yepxksmccsjdemcjb7gmq4gkmtccuonvnlrwkbgfvvkgv2f/eikfpblgmncjvdx2h/zxizsihacvlfqhcj2qefymxiud5+fyskt4zzgape2lerphc/t2rkiplapnztwc3xzuz/tx6qh1d+zmkraojpytew5vgnebylhjajvppmakgsmb9ioiasug3cq5gq3owtv6htqlug7xrv5krrxmdofnjlxizrofrvqg1hij7rk3qznqwx6936wlswrglmgp2r9fkdituanw==</latexit> Simple Scaling Relation Offers Favorable Prospect of Achieving RMP ELM Suppression in ITER Low rotation RMP ELM suppression is hard to achieve, hypothesized to be a result of inward movement of Er= 1!?,e also hypothesized 2, movement is typically correlated with Er= movement Relation for Er=, divergence free flow: V = k( )B +!( )R ˆ' ) ITER needs less rotation because of: Larger gradient scale length (larger size) Larger poloidal field rp nze =!RB Edge C 6+ Rotation (km/s) ELMing Suppressed t (s) 1 #slices (a.u.) 5-9 krad/s of pedestal top rotation is lower limit for suppression in DIII-D, translates to.2-.5 krad/s for ITER, <3 krad/s prediction Effect of RMP field on rotation prediction still needed to fully answer this question!24 [1] Paz-Soldan, Nucl. Fusion (in review) [2] Moyer, Phys. Plasmas 24, 1251 (17)

25 Conclusions Edge rotation prediction for ITER is made with increased confidence: 3-1 krad/s Fast-ion effect on results is relatively small while reducing discrepancies between predictions Neutral particle induced transport found to be small ITER, though large and with relatively small NBI torque, will still have significant enough ExB to decrease turbulent transport Prospect of RMP ELM suppression is good These rotation predictions must now be ω (krad/s) (kev) Te No Rotation With Rotation (kev) ne (1 19 /m 3 ) Ti !25 integrated with effects from intrinsic and applied 3D fields

26 BACKUP SLIDES!26

27 Intrinsic Rotation Does Not Vary with Gross Change in Neutrals Associated with Divertor Detachment!27 Detached divertors have higher neutral particle pressures These conditions were created with significant main-chamber gas fueling in order to increase plasma density These changes are expected to increase neutral densities inside the confined plasma, but this causes no significant change to the intrinsic rotation So long as Ti does not begin to drop This result supports conclusions drawn from open/closed divertor comparisons J sat (A/cm 2 ) Neut. Press. (mtorr) T i (kev) ω (krad/s) (a) (b) (c) (d) Time (s) NBI Blips Detachment Onset

28 Dimensionless Parameter Scan Executed in ECH H-modes in DIII-D Achieved Desired Variation in was decreased by ~3%, the expected range achievable in DIII-D with limitations on field β variation due to ECH absorption 6 2 Change in Zeff is likely due to a change in carbon source due to a hard to control change in boundary conditions This is a potential confounding factor for the results, though previous work has not seen causal changes in intrinsic rotation with Zeff (a) (c) ν (b) (d) Z eff !28

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sha1_base64="sacc3ix45qof2bhp89/macalqwy=">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</latexit> <latexit sha1_base64="sacc3ix45qof2bhp89/macalqwy=">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</latexit> Simple Scaling Relation Offers Favorable Prospect of Achieving RMP ELM Suppression in ITER RMP ELM Suppression at low rotation is thought to be difficult due to the movement of the Er= crossing to lower minor radius Using the divergence-free form of velocity: V = k( )B +!( )R ˆ' a relation for Er= can be made into scaling requirement for Mach! number rp nze =!RB ) rp nze =!RB M = q( 1 T + 1 n ) R p T/m/B/a R p T/m/B/a ω is the toroidal rotation frequency if poloidal rotation is zero, B approximated as toroidal field to make factor of q We will assume the normalized gradient scale lengths will NOT change in ITER 5-9 krad/s of pedestal top rotation is current lower limit for RMP ELM suppression in DIII-D, yields a lower limit of.2-.5 krad/s for ITER, <3 krad/s prediction Effect of RMP ELM suppression on rotation prediction still needed to fully answer this question!29

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