Hybrid iterative approach for simulation of radio-frequency fields in plasma
Abstract
In this work, a novel iterative approach for solving discretized linear wave equations in a frequency domain, which combines time evolution with iterative relaxation schemes, is presented. In this hybrid approach, each iteration cycle consists of evolution of electromagnetic (EM) fields in time over a specified number of field periods followed by several iterative relaxations. Provided that there is sufficient dissipation, both the time evolution and the iterative relaxations contribute to the convergence of the EM fields to the solution of the formulated full wave boundary value problem. Time evolution rapidly distributes EM fields, propagating with group velocity, over the simulation domain, while the iterative relaxations smooth the fields, reducing the numerical errors such that iteration cycles converge to a steady state solution, approximating the solution of the formulated problem. This approach is intended for large scale simulations which are beyond the capabilities of direct solvers presently used for solving wave equations in the frequency domain. Lastly, the technique is demonstrated for solving wave equations on a regular grid using a cold plasma dielectric model with collisions for 2D modeling of EM fields in tokamak in an electron cyclotron frequency range.
- Authors:
-
- FAR-TECH, Inc., San Diego, CA (United States)
- Publication Date:
- Research Org.:
- FAR-TECH, Inc., San Diego, CA (United States); Univ. of California, Oakland, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1540222
- Alternate Identifier(s):
- OSTI ID: 1463936
- Grant/Contract Number:
- SC0011863; AC02-05CH11231
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics of Plasmas
- Additional Journal Information:
- Journal Volume: 25; Journal Issue: 8; 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
Citation Formats
Svidzinski, V. A., Kim, J. S., Zhao, L., Galkin, S. A., and Spencer, J. A. Hybrid iterative approach for simulation of radio-frequency fields in plasma. United States: N. p., 2018.
Web. doi:10.1063/1.5037110.
Svidzinski, V. A., Kim, J. S., Zhao, L., Galkin, S. A., & Spencer, J. A. Hybrid iterative approach for simulation of radio-frequency fields in plasma. United States. https://doi.org/10.1063/1.5037110
Svidzinski, V. A., Kim, J. S., Zhao, L., Galkin, S. A., and Spencer, J. A. Fri .
"Hybrid iterative approach for simulation of radio-frequency fields in plasma". United States. https://doi.org/10.1063/1.5037110. https://www.osti.gov/servlets/purl/1540222.
@article{osti_1540222,
title = {Hybrid iterative approach for simulation of radio-frequency fields in plasma},
author = {Svidzinski, V. A. and Kim, J. S. and Zhao, L. and Galkin, S. A. and Spencer, J. A.},
abstractNote = {In this work, a novel iterative approach for solving discretized linear wave equations in a frequency domain, which combines time evolution with iterative relaxation schemes, is presented. In this hybrid approach, each iteration cycle consists of evolution of electromagnetic (EM) fields in time over a specified number of field periods followed by several iterative relaxations. Provided that there is sufficient dissipation, both the time evolution and the iterative relaxations contribute to the convergence of the EM fields to the solution of the formulated full wave boundary value problem. Time evolution rapidly distributes EM fields, propagating with group velocity, over the simulation domain, while the iterative relaxations smooth the fields, reducing the numerical errors such that iteration cycles converge to a steady state solution, approximating the solution of the formulated problem. This approach is intended for large scale simulations which are beyond the capabilities of direct solvers presently used for solving wave equations in the frequency domain. Lastly, the technique is demonstrated for solving wave equations on a regular grid using a cold plasma dielectric model with collisions for 2D modeling of EM fields in tokamak in an electron cyclotron frequency range.},
doi = {10.1063/1.5037110},
journal = {Physics of Plasmas},
number = 8,
volume = 25,
place = {United States},
year = {Fri Aug 10 00:00:00 EDT 2018},
month = {Fri Aug 10 00:00:00 EDT 2018}
}
Web of Science
Works referenced in this record:
Computational studies on scattering of radio frequency waves by density filaments in fusion plasmas
journal, October 2017
- Ioannidis, Zisis C.; Ram, Abhay K.; Hizanidis, Kyriakos
- Physics of Plasmas, Vol. 24, Issue 10
Iterative addition of parallel temperature effects to finite-difference simulation of radio-frequency wave propagation in plasmas
journal, March 2014
- Green, D. L.; Berry, L. A.
- Computer Physics Communications, Vol. 185, Issue 3
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
journal, March 1982
- Paige, Christopher C.; Saunders, Michael A.
- ACM Transactions on Mathematical Software, Vol. 8, Issue 1
An iterative method for the Helmholtz equation
journal, March 1983
- Bayliss, Alvin; Goldstein, Charles I.; Turkel, Eli
- Journal of Computational Physics, Vol. 49, Issue 3
Space Charge Waves in Cylindrical Plasma Columns
journal, November 1959
- Trivelpiece, A. W.; Gould, R. W.
- Journal of Applied Physics, Vol. 30, Issue 11
Application of the Finite-Difference Time-Domain Method to Sinusoidal Steady-State Electromagnetic-Penetration Problems
journal, August 1980
- Taflove, Allen
- IEEE Transactions on Electromagnetic Compatibility, Vol. EMC-22, Issue 3
Comparison of multigrid and incomplete LU shifted-Laplace preconditioners for the inhomogeneous Helmholtz equation
journal, May 2006
- Erlangga, Y. A.; Vuik, C.; Oosterlee, C. W.
- Applied Numerical Mathematics, Vol. 56, Issue 5
Hot plasma dielectric response to radio-frequency fields in inhomogeneous magnetic field
journal, November 2016
- Svidzinski, V. A.; Kim, J. S.; Spencer, J. A.
- Physics of Plasmas, Vol. 23, Issue 11
VORPAL: a versatile plasma simulation code
journal, May 2004
- Nieter, Chet; Cary, John R.
- Journal of Computational Physics, Vol. 196, Issue 2
Particle simulation of lower hybrid wave propagation in fusion plasmas
journal, August 2014
- Bao, J.; Lin, Z.; Kuley, A.
- Plasma Physics and Controlled Fusion, Vol. 56, Issue 9
Time-Domain Modeling of RF Antennas and Plasma-Surface Interactions
journal, January 2017
- Jenkins, Thomas G.; Smithe, David N.
- EPJ Web of Conferences, Vol. 157
Plasma wave simulation based on a versatile finite element method solver
journal, May 2010
- Shiraiwa, S.; Meneghini, O.; Parker, R.
- Physics of Plasmas, Vol. 17, Issue 5
Possibility of a direct solution of Vlasov–Maxwell equations in tokamaks in the ion cyclotron range of frequencies
journal, February 2001
- Svidzinski, V. A.; Swanson, D. G.
- Physics of Plasmas, Vol. 8, Issue 2
Numerical simulation of ion cyclotron heating of hot tokamak plasmas
journal, October 1988
- Brambilla, M.; Krücken, T.
- Nuclear Fusion, Vol. 28, Issue 10
Advances in Iterative Methods and Preconditioners for the Helmholtz Equation
journal, December 2007
- Erlangga, Yogi A.
- Archives of Computational Methods in Engineering, Vol. 15, Issue 1
Advances in full-wave modeling of radio frequency heated, multidimensional plasmas
journal, May 2002
- Jaeger, E. F.; Berry, L. A.; D’Azevedo, E.
- Physics of Plasmas, Vol. 9, Issue 5
All-orders spectral calculation of radio-frequency heating in two-dimensional toroidal plasmas
journal, May 2001
- Jaeger, E. F.; Berry, L. A.; D’Azevedo, E.
- Physics of Plasmas, Vol. 8, Issue 5
Scattering of radio frequency waves by cylindrical density filaments in tokamak plasmas
journal, February 2016
- Ram, Abhay K.; Hizanidis, Kyriakos
- Physics of Plasmas, Vol. 23, Issue 2
Recent progress in IC wave codes at IPP Garching
conference, January 1997
- Brambilla, Marco
- The twelfth topical conference on radio frequency power in plasmas, AIP Conference Proceedings
Finite-difference time-domain simulation of fusion plasmas at radiofrequency time scales
journal, May 2007
- Smithe, David N.
- Physics of Plasmas, Vol. 14, Issue 5
Full wave simulation of lower hybrid waves in Maxwellian plasma based on the finite element method
journal, September 2009
- Meneghini, O.; Shiraiwa, S.; Parker, R.
- Physics of Plasmas, Vol. 16, Issue 9
Modeling RF waves in spatially dispersive inhomogeneus plasma using an iterative wavelet spectral method
journal, January 2017
- Vallejos, Pablo; Johnson, Thomas; Hellsten, Torbjörn
- EPJ Web of Conferences, Vol. 157
A Multigrid Method Enhanced by Krylov Subspace Iteration for Discrete Helmholtz Equations
journal, January 2001
- Elman, Howard C.; Ernst, Oliver G.; O'Leary, Dianne P.
- SIAM Journal on Scientific Computing, Vol. 23, Issue 4
Modeling of Electron Cyclotron Heating in Large Tokamaks and ITER with the 3-D Full-Wave Code STELEC
journal, May 2011
- Vdovin, V.
- Fusion Science and Technology, Vol. 59, Issue 4
DIII-D Electron Cyclotron Heating System Status and Upgrades
journal, December 2016
- Cengher, Mirela; Lohr, John; Gorelov, Yuri
- IEEE Transactions on Plasma Science, Vol. 44, Issue 12