11
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

Realtime visualization and optimization of vacuum surfaces - Boyd Blackwell, ANU

Embed Size (px)

DESCRIPTION

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

Citation preview

Page 1: Realtime visualization and optimization of vacuum surfaces  - Boyd Blackwell, ANU

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

Page 2: Realtime visualization and optimization of vacuum surfaces  - Boyd Blackwell, ANU

• 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

Page 3: Realtime visualization and optimization of vacuum surfaces  - Boyd Blackwell, ANU

• 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

Page 4: Realtime visualization and optimization of vacuum surfaces  - Boyd Blackwell, ANU

• 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

Page 5: Realtime visualization and optimization of vacuum surfaces  - Boyd Blackwell, ANU

• 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

Page 6: Realtime visualization and optimization of vacuum surfaces  - Boyd Blackwell, ANU

• 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

Page 7: Realtime visualization and optimization of vacuum surfaces  - Boyd Blackwell, ANU

• 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

Page 8: Realtime visualization and optimization of vacuum surfaces  - Boyd Blackwell, ANU

• 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

Page 9: Realtime visualization and optimization of vacuum surfaces  - Boyd Blackwell, ANU

• 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

Page 10: Realtime visualization and optimization of vacuum surfaces  - Boyd Blackwell, ANU

• 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”

Page 11: Realtime visualization and optimization of vacuum surfaces  - Boyd Blackwell, ANU

• 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