8 Feb 99 Quasi-symmetry - Boyd Blackwell 1

Quasi Symmetric StellaratorsBoyd Blackwell, ANU

• History of Stellarator Optimisation– sigma optimisation, j|| minimisation

• Quasi-Symmetry– QHS, QAS, QOS, QBS

• The (US)NCSX, a QAS machine

• Flexibility– in transform and spectrum

• Real Time Surface Calculations

• QAS Design studies

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Introduction• Stellarator: magnetic surfaces generated entirely by

currents external to plasma

• Nested magnetic surfaces– magnetic field cover nested surfaces before closing on

themselves

• Rotational transform: twist per turn (=1/q), generated by:

• axially rotating multipole fields (torsatron/stell.)

• axially rotating magnetic axis (heliac/helias)

• Magnetic Coordinates: curvilinear coord. system in which field lines are straight

– Boozer - Jacobian = 1/|B|2

spectra in terms of =B.dl

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Optimisation: brief history– first device - figure 8 stellarator

• finding/maximizing surfaces - ‘60s-‘70s– transform improves Eq. and Stab.

– low order fields/symmetries reduce islands

• transport optimisation– 1980-2: sigma optimisation reduces 1/ transport

(helical pitch modulation) (single periodicity)

– modular windings

• j|| minimisation ~ indept

– W-7AS, 1983

– separation of physics and coil design(Merkel, 1987)

W7-X, 1991

• quasi helical symmetry• Nuhrenberg and Zille, 1988

• quasi axisymmetry• Garabedian 1996

( quasi isodynamicity/omnigeneity/bumpy...)

collisionality

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Quasi-Symmetry

• QHS, QAS, QOS, QBS

• W7X- beta indep

• QO - alpha indep

• need helical -> iota

• single periodicity -> transport

• QAS for low aspect ratio

• Fourier c.f. Spatial Optimisation -Boozer paper 1997

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The (US)NCSX, a QAS machine

Garabedian’s concept

3 Field period saddle coil for

PBX

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Flexibility

• in transform– optimum path may be “along field

lines”

• in Boozer spectrum

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QAS Design studies

• simple elements for flexibility

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Conforming Stellarator Flexibility Winding

• L=2, M=1 stellarator winding shown in

relation to the plasma to which it conforms.

The main saddle coils are omitted for clarity

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Comparison of helical flexibility windings

Name Current(kA)

Geometry L M Deltaiota(0)

Deltaiota(a)

Cost (MA-m)

/unit iota

Sc009 - (base) - - - -

Gl2076 75 Conf (alone) 2 -1 -0.2 0.054 0.05 19

Sc044 37.5 Conforming 2 -1 -0.2 0.13 4

Sc045 25 Conf 2 -1 -0.2 0.08 4

Sc046 75 Conf 4 -1 0 0.09 0.01 12

Sc048(50) 90 (-90) Elliptical 4 -1 +0.2 0.06 -0.03 28

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• Application: heliac configuration studies and QAS flexibility winding studies

• 3D spline calculation of B from large arrays (~100MB)

• linear combination of arrays for TFC, Ring provide instant adjustment of current ratios and configurations

• variable geometry conductors not allowed, but simplified model can be evaluated on top of accurate model of the rest of the geometry.

• Traces at ~20K steps/second surfaces in secs.

– BLINE code by Antony Searle

• Demonstration at Remote Data Access Poster

Real Time 3D B Field and Surface Calculations

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Conclusions

• Quasi helical symmetry consistent with high transform and good orbits.

• Quasi axi-symmetry consistent with low aspect ratio, but requires internal currents to generate enough transform - at high pressure, these currents are approximated by the bootstrap current

• QO is a weaker condition than QA, QH– QO optimization of QAS? Best of both?

• Flexibility is possible with Qsym, but often other parameters degrade (esp. symmetry)

• H-1NF has comparable helical and toroidal components (mixed helicity), but is optimised for flexibility.