Reactor Configuration Development for ARIES-CS

1. Reactor Configuration Development for ARIES-CS L. P. Ku and the ARIES-CS Team Princeton Plasma Physics Laboratory Princeton University, Princeton, NJ 08543

2. Abstract • Progress has been made in developing new classes of quasi-axially symmetric configurations for ARIES-CS that have good a particle confinement properties and good integrity of equilibrium flux surfaces at high b.

3. For each new class of configurations, we have designed coils to ensure that the new configurations are realizable and engineering-wise feasible. • R/Dmin (Coil-Plasma) ≤ 6 • R/Dmin (Coil-Coil) ≤ 10. • The physics and coil properties of new configurations allow power producing reactors of ~2 GW be designed with R<9 m with DT fuels and with a full breeding blanket. The good quasi-axisymmetry limits the energy loss of a to < 10%.

4. We showcase two new classes of configurations • Configurations with low magnetic shear even in the presence of large amount of bootstrap current. • Configurations of very low aspect ratios (A~2.5)

5. ARIES-CS is a four-year, multi-institution program to study compact stellarator reactor systems. What Is ARIES-CS

6. F. Najmabadi, UCSD

7. Goals of Configuration Design Study • Identify plasma engineering issues relevant to a compact stellarator reactor • Find configurations that are optimized with respect to the components critical to reactor performance • Aspect ratios versus QA • a loss and its minimization • Equilibrium and MHD b limits • Integrity of flux surfaces

8. Minimum requirements in configuration optimization for MHD stable QA plasmas at high b are not well known at present. The following are “acceptance criteria” generally considered§. • Maximum residues of non-axisymmetry in magnetic spectrum. • neo-classical transport << anomalous transport • ovall allowable “noise” content < ~2%. • effective ripple in 1/n transport, e-eff < ~1% • ripple transport and energetic particle loss • a energy loss < ~10% • rotational damping (?) • Stability beta limits based on linear, ideal MHD theories. • vertical modes • interchange stability • V″~2-4%. • LHD, CHS stable while having a hill.

9. < 1/2 • ballooning modes • stable to infinite-n modes (eigenvalues calculated by COBRA code). • LHD exceeds infinite-n results. High-n calculation typically gives higher b limits. • kink modes • stable to n=1 and 2 modes without a conducting wall (eigenvalues calculated by Terpsichore code). • W7AS results showed mode (2,1) saturation and plasma remained quiescent. • tearing modes • di/ds > 0 • Equilibrium and equilibrium beta limits • Shafranov shift • large islands associated with low order rational surfaces • flux loss due to all isolated islands < 5% • overlapping of islands due to high shears associated with the bootstrap current • limitdi/ds §The ability to achieve our goals is often compromised by the conflicting demands of various constraints. Typically, we impose different weights depending upon the characteristics of a configuration we are looking for. There is also an issue of convergence and accuracy in numerical calculations.

10. Configuration Design Targets (Cont.) To establish minimum requirements for coil design optimization, we need more feedback from and iteration with systems analysis and engineering design. Presently, we include • Coil design • coil to coil and coil to plasma separation • R/Dmin(c-c) < 12 • R/Dmin(c-p) < 6 • radius of curvature and complexity • Bmax/B0 ~2.5 for 0.3 m x 0.3 m conductor @R~8 m. • adequate space for pumping, diagnostics, plasma heating and maintenance • R/Dout (c-p) < Ap (R/<a>)

11. Methods of Exploring Configuration Space • Broaden search of aspect ratio – rotational transform space, identifying regions endowed with particularly interesting features. • Build sophisticated computational systems to design configurations and coils which target the physics and engineering goals*. * See companion poster : Modular Coil Design for the Ultra-Low Aspect Ratio Quasi-Axially Symmetric Stellarator MHH2

12. Plasma Optimization System • Select p, J profiles, b, B, FP • Iota target • MHD stability target (Mercier, ballooning, kink) • Transport target (QA, ripple) • Coil target (complexity, current density) Constraints/weights Initial “guess”. Plasma boundary represented as Fourier coefficients. ballooning 1) Evaluate equilibrium (VMEC, NSTAB), 2) Jacobian calculations, 3) determine direction of descent, 4) perform functional minimization (Levenberg-Marquardt, GA). kink a loss transport shape/position coil complexity No Targets met? Modify weights Yes Flux surface quality, islands healing, PIES Refined calculation and detailed analysis

13. I. SNS family of configurations KJC167 – a showcase for essentially flat iota profile, demonstrating the existence of excellence of flux surface integrity Plane and perspective views of last LCMS geometry and |B| in real space.

14. < 1/2 Why low overall shear is of interest? • The integrity of equilibrium flux surfaces places a limit on the attainable beta • Shafranov shift • Formation of magnetic islands • Spacing between island chains and magnetic field stochasticity • We generally require • Shafranov shift • large islands associated with low order rational surfaces • flux loss due to all isolated islands < 5% • overlapping of islands due to high shears associated with the bootstrap current • limit di/ds

15. How flux surface integrity might be achieved in QAS? • Bootstrap currents in QAS are expected to be of similar magnitude to those in tokamaks. • High magnetic shear possible • Rotational transform crossing large number of rational surfaces likely • Rational surfaces may be close to each other • One solution is to carefully tailor the rotational transform profile • Select regions free of low order resonances • Shape the plasma such that the rising rotational transform due to the bootstrap current is compensated for by the decreasing transform from the shaping.

16. 9/16 6/11 9/17 KJC167 is a 3 field-period, aspect ratio 6 configuration of the SNS family in which the iota profile is selected to minimize the impact of low order resonance on the flux surface integrity. In this case, the external iota has a strong negative shear, but the iota at operating b is expected to have a small but positive shear in most of the plasma volume. Shear ~5% Total transform including contribution from bootstrap current at 6% b. External transform from plasma shaping

17. Excellent quality of flux surfaces is observed in most of the plasma for KJC167 at 6% b as seen below based on a PIES calculation. Equilibrium calculated by PIES @6% b. Poincaré plot in r-q at j=0. In Cartesian m=16 PIES and VMEC solutions are consistent. Equilibrium calculated by VMEC

18. Minimizing non-axisymmetric residues and effective ripples resulted in good quasi-axisymmetry. The effective ripple @s=1 is only 0.35% at 6% b and the overall “noise” is <2.5%. Loss of a energy is ~8% in one slowing down time in our model calculation. |B| on last LCMS in U-V space Effective ripple ~2.5% @s=1 0.5% Ovall “noise” content vacuum Eight major non-symmetric components in the magnetic spectrum plotted as function of normalized toroidal flux. With pressure at 6% b

19. KJC167 is stable to the m=1, n=0 vertical mode according to the Terpsichore calculation (no feedback control necessary) and is slightly unstable to both low and high-n internal modes at b=4%. Infinite-n ballooning modes (Cobra calculation) @ Low-n modes g• R/vA~0.001 6% b P-profile 5% b 3% b J-profile 2% b Note:stability analyses were based on the pressure and current profiles given above. Profiles may be further optimized to improve MHD stabilities to both the local and global modes.

20. KJC167 may be unstable to free-boundary modes for b~6% according to the Terpsichore calculation primarily due to the m=2, n=1 mode, but it could be made stable with more flux surface shaping to improve the local shear. It may also be made more stable by choosing more optimized pressure and current profiles. g • R/vA~0.15 Radial displacement eigenfunction N=0 N=1 Plasma-wall interface Wall @3.5x plasma-vacuum interface

21. A proposed design for the modular coils is to have 6 coils/period with coil aspect ratio R/Dmin(C-P)~6. The example given here, KJC167-M05, based on equal coil currents, has smooth contours with small toroidal excursion. Coil contours viewed on “U-V” plane of the winding surface in one field period.

22. II. MHH2 Family of Configurations MHH2-K14 – a showcase for very low aspect ratio A~2.65 configuration having low field ripples and excellent confinement of a particles. Plane and perspective views of the last LCMS geometry and |B| in real space.

23. Why low aspect ratio is of interest? • Fusion power, P, is inversely proportional to the square of plasma aspect ratio, A • A = R/<a>, R=major radius, <a>=average minor radius • P  B4b2R3/A2 • Lower A allows lower B or b or R. • Smaller sized-reactor (R) • Less stress and power for magnets (B) • Less MHD stability issues (b)

24. MHH2-K14 is a configuration of the ultra-low A family with relatively simple shaping and optimized for quasi-axisymmetry at 5% b without any other driven currents. Expected at 5% b with NCSX-like pressure/current profile Assumed in configuration optimization External transform due to plasma shaping LCMS in four toroidal angles over half period. Rotational transform as function of toroidal flux.

25. MHH2-K14 has reasonably good QA, but it is not as good as 1104. The B(2,1) and B(3,2) components remain to be significant in the magnetic spectrum. The loss of a energy is still reasonable, being < 10% (~6% in one slowing down time in our model calculation). (2,1) (0,1) (0,2) (3,2) Max. “noise” content ~3.4% @s=1 |B| on last LCMS in U-V space Eight major non-symmetric components in the magnetic spectrum plotted as function of normalized toroidal flux.

26. Plots of |B| along field lines show an increased amount of secondary ripples and the epsilon-effective (calculated by the NEO code) at the edge is now ~0.8%. r/a=0.5 r/a=0.7 effevtive ripple (1/n) |B| versus poloidal angle q in radians along field lines starting @ j=0, q=0.

27. A vacuum magnetic well, ~4% @ s=1, was imposed as one of the constraints in the configuration optimization. Total @ 5% b, p  (1-s1.5)1.5 From plasma shaping. Well depth=3.8% @s=1. Magnetic well depth as function of normalized toroidal flux.

28. But it is slightly unstable to both low- and high-n internal modes at b=4%. Low-n modesg• R/vA~0.0009 Infinite-n ballooning modes(Cobra calculation) p  (1-s1.5)1.5 5% b Radial displacement eigenfunction 3% b 2% b

29. MHH2-K14 may be also unstable to the external modes for b>5% according to the Terpsichore calculation, primarily due to modes of intermediate toroidal mode numbers 5 and 7. g • R/vA~0.12 Radial displacement eigenfunction Plasma-wall interface Wall @3.5x plasma average minor radius

30. No. of Coils: 8/period Different Types of Coils: 4 R/Dmin (coil-plasma)=5.5 R/Dmin (coil-coil)=10.3 I /R-B (max)=0.32 MA/m-T B(max)/B(0) = 1.9 for 0.4 m x 0.4 m conductor A modular coil design for MHH2-K14 (K14LA). Details: see the companion paper.

31. Summary & Conclusions • Taking advantage of recent experimental results which generally showed that stellarator plasmas are more resilient to MHD perturbations than predicted by the linerar theories, we searched the rotational transform-aspect ratio space for configurations endowed with better quasi-axisymmetry, low a-particale loss and better integrity of flux surfaces at high equilibrium beta. • We have found configurations whose rotational transform have small but positive shear even with the presence of large amounts of bootstrap current, making the avoidance of low order rational surfaces possible. We have also found configurations in two field periods having very low aspect ratios, making reactors of high power density and smaller sizes likely. • The most attractive configurations will ultimately be determined by results of systems optimization and other constraints arising from engineering designs. To this end, we have included in our effort also the initial coil designs to ensure the realizability of the configurations we found and have provided configuration and coil parameters to the systems study to allow a better understanding of the optimal parameters for a competitive power plant.