Advanced Tokamak Modeling for FIRE

1. Advanced Tokamak Modeling for FIRE C. Kessel, PPPL NSO/PAC Meeting, University of Wisconsin, July 10-11, 2001

2. Systems Analysis of Burning AT Plasmas in FIRE • Using the FIRE baseline (R=2.0 m, A=3.8)solutions are found which satisfy: • Power balance with Q=10 • PCD< Paux=5Palpha/Q, hCD= 0.45 A/W-m2 from CD calculations • Pfusion< 250 MW,Palpha< 50 MW • While varying • BT(6.5 - 9.5 T) • q95 (3.1-4.7) • n(0)/<n> (1.25-2.0) • bN(2.5-4.5) • n/nGr (0.45-0.85)

3. Applying Constraints Shows Viable Q=10 Burning AT Plasmas Exist

4. System Analysis Is Searching for Lowest H98 Factors for AT Plasmas Each bN has a best (Bt, q95) combination to get lowest H98 bN = 2.5; Bt=9.5, q95=4.3 bN = 3.0; Bt=8.5, q95=3.7 bN = 3.5; Bt=7.5, q95=3.5 Highest n(0)/<n> leads to lowest H98 Highest allowed n/nGr leads to lowest H98

5. Quasi-Stationary AT Burning Plasmas are the Primary Focus • Plasma current is ramped up with inductive and non-inductive current to produce a quasi-stationary plasma at the beginning of flattop • The safety factor is held by non-inductive current • Bootstrap current • LHCD off-axis • ICRF/FW on axis • Flattop times 2-4 x tjdiff (30-60 s) • Q=5-10 • 1.0 < H(y,2) < 1.8 transient burning AT plasmas can be produced with inductive current long pulse DD (non-burning) plasmas can be created with pulse lengths up to >200 s at Bt=4 T, Ip=2 MA

6. FIRE Can Access Various Pulse Lengths by Varying BT

7. Ideal MHD Stability and LHCD Analysis Identifies an AT Plasma Target q(min) = 2.1-2.2, r/a(min) = 0.8, Ip(MA) < 5.5, Bt(T) = 8.5 • No n=1 stabilization • bN = 2.5 • fbs < 0.55 • With n=1 stabilization • bN = 3.6 • fbs < 0.75 *plasmas with qmin = 1.3-1.4 also identified, but these have (3,2) and (2,1) NTMs, and no improvement in bN when n=1 is stabilized (for feedback approach, not rotation method) **pockets of n=1 stability at qmin just above integer values are found, although the depth of the pocket is unclear ***LHCD calculations show that waves can not penetrate inside of r/a = 0.5-0.6 for typical plasma parameters

8. qmin = 2.1, r/a(qmin) = 0.8, Ip = 5.3 MA, BT = 8.5 T, R/a = 3.8, (5,2) and (3,1) NTM’s, allows wider range for value of qmin, n(0)/<n> = 1.5 Benefit of n=1 RWM Stabilization LHCD shape and location approximation from ray-tracing calculations n=1 not stabilized bN = 2.55 fbs = 0.55 ILH = 2.2 MA IBS = 3.0 MA n=1 stabilized bN = 3.6 fbs = 0.75 ILH = 1.4 MA IBS = 3.8 MA

9. Plasma rotation theory Require rotation of 1-10% of Alfven speed Conducting shell located inside the critical ideal wall and outside the critical resistive wall* Dissipation mechanism in plasma Error field control (DIII-D experience) Feedback control theory Require feedback coils to produce field with given toroidal mode number (n=1) Conducting shell to slow instability growth time to feedback timescales* Field sensors preferably between conducting shell and plasma Rotation or Feedback Coil for n=1 External Kink Mode (RWM) Stabilization on FIRE *for rotation detailed wall geometry is important, for feedback it is not

10. FIRE is Examining Ways to Feedback Control RWM/Kink Modes Is rotation better or worse than feedback coils with a realistic partial wall? Feedback Coils: n=2 sets limit bN=3.6 Rotation: (NBI) continuous wall on outboard side, n=1 bN>4.5, with n=2,3 setting the limit model partial wall on outboard side, n=1 bN=3.45, n=2 limit??

11. 30 MW ICRF (ion heating) for ELMy H-mode; 4 ports, 100-150 MHz <10 MW ICRF/FW (electron heating/CD) for AT mode; 1 (or 2) ports, 90-110 MHz, phasable Want to use same ICRF equipment 20 MW LHCD (electron heating/CD) for AT mode; 2-3 ports, 5.6 GHz, n|| =2.0-2.5 For NTM control ?? MW ECH/ECCD (electron heating/CD) for startup External Current Drive and Heating for FIRE

12. ICRF/FW (T.K. Mau) ne(0) = 3.4 x 10^20 Te(0) = 20 keV Zeff = 1.4, bN = 2.55, Bt = 8.5 T w = 100 MHz n|| = 2.0 PFW = 3.6 MW IFW = 0.30 MA LHCD (LSC code) ne(0) = 4.5 x 10^20 n(0)/<n> = 1.5 Te(0) = 22 keV Zeff = 1.45, bN = 3.5, Bt = 8.5 T w = 5.6 GHz n|| = 2.0, Dn|| = 0.3 PLH = 20 MW ILH = 1.7 MA RFCD Analysis for FIRE Burning AT Plasmas CD efficiencies and deposition depend on details of n and T profiles

13. LHCD Calculation for FIRE with LSC Ray-Tracing Code PLH = 17.5 MW ILH = 1.65 MA n|| = 1.90, Dn|| = 0.3, w = 5.6 GHz IBS = 3.8 MA, Ip = 5.5 MA bN = 3.8, ne(0) = 4.6 x 10^20 n(0)/<n> = 1.4

14. Dynamic Burning AT Simulations with TSC-LSC for FIRE Ip=5.5 MA, Bt=8.5 T, Q=7.5, bN=3.0, b=4.4%, PLH=20 MW, ILH=1.7 MA, IBS=3.5 MA, IFW=0.35 MA H(y,2)=1.6

15. Dynamic Burning AT Simulations with TSC-LSC for FIRE Plasma becomes quasi-stationary after 10 s

16. Target AT plasmas found by systems study Continue ideal MHD stability search Pressure profile and q* variations Edge profile effects n=1 stabilized plasmas NTM requirements Examine DIII-D AT experiments Examine C-Mod AT experiments CD analysis Reduce PCD, raise fbs LHCD, HHFW, NBI ICRF/FW ECH/ECCD TSC-LSC dynamic discharge simulations Plasma formation in shortest time Energy and particle transport models Control of j, n, T Future Work for FIRE Burning AT Plasma Development

17. Conclusions • Systems analysis shows range of Q=10 burning AT plasmas with H98 > 1.4 • qmin around 2.1-2.2 is found to provide a good combination of • Beta limit with and without n=1 stabilization--increase these • High plasma current--not too high • Elimination of (3,2) and (2,1) NTM’s--but (5,2) and (3,1) exist • Lower CD power --need to reduce this • Less than 2 MA of LHCD is required, leading to powers of 20 MW from LSC lower hybrid calculations • Stabilization of n=1 RWM would yeild attractive configuratons; rotation versus feedback coils? • Need to find techniques for density profile peaking to enhance bootstrap current and reduce LHCD power • TSC-LSC simulations indicate that we can create quasi-stationary plasmas for flattop burn