Realtime visualization and optimization of vacuum surfaces - Boyd Blackwell, ANU Real time tracing code BLINE (Summer Scholar: Antony Searle, ANU) –multi-thread/processor –mesh accuracy –speed –hierarchial system element/mesh structure Perturbation method for iota (Summer Scholar: Ben McMillan, ANU/UMelb) Real-time optimization by simulated annealing –demonstration

Simplest possible geometries with closed surfaces that resemble real geometries, for testing codes –fast direct evaluation, exact –iota ~ 1 –aspect ratio ~ 5-10 –highly 3D –enclose no conductors “triator” –4 simple elements (finite filaments) –iota ~ 0.6, bean shaped, (similar to Tom Todds?) “1 element” toroidal helix –slow evaluation Minimal Confinement Geometries

cubic tri-spline on regular rectangular meshes copy of mesh in neighbourood stored to better fit in CPU cache – derivatives stored only in local mesh (4 point eval from main mesh) mesh hierarchy underneath the hierarchy of magnetic macro-elements –e.g. H-1 has 3 meshes for main field, but one coarse mesh for VF coils –allows quick configuration exploration by varying currents (linear combination I 1 M 1 + I 2 M 2 + I 3 M 3 ) mesh filled on demand and/or in background –(see also Gourdon code, Zacharov’s code (Hermite polynomials)) Mesh Interpolation H-1 TFC VF 3 ea. 32×128×32

Meshes of 10-50MByte are adequate even near edge –distance to nearest conductor recorded in each cell, automatically revert to direct calculation if too close. Mesh Convergence 5th order or better in  x

windows threads (posix under linux) (MISD) –needs semaphore system (e.g. no tracing while loading a new mesh) multi-threaded code runs fine on single processor –some priority tuning useful on single processor initial scheme –tracing thread, display thread and mesh-filling threads –large caches on Intel machines favour each thread working in distant memory locations multi-threading  object oriented coding Multi-processing

Find a nearby rational surface by iteration ~middle order –say ~ 30 circuits Store B and derivatives along this closed path For each variation in the perturbing winding, integrate  x   B/B 0 where  B is the perturbing field and B 0 the original field (Alternatively integrate cpt of  B in surface, normalized to B 0 and the puncture spacing at that point ~ Boozer  ) Perturbation Calculation of iota BB B0B0

Check   /  I by ultra high accuracy (1e-7) direct calculation of  correction for area change can be significant Accuracy of   /  I Perturbation result: cf 0.304

Minimization by steepest descent (but multi-variate) Simulated annealing –virtual temperature T –accept a new configuration even if slightly worse (up to T) –“heat” to explore new configurations –“cool” to home in on optimum Annealing more tolerant of occasional anomalies in goodness function, e.g. local minima or discontinuities (resonances) Machine Optimization of iota

Constrain conductor to lie inside a torus, N=3 –(actually end-point and middle point fixed) Seek maximum transform for length  current Result is very close to the flexible heliac “Reinvent” helical conductor in flexible heliac

Constrain conductor to lie on a cylinder, N=3 Seek maximum transform near the axis of a heliac per unit length  current Reproduces approximate “sawtooth coil” R>Rmin constraint  “sawtooth coil”

Very useful for following particles out of machine (so far, not a drift calculation) Very quick (50k/sec) configuration evaluation for varying current ratios in existing coil system (e.g. H-1 flexibility studies) Fast evaluation (10k/sec) of new winding (“simple”) in arbitrarily complex existing configuration Iota perturbation calculation works, and is fast. Well calculation implemented, but not debugged Possibly extend to island width as in Rieman & Boozer 1983 optimization principle demonstrated “standard results” recovered real time operation  possibility of human guidance during optimization Develop/find “Meta-Language” for description of symmetries and constraints Conclusions and Future Work