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 –P CD < P aux = 5P alpha / Q,  CD = 0.45 A/W-m2 from CD calculations –P fusion < 250 MW, P alpha < 50 MW While varying –B T (6.5 - 9.5 T) –q95 (3.1-4.7) –n(0)/ (1.25-2.0) –  N (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  N has a best (Bt, q95) combination to get lowest H98  N = 2.5; Bt=9.5, q95=4.3  N = 3.0; Bt=8.5, q95=3.7  N = 3.5; Bt=7.5, q95=3.5 Highest n(0)/ 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  jdiff (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 B T

7. Ideal MHD Stability and LHCD Analysis Identifies an AT Plasma Target No n=1 stabilization –  N = 2.5 – f bs < 0.55 With n=1 stabilization –  N = 3.6 – f bs < 0.75 *plasmas with q min = 1.3-1.4 also identified, but these have (3,2) and (2,1) NTMs, and no improvement in  N when n=1 is stabilized (for feedback approach, not rotation method) **pockets of n=1 stability at q min 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 q(min) = 2.1-2.2, r/a(min) = 0.8, Ip(MA) < 5.5, Bt(T) = 8.5

8. Benefit of n=1 RWM Stabilization n=1 stabilized  N = 3.6 f bs = 0.75 I LH = 1.4 MA I BS = 3.8 MA n=1 not stabilized  N = 2.55 f bs = 0.55 I LH = 2.2 MA I BS = 3.0 MA q min = 2.1, r/a(q min ) = 0.8, I p = 5.3 MA, B T = 8.5 T, R/a = 3.8, (5,2) and (3,1) NTM’s, allows wider range for value of q min, n(0)/ = 1.5 LHCD shape and location approximation from ray-tracing calculations

9. Rotation or Feedback Coil for n=1 External Kink Mode (RWM) Stabilization on FIRE 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 *for rotation detailed wall geometry is important, for feedback it is not

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

11. External Current Drive and Heating for FIRE 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

12. RFCD Analysis for FIRE Burning AT Plasmas ICRF/FW (T.K. Mau) n e (0) = 3.4 x 10^20 T e (0) = 20 keV Z eff = 1.4,  N = 2.55, Bt = 8.5 T –  = 100 MHz – n|| = 2.0 –P FW = 3.6 MW –I FW = 0.30 MA LHCD (LSC code) n e (0) = 4.5 x 10^20 n(0)/ = 1.5 T e (0) = 22 keV Z eff = 1.45,  N = 3.5, Bt = 8.5 T –  = 5.6 GHz – n|| = 2.0,  n|| = 0.3 –P LH = 20 MW –I LH = 1.7 MA CD efficiencies and deposition depend on details of n and T profiles

13. LHCD Calculation for FIRE with LSC Ray-Tracing Code P LH = 17.5 MW I LH = 1.65 MA n|| = 1.90,  n|| = 0.3,  = 5.6 GHz I BS = 3.8 MA, I p = 5.5 MA  N = 3.8, n e (0) = 4.6 x 10^20 n(0)/ = 1.4

14. Dynamic Burning AT Simulations with TSC-LSC for FIRE Ip=5.5 MA, Bt=8.5 T, Q=7.5,  N =3.0,  =4.4%, P LH =20 MW, I LH =1.7 MA, I BS =3.5 MA, I FW =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. Future Work for FIRE Burning AT Plasma Development 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

17. Conclusions Systems analysis shows range of Q=10 burning AT plasmas with H98 > 1.4 q min 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