realtime visualization and optimization of vacuum surfaces boyd blackwell anu n.
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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

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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
minimal confinement geometries
Minimal Confinement Geometries
  • 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
mesh interpolation
Mesh Interpolation
  • 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))

H-1

TFC

VF

3 ea. 32×128×32

mesh convergence
Mesh Convergence
  • Meshes of 10-50MByte are adequate even near edge
    • distance to nearest conductorrecorded in each cell, automatically revert to direct calculation if too close.

5th order or better in x

multi processing
Multi-processing
  • 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
perturbation calculation of iota
Perturbation Calculation of iota

B

B0

  • 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 )
accuracy of i
Accuracy of / I
  • Check / I by ultra highaccuracy (1e-7) directcalculation of 
  • correction for area changecan be significant

Perturbation result: 0.315 cf 0.304

machine optimization of iota
Machine Optimization of iota
  • 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)
reinvent helical conductor in flexible heliac
“Reinvent” helical conductor in flexible heliac
  • 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
r rmin constraint sawtooth coil
R>Rmin constraint  “sawtooth coil”
  • 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”
conclusions and future work
Conclusions and Future Work
  • 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