TY - JOUR
T1 - Fast neural Poincaré maps for toroidal magnetic fields
AU - Burby, J. W.
AU - Tang, Q.
AU - Maulik, R.
N1 - Funding Information:
We extend our gratitude to Xianzhu Tang for a number of helpful discussions. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility. Research presented in this article was supported by the Los Alamos National Laboratory LDRD program under project number 20180756PRD4. Research was also supported by the U.S. Department of Energy through the Fusion Theory Program of the Office of Fusion Energy Sciences, and the Tokamak Disruption Simulation (TDS) SciDAC partnerships between the Office of Fusion Energy Science and the Office of Advanced Scientific Computing. We gratefully acknowledge the computing resources provided and operated by the Joint Laboratory for System Evaluation (JLSE) at Argonne National Laboratory. This material is based upon work supported by the U.S. Department of Energy (DOE), Office of Science, Office of Advanced Scientific Computing Research, under Contract No. DE-AC02-06CH11357.
Publisher Copyright:
© Not subject to copyright in the USA. Contribution of Department of Energy.
PY - 2021/2
Y1 - 2021/2
N2 - Poincaré maps for toroidal magnetic fields are routinely employed to study gross confinement properties in devices built to contain hot plasmas. In most practical applications, evaluating a Poincaré map requires numerical integration of a magnetic field line, a process that can be slow and that cannot be easily accelerated using parallel computations. We propose a novel neural network architecture, the HénonNet, and show that it is capable of accurately learning realistic Poincaré maps from observations of a conventional field-line-following algorithm. After training, such learned Poincaré maps evaluate much faster than the field-line integration method. Moreover, the HénonNet architecture exactly reproduces the primary physics constraint imposed on field-line Poincaré maps: flux preservation. This structure-preserving property is the consequence of each layer in a HénonNet being a symplectic map. We demonstrate empirically that a HénonNet can learn to mock the confinement properties of a large magnetic island by using coiled hyperbolic invariant manifolds to produce a sticky chaotic region at the desired island location. This suggests a novel approach to designing magnetic fields with good confinement properties that may be more flexible than ensuring confinement using KAM tori.
AB - Poincaré maps for toroidal magnetic fields are routinely employed to study gross confinement properties in devices built to contain hot plasmas. In most practical applications, evaluating a Poincaré map requires numerical integration of a magnetic field line, a process that can be slow and that cannot be easily accelerated using parallel computations. We propose a novel neural network architecture, the HénonNet, and show that it is capable of accurately learning realistic Poincaré maps from observations of a conventional field-line-following algorithm. After training, such learned Poincaré maps evaluate much faster than the field-line integration method. Moreover, the HénonNet architecture exactly reproduces the primary physics constraint imposed on field-line Poincaré maps: flux preservation. This structure-preserving property is the consequence of each layer in a HénonNet being a symplectic map. We demonstrate empirically that a HénonNet can learn to mock the confinement properties of a large magnetic island by using coiled hyperbolic invariant manifolds to produce a sticky chaotic region at the desired island location. This suggests a novel approach to designing magnetic fields with good confinement properties that may be more flexible than ensuring confinement using KAM tori.
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U2 - 10.1088/1361-6587/abcbaa
DO - 10.1088/1361-6587/abcbaa
M3 - Article
AN - SCOPUS:85098271146
SN - 0741-3335
VL - 63
JO - Plasma Physics and Controlled Fusion
JF - Plasma Physics and Controlled Fusion
IS - 2
M1 - 024001
ER -