Exploration of Compact Stellarators as Power Plants: Initial Results from ARIES-CS Study

Exploration of Compact Stellarators as Power Plants: Initial Results from ARIES-CS Study Farrokh Najmabadi, Long-Poe Ku Jim Lyon, Rene Raffray, and the ARIES Team September 23, 2004 OFES Electronic copy: http://aries.ucsd.edu/najmabadi/talks UCSD IFE Web Site: http://aries.ucsd.edu/ife

For ARIES Publications, see: http://aries.ucsd.edu/ For ARIES Publications, see: http://aries.ucsd.edu/

Exploration and Optimization of Compact Stellarators as Power Plants -- Motivations Timeliness: Initiation of of NCSX NCSX and and QPS QPS experiments in in US; US; PE PE experiments in injapan (LHD) (LHD) and and Germany (W7X (W7X under under construction). Progress in in our our theoretical understanding, new new experimental results, results, and and development of of a a host host of of sophisticated physics physics tools. tools. Benefits: Such Such a a study study will will advance advance physics physics and and technology of of compact stellarator concept concept and and addresses concept concept attractiveness issues issues that that are are best best addressed in in the the context context of of power power plant plant studies, studies, e.g., e.g., α particle particle loss loss Divertor (location, particle particle and and energy energy distribution and and management) Practical coil coil configurations. NCSX NCSX and and QPS QPS plasma/coil configurations are are optimized for for most most flexibility for for scientific investigations at at PoP PoPscale. Optimum plasma/coil configuration for for a a power power plant plant (or (or even even a a PE PE experiment) will will be be different. Identification of of such such optimum configuration will will help help define define key key R&D R&D for for compact stellarator research research program.

ARIES-Compact Stellarator Program Has Three Phases FY03/FY04: Exploration of of Plasma/coil Configuration and and Engineering Options 1. 1. Develop physics physics requirements and and modules (power (power balance, balance, stability, α FY04/FY05: Exploration of of confinement, divertor, etc.) etc.) Configuration Design Design Space Space 2. 2. Develop engineering requirements and and 1. 1. Physics: Physics: β, β, aspect aspect ratio, ratio, number number of of constraints. periods, periods, rotational transform, sheer, sheer, etc. etc. 3. 3. Explore Explore attractive coil coil topologies. 2. 2. Engineering: configuration optimization, management of of space space between between plasma plasma and and coils, coils, etc. etc. 3. 3. Choose Choose one one configuration for for detailed detailed design. design. FY05/FY06: Detailed system system design design and and optimization

Configuration Development for ARIES Compact Stellarator Reactors Long-Poe Ku Princeton Plasma Physics Laboratory Department of Energy, Office of Fusion Energy Sciences September 23, 2004

Outline of Presentation What we have been studying and why, what our goals are. How we do it. Highlight of results. What s next.

The discovery of quasi-axially symmetric stellarators opens up the possibility of designing fusion reactors that have tokamak transport and stellarator stability. In 3-D magnetic field topology, particle drift trajectories depend only on the strength of the magnetic field, not on the vector components of the field nor on the shape of the magnetic flux surfaces. QA tokamak-like field topology good particle confinement. Stellarators with externally supplied poloidal flux have shown resilience to plasma disruption and the achieved β s have exceeded limits predicted by linear MHD theories. QA can be achieved at lower aspect ratios with smaller number of field periods. more compact device (R<10 m), bootstrap can be used to our advantage to supplement rotational transform, shown to have favorable MHD stability at high beta.

There are many stellarator reactors studied in the past based on a variety of confinement concepts but all have large sizes. We aim at QA reactors having sizes competitive with advanced tokamaks. Helias Reactors based on the concept of W7X (linked mirror, omnigeneous): HSR5/22, 5-field period, A=10, R=22 m, B=5 T, B max =10 T, P f =3 GW, β~4%. HSR4/18, 4-field period, A=8, R=18 m. HSR3/15, 3-field period, A=6, R=15 m. SPPS, Modular Helias-like Heliac (QA) MHH4, 4-field period, A=8.54, R=13.95 m, B=4.94 T, B max =14.5 T. Haliotron/Torsatron (classical l=2 stellarator) FFHR, 10-field period, A=10, R=10-20 m.

Tokamak-like magnetic field topology can be achieved approximately by three dimensional shaping of the plasma without relying on toroidal current. Because we can only find approximate solutions, configurations are not unique. The normally over-determined system allows one to impose further constraints, such as MHD stability to the kink or ballooning modes, the shape and magnitude of rotational transform and so on, in the solution. Optimization of solution is sought once a set of constraints are defined. The configuration space is immense, however.

Plasma boundary represented as Fourier harmonics ballooning kink α loss transport shape/position coil complexity Plasma optimization Initial guess, boundary as independent variables Constraints/weights 1) Evaluate equilibrium (VMEC, NSTAB), 2) Jacobian calculation, 3) determine direction of descent, 4) perform functional minimization (Levenberg-Marquardt, GA). 1) Select p, J profiles, β, B, FP 2) Iota target 3) MHD stability target (Mercier, ballooning, kink) 4) Transport target (QA, ripple) 5) Coil target (complexity, current density) Targets met? Yes No Modify weights Flux surface quality, islands healing, PIES Refined calculation and detailed analysis

An important element in our effort is to find coils that would produce the desirable plasma with low complexity and good engineering properties. For coil design, we want, on the last closed magnetic surface, B norm (coil) = -B norm (plasma pressure) In seeking the solution, we also try to maximize min (coil-plasma), min (coil-coil) and minimize B max /B 0 to the extent possible. Again, optimization process is invoked since there may involve a large number of independent variables (> 100) as well as constraints.

Coil Design and Optimization 1) Winding surface 2) Number of coils 3) Coil representation 4) Coil currents Constraints & weights 1) Radius of curvature 2) Coil-coil separation 3) Coil plasma separation 4) Coil length 5) Linear current density 6) Coil currents Initial coil parameters Evaluate B n from coils, calculate residual B n on LCFS, calculate Jacobian, find direction of descent, perform functional minimization (LM). Target met? Yes No Equilibrium data from optimized plasma Evaluate B n due to plasma current on LCFS Modify weights

We have refined, improved and expand configurations developed in the NCSX project and discovered new classes of configurations as well. We have explored configuration space with respect to plasma aspect ratio, number of field periods, rotational transform both magnitude and shear, vacuum magnetic well depth, linear and non-linear MHD stabilities. We have devised ways to minimize the loss of α particles. We have investigated ways to mitigate the problem of magnetic islands and methods to improve flux surface integrity. We have studied coil topology to improve their overall physics and engineering performance.

Three classes of QA configurations may be of interest for further reactor studies. NCSX-like SNS-QA MHH-2 These are not the only possibilities, nor are they the only configurations we studied.

NCSX-like configurations Good QA, low effective ripple (<1%), α energy loss 15% in 1000 m 3 device. Stable to MHD modes at β 4% Coils can be designed with aspect ratio 6 and are able to yield plasmas that capture all essential physics properties. Resonance perturbation can be minimized. Footprints of escaping α on LCMS for the α- loss improved configuration B5D. Energy loss ~12% in model calculation. Optimization of modular coils has led to configurations with coil aspect ratios < 6, hence reactors of smaller sizes are realizable. Poloidal Angle Toroidal Angle Heat load maybe localized and high (~a few MW/m 2 ) For R=8.25 m min (c-p)=1.4 m min (c-c)=0.83 m I max =16.4 MA @6.5 T B max /B 0 ~2 for 0.4 m x 0.4 m conductor

SNS-QA configurations Aimed particularly at having good flux surface quality. Characterized by strong negative magnetic shear from shaping coils. Have excellent QA and good α confinement characteristic (loss ~10%). Inherently deep magnetic well in 2 and 3 field periods. 3/16 3/17 2/11 Total including bootstrap current expected at 6% β A case having excellent flux surface quality has been identified at 6% β. Rotational Transform 1/6 2/13 1/7 2/15 1/8 Transform due to 3D shaping Poincaré plot for KJC167 based on a PIES calculation. Normalized Toroidal Flux Label

MHH2 Small plasma aspect ratio (A<3.5) in 2 field periods. Simple shape, clean coils. MHH2 with A=3.7 and 16 coils MHH2 with A=2.7 and 8 coils

Summary The physics basis of QA as candidate for compact stellarator reactors has been assessed. New configurations have been developed, others refined and improved, all aimed at low plasma aspect ratios, hence compact size at a given fusion power. Configurations with excellent QA have been found with A 6. Configurations with both 2 and 3 field periods possible. Progress has been made to reduce loss of α particles. Losses ~10% have been achieved. This is still higher than desirable, however. Numerical calculations using codes based on linear, ideal MHD theories show that stability to the kink, ballooning, and Mercier modes may be attained in most cases but at the expense of reduced QA and increased complexity of plasma shape. Recent experimental results indicated that linear, ideal MHD stability theories may be too pessimistic, however. Modular coils are designed to examine the geometric complexity and to understand the constraints imposed by the maximum allowable field, desirable coil-plasma separation, coil-coil spacing, and other coil parameters. Adequate space available for blanket/shield without the need of having unduly large reactors, although in some cases ingenuity needed in designs. Strong incentive to simplify coils for remote maintenance without compromising the fundamental requirement of meeting physics objectives.

.. And beyond Codes and numerical issues and configuration robustness Development of configurations relies on numerical calculations. There are assumptions/approximations, numerical errors, etc. How robust a configuration is? How we can make it more robust? Existence of nested flux surfaces, number of Fourier modes, convergence, etc. Codes for equilibrium and stability calculations (NSTAB, VMEC, ) Data base and adequacy of physics basis There are no data yet for QA devices. Data from other types of stellarators are encouraging, especially with respect to MHD stability (experiments exceed prediction based on linear theory). How we should extrapolate the available data in designing reactors years away? Have we sampled enough configuration space? Are there attractive regions missed? It requires tremendous resource to survey the landscape. We only manage to explore a little farther from where we were. How about other symmetries? Do other symmetries necessarily conflict with compactness? Can we take advantage of other symmetry approach?

There Are Unique Integration Issues Associated with a Compact Stellarator Maintenance and assembly - 3-D assessment of possible schemes (field-period based and port-based) Coil structure Shielding requirement (minimum distance) Alpha losses and impact on PFC - Divertor Power core - Scoping analysis of possible concepts (blanket/shield thickness, size, performance) September 23, 2004/ARR

Initial Configurations for ARIES-CS Phase I Scoping Studies Parameter 3-field period (NCSX) 2-field period (MHH2) Coil-plasma distance, (m) 1.2 1.4 <R> (m) 8.3 7.5 <a> (m) 1.85 2.0 Aspect ratio 4.5 3.75 β (%) 4.1 4.0 Number of coils 18 16* B o (T) 5.3 5.0 B max (T) 14.4 14.4 Fusion power (GW) 2 2 Avg. wall load (MW/m 2 ) 2.0 2.7 September *Cases 23, 2004/ARR of 12 and 8 coils also considered for 2-field period configuration.

Coil Structure Design for CS to Accommodate Load within One Field Period and Provide Openings for Coolant and Support Access Planar coil for illustration Actual geometry No net forces between coils from one field period to the other. Out-of plane forces acting between neighbouring coils inside a field period reacted by inter-coil structure. Large centering forces need to be reacted by strong bucking cylinder. Design can be adapted to be used with either field-period-based or port-based maintenance schemes. September 23, 2004/ARR

Field-Period Based Maintenance Scheme With External Vacuum Vessel Radial movement of a field period unit without disassembling coils in order to avoid unacceptably long down time. Key issue is minimum distance between plasma and coil for clearance (3-D assessment to demonstrate possibility). Advantage of nearly no weight limit on blanket (use of air cushions) but local limit on thickness of blanket for clearance However, better suited for 3-field period or more because of scale of field period unit movement. Cross section of 3 field-period configuration at 0 illustrating the layout for field-period based maintenance. September 23, 2004/ARR

Port-Based Maintenance Approach ITER-like rail system extremely challenging in CS geometry due to roller coaster effect and to non-uniform plasma shape and space Preferable to design maintenance based on articulated boom only - required reach a function of machine size and number of ports Maintenance through limited number of ports - Compatible with 2 or 3 field-period - Constraints on module weight Maintenance through ports between each pair of adjacent coil - Seems only possible with 2-field period for reasonable-size reactor (space availability) - heavier blanket module possible September 23, 2004/ARR

ARIES-CS Divertor Further effort to minimize alpha losses Need tools to estimate location and heat fluxes - Collaboration with Garching colleagues (Dr. Erika Strumberger - Code development under way (H. McGuinness from RPI in Garching and then working visit at UCSD) - Suite of codes to be adapted for ARIES-CS: MFBE + GOURDON + GEOM He cooling most probably for ARIES-CS divertor - Compatible with He coolant for blanket - Collaboration with FZK on divertor design (T. Ihli as visiting scientist at UCSD for 6 months next year to work on this) Major effort for Phase II September 23, 2004/ARR

We have Performed a Scoping Study of Possible Blanket Concepts Most Applicable for a Compact Stellarator Key parameters - Thickness of blanket as compared to available space - Possibility of design based on modular and/or larger unit (module size and weight important for port-based maintenance) - Breeding performance since, to minimize power plant size, we shield-only regions locally where the plasma to coil distance is a minimum (a few % coverage) - Cycle efficiency (emphasizing Brayton cycle to avoid safety concerns associated with steam) We are converging on two concepts: - Self-cooled Pb-17Li concept with SiC f /SiC (ARIES-AT) - Pb-17Li/He dual coolant concept with ferritic steel (similar to ARIES-ST) - Interesting to see that blanket concepts can be adapted to different MFE configurations - Similar concepts have also been studied abroad - Impact of ARIES on design and R&D - e.g. Pb-17Li/He dual coolant concept in EU (FZK) and now for September US ITER 23, 2004/ARR TBM ODS Layers Plated to the FW He System 2 1 Pb-17Li 2 1 2 1 EUROFER Structure (FW+Grids) Shield 1 2 SiC f /SiC Channel Inserts

We Have Addressed the Unique Integration Issues Associated with a Compact Stellarator and Help Define Design Windows Maintenance and assembly - Minimum distance between plasma/coil may be set by assembly/maintenance and not by shielding. - Maintenance and assembly scheme influenced by coil configuration (2-field period or 3-field period). Coil structure - A feasible coil support structure has been worked out. Shielding requirement (minimum distance) - Localized shielding is possible while achieving sufficient TBR. Alpha losses and impact on PFC - Divertor is a critical system. High alpha losses is a major concern. Power core - Blankets comparable to those developed for tokamaks can be utilized. September 23, 2004/ARR

Results of ARIES-CS Phase I Effort Presented at 16 th TOFE Invited Oral Papers for ARIES Special Session 1. F. Najmabadi and the ARIES Team, Overview of ARIES-CS Compact Stellarator Study 2. P. Garabedian, L. P. Ku, and the ARIES Team, Reactors with Stellarator Stability and Tokamak Transport 3. J.F. Lyon, L. P. Ku, P. Garabedian and the ARIES Team, Optimization of Stellarator Reactor Parameters 4. A. R. Raffray, L. El-Guebaly, S. Malang, X. Wang and the ARIES Team, Attractive Design Approaches for Compact Stellarator 5. L. El-Guebaly, R. Raffray, S. Malang, J. Lyon, L.P. Ku and the ARIES Team, "Benefits of Radial Build Minimization and Requirements Imposed on ARIES-CS Stellarator Design" Contributed Papers 6. L. El-Guebaly, P. Wilson, D. Paige and the ARIES Team, "Initial Activation Assessment for ARIES-CS Stellarator Power Plant" 7. L. El-Guebaly, P. Wilson, D. Paige and the ARIES Team "Views on Clearance Issues Facing Radwaste Management of Fusion Power Plants" 8. S. Abdel-Khalik, S. Shin, M. Yoda, and the ARIES Team, "Design Constraints for Liquid- Protected Divertors" 9. X. Wang, S. Malang, A. R. Raffray and the ARIES Team, Maintenance Approaches for ARIES- CS Power 10. A. R. Raffray, S. Malang, L. El-Guebaly, X. Wang and the ARIES Team, Ceramic Breeder Blanket for ARIES-CS September 23, 2004/ARR

Determination of ARIES Compact Stellarator Reactor Parameters J. F. Lyon, ORNL for the ARIES Team OFES ARIES Briefing Sept.23, 2004

Goal: Stellarator Reactors Similar in Size to Tokamak Reactors Need a factor of 2-4 reduction => compact stellarators Plasma Aspect Ratio <R>/<a> 12 10 8 6 4 Tokamak Reactors 2 Compact Stellarator Reactors SPPS LHD-R HSR-4 Stellarator Reactors 4 8 12 16 20 24 Average Major Radius <R> (m) HSR-5

Interaction between ARIES & CS Programs Integrated Plasma and Coil Optimization NCSX, QPS Experiments Theory Candidate Plasma and Coil Geometry Compact Stellarator Development Determination of Parameters and Assessment as Reactor ARIES CS Study Information to Improve CS Plasma, Coil and Reactor Concept NCSX, QPS Programs Theory Sensitivity to confinement, β limits, profiles, divertor, α losses Attractive Reactor Option

Parameter Determination Integrates Plasma/Coil Geometry and Reactor Constraints Plasma & Coil Geometry Shape of last closed flux surface and <R axis >/<a plasma >, β limit?? Shape of modular coils and B max,coil /B axis vs coil cross section, <R coil >/<R axis >, min /<R axis > Alpha-particle loss fraction Reactor Constraints Blanket and shield thickness B max,coil vs j coil for superconductor Acceptable wall power loading Access for assembly/disassembly Component costs/volume Parameter Determination <R axis >, <a plasma >, <B axis > B max,coil, coil cross section, gaps n e,i,z (r),t e,i (r), <β>, P fusion, P rad, etc. Operating point, path to ignition Cost of components, operating cost cost of electricity

Staged Approach in Defining Parameters 0-D scoping study determines device parameters calculates <R axis >, <B axis >, <β>, <p n,wall >, B max, j coil, etc. subject to limits and constraints 1-D power balance determines plasma parameters and path to ignition incorporates density and temperature profiles; overall power balance; radiation, conduction, alpha-particle losses 1-D systems cost optimization code calculates self-consistent temperature profiles, power balance calculates reactor component and operating costs Examine sensitivity to models, assumptions and constraints at each stage

Four Configurations Have Been Studied NCSX MHH2 port or sector (end) access access through ports QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture. both quasi-axisymmetric Key Configuration Properties NCSX-1 NCSX-2 MHH2-8 MHH2-16 Plasma aspect ratio A p = <R>/<a> 4.50 4.50 2.70 3.75 Wall (plasma) surface area/<r> 2 11.80 11.95 19.01 13.37 Min. plasma-coil separation ratio <R >/ min 5.90 6.88 4.91 5.52 Min. coil-coil separation ratio <R>/(c-c) min 10.07 9.38 7.63 13.27 Total coil length/<r> 89.7 88.3 44.1 64.6 B max,coil /<B axis > for 0.4-m x 0.4-m coil pack 2.10 1.84 3.88 2.77 <R coil >/<R> constant for each case, can t change separately

B max /B axis Depends on Coil Cross Section 8 7 6 square coil pack cross section (k = 1) 1 0.95 0.64 m 2 0.49 m 2 0.36 m 2 0.25 m 2 B max /<B axis > 5 4 3 2 NCSX-2 MHH2-8 MHH2-16 NCSX-1 B max (k)/ B max (1) 0.9 0.85 NCSX-2 with A = 6.9 0.16 m 2 0.09 m 2 d 2 = 0.04 m 2 1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 d = (cross section) 1/2, m 0.8 1 3 5 7 9 k = coil width/radial depth Larger plasma-coil spacings lead to more convoluted coils and higher B max /<B axis > Minimum coil-coil separation distance determines k max

NCSX-1 Values Limited to p n,max = 5 MW/m 2 j (MA/m 2 ) 200 150 100 50 1 1.5 decreasing d 2 j SC 2.5 3 3.33 <p > (MW/m 2 ) n,wall 0 6 8 10 12 14 16 B max (T) <R> (m), <B axis > (T) 12 11 10 9 8 7 6 5 4 NCSX-1 cases <R> <R > min, blanket <R > min, no blanket <B > axis 1 1.5 2 2.5 3 3.5 <p n,wall > (MW/m 2 ) <R> = 6.22 m, <B axis > = 6.48 T, B max = 12.65 T j coil approximately constant <R>, <B axis >, B max & d are constrained for other cases by radial build to lower <p n,wall > (2.13 2.67 MW/m 2 )

Main Reactor Parameters from 0-D Study NCSX-1 NCSX-2 MHH2-8 MHH2-16 <p n,wall > (MW/m 2 ) 3.33 2.67 2.13 2.4 <R> (m) 6.22 6.93 6.19 6.93 <a> (m) 1.38 1.54 2.29 1.85 <B axis > (T) 6.48 5.98 5.04 5.46 B max (T) 12.65 10.9 14.9 15.2 j coil (MA/m 2 ) 114 119 93 93 k max 3.30 5.0 2.78 1.87 coil width (m) 0.598 0.719 0.791 0.502 coil depth (m) 0.181 0.144 0.286 0.268 radial gap (m) 0.026 0.012 0.007 0.005 Coil volume (m 3 ) 60.3 63.4 61.4 60.3 Wall area (m 2 ) 480 600 750 667 Wall (blanket, shield, structure, vacuum vessel) area smallest for NCSX-1case, chosen for more detailed study

NCSX-1: τ E /τ E ISS-95 = 4.2, <T> = 9.5 kev, <n> = 3.5 10 20 m 3, <β> = 6.1% H-ISS95 = τ E /τ E ISS-95 100 ignition contour (P in = 0) operating point 10 thermally stable branch 20 20 20 6% <β> 2-GW P fus 20 100 n Sudo P in = 10 MW τ E ISS-95 = 0.26P heating 0.59 <n e > 0.51 <B axis > 0.83 <R> 0.65 <a> 2.21 ι 2/3 0.4

Plasma Parameters from 1-D Power Balance NCSX-1 NCSX-2 MHH2-8 MHH2-16 <R> (m) 6.22 6.93 6.19 6.93 <a> (m) 1.38 1.54 2.29 1.85 <B axis > (T) 6.48 5.98 5.04 5.46 H-ISS95 4.15 4.20 3.75 4.10 n (10 20 m 3 ) 3.51 2.89 2.05 2.43 f DT 0.841 0.837 0.837 0.839 f He 0.049 0.051 0.051 0.050 T (kev) 9.52 9.89 9.92 9.74 β, (%) 6.09 6.12 6.13 6.09 ISS-95 of 3.75 to 4.2 is required; present stellarator experiments have up to 2.5 ISS-2004 scaling ~ 2 x ISS-95 and has ε eff 0.4 improvement, so compact stellarators should have high H-ISS values

H-ISS95 Is Sensitive to Some Assumptions 6.5 8 6 <β> (%) 7 5.5 5 6 <β> (%) 4.5 5 4 3.5 H-ISS95 NCSX-1 Case 4 H-ISS95 NCSX-1 Case 3 0 0.05 0.1 0.15 0.2 0.25 0.3 Fraction of Alpha-Particle Power Lost 3 4 6 8 10 12 τ He */τ E Need to control alpha-particle power loss and helium recycling back into plasma -- both divertor issues Results are relatively insensitive to profile assumptions

Next Steps Analysis of newer plasma configurations with low alpha-particle losses when coils are developed Refinement of parameters with the 1-D systems/ cost optimization code

Reactor Issues for CS Experiments Density and temperature profiles were assumed What are reasonable transport coefficients (D, χ)? ambipolar electric field? bootstrap current? Is neoclassical impurity model OK? Is n(r) hollow? Required confinement multiplier H-ISS95 is ~ 4 How does confinement scale with plasma and configuration parameters at low aspect ratio? Does quasi-symmetry, smaller ε eff and reduced flow damping lead to improved confinement? β limit is assumed -- no credible model exists What are β limits and dependence on configuration parameters? Power density to the divertor is very high Can power density on the divertor be reduced? Can radiated power to the wall be increased? Alpha-particle losses are high at present What are energetic ion losses? Can they be reduced?

Summary Parameter determination integrates plasma & coil geometry with physics & engineering constraints and assumptions Initial results lead to factor ~2 smaller stellarator reactors (<R> = 6 7 m), closer to tokamaks in size Results are relatively insensitive to profile assumptions but sensitive to helium accumulation and alpha-particle losses Next step is to refine results with the 1-D systems/ cost optimization code Study points up uncertainties in reactor physics assumptions that CS experiments can help clarify

BACKUP

ISS-95 Confinement Scaling Is Being Updated τ ISS 04 v 3 E = 0.148a 2.33 R 0.64 P 0.61 n 0.55 e B 0.85 ι 0.41 2/3 τ Bohm ρ * 0.90 β 0.14 ν * 0.01 b H. Yamada, J. Harris et al. EPS 2004 ~ε eff 0.4? Determine τ E increase with lower ε eff in HSX, NCSX, QPS

Systems Optimization Approach Minimizes core cost or size or COE with constraints for a particular plasma and coil geometry using a nonlinear constrained optimizer with a large number of variables Large number of constraints allowed (=, <, or >) P electric, ignition margin, β limit, ISS-95 multiplier, radial build, coil j and B max, plasma-coil distance, blanket and shielding thicknesses, TBR, access for divertors and maintenance, etc. Large number of fixed parameters for plasma and coil configuration, plasma parameters and profiles, transport coefficients, cost component algorithms, and engineering model parameters Calculates (and iterates on) a large number of variables plasma: T e (r), T i (r), n e (r), n e (r), E r (r), β, Z eff, H-ISS95, power components (coronal and bremsstrahlung radiation, α => i, α => e), α losses, etc. coils: max. & min. width/depth of coils, clearance between coils, components volumes and costs, j, B max, forces reactor variables: B 0, <R>, blanket volumes, TBR, neutron wall loading, P electric, divertor area, access between coils, radial build, etc. costs: equipment cost, annual operating cost, total project cost, CoE

MHHOPT Reactor Optimization Code input: physics, coil, costing, and reactor component parameters and constraints output: all parameters and profiles plasma solver: T e (r), T i (r), n e (r), n i (r), E r (r), β, Z eff, P rad, P fusion, P α,loss, P wall, P divertor, τ E, etc. nonlinear optimizer: optimizes targets with constraints masses of coil and structure, j, B max blanket volumes, TBR, access, radial build forces on coil and structure evaluate all parameters & constraints costs of all ARIES accounts, P electric