Development of a Systematic, Self-consistent Algorithm for the K-DEMO Steady-state Operation Scenario

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1 Development of a Systematic, Self-consistent Algorithm for the K-DEMO Steady-state Operation Scenario J.S. Kang 1, J.M. Park 2, L. Jung 3, S.K. Kim 1, J. Wang 1, D. H. Na 1, C.-S. Byun 1, Y. S. Na 1, and Y. S. Hwang 1 1 Seoul National University, Seoul, Republic of Korea 2 Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA 3 National Fusion Research Institute, Daejeon, Republic of Korea contact : 26 th IAEA Fusion Energy Conference Oct 22, 2016

2 K-DEMO Goal: Demonstrate a Net Electricity Generation 1 st phase High B T 2 nd phase High B T & β N Pressure Limit B T β N I P f BS B T β N /I P β N KSTAR 2 nd Phase 3000 MW 3.5 T β N ~ 5 1 st Phase 2000 MW ITER Q ~ 5 Steady-state 5.3 T β N ~ 3 Scope of This Study B T 1/21

3 K-DEMO Design Parameters Major Radius (R) Minor Radius (a) 6.8 m 2.1 m Toroidal Magnetic Field Elongation / Triangularity 7.4 T 2.0 / 0.6 β N < 4 Fusion Power (P F ) 2000 MW (1 st ) 3000 MW (2 nd ) Fusion Gain 20 Divertor Operation Double-null < K-DEMO Magnet & Divertor Analysis [1]> Size & aspect ratio similar to those of ITER & KSTAR. Nb 3 Sn configuration/stress analysis/test fabrication. Tungsten mono-block type divertor, RAFM cooling tube, high pressure water-cooling. Ceramic pebble type breeder blanket, high pressure water cooling. [1] Kim, K., et al, Design concept of K-DEMO for near-term implementation, Nucl. Fusion 55 (2015) /21

4 0-D System Analysis to Identify Fusion Performance & Operating Regime <Operation Regime for K-DEMO[1]> [1] Kang, J.S., et al, Fusion. Eng. Des , Part A (2016) D power balance P F = 2000 MW, Q = 20 n eavg = 0.87x10 20 m -3, T e = 20.0 kev 3/21

5 0-D System Analysis to Identify Fusion Performance & Operating Regime <Operation Regime for K-DEMO[1]> [1] Kang, J.S., et al, Fusion. Eng. Des , Part A (2016) D power balance P F = 2000 MW, Q = 19 n eavg = 1.2x10 20 m -3, T e = 20.0 kev Burning plasma profile effect (self H/CD) change optimum operation regime. Pressure Profile α heating & bootstrap Current Profile Heat Diffusion Need a self-consistent integrated modeling! 4/21

6 Previous K-DEMO Integrated Modelling Target pressure and current profile are achieved intuitively. <1-D KDEMO n, T, J profile[1]> Modelling with prescribed heating schemes (1) 1 beam 1 MeV 100 MW on-axis (2) 2 beams, on-axis (1.5 MeV 50 MW) off-axis (0.6 MeV 50 MW) (3) 2 beams, on-axis (1.3 MeV 40 MW) off axis (0.8 MeV 80 MW) (4) (5) (6) Try Select the maximum fusion gain one Systematic approach is required! [1] Kang, J.S., et al, Fusion. Eng. Des , Part A (2016) /21

7 A Systematic Algorithm for K-DEMO Burning Plasma Design is Developed o Find p & j profiles and corresponding H&CD specification to maximize Q, systematically and self-consistently. f ( p, j ) = max {Q} p : pressure profile j : current profile High performance steady state operation needs optimization of P&J profiles. Burning plasma algorithm must integrate various physics/engineering. Optimization Algorithm Consider Constraints Confinement MHD stability H/CD 6/21

8 Previous Flowchart of K-DEMO Target P&J 0D Analysis <n> <T> I P Solve Equilibrium with prescribed q H/CD Configuration No Select with Highest Q Check target performance Stable Equilibria & Check Check P F P F Solve Plasma Transport 7/21

9 K-DEMO Burning Plasma Target Scenario Algorithm Flowchart Confinement, Stability, and H/CD are simultaneously satisfied. Systematic 0D Analysis <p> I P Pressure & Current Variation P(ρ) J(ρ) Stable Equilibria & P F Check No, vary P&J Shape No I P No, other equilibrium for high f BS Find relevant H/CD Deposition Select with Highest Q Check P F Solve Plasma Transport 8/21

10 FASTRAN/IPS is Adopted for Numerical Apparatus to Integrated Numerical Package Implement Algorithm Algorithm - Operation Supervisor Standard Data Model (Plasma State File) TGLF RF Sources CURRAY Energetic particle sources (NB) NUBEAM Transport FASTRAN Turbulent transport coeff. Neoclassical coeff. Chang-Hinton Sauter MHD equilibrium ESC MHD stability DCON MISHIKA1 0D system Analysis Driver : ITERATIVE SOLUTION of d/dt=0 9/21

11 Loop 1: Find Stable Equilibrium Satisfying P F Confinement & Stability 0D Analysis <p> I P Pressure & Current Variation P(ρ) J(ρ) Stable Equilibria & P F Check No, vary P&J Shape No I P No, other equilibrium for high f BS Find relevant H/CD Deposition Select with Highest Q Check P F Solve Plasma Transport 10/21

12 Loop 1: Find Stable Equilibrium Satisfying P F Target P&J Profiles are Explored. Pressure & Current Variation P(ρ) J(ρ) Stable Equilibria & P F Check No, vary P&J Shape Control Knobs p axis, α, β, p ped, j axis, j peak, ρ peak, ρ boundary Δped = 0.1 benchmark from ITER. 11/21

13 Loop 1: Find Stable Equilibrium Satisfying P F Target P&J Profiles are Explored. Pressure & Current Variation P(ρ) J(ρ) Stable Equilibria & P F Check No, vary P&J Shape P F Evaluation with T i / n i Ion Temperature (kev) (T i T e ) Ion Density (10 19 m -3 ) Z eff Z imp f imp from ITER Prescribed n e (f GW = 1) n axis /n ped = 0.8 n ped /n sep = Radius, ρ 12/21

14 Loop 1: Find Stable Equilibrium Satisfying P F Target P&J Profiles are Explored. Pressure & Current Variation P(ρ) J(ρ) Stable Equilibria & P F Check No, vary P&J Shape Linear Ideal MHD Evaluation with DCON[1] & MISHIKA1[2] T ped < ideal MHD P-B mode [3] limit. n = 3 mode structure X [a.u] [1] Glasser, A. H., et al., Bulletin of the American Physical Society Vol. 42, p (1997). [2] Mikhailovskii, A. B., et al., Plasma physics reports, 23(10), p. 844 (1997). Normalized flux N [3] Snyder, P. B., et al., Physics of Plasmas 9 (2002) /21

15 Loop 2: Determine External H/CD Configuration H/CD & Confinement 0D Analysis <p> I P Pressure & Current Variation P(ρ) J(ρ) Stable Equilibria & P F Check No, vary P&J Shape No, other equilibrium for high f BS Find relevant H/CD Deposition No I P Select with Highest Q Check P F Solve Plasma Transport 14/21

16 P (MW/m 3 ) Jφ (MA/m 2 ) Loop 2: Determine External H/CD Configuration 1. Scanning H/CD control knobs to match J EXT = J TOT - J BS Pressure & Current Variation J EXT P CD H ρ P(ρ) J(ρ) No, vary P&J Shape Stable Equilibria & P F Check No, other equilibrium for high f BS Control Knobs E Beam, P NB, Port location RF frequency, wave number NB&FW choice with ITER technology. Find relevant H/CD Deposition 15/21

17 P (MW/m 3 ) Loop 2: Determine External H/CD Configuration 2. 1-D power balance analysis P α P PB H P con + P rad ρ Pressure & Current Variation P(ρ) J(ρ) No, vary P&J Shape Stable Equilibria & P F Check Calculate P H PB to match 1-D power balance. P H PB = P α - ( P con + P rad ) No, other equilibrium for high f BS Find relevant H/CD Deposition P CON from diffusion model & n,t profile P α P RAD from n, T profile(loop 1 Result) 16/21

18 P (MW/m 3 ) Loop 2: Determine External H/CD Configuration 3. Compare P H CD & P H PB (1) P H CD ~ P H PB (2) P H CD > P H PB (3) P H CD < P H EXT (Discard) Pressure & Current Variation P(ρ) J(ρ) Stable Equilibria & P F Check 1 No, vary P&J Shape P H PB P H CD ρ No, other equilibrium for high f BS P H CD > P H PB (2) Consider required H/CD alignment together. Solve Plasma Transport Find relevant H/CD Deposition (1) P H CD ~ P H PB 17/21

19 Loop 3: Check Self-consistency between Plasma Profiles and H/CD Configuration by Integrated Modelling 0D Analysis <p> I P Pressure & Current Variation P(ρ) J(ρ) Stable Equilibria & P F Check No, vary P&J Shape No, other equilibrium for high f BS Find relevant H/CD Deposition No I P Select with Highest Q Check P F Solve Plasma Transport 18/21

20 Jφ (MA/m 2 ) An Optimum Target P&J is Attained through Algorithm with Integrated Transport Modeling A fully non-inductive target plasma is finally achieved Temperature (kev) T i Radius, ρ T e Density (10 19 m -3 ) n e Radius, ρ Total Bootstrap Radius, ρ n i Result 0 D P F (MW) Q (Fusion Gain) P NB (MW) I P (MA) f BS 77 % 75 % β N H 98y T ped n ped 8.3 kev m -3 19/21

21 Safety factor, q Jφ (MA/m 2 ) Discussion of Derived H/CD Specification Total Bootstrap Off-axis NB provide broad J Profile - improved confinement. NB Single 110MW 500keV NB injection - Alignment with less-bootstrap region. - Even half of ITER NBI beam energy. q min > 2 is set to avoid tearing modes Radius, ρ 20/21

22 Conclusion & Future Work A systematic scenario optimization algorithm maximizing the fusion gain is newly established by integrating equilibrium, confinement, stability, and current drive requirement, self-consistently. Target pressure & current profile for K-DEMO is derived with designed algorithm. fusion power of 2080 MW, fusion gain Q of 18.8 and normalized beta β N of Particle Transport/plasma rotation/more detailed stability are planned. Particle transport and plasma rotation are also key control knobs for stable fusion power production and they will be updated to the systematic algorithm in the near future. Pedestal structure and plasma shaping optimization are expected to address more efficient/accurate target scenario. 21/21

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