Evaluation of the Abel inversion integral in O-mode plasma reflectometry using Chebyshev-Gauss quadrature

E. Leppink; C. Lau; Y. Lin; S. J. Wukitch

doi:10.1063/5.0132246

Evaluation of the Abel inversion integral in O-mode plasma reflectometry using Chebyshev-Gauss quadrature

E. Leppink, C. Lau, Y. Lin, S. J. Wukitch

Diagnostics and Control

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2 Scopus citations

Abstract

The Abel transform is often used to reconstruct plasma density profiles from O-Mode polarized reflectometry diagnostics. However, standard numerical trapezoidal evaluation of the Abel inversion integral can be computationally expensive for a large number of evaluation points, and an endpoint singularity exists on the upper-bound of the integral, which can result in an increased error. In this work, Chebyshev-Gauss quadrature is introduced as a new method to evaluate the Abel inversion integral for the problem of O-Mode plasma reflectometry. The method does not require numerical evaluation of an integral singularity and is shown to have similar accuracy compared to existing methods while being computationally efficient.

Original language	English
Article number	063506
Journal	Review of Scientific Instruments
Volume	94
Issue number	6
DOIs	https://doi.org/10.1063/5.0132246
State	Published - Jun 1 2023

Funding

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, using the DIII-D National Fusion Facility, a DOE Office of Science user facility, under Award Nos. DE-FC02-04ER54698 and DE-SC0014264.

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10.1063/5.0132246

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abstract = "The Abel transform is often used to reconstruct plasma density profiles from O-Mode polarized reflectometry diagnostics. However, standard numerical trapezoidal evaluation of the Abel inversion integral can be computationally expensive for a large number of evaluation points, and an endpoint singularity exists on the upper-bound of the integral, which can result in an increased error. In this work, Chebyshev-Gauss quadrature is introduced as a new method to evaluate the Abel inversion integral for the problem of O-Mode plasma reflectometry. The method does not require numerical evaluation of an integral singularity and is shown to have similar accuracy compared to existing methods while being computationally efficient.",

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AU - Lau, C.

AU - Lin, Y.

AU - Wukitch, S. J.

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AB - The Abel transform is often used to reconstruct plasma density profiles from O-Mode polarized reflectometry diagnostics. However, standard numerical trapezoidal evaluation of the Abel inversion integral can be computationally expensive for a large number of evaluation points, and an endpoint singularity exists on the upper-bound of the integral, which can result in an increased error. In this work, Chebyshev-Gauss quadrature is introduced as a new method to evaluate the Abel inversion integral for the problem of O-Mode plasma reflectometry. The method does not require numerical evaluation of an integral singularity and is shown to have similar accuracy compared to existing methods while being computationally efficient.

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Evaluation of the Abel inversion integral in O-mode plasma reflectometry using Chebyshev-Gauss quadrature

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