Realtime visualization and optimization of vacuum surfaces Boyd Blackwell, ANU

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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

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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

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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, Zacharovs code (Hermite
  polynomials))

H-1
TFC
VF
3 ea. 3212832
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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
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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

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Perturbation Calculation of iota

• 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 ?)

?B
B0
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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
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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)

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Reinvent helical conductor in flexible heliac

• Constrain conductor to lie inside a torus, N3
• (actually end-point and middle point fixed)
• Seek maximum transform for length ? current
• Result is very close to the flexible heliac

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RgtRmin constraint ? sawtooth coil

• Constrain conductor to lie on a cylinder, N3
• Seek maximum transform near the axis of a heliac
  per unit length ? current
• Reproduces approximate sawtooth coil

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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