Dependence of Achievable β N on Discharge Shape and Edge Safety Factor in DIII D Steady-State Scenario Discharges

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1 Dependence of Achievable β N on Discharge Shape and Edge Safety Factor in DIII D Steady-State Scenario Discharges by J.R. Ferron with T.C. Luce, P.A. Politzer, R. Jayakumar, * and M.R. Wade *Lawrence Livermore National Laboratory. Oak Ridge National Laboratory Presented at the American Physical Society Division of Plasma Physics Meeting Long Beach, California DIII D NATIONAL FUSION FACILITY October 29 through November 2, 21 QTYUIOP

2 Motivation

3 high fi N is an important component of the Motivation: parameter set for a steady-state, advanced self-consistent Optimum discharge has relatively high q (including q(), q min, q 95 ) for BS, high fi N for power output. f Low density requires pumping of H-mode divertor exhaust. tokamak discharge High fifi E / (fi N =q)(h 89 =q ff ) for fusion power output. High bootstrap fraction f BS / fi P / qfi N for steady state. High fi N enhances off-axis ECCD efficiency. Low density required for efficient electron cyclotron current drive (ECCD). 2

4 Background

5 of fi N was sought within the constraints of the Optimization tokamak scenario advanced Prior to upper divertor bae installation (1999), fi N H 89 ß 1, fi N ß 3:7 sustained in = 2, ffi = :9 shape.» Achievable fi N (ß 3:4) reduced in lower elongation, triangularity (» = 1:7, = :7) shape compatible with pumping after divertor bae installation ffi Leads to 21 investigation of the effect of variation in shape and q 95 (by changing T ) on achievable fi N. B (2) operation at B T = 1:6T for ECCD. Data set shows a dependence of the achievable fi N on the shape parameter S = (I=aB)q 95. 3

6 HIGH NORMALIZED PERFORMANCE (~1) SUSTAINED FOR 5 τ E IN κ = 2, δ =.9 SHAPE l i β N β N H 89 β ~ < 4.7% 4 3 q() f q min bs ~ n = 1 Mirnov Ampl. (G) n = 1 Saddle Loop (G) DIII D NATIONAL FUSION FACILITY SAN DIEGO I p (MA) x 1 P NB (MW) <n e > Time (ms) 251 1/JRF/wj

7 OBSERVED β N LIMIT HAS A SIGNIFICANT DEPENDENCE ON PLASMA SHAPE Comparison between shapes available before and after divertor bae installation S = Data windowed to.75 < l i <.85, β N > 4 l i S = 6.7 Maximum β N Pumping Shape κ = 1.8; δ =.6 Optimized 3. Shape S (I/aB) q κ = 2.; δ =.9 95 DIII D NATIONAL FUSION FACILITY SAN DIEGO Experimental scans at constant I/aB 251 1/JRF/wj

8 Experimental results

9 Experimentally achievable fi N increased at higher q 95 fi N = 4:1 sustained at B T = 1:85T in» = 1:8, ffi = :7 shape (compared to N = 3:4 at B T = 1:6T). fi No improvement in fi N was found by varying the discharge shape near the pumping geometry. Resistive fi N limited, high performance phase terminated by instability: ELMs Neoclassical Above In Improvement over fi N in the older higher elongation, triangularity shape. Provides a satisfactory fi N value for an ECCD target. wall modes (RWM). tearing modes (NTM) at m=n = 2=1. Maximum fi N : to 5:5`i. Up the ideal, no-wall n = 1 limit. some cases, close to the ideal-wall limit. 4

10 EXPERIMENTAL STUDIES INDICATE β N INCREASES WITH INCREASING q 95 Increasing DRSEP causes a drop in the shape parameter S = (I/aB) q 95 and q 95 itself studies indicated variation of RWM β limit with shape parameter and q < l i <.85 β N > 4l i < l i <.85 β N > 4l i 4.75 < S < Maximum β N Maximum β N S = (I/aB) q q 95 DIII D NATIONAL FUSION FACILITY SAN DIEGO 251 1/JRF/wj

11 CONDITIONS CONDUCIVE TO HIGH f BS AND HIGH βτ (β N = 4, H 89 = 3 WITH q min > 1.5) SUSTAINED FOR 5τ E <β> H 89P β N β p β N H 89P n = 1 B θ ( < 1 KHz) n = 1 B ( > 1 KHz) D α β N / l i q q min I p /1 (MA) 5 P NBI (MW) <n e > (1 19 m 3 ) DIII D NATIONAL FUSION FACILITY SAN DIEGO Time (ms) 13-1/jy

12 systematic variation in fi N resulted from many small variations No the standard pumping shape about No opportunity to optimize most shapes. Further analysis and modeling comparison required. standard pumping triangularity increased triangularity 4 BETAN BETAN BETAN BETAN BETAN BETAN 166 large inside gap (increased triangularity) normalized beta 2 1 Bt = 1.85 T upper bias increased squareness time (ms)

13 β N ~ 4 HAS BEEN ACHIEVED WITH THE UPWARD SHAPE BIAS REQUIRED TO MAINTAIN DENSITY CONTROL Pumped Shape 8 4 Density ( 1 19 m 3 ) Unpumped Pumped Unpumped Shape 4 β N 2 ~ 4 n = 1 B θ (G) Time (ms) 15 2 DIII D NATIONAL FUSION FACILITY SAN DIEGO 251 1/JRF/wj

14 ERROR FIELD CORRECTION AND RWM FEEDBACK STABILIZATION HAVE ALSO BEEN SUCCESSFUL IN IMPROVING THE ACHIEVABLE β N C79 current (A) β N Mirnov signal (a.u.) RWM feedback Normal error field correction Enhanced error field correction Rotation at q = 2 surface Central Rotation DIII D NATIONAL FUSION FACILITY SAN DIEGO Time (ms) /JRF/wj

15 Modeling of no-wall limit

16 based on ideal n = 1 no-wall theory cannot account for Modeling changes in fi N observed in the experiment the Decreases In contrast to the experiment, the predicted no-wall n = 1 limit: Is Is q 95 increases. as Scan of B T at constant shape. Λ Λ Change in I p at constant shape. Modeling also predicts that the no-wall n = 1 limit: Is Current Ideal lower in the higher elongation, triangularity shape. optimized at lower q(). not strongly dependent on details of the pressure gradient profile shape. Modeling: computed with the code TOQ. Equilibria and pressure gradient profiles modeled from measured experimental profiles. stability computed with GATO with or without a conformal wall or a wall at the DIII-D vessel position. 6

17 modeling results show that the marginal value of fi N is Stability or decreasing as B T and q 95 are increased constant No-wall fi N limit for n = 1 from GATO/TOQ. 3.8 q() = 1.27 q, safety factor model q profiles Bt=2.1 T Bt=1.6 T normalized flux exp normalized beta stability margin q()= 1.27 q() varies with toroidal field q()= q toroidal field (T) 7

18 increase in the ideal, no-wall, n = 1 stability limit with extra No has been found in initial modeling results shaping 1*1 6 8*1 5 6*1 5 4*1 5 2* pressure gradient marginally stable profiles q, safety factor "13315" "98549" TOQ model of » = 1:8, ffi = :6, q 95 = 4 marginally stable at fi N = 3: "98549" 2 1.5* *1 6 current density "13315" "13315" Reducing q 95 (increasing Ip) increases normalized beta limit 5.*1 5 "98549"» = 2:, ffi = :8, q 95 = 5:3 marginally stable at fi N = 3: normalized flux model of (fi N = 3:66 at q 95 = 4) 8

19 of the fi N limit to the model profiles was studied for Sensitivity more strongly shaped case the fi N.5. most Strongly shaped H-mode type J profile experiment-type J profile (q() ß 1:27) (q() ß 1:6) H-mode P profile Experiment-type P profile *1 5 5 q, safety factor P, total pressure limit varies by at 1.*1 5 discharge had *1 4 experimenttype an unusually broad 2 1 pressure profile. 1.5*1 6 1*1 6 J, current density 8*1 5 pressure gradient 1.*1 6 H-mode type profiles 6*1 5 5.*1 5 4*1 5 experiment-type profiles normalized radius 2*1 5 measured experiment profiles normalized radius 9

20 Effect of an ideal wall

21 in fi N achieved by Increases the no-wall limit by a wider margin exceeding The no-wall limit is exceeded if the ideal wall stability. The more the no-wall limit N = 3:7 fi T = 1:6T B 1-1 must be present for 1-2 fi N = 4;B T = 1:85T;» = 1:8 is exceeded, the closer the stabilizing wall must be to the plasma. normalized growth rate » = 2: 1-6 fi N = 3:4;B T = 1:6T;» = 1: equivalent DIII-D wall position conformal wall position minor radius 1 1

22 fi N achievable with an ideal wall determined by Maximum stability versus wall position modeling T = 1:85T B = 1:8, ffi = :7) (» B T = 2:1T = 2:, ffi = :9» T = 1:6T) (B = 1:27 q() T = 2:1T, (B Little difference 4.5 in response to B T = 1:6T (» = 1:8, ffi = :7) change in wall position as shape and B T (i.e. q 95 ) are varied. normalized beta » = 1:8, ffi = :7) Equivalent DIII-D wall position conformal wall position (factor times minor radius) (» = 1:8, ffi = :7) 11

23 experimental discharges with fi N 4 are near the ideal Some n = 1 stability limit wall q, safety factor 2.* *1 5 Effect of wall depends on details of the equilibrium in 3 examples with fi N 4. P, total pressure normalized growth rate *1 1.*1 6 J, current density 1.*1 5 5.* *1 1.*1 6 Pressure gradient equivalent DIII-D wall position conformal wall position minor radius 1 5.* normalized radius 5.* normalized radius 12

24 Summary

25 The advanced tokamak steady-state scenario required a method to increase achievable N in the lower», ffi pumping shape. fi q An increase to fi N > 4 was achieved by a 15% increase in B T. Improved 95 is thought to be the key parameter. The higher fi N values cannot be accounted for by an increase in the no-wall N limit. fi Discharges at q 95 ß 5, fi N ß 4:1 appear to be close to the ideal wall limit. Further increases in the ideal wall limit appear possible through changes in profiles. Summary error field correction may be an enabling factor. Increase in fi N likely results from a closer approach to the ideal wall fi N limit. 13

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