A statistical study of gyro-averaging effects in a reduced model of drift-wave transport

J. D. Da Fonseca; D. Del-Castillo-Negrete; I. M. Sokolov; I. L. Caldas

doi:10.1063/1.4961430

A statistical study of gyro-averaging effects in a reduced model of drift-wave transport

J. D. Da Fonseca, D. Del-Castillo-Negrete, I. M. Sokolov, I. L. Caldas

Plasma Theory and Modeling

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Abstract

A statistical study of finite Larmor radius (FLR) effects on transport driven by electrostatic drift-waves is presented. The study is based on a reduced discrete Hamiltonian dynamical system known as the gyro-averaged standard map (GSM). In this system, FLR effects are incorporated through the gyro-averaging of a simplified weak-turbulence model of electrostatic fluctuations. Formally, the GSM is a modified version of the standard map in which the perturbation amplitude, K₀, becomes K0J0(ρ), where J₀ is the zeroth-order Bessel function and ρ is the Larmor radius. Assuming a Maxwellian probability density function (pdf) for ρ, we compute analytically and numerically the pdf and the cumulative distribution function of the effective drift-wave perturbation amplitude K0J0(ρ). Using these results, we compute the probability of loss of confinement (i.e., global chaos), P_c, and the probability of trapping in the main drift-wave resonance, P_t. It is shown that P_c provides an upper bound for the escape rate, and that P_t provides a good estimate of the particle trapping rate. The analytical results are compared with direct numerical Monte-Carlo simulations of particle transport.

Original language	English
Article number	082308
Journal	Physics of Plasmas
Volume	23
Issue number	8
DOIs	https://doi.org/10.1063/1.4961430
State	Published - Aug 1 2016

Funding

This work was made possible through financial support from the So Paulo Research Foundation (FAPESP, Brazil) under Grant No 2011/19296-1, CNPq (Grant No. 203460/2014-6), FAPESP (Grant No. 2012/10240-6), and DFG (IRTG 1740). J.D.F. acknowledges Roberto Venegeroles (UFABC, Brazil) for valuable discussions and the hospitality of the Institute of Physics at the Humboldt University in Berlin, where part of the work was conducted. D.d.C.N. acknowledges support from the Office of Fusion Energy Sciences of the U.S. Department of Energy at Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U.S. Department of Energy under Contract No. DE-AC05-00OR22725

Funders	Funder number
Roberto Venegeroles
UFABC
U.S. Department of Energy	DE-AC05-00OR22725
Fusion Energy Sciences
Oak Ridge National Laboratory
Institute of Physics
Deutsche Forschungsgemeinschaft	IRTG 1740
Fundação de Amparo à Pesquisa do Estado de São Paulo	2011/19296-1
Conselho Nacional de Desenvolvimento Científico e Tecnológico	2012/10240-6, 203460/2014-6

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10.1063/1.4961430

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title = "A statistical study of gyro-averaging effects in a reduced model of drift-wave transport",

abstract = "A statistical study of finite Larmor radius (FLR) effects on transport driven by electrostatic drift-waves is presented. The study is based on a reduced discrete Hamiltonian dynamical system known as the gyro-averaged standard map (GSM). In this system, FLR effects are incorporated through the gyro-averaging of a simplified weak-turbulence model of electrostatic fluctuations. Formally, the GSM is a modified version of the standard map in which the perturbation amplitude, K0, becomes K0J0(ρ), where J0 is the zeroth-order Bessel function and ρ is the Larmor radius. Assuming a Maxwellian probability density function (pdf) for ρ, we compute analytically and numerically the pdf and the cumulative distribution function of the effective drift-wave perturbation amplitude K0J0(ρ). Using these results, we compute the probability of loss of confinement (i.e., global chaos), Pc, and the probability of trapping in the main drift-wave resonance, Pt. It is shown that Pc provides an upper bound for the escape rate, and that Pt provides a good estimate of the particle trapping rate. The analytical results are compared with direct numerical Monte-Carlo simulations of particle transport.",

author = "{Da Fonseca}, {J. D.} and D. Del-Castillo-Negrete and Sokolov, {I. M.} and Caldas, {I. L.}",

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AU - Caldas, I. L.

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N2 - A statistical study of finite Larmor radius (FLR) effects on transport driven by electrostatic drift-waves is presented. The study is based on a reduced discrete Hamiltonian dynamical system known as the gyro-averaged standard map (GSM). In this system, FLR effects are incorporated through the gyro-averaging of a simplified weak-turbulence model of electrostatic fluctuations. Formally, the GSM is a modified version of the standard map in which the perturbation amplitude, K0, becomes K0J0(ρ), where J0 is the zeroth-order Bessel function and ρ is the Larmor radius. Assuming a Maxwellian probability density function (pdf) for ρ, we compute analytically and numerically the pdf and the cumulative distribution function of the effective drift-wave perturbation amplitude K0J0(ρ). Using these results, we compute the probability of loss of confinement (i.e., global chaos), Pc, and the probability of trapping in the main drift-wave resonance, Pt. It is shown that Pc provides an upper bound for the escape rate, and that Pt provides a good estimate of the particle trapping rate. The analytical results are compared with direct numerical Monte-Carlo simulations of particle transport.

AB - A statistical study of finite Larmor radius (FLR) effects on transport driven by electrostatic drift-waves is presented. The study is based on a reduced discrete Hamiltonian dynamical system known as the gyro-averaged standard map (GSM). In this system, FLR effects are incorporated through the gyro-averaging of a simplified weak-turbulence model of electrostatic fluctuations. Formally, the GSM is a modified version of the standard map in which the perturbation amplitude, K0, becomes K0J0(ρ), where J0 is the zeroth-order Bessel function and ρ is the Larmor radius. Assuming a Maxwellian probability density function (pdf) for ρ, we compute analytically and numerically the pdf and the cumulative distribution function of the effective drift-wave perturbation amplitude K0J0(ρ). Using these results, we compute the probability of loss of confinement (i.e., global chaos), Pc, and the probability of trapping in the main drift-wave resonance, Pt. It is shown that Pc provides an upper bound for the escape rate, and that Pt provides a good estimate of the particle trapping rate. The analytical results are compared with direct numerical Monte-Carlo simulations of particle transport.

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A statistical study of gyro-averaging effects in a reduced model of drift-wave transport

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