Modeling of resistive plasma response in toroidal geometry using an asymptotic matching approach

Wang, Zhirui; Glasser, Alan H.; Brennan, Dylan; Liu, Yueqiang; Park, Jongkyu

doi:10.1063/5.0020010

Title: Modeling of resistive plasma response in toroidal geometry using an asymptotic matching approach

Abstract

The method of solving the linear resistive plasma response, based on the asymptotic matching approach, is developed for full toroidal tokamaks by upgrading the resistive DCON code [A. H. Glasser, Z. R. Wang, and J.-K. Park, Phys. Plasmas 23, 112506 (2016)]. The derived matching matrix, asymptotically matching the outer and inner regions, indicates that the applied three dimension (3-D) magnetic perturbations contribute additional small solutions at each resonant surface due to the toroidal coupling of poloidal modes. In contrast, the resonant harmonic only affects the corresponding resonant surface in the cylindrical plasma. Additionally, the solution of the ideal outer region is critical to the asymptotic matching and is challenging in toroidal geometry due to the singular power series solution at the resonant surfaces. Thus, a systematic verification of the outer region Δ' matrix is made by reproducing the well-known analytical Δ' result in Furth et al. [Phys. Fluids 16, 1054–1063 (1073)] and by making a quantitative benchmark with the PEST3 code [A. Pletzer and R. L. Dewar, J. Plasma Phys. 45, 427–451 (1991)]. Finally, the reconstructed numerical solution of the resistive plasma response from the toroidal matching matrix is presented. Compared with the ideal plasma response, the global structure ofmore »« less

Authors:

^[1];

^[2];

^[3];

^[4];

^[1]

Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Fusion Theory and Computation, Inc., Kingston, WA (United States)
Princeton Univ., NJ (United States)
General Atomics, San Diego, CA (United States)

Publication Date:: Tue Dec 01 00:00:00 EST 2020

Research Org.:: Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Fusion Energy Sciences (FES)

OSTI Identifier:: 1819056

Alternate Identifier(s):: OSTI ID: 1970623

Grant/Contract Number:: AC02-09CH11466

Resource Type:: Accepted Manuscript

Journal Name:: Physics of Plasmas

Additional Journal Information:: Journal Volume: 27; Journal Issue: 12; Journal ID: ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; plasma confinement; dimensional analysis; functions and functionals; finite-element analysis; power series; tokamaks; plasma instabilities; control theory

Citation Formats


                    Wang, Zhirui, Glasser, Alan H., Brennan, Dylan, Liu, Yueqiang, and Park, Jongkyu. Modeling of resistive plasma response in toroidal geometry using an asymptotic matching approach.  United States: N. p., 2020. 
Web.  doi:10.1063/5.0020010.

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                    Wang, Zhirui, Glasser, Alan H., Brennan, Dylan, Liu, Yueqiang, & Park, Jongkyu. Modeling of resistive plasma response in toroidal geometry using an asymptotic matching approach.  United States.  https://doi.org/10.1063/5.0020010

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                    Wang, Zhirui, Glasser, Alan H., Brennan, Dylan, Liu, Yueqiang, and Park, Jongkyu. Tue .  
"Modeling of resistive plasma response in toroidal geometry using an asymptotic matching approach".  United States.  https://doi.org/10.1063/5.0020010.  https://www.osti.gov/servlets/purl/1819056.

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@article{osti_1819056,

  title        = {Modeling of resistive plasma response in toroidal geometry using an asymptotic matching approach},

  author       = {Wang, Zhirui and Glasser, Alan H. and Brennan, Dylan and Liu, Yueqiang and Park, Jongkyu},

  abstractNote = {The method of solving the linear resistive plasma response, based on the asymptotic matching approach, is developed for full toroidal tokamaks by upgrading the resistive DCON code [A. H. Glasser, Z. R. Wang, and J.-K. Park, Phys. Plasmas 23, 112506 (2016)]. The derived matching matrix, asymptotically matching the outer and inner regions, indicates that the applied three dimension (3-D) magnetic perturbations contribute additional small solutions at each resonant surface due to the toroidal coupling of poloidal modes. In contrast, the resonant harmonic only affects the corresponding resonant surface in the cylindrical plasma. Additionally, the solution of the ideal outer region is critical to the asymptotic matching and is challenging in toroidal geometry due to the singular power series solution at the resonant surfaces. Thus, a systematic verification of the outer region Δ' matrix is made by reproducing the well-known analytical Δ' result in Furth et al. [Phys. Fluids 16, 1054–1063 (1073)] and by making a quantitative benchmark with the PEST3 code [A. Pletzer and R. L. Dewar, J. Plasma Phys. 45, 427–451 (1991)]. Finally, the reconstructed numerical solution of the resistive plasma response from the toroidal matching matrix is presented. Compared with the ideal plasma response, the global structure of the response can be affected by the small finite island at the resonant surfaces.},

  doi          = {10.1063/5.0020010},

  journal      = {Physics of Plasmas},

  number       = 12,

  volume       = 27,

  place        = {United States},

  year         = {Tue Dec 01 00:00:00 EST 2020},

  month        = {Tue Dec 01 00:00:00 EST 2020}

}

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Title: Modeling of resistive plasma response in toroidal geometry using an asymptotic matching approach

Abstract

Citation Formats

Computation of three-dimensional tokamak and spherical torus equilibria journal, May 2007

Experimental tests of linear and nonlinear three-dimensional equilibrium models in DIII-D journal, July 2015

Current sheets and nonlinear growth of the m =1 kink‐tearing mode journal, December 1989

Neoclassical toroidal viscosity and error-field penetration in tokamaks journal, May 2008

A necessary condition for hydromagnetic stability of plasma with axial symmetry journal, September 1960

Verification of the ideal magnetohydrodynamic response at rational surfaces in the VMEC code journal, January 2016

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Drift-magnetohydrodynamical model of error-field penetration in tokamak plasmas journal, March 2006

Calculations of two-fluid linear response to non-axisymmetric fields in tokamaks journal, May 2012

Computation of resistive instabilities by matched asymptotic expansions journal, November 2016

Resistive instabilities in a tokamak journal, January 1976

Theory comparison and numerical benchmarking on neoclassical toroidal viscosity torque journal, April 2014

The locking and unlocking thresholds for tearing modes in a cylindrical tokamak journal, March 2016

Forced magnetic reconnection journal, January 1985

Stable compression of a spherical tokamak plasma journal, March 2020

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Validation of the linear ideal magnetohydrodynamic model of three-dimensional tokamak equilibria journal, March 2010

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The direct criterion of Newcomb for the ideal MHD stability of an axisymmetric toroidal plasma journal, July 2016

Understanding edge-localized mode mitigation by resonant magnetic perturbations on MAST journal, March 2013

Non-ideal stability: variational method for the determination of the outer-region matching data journal, June 1991

Effects of resistivity and rotation on the linear plasma response to non-axisymmetric magnetic perturbations on DIII-D journal, January 2015

Tearing mode in the cylindrical tokamak journal, January 1973

A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures journal, October 1970

Importance of plasma response to nonaxisymmetric perturbations in tokamaks journal, May 2009

Dynamics of resonant magnetic field penetration and plasma rotation journal, November 2016

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Energy release and plasma heating by forced magnetic reconnection journal, May 1998

Linear Stability of Resistive MHD Modes: Axisymmetric Toroidal Computation of the Outer Region Matching Data journal, December 1994

Self-consistent perturbed equilibrium with neoclassical toroidal torque in tokamaks journal, March 2017

Rotation and Locking of Magnetic Islands journal, March 1997

Stability Criterion for Arbitrary Hydromagnetic Equilibria journal, January 1962

Cross-machine comparison of resonant field amplification and resistive wall mode stabilization by plasma rotation journal, May 2006

Mode locking and island suppression by resonant magnetic perturbations in Rutherford regime journal, March 2015

Edge localized mode control with an edge resonant magnetic perturbation journal, May 2005

Forced Magnetic Reconnection and Field Penetration of an Externally Applied Rotating Helical Magnetic Field in the TEXTOR Tokamak journal, August 2006

3D field phase-space control in tokamak plasmas journal, September 2018

The physics of edge resonant magnetic perturbations in hot tokamak plasmas journal, May 2006

RMP enhanced transport and rotational screening in simulations of DIII-D plasmas journal, September 2008

Numerical solution of the resistive magnetohydrodynamic boundary layer equations journal, January 1984

CORSICA modelling of ITER hybrid operation scenarios journal, August 2016

Resistive instabilities in general toroidal plasma configurations journal, January 1975

Role of plasma response in displacements of the tokamak edge due to applied non-axisymmetric fields journal, June 2013

Theory of edge localized mode suppression by static resonant magnetic perturbations in the DIII-D tokamak journal, April 2020

Resistive versus ideal plasma response to RMP fields in DIII-D: roles of q 95 and X-point geometry journal, June 2019

The interaction of resonant magnetic perturbations with rotating plasmas journal, March 1991

A robust solution for the resistive MHD toroidal Δ′ matrix in near real-time journal, August 2018

Identification of multi-modal plasma responses to applied magnetic perturbations using the plasma reluctance journal, May 2016

Interaction of tearing modes with external structures in cylindrical geometry (plasma) journal, July 1993

Effects of resistivity on linear plasma responses to resonant magnetic perturbations in tokamak plasmas journal, September 2016

Role of singular layers in the plasma response to resonant magnetic perturbations journal, July 2012

Measurement of 3D plasma response to external magnetic perturbations in the presence of a rotating external kink journal, October 2013

Shielding of resonant magnetic perturbations in the long mean-free path regime journal, October 2003

Edge stability and transport control with resonant magnetic perturbations in collisionless tokamak plasmas journal, May 2006

Finite-Resistivity Instabilities of a Sheet Pinch journal, January 1963

Nonlinear dynamics of feedback modulated magnetic islands in toroidal plasmas journal, December 2000

Error Field Amplification and Rotation Damping in Tokamak Plasmas journal, May 2001

Nonambipolar Transport due to Electrons with 3D Resistive Response in the KSTAR Tokamak journal, August 2019

Suppression of Large Edge-Localized Modes in High-Confinement DIII-D Plasmas with a Stochastic Magnetic Boundary journal, June 2004

Neoclassical plasma viscosity and transport processes in non-axisymmetric tori journal, November 2015

Three-Dimensional Drift Kinetic Response of High- β Plasmas in the DIII-D Tokamak journal, April 2015

Nonambipolar Transport by Trapped Particles in Tokamaks journal, February 2009

Computation of three-dimensional tokamak and spherical torus equilibria
journal, May 2007

Experimental tests of linear and nonlinear three-dimensional equilibrium models in DIII-D
journal, July 2015

Current sheets and nonlinear growth of the m =1 kink‐tearing mode
journal, December 1989

Neoclassical toroidal viscosity and error-field penetration in tokamaks
journal, May 2008

A necessary condition for hydromagnetic stability of plasma with axial symmetry
journal, September 1960

Verification of the ideal magnetohydrodynamic response at rational surfaces in the VMEC code
journal, January 2016

Non-linear modeling of the plasma response to RMPs in ASDEX Upgrade
journal, September 2016

Bifurcated states of a rotating tokamak plasma in the presence of a static error-field
journal, September 1998

Nonlinear growth of the tearing mode
journal, January 1973

Drift-magnetohydrodynamical model of error-field penetration in tokamak plasmas
journal, March 2006

Calculations of two-fluid linear response to non-axisymmetric fields in tokamaks
journal, May 2012

Computation of resistive instabilities by matched asymptotic expansions
journal, November 2016

Resistive instabilities in a tokamak
journal, January 1976

Theory comparison and numerical benchmarking on neoclassical toroidal viscosity torque
journal, April 2014

The locking and unlocking thresholds for tearing modes in a cylindrical tokamak
journal, March 2016

Forced magnetic reconnection
journal, January 1985

Stable compression of a spherical tokamak plasma
journal, March 2020

RMP ELM suppression in DIII-D plasmas with ITER similar shapes and collisionalities
journal, January 2008

Validation of the linear ideal magnetohydrodynamic model of three-dimensional tokamak equilibria
journal, March 2010

Full toroidal plasma response to externally applied nonaxisymmetric magnetic fields
journal, December 2010

The direct criterion of Newcomb for the ideal MHD stability of an axisymmetric toroidal plasma
journal, July 2016

Understanding edge-localized mode mitigation by resonant magnetic perturbations on MAST
journal, March 2013

Non-ideal stability: variational method for the determination of the outer-region matching data
journal, June 1991

Effects of resistivity and rotation on the linear plasma response to non-axisymmetric magnetic perturbations on DIII-D
journal, January 2015

Tearing mode in the cylindrical tokamak
journal, January 1973

A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures
journal, October 1970

Importance of plasma response to nonaxisymmetric perturbations in tokamaks
journal, May 2009

Dynamics of resonant magnetic field penetration and plasma rotation
journal, November 2016

Observation of a Multimode Plasma Response and its Relationship to Density Pumpout and Edge-Localized Mode Suppression
journal, March 2015

Pedestal Bifurcation and Resonant Field Penetration at the Threshold of Edge-Localized Mode Suppression in the DIII-D Tokamak
journal, March 2015

Ideal plasma response to vacuum magnetic fields with resonant magnetic perturbations in non-axisymmetric tokamaks
journal, September 2015

Energy release and plasma heating by forced magnetic reconnection
journal, May 1998

Linear Stability of Resistive MHD Modes: Axisymmetric Toroidal Computation of the Outer Region Matching Data
journal, December 1994

Self-consistent perturbed equilibrium with neoclassical toroidal torque in tokamaks
journal, March 2017

Rotation and Locking of Magnetic Islands
journal, March 1997

Stability Criterion for Arbitrary Hydromagnetic Equilibria
journal, January 1962

Cross-machine comparison of resonant field amplification and resistive wall mode stabilization by plasma rotation
journal, May 2006

Mode locking and island suppression by resonant magnetic perturbations in Rutherford regime
journal, March 2015

Edge localized mode control with an edge resonant magnetic perturbation
journal, May 2005

Forced Magnetic Reconnection and Field Penetration of an Externally Applied Rotating Helical Magnetic Field in the TEXTOR Tokamak
journal, August 2006

3D field phase-space control in tokamak plasmas
journal, September 2018

The physics of edge resonant magnetic perturbations in hot tokamak plasmas
journal, May 2006

RMP enhanced transport and rotational screening in simulations of DIII-D plasmas
journal, September 2008

Numerical solution of the resistive magnetohydrodynamic boundary layer equations
journal, January 1984

CORSICA modelling of ITER hybrid operation scenarios
journal, August 2016

Resistive instabilities in general toroidal plasma configurations
journal, January 1975

Role of plasma response in displacements of the tokamak edge due to applied non-axisymmetric fields
journal, June 2013

Theory of edge localized mode suppression by static resonant magnetic perturbations in the DIII-D tokamak
journal, April 2020

Resistive versus ideal plasma response to RMP fields in DIII-D: roles of q ₉₅ and X-point geometry
journal, June 2019

The interaction of resonant magnetic perturbations with rotating plasmas
journal, March 1991

A robust solution for the resistive MHD toroidal Δ′ matrix in near real-time
journal, August 2018

Identification of multi-modal plasma responses to applied magnetic perturbations using the plasma reluctance
journal, May 2016

Interaction of tearing modes with external structures in cylindrical geometry (plasma)
journal, July 1993

Effects of resistivity on linear plasma responses to resonant magnetic perturbations in tokamak plasmas
journal, September 2016

Role of singular layers in the plasma response to resonant magnetic perturbations
journal, July 2012

Measurement of 3D plasma response to external magnetic perturbations in the presence of a rotating external kink
journal, October 2013

Shielding of resonant magnetic perturbations in the long mean-free path regime
journal, October 2003

Edge stability and transport control with resonant magnetic perturbations in collisionless tokamak plasmas
journal, May 2006

Finite-Resistivity Instabilities of a Sheet Pinch
journal, January 1963

Nonlinear dynamics of feedback modulated magnetic islands in toroidal plasmas
journal, December 2000

Error Field Amplification and Rotation Damping in Tokamak Plasmas
journal, May 2001

Nonambipolar Transport due to Electrons with 3D Resistive Response in the KSTAR Tokamak
journal, August 2019

Suppression of Large Edge-Localized Modes in High-Confinement DIII-D Plasmas with a Stochastic Magnetic Boundary
journal, June 2004

Neoclassical plasma viscosity and transport processes in non-axisymmetric tori
journal, November 2015

Three-Dimensional Drift Kinetic Response of High- $β$ Plasmas in the DIII-D Tokamak
journal, April 2015

Nonambipolar Transport by Trapped Particles in Tokamaks
journal, February 2009