Development and Scope of ARIES Systems Code Zoran Dragojlovic A. René Raffray Farrokh Najmabadi ARIES-“TNS” Project Meeting April 3 and 4, 2007 University of California in San Diego

Purpose of Code To allow the possibility of a wide trade-off study while using the actual design points instead of “fudge factors”. In the ARIES Next Step project, this code will help establish a database to understand impacts of different physics and technology on a prototypical power plant so that necessary assessments can be made. Previous code was built layer-by-layer until it became too cumbersome to be used for an effective study. Major shortcomings include: –Optimization process was not transparent, the final answer was sometimes hard to explain or justify. –Inaccurate geometry. –Lack of user-friendly pre and post processing interface. –Lack of documentation. We are building a new ARIES systems code. –Programming is being done “from scratch”, as opposed to building on top of the existing code. –Initially, we may borrow parts of the existing code that are correct, such as the costing algorithms but a different optimization process will be employed.

Requirements Transparent system optimization that shows trends instead of single data points. Lean and time efficient processing. Total CPU time per optimization case should be reasonable (~30 min, for example). Accurate geometry with adjustable resolution. Easy to use pre and post-processing interface. Ample amount of documentation (manual, comments within the code, etc.)

The Systems Analysis Approach –Sequential loops will be implemented instead of nonlinear search. Physics. –Plasma shapes and parameters from a wide range of possible operating points will be provided in order to calculate the wall loads. Data will be based on Fusion Ignition Research Experiment (FIRE), PPPL. Engineering. –Inboard radial build based on the wall loads, primarily due to neutrons. –Outboard radial build is based on engineering and maintenance requirements. –Power flow –Implement example configurations based on past studies for more efficient programming Costing Analysis. –Initially, the costing algorithms will be implemented from the previously used ARIES systems code. –Costing accounts will be modified, as needed.

Pre-Defined Example Configurations The pre-defined configurations, A, B, C, etc. will be based on past studies and will allow a “plug and play” mode of use for more efficient analysis. Blanket A radial build … Power … ……………… B C Shield A radial build … Power … ……………… B C Divertor A radial build … Power … ……………… B C Coil A radial build... … Power … ……………… B C

Responsibility and Scope 3 year ARIES Next Step Project and beyond. PhysicsCharles KesselPrinceton Plasma Physics Laboratory Systems Code + Engineering Zoran Dragojlovic René Raffray Farrokh Najmabadi University of California in San Diego Costing Analysis + Engineering Laila El-GuebalyUniversity of Wisconsin Costing AnalysisLester WaganerThe Boeing Company Magnet AlgorithmMassachusetts Institute of Technology

Current Accomplishments 3-D TOKAMAK geometry is built. Various spatial integrals such as volumes and areas of different parts can be evaluated, as needed for the engineering and costing analysis. Implemented a power flow scheme. All the relevant algorithms are written in Fortran. The graphic representation of data is generated by using a suite of Matlab scripts (single command).

Choice of a Programming Language Benchmark reports of 2004 and later indicate that the two competing languages of choice for numerical computing are still Fortran and C++. There are three possible choices: using Fortran only, using C++ only and combining Fortran and C++. Both languages are suitable for the purpose, portable and can make user friendly applications. Fortran Only: Fastest for numerical computing in general. Superior handling of numerical arrays. When the Fortran code is optimized for performance, it looks simpler and easier to understand than when C++ is optimized for performance. Easy to link with other relevant codes that are also written in Fortran. C++ Only: Latest brands of compilers are almost as fast as Fortran. Perceived to be a more modern language, popular among computer scientists as a tool for programming operating systems. Fortran & C++: Use C++ for handling data structures and dynamic memory allocation. Use Fortran for all numerical computations. I already have experience employing this strategy in SPARTAN.

Geometry Started from the plasma shape as a reference point, built the geometry around it by using ARIES-AT CAD drawings and radial builds from design book. Tested the geometry for random variations in plasma shape to make sure that everything fits together. Tested the volumes and surface areas of the ARIES-AT power core by comparison with the Pro-E values from design book. ARIES-AT Geometry Generated by Systems Code

Examples of Geometrical Features Maintenance Port Detail of Divertor Region The new systems code generates geometry that is truly 3-D. An example is the maintenance port, shown above. Divertors are represented by Bezier curves, which allows the user to prescribe an arbitrary angle between the divertor and the last closed magnetic surface. Arbitrary gaps between adjacent parts are allowed.

Power Core Volumes and Surface Areas Match the ARIES-AT Design Book Values (Pro-Engineer) Volumes Design Book [m 3 ] New Systems Code [m 3 ] Error Relative to Design Book [%] Plasma Blankets Shield Divertor Power Core Sector Surface Areas Design Book [m 2 ] New Systems Code [m 2 ] Error Relative to Design Book [%] First Wall Divertor –Inboard –Outboard –Dome Total Div CAD Drawing Systems Code

Power Flow Power flow algorithm was implemented simultaneously with geometry. ARIES-AT design study was used as a model. Efficiency of the Brayton cycle is estimated based on the average neutron flux on the first wall. The flow chart is generated automatically by a Matlab script. [MW] P N DD – power from neutrons in D-D reaction. P N DT – power from neutrons in D-T reaction. P CP – charged particle fusion product power.

A Simple Optimization Test This test was done in collaboration with Charles Kessel, PPPL. The motivation was to incorporate the new geometry into the existing physics and engineering codes and make a step beyond testing surface areas and volumes against the ARIES-AT design book. Test runs: Charles Kessel: –Generated 165,000 physics operating points close to ARIES-AT specs. –Assembled a code that tests the operating points for engineering limits, such as: »first wall heat flux »divertor peak heat flux »TF peak field limit/superconducting current density limit »bucking cylinder criteria »PF coil peak field/superconducting current density limit »resulting inboard radial build with assumed thicknesses for the FW, blanket, shield, and VV from ARIES-AT neutronics analysis. –Final outcome: 120 data points that survived all the engineering limits. Zoran Dragojlovic: –Generated geometry for the 120 data points, eliminated 23 points based on geometry. –For the remaining points, used the power flow algorithm to estimate the trends that maximize the net electric power.

Input Data for Geometry and Power Flow Algorithms 120 data points with 83 different parameters describing –Plasma shape and physics. –Inboard radial thicknesses. –Electrical and magnetic data for coils. –Power distribution with electric power as a final outcome. Parameters I used as input are: –Plasma shape ( 5.1 m ≤ R ≤ 7.8 m, m ≤ a ≤ 1.95 m). –Inboard radial thicknesses. –Fusion power (2.137 GW ≤ P fusion ≤ GW).  = 0.7

Optimization Based on Trends in Net Electric Power “level 1” “level 2” “level 3” “level 4” A fictitious cost of electricity distribution. Possible optimal solution. A single optimal data point as a possible outcome of nonlinear search. COE (fictitious) The net electric power was estimated by the new power flow diagram. The values are within 4-5% from those provided by Chuck Kessel. The data points were then ordered in the increasing sequence based on the net electric power. The diagram above indicates the existence of 4 distinctive groups or “levels” with low variations of power within each group. The fictitious cost of electricity distribution is drawn above to illustrate the need for understanding trends within similar solutions (such as the one marked as “level 3”) instead of using a single optimal data point.

Variation in Geometry Within the Range of Optimal Solutions (“level 3”) Group of data points with similar net electric power (“level 3”) allows for a variety of different chamber sizes. R = 5.4 m R = 7.2 m a = 1.35 m a = 1.8 m

Comparison Between Levels 3 and 4 Both groups of data points feature the same variation in plasma size. However, most of the data points in the lower electric power group (level 3) have the major radius of 7 m or larger. In the higher electric power group, on the other hand, most of the data points are under 6 m in the major radius. This observation serves as an example of how optimization can be formulated to identify trends within similar solutions instead of single point outcomes of nonlinear search. Level 3: P net electric = 955 MW Level 4: P net electric = 960 MW

Plan of Development DeliverablesCriteria of SuccessDurationDate Expected Engineering Algorithms Radial and vertical builds implemented. Pre-defined example configurations for blanket, shield, divertor and coil available. 2-3 months June 2007 Costing Algorithms (simultaneously with engineering algorithms) Costing algorithms extracted from the previous systems code, verified and implemented. 2-4 weeks June 2007 Test for Cost of Electricity Ability to compare the results from the new and old systems code. Discrepancies are expected, within reason. A huge discrepancy would indicate a possible error in the new algorithm. 1 monthJuly 2007

Conclusions and Discussion Development of the ARIES systems code is gaining momentum, as demonstrated today. Initial achievements include: –Accurate geometry, with the resolution that can be adjusted to fit the needs of the analysis. –Power flow diagram is available as the first stage of implementation of the engineering algorithms. Radial and vertical build are expected in the near future. –Geometry and power flow diagram can be integrated to perform a simple optimization, as shown in the example with data from Chuck Kessel. We have suggested the basic requirements for the code and set the milestones in the algorithm development. Both are open for discussion.