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This study focuses on the systems analysis and ideal MHD stability of burning AT plasmas in the FIRE fusion reactor. It explores various parameters such as plasma current, q(min), bN, and feedback control methods for stabilizing instabilities.
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Advanced Tokamak Modeling for FIRE C. Kessel, PPPL NSO/PAC Meeting, University of Wisconsin, July 10-11, 2001
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)
Applying Constraints Shows Viable Q=10 Burning AT Plasmas Exist
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
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
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
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
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
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??
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
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
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
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
Dynamic Burning AT Simulations with TSC-LSC for FIRE Plasma becomes quasi-stationary after 10 s
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
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