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Title: Action-angle formulation of generalized, orbit-based, fast-ion diagnostic weight functions

Due to the usually complicated and anisotropic nature of the fast-ion distribution function, diagnostic velocity-space weight functions, which indicate the sensitivity of a diagnostic to different fast-ion velocities, are used to facilitate the analysis of experimental data. Additionally, when velocity-space weight functions are discretized, a linear equation relating the fast-ion density and the expected diagnostic signal is formed. In a technique known as velocity-space tomography, many measurements can be combined to create an ill-conditioned system of linear equations that can be solved using various computational methods. However, when velocity-space weight functions (which by definition ignore spatial dependencies) are used, velocity-space tomography is restricted, both by the accuracy of its forward model and also by the availability of spatially overlapping diagnostic measurements. In this work, we extend velocity-space weight functions to a full 6D generalized coordinate system and then show how to reduce them to a 3D orbit-space without loss of generality using an action-angle formulation. Moreover, we show how diagnostic orbit-weight functions can be used to infer the full fast-ion distribution function, i.e., orbit tomography. In depth derivations of orbit weight functions for the neutron, neutral particle analyzer, and fast-ion D-α diagnostics are also shown
Authors:
ORCiD logo [1] ;  [1]
  1. Univ. of California, Irvine, CA (United States)
Publication Date:
Grant/Contract Number:
AC02-09CH11466; FC02-04ER54698
Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 24; Journal Issue: 9; Journal ID: ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)
Research Org:
Princeton Univ., NJ (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS
OSTI Identifier:
1474286
Alternate Identifier(s):
OSTI ID: 1374930

Stagner, L., and Heidbrink, W. W.. Action-angle formulation of generalized, orbit-based, fast-ion diagnostic weight functions. United States: N. p., Web. doi:10.1063/1.4990391.
Stagner, L., & Heidbrink, W. W.. Action-angle formulation of generalized, orbit-based, fast-ion diagnostic weight functions. United States. doi:10.1063/1.4990391.
Stagner, L., and Heidbrink, W. W.. 2017. "Action-angle formulation of generalized, orbit-based, fast-ion diagnostic weight functions". United States. doi:10.1063/1.4990391. https://www.osti.gov/servlets/purl/1474286.
@article{osti_1474286,
title = {Action-angle formulation of generalized, orbit-based, fast-ion diagnostic weight functions},
author = {Stagner, L. and Heidbrink, W. W.},
abstractNote = {Due to the usually complicated and anisotropic nature of the fast-ion distribution function, diagnostic velocity-space weight functions, which indicate the sensitivity of a diagnostic to different fast-ion velocities, are used to facilitate the analysis of experimental data. Additionally, when velocity-space weight functions are discretized, a linear equation relating the fast-ion density and the expected diagnostic signal is formed. In a technique known as velocity-space tomography, many measurements can be combined to create an ill-conditioned system of linear equations that can be solved using various computational methods. However, when velocity-space weight functions (which by definition ignore spatial dependencies) are used, velocity-space tomography is restricted, both by the accuracy of its forward model and also by the availability of spatially overlapping diagnostic measurements. In this work, we extend velocity-space weight functions to a full 6D generalized coordinate system and then show how to reduce them to a 3D orbit-space without loss of generality using an action-angle formulation. Moreover, we show how diagnostic orbit-weight functions can be used to infer the full fast-ion distribution function, i.e., orbit tomography. In depth derivations of orbit weight functions for the neutron, neutral particle analyzer, and fast-ion D-α diagnostics are also shown},
doi = {10.1063/1.4990391},
journal = {Physics of Plasmas},
number = 9,
volume = 24,
place = {United States},
year = {2017},
month = {8}
}