Time-dependent probability density functions and information geometry in a stochastic prey-predator model of fusion plasmas

Patrick Fuller; Eun Jin Kim; Rainer Hollerbach; Bogdan Hnat

doi:10.1063/5.0193622

Time-dependent probability density functions and information geometry in a stochastic prey-predator model of fusion plasmas

Patrick Fuller, Eun Jin Kim, Rainer Hollerbach, Bogdan Hnat

Research Centre for Fluid and Complex Systems

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

66 Downloads (Pure)

Abstract

A stochastic, prey-predator model of the low to high confinement transition is presented. The model concerns the interaction of a turbulent fluctuation amplitude, zonal flow shear, and the ion density gradient. Delta-correlated noise terms are used to construct Langevin equations for each of the three variables, and a Fokker-Planck equation is subsequently derived. A time-dependent probability distribution function is solved and a number of diagnostic quantities are calculated from it, including the information rate and length. We find the marginal probability distribution functions to be strongly non-Gaussian and frequently multi-modal, showing the coexistence of dithering and H-mode solutions over time. The information rate and length are shown to be useful diagnostics to investigate self-regulation between the variables, particularly the turbulence and zonal flow shear.

Original language	English
Article number	092506
Number of pages	21
Journal	Physics of Plasmas
Volume	31
Issue number	9
DOIs	https://doi.org/10.1063/5.0193622
Publication status	Published - 11 Sept 2024

Bibliographical note

All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

Funder

This research is in part supported by Brain Pool Program funded by the Ministry of Science and ICT through the National Research Foundation of Korea (RS-2023-00284119).

Funding

This research is in part supported by Brain Pool Program funded by the Ministry of Science and ICT through the National Research Foundation of Korea (RS-2023-00284119).

Funders	Funder number
Ministry of Science and ICT	RS-2023-00284119
National Research Foundation of Korea	RS-2023-00284119

Keywords

Physical quantities
Signal processing
Message passing interface
Probability theory
Plasmas
Tokamaks
Fluid flows
Turbulence simulations
Turbulent flows
Stochastic processes

ASJC Scopus subject areas

Condensed Matter Physics

Access to Document

10.1063/5.0193622Licence: CC BY

Kim2024VoRFinal published version, 5.67 MBLicence: CC BY

Cite this

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title = "Time-dependent probability density functions and information geometry in a stochastic prey-predator model of fusion plasmas",

abstract = "A stochastic, prey-predator model of the low to high confinement transition is presented. The model concerns the interaction of a turbulent fluctuation amplitude, zonal flow shear, and the ion density gradient. Delta-correlated noise terms are used to construct Langevin equations for each of the three variables, and a Fokker-Planck equation is subsequently derived. A time-dependent probability distribution function is solved and a number of diagnostic quantities are calculated from it, including the information rate and length. We find the marginal probability distribution functions to be strongly non-Gaussian and frequently multi-modal, showing the coexistence of dithering and H-mode solutions over time. The information rate and length are shown to be useful diagnostics to investigate self-regulation between the variables, particularly the turbulence and zonal flow shear.",

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author = "Patrick Fuller and Kim, \{Eun Jin\} and Rainer Hollerbach and Bogdan Hnat",

note = "All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).",

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AU - Fuller, Patrick

AU - Kim, Eun Jin

AU - Hollerbach, Rainer

AU - Hnat, Bogdan

N1 - All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

PY - 2024/9/11

Y1 - 2024/9/11

N2 - A stochastic, prey-predator model of the low to high confinement transition is presented. The model concerns the interaction of a turbulent fluctuation amplitude, zonal flow shear, and the ion density gradient. Delta-correlated noise terms are used to construct Langevin equations for each of the three variables, and a Fokker-Planck equation is subsequently derived. A time-dependent probability distribution function is solved and a number of diagnostic quantities are calculated from it, including the information rate and length. We find the marginal probability distribution functions to be strongly non-Gaussian and frequently multi-modal, showing the coexistence of dithering and H-mode solutions over time. The information rate and length are shown to be useful diagnostics to investigate self-regulation between the variables, particularly the turbulence and zonal flow shear.

AB - A stochastic, prey-predator model of the low to high confinement transition is presented. The model concerns the interaction of a turbulent fluctuation amplitude, zonal flow shear, and the ion density gradient. Delta-correlated noise terms are used to construct Langevin equations for each of the three variables, and a Fokker-Planck equation is subsequently derived. A time-dependent probability distribution function is solved and a number of diagnostic quantities are calculated from it, including the information rate and length. We find the marginal probability distribution functions to be strongly non-Gaussian and frequently multi-modal, showing the coexistence of dithering and H-mode solutions over time. The information rate and length are shown to be useful diagnostics to investigate self-regulation between the variables, particularly the turbulence and zonal flow shear.

KW - Physical quantities

KW - Signal processing

KW - Message passing interface

KW - Probability theory

KW - Plasmas

KW - Tokamaks

KW - Fluid flows

KW - Turbulence simulations

KW - Turbulent flows

KW - Stochastic processes

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VL - 31

JO - Physics of Plasmas

JF - Physics of Plasmas

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ER -

Time-dependent probability density functions and information geometry in a stochastic prey-predator model of fusion plasmas

Abstract

Bibliographical note

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Funding

Keywords

ASJC Scopus subject areas

Access to Document

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