Designing stellarator coils by a modified Newton method using FOCUS

Zhu, Caoxiang; Hudson, Stuart R.; Song, Yuntao; Wan, Yuanxi

doi:10.1088/1361-6587/aab8c2

Title: Designing stellarator coils by a modified Newton method using FOCUS

Abstract

To find the optimal coils for stellarators, nonlinear optimization algorithms are applied in existing coil design codes. However, none of these codes have used the information from the second-order derivatives. In this paper, we present a modified Newton method in the recently developed code FOCUS. The Hessian matrix is calculated with analytically derived equations. Its inverse is approximated by a modified Cholesky factorization and applied in the iterative scheme of a classical Newton method. Using this method, FOCUS is able to recover the W7-X modular coils starting from a simple initial guess. Results demonstrate significant advantages.

Authors:

^[1]; Hudson, Stuart R. ^[2]; Song, Yuntao ^[3]; Wan, Yuanxi ^[1]

Univ. of Science and Technology of China, Hefei (China)
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Chinese Academy of Sciences (CAS), Hefei (China)

Publication Date:: Thu Mar 22 00:00:00 EDT 2018

Research Org.:: Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1430525

Grant/Contract Number:: AC02-09CH11466; No. 201506340040

Resource Type:: Accepted Manuscript

Journal Name:: Plasma Physics and Controlled Fusion

Additional Journal Information:: Journal Volume: 60; Journal Issue: 6; Journal ID: ISSN 0741-3335

Publisher:: IOP Science

Country of Publication:: United States

Language:: English

Subject:: 70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Citation Formats


                    Zhu, Caoxiang, Hudson, Stuart R., Song, Yuntao, and Wan, Yuanxi. Designing stellarator coils by a modified Newton method using FOCUS.  United States: N. p., 2018. 
Web.  doi:10.1088/1361-6587/aab8c2.

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                    Zhu, Caoxiang, Hudson, Stuart R., Song, Yuntao, & Wan, Yuanxi. Designing stellarator coils by a modified Newton method using FOCUS.  United States.  https://doi.org/10.1088/1361-6587/aab8c2

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                    Zhu, Caoxiang, Hudson, Stuart R., Song, Yuntao, and Wan, Yuanxi. Thu .  
"Designing stellarator coils by a modified Newton method using FOCUS".  United States.  https://doi.org/10.1088/1361-6587/aab8c2.  https://www.osti.gov/servlets/purl/1430525.

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@article{osti_1430525,

  title        = {Designing stellarator coils by a modified Newton method using FOCUS},

  author       = {Zhu, Caoxiang and Hudson, Stuart R. and Song, Yuntao and Wan, Yuanxi},

  abstractNote = {To find the optimal coils for stellarators, nonlinear optimization algorithms are applied in existing coil design codes. However, none of these codes have used the information from the second-order derivatives. In this paper, we present a modified Newton method in the recently developed code FOCUS. The Hessian matrix is calculated with analytically derived equations. Its inverse is approximated by a modified Cholesky factorization and applied in the iterative scheme of a classical Newton method. Using this method, FOCUS is able to recover the W7-X modular coils starting from a simple initial guess. Results demonstrate significant advantages.},

  doi          = {10.1088/1361-6587/aab8c2},

  journal      = {Plasma Physics and Controlled Fusion},

  number       = 6,

  volume       = 60,

  place        = {United States},

  year         = {Thu Mar 22 00:00:00 EDT 2018},

  month        = {Thu Mar 22 00:00:00 EDT 2018}

}

Copy to clipboard

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https://doi.org/10.1088/1361-6587/aab8c2

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Cited by: 17 works

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Works referencing / citing this record:

Hessian matrix approach for determining error field sensitivity to coil deviations
journal, April 2018

Zhu, Caoxiang; Hudson, Stuart R.; Lazerson, Samuel A.
Plasma Physics and Controlled Fusion, Vol. 60, Issue 5
DOI: 10.1088/1361-6587/aab6cb

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Title: Designing stellarator coils by a modified Newton method using FOCUS

Abstract

Citation Formats

Computation of three-dimensional tokamak and spherical torus equilibria journal, May 2007

An Algorithm for Least-Squares Estimation of Nonlinear Parameters journal, June 1963

Magnetic islands and perturbed plasma equilibria journal, July 2003

Enhanced simulated annealing for globally minimizing functions of many-continuous variables journal, June 1997

Stochasticity reduction journal, January 1986

Quasi-helically symmetric toroidal stellarators journal, May 1988

Explicit spectrally optimized Fourier series for nested magnetic surfaces journal, July 1998

Innovations in compact stellarator coil design journal, March 2001

Stable stellarators with medium β and aspect ratio journal, February 1986

Optimization of the current potential for stellarator coils journal, February 2000

Convergence Conditions for Ascent Methods. II: Some Corrections journal, April 1971

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Solving the 3D MHD equilibrium equations in toroidal geometry by Newton’s method journal, January 2006

Solution of stellarator boundary value problems with external currents journal, May 1987

Stellarator coil design and plasma sensitivity journal, December 2010

A New Modified Cholesky Factorization journal, November 1990

Constructing integrable high-pressure full-current free-boundary stellarator magnetohydrodynamic equilibrium solutions journal, September 2003

Efficient magnetic fields for supporting toroidal plasmas journal, March 2016

An improved current potential method for fast computation of stellarator coil shapes journal, February 2017

Automated Optimization of Stellarator Coils journal, March 1998

Designing Coils for Compact Stellarators journal, March 2002

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Calculation of cantori for Hamiltonian flows journal, November 2006

A Nonlinear Conjugate Gradient Method with a Strong Global Convergence Property journal, January 1999

Stellarator symmetry journal, January 1998

Physics and Engineering Design for Wendelstein VII-X journal, January 1990

Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces journal, January 1997

Particle swarm optimization conference, January 1995

Physics design of a high-bbeta quasi-axisymmetric stellarator journal, December 1999

Datasets of seed mucilage traits for Arabidopsis thaliana natural accessions with atypical outer mucilage journal, March 2021

Particle swarm optimization: An overview journal, August 2007

Hessian matrix approach for determining error field sensitivity to coil deviations journal, April 2018

Computation of three-dimensional tokamak and spherical torus equilibria
journal, May 2007

An Algorithm for Least-Squares Estimation of Nonlinear Parameters
journal, June 1963

Magnetic islands and perturbed plasma equilibria
journal, July 2003

Enhanced simulated annealing for globally minimizing functions of many-continuous variables
journal, June 1997

Stochasticity reduction
journal, January 1986

Quasi-helically symmetric toroidal stellarators
journal, May 1988

Explicit spectrally optimized Fourier series for nested magnetic surfaces
journal, July 1998

Innovations in compact stellarator coil design
journal, March 2001

Stable stellarators with medium β and aspect ratio
journal, February 1986

Optimization of the current potential for stellarator coils
journal, February 2000

Convergence Conditions for Ascent Methods. II: Some Corrections
journal, April 1971

Convergence Conditions for Ascent Methods
journal, April 1969

Solving the 3D MHD equilibrium equations in toroidal geometry by Newton’s method
journal, January 2006

Solution of stellarator boundary value problems with external currents
journal, May 1987

Stellarator coil design and plasma sensitivity
journal, December 2010

A New Modified Cholesky Factorization
journal, November 1990

Constructing integrable high-pressure full-current free-boundary stellarator magnetohydrodynamic equilibrium solutions
journal, September 2003

Efficient magnetic fields for supporting toroidal plasmas
journal, March 2016

An improved current potential method for fast computation of stellarator coil shapes
journal, February 2017

Automated Optimization of Stellarator Coils
journal, March 1998

Designing Coils for Compact Stellarators
journal, March 2002

Engineering optimization of stellarator coils lead to improvements in device maintenance
conference, May 2015

Calculation of cantori for Hamiltonian flows
journal, November 2006

A Nonlinear Conjugate Gradient Method with a Strong Global Convergence Property
journal, January 1999

Stellarator symmetry
journal, January 1998

Physics and Engineering Design for Wendelstein VII-X
journal, January 1990

Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces
journal, January 1997

Particle swarm optimization
conference, January 1995

Physics design of a high-bbeta quasi-axisymmetric stellarator
journal, December 1999

Datasets of seed mucilage traits for Arabidopsis thaliana natural accessions with atypical outer mucilage
journal, March 2021

Particle swarm optimization: An overview
journal, August 2007

Hessian matrix approach for determining error field sensitivity to coil deviations
journal, April 2018