Linear stability analysis via simulated annealing and accelerated relaxation
Abstract
Simulated annealing (SA) is a kind of relaxation method for finding equilibria of Hamiltonian systems. A set of evolution equations is solved with SA, which is derived from the original Hamiltonian system so that the energy of the system changes monotonically while preserving Casimir invariants inherent to noncanonical Hamiltonian systems. The energy extremum reached by SA is an equilibrium. Since SA searches for an energy extremum, it can also be used for stability analysis when initiated from a state where a perturbation is added to an equilibrium. The procedure of the stability analysis is explained, and some examples are shown. Because the time evolution is computationally time consuming, efficient relaxation is necessary for SA to be practically useful. An acceleration method is developed by introducing time dependence in the symmetric kernel used in the double bracket, which is part of the SA formulation described here. An explicit formulation for low-beta reduced magnetohydrodynamics (MHD) in cylindrical geometry is presented. Since SA for low-beta reduced MHD has two advection fields that relax, it is important to balance the orders of magnitude of these advection fields.
- Publication Date:
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1891581
- Grant/Contract Number:
- FG05-80ET-53088
- Resource Type:
- Publisher's Accepted Manuscript
- Journal Name:
- Physics of Plasmas
- Additional Journal Information:
- Journal Name: Physics of Plasmas Journal Volume: 29 Journal Issue: 10; Journal ID: ISSN 1070-664X
- Publisher:
- American Institute of Physics
- Country of Publication:
- United States
- Language:
- English
Citation Formats
Furukawa, M., and Morrison, P. J. Linear stability analysis via simulated annealing and accelerated relaxation. United States: N. p., 2022.
Web. doi:10.1063/5.0101095.
Furukawa, M., & Morrison, P. J. Linear stability analysis via simulated annealing and accelerated relaxation. United States. https://doi.org/10.1063/5.0101095
Furukawa, M., and Morrison, P. J. Mon .
"Linear stability analysis via simulated annealing and accelerated relaxation". United States. https://doi.org/10.1063/5.0101095.
@article{osti_1891581,
title = {Linear stability analysis via simulated annealing and accelerated relaxation},
author = {Furukawa, M. and Morrison, P. J.},
abstractNote = {Simulated annealing (SA) is a kind of relaxation method for finding equilibria of Hamiltonian systems. A set of evolution equations is solved with SA, which is derived from the original Hamiltonian system so that the energy of the system changes monotonically while preserving Casimir invariants inherent to noncanonical Hamiltonian systems. The energy extremum reached by SA is an equilibrium. Since SA searches for an energy extremum, it can also be used for stability analysis when initiated from a state where a perturbation is added to an equilibrium. The procedure of the stability analysis is explained, and some examples are shown. Because the time evolution is computationally time consuming, efficient relaxation is necessary for SA to be practically useful. An acceleration method is developed by introducing time dependence in the symmetric kernel used in the double bracket, which is part of the SA formulation described here. An explicit formulation for low-beta reduced magnetohydrodynamics (MHD) in cylindrical geometry is presented. Since SA for low-beta reduced MHD has two advection fields that relax, it is important to balance the orders of magnitude of these advection fields.},
doi = {10.1063/5.0101095},
journal = {Physics of Plasmas},
number = 10,
volume = 29,
place = {United States},
year = {Mon Oct 10 00:00:00 EDT 2022},
month = {Mon Oct 10 00:00:00 EDT 2022}
}
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