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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 - PowerPoint PPT Presentation
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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 I1M1 + I2M2 + I3M3)
• mesh filled on demand and/or in background– (see also Gourdon code, Zacharov’s code (Hermite polynomials))
Mesh Interpolation
H-1
TFCVF
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/B0 where B is the perturbing field
and B0 the original field
• (Alternatively integrate cpt of B in surface, normalized to B0 and the puncture spacing at that point ~ Boozer )
Perturbation Calculation of iota
BB0
• Check / I by ultra highaccuracy (1e-7) directcalculation of
• correction for area changecan be significant
Accuracy of / I
Perturbation result: 0.315 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
Recommended