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
Motivation
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
Background
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). 1999-2 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
HIGH NORMALIZED PERFORMANCE (~1) SUSTAINED FOR 5 τ E IN κ = 2, δ =.9 SHAPE 4 2 12 8 4 4 l i β N β N H 89 β ~ < 4.7% 4 3 q() f q min bs ~.5 2 1 3 2 1 n = 1 Mirnov Ampl. (G) n = 1 Saddle Loop (G) 1 15 1 5 DIII D NATIONAL FUSION FACILITY SAN DIEGO I p (MA) x 1 P NB (MW) <n e > 5 1 15 2 25 Time (ms) 251 1/JRF/wj
OBSERVED β N LIMIT HAS A SIGNIFICANT DEPENDENCE ON PLASMA SHAPE Comparison between shapes available before and after divertor bae installation S = 5.2 4.5 Data windowed to.75 < l i <.85, β N > 4 l i S = 6.7 Maximum β N 4. 3.5 Pumping Shape κ = 1.8; δ =.6 Optimized 3. Shape 4.5 5. 5.5 6. 6.5 7. 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
Experimental results
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
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 1999-2 studies indicated variation of RWM β limit with shape parameter and q 95 4.5.75 < l i <.85 β N > 4l i 1999 2 21 4.5.75 < l i <.85 β N > 4l i 4.75 < S < 5.25 1999 2 21 Maximum β N 4. 3.5 Maximum β N 4. 3.5 3. 4.5 5. 5.5 6. 6.5 7. S = (I/aB) q 95 3. 3.5 4. 4.5 5. 5.5 6. q 95 DIII D NATIONAL FUSION FACILITY SAN DIEGO 251 1/JRF/wj
CONDITIONS CONDUCIVE TO HIGH f BS AND HIGH βτ (β N = 4, H 89 = 3 WITH q min > 1.5) SUSTAINED FOR 5τ E 5 4 3 2 1 15 <β> H 89P β N β p 16795 1 β N H 89P 5 15 1 5 1 n = 1 B θ ( < 1 KHz) n = 1 B ( > 1 KHz) D α β N / l i 3. 2.5 2. 1.5 q q min 1. 15 1 I p /1 (MA) 5 P NBI (MW) <n e > (1 19 m 3 ) 5 1 15 2 DIII D NATIONAL FUSION FACILITY SAN DIEGO Time (ms) 13-1/jy
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 16568 BETAN 16581 BETAN 16589 BETAN 16592 3 BETAN 16685 BETAN 166 large inside gap (increased triangularity) normalized beta 2 1 Bt = 1.85 T upper bias increased squareness 5 1 15 2 time (ms) 166 1275. 16685 1625. 16592 135. 16589 1525. 16581 13. 16568 15. 5
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 16795 17181 Pumped Unpumped Shape 4 β N 2 ~ 4 n = 1 B θ (G) 2 5 1 Time (ms) 15 2 DIII D NATIONAL FUSION FACILITY SAN DIEGO 251 1/JRF/wj
ERROR FIELD CORRECTION AND RWM FEEDBACK STABILIZATION HAVE ALSO BEEN SUCCESSFUL IN IMPROVING THE ACHIEVABLE β N 4 3 2 1 4.2 4. 3.8 3.6 3.4 3.2 3. C79 current (A) β N Mirnov signal (a.u.) RWM feedback Normal error field correction 1756 17516 17514 Enhanced error field correction 25 2 15 1 5 5 4 3 2 Rotation at q = 2 surface Central Rotation DIII D NATIONAL FUSION FACILITY SAN DIEGO 1 5 1 Time (ms) 15 2 251 1/JRF/wj
Modeling of no-wall limit
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
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 6 5 4 3 2 model q profiles Bt=2.1 T Bt=1.6 T 1..2.4.6.8 1. normalized flux exp 13315.188 normalized beta stability margin 3.4 3. 2.6 q()= 1.27 q() varies with toroidal field q()= 1.65 4. q 95 5.3 1.5 1.7 1.9 2.1 toroidal field (T) 7
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*1 5 6 5 pressure gradient marginally stable profiles q, safety factor "13315" "98549" TOQ model of 13315.188» = 1:8, ffi = :6, q 95 = 4 marginally stable at fi N = 3:74 4 3 "98549" 2 1.5*1 6 1 1.*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 = 3:48..2.4.6.8 1. normalized flux model of 98549.19 (fi N = 3:66 at q 95 = 4) 8
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 3.52 3.15 Experiment-type P profile 3.34 3.62 6 1.5*1 5 5 q, safety factor P, total pressure limit varies by at 1.*1 5 discharge had 4 3 5.*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..2.4.6.8 1. normalized radius 2*1 5 measured experiment profiles..2.4.6.8 1. normalized radius 9
Effect of an ideal wall
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 1-3 1-4 1-5» = 2: 1-6 fi N = 3:4;B T = 1:6T;» = 1:8 1. 1.5 2. 2.5 equivalent DIII-D wall position conformal wall position minor radius 1 1
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 4. 3.5» = 1:8, ffi = :7) Equivalent DIII-D wall position 3. 1.4 1.6 1.8 2. 2.2 2.4 conformal wall position (factor times minor radius) (» = 1:8, ffi = :7) 11
experimental discharges with fi N 4 are near the ideal Some n = 1 stability limit wall 1-1 6 5 q, safety factor 2.*1 5 1.5*1 5 Effect of wall depends on details of the equilibrium in 3 examples with fi N 4. P, total pressure normalized growth rate 1-3 1-5 4 3 2 1.2.4.6.8 1. 6. 1.5*1 1.*1 6 J, current density 1.*1 5 5.*1 4.2.4.6.8 1. 6. 1.5*1 1.*1 6 Pressure gradient equivalent DIII-D wall position 1. 1.5 2. 2.5 conformal wall position minor radius 1 5.*1 5..2.4.6.8 1. normalized radius 5.*1 5..2.4.6.8 1. normalized radius 12
Summary
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