Quasioptical modeling of wave beams with and without mode conversion. I. Basic theory
Abstract
This work opens a series of papers where we develop a general quasi-optical theory for mode-converting electromagnetic beams in plasma and implement it in a numerical algorithm. Here, the basic theory is introduced. We consider a general quasimonochromatic multicomponent wave in a weakly inhomogeneous linear medium with no sources. For any given dispersion operator that governs the wave field, we explicitly calculate the approximate operator that governs the wave envelope ψ to the second order in the geometrical-optics parameter. Then, we further simplify this envelope operator by assuming that the gradient of ψ transverse to the local group velocity is much larger than the corresponding parallel gradient. This leads to a parabolic differential equation for ψ (“quasioptical equation”) on the basis of the geometrical-optics polarization vectors. Scalar and mode-converting vector beams are described on the same footing. Here, we also explain how to apply this model to electromagnetic waves in general. In the next papers of this series, we report successful quasioptical modeling of radio frequency wave beams in magnetized plasma based on this theory.
- Authors:
-
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Nagoya Univ., Aichi (Japan)
- National Inst. for Fusion Science, Gifu (Japan)
- Publication Date:
- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA); Japan Society for the Promotion of Science (JSPS)
- Contributing Org.:
- National Institute of Fusion Science, Japan. This work was supported by JSPS KAKENHI Grant No. JP17H03514 and by the U.S. DOE through Contract No. DE-AC02-09CH11466 and by the Laboratory Directed Research and Development program at Sandia National Laboratories, under Contract No. DE-NA-0003525.
- OSTI Identifier:
- 1634798
- Alternate Identifier(s):
- OSTI ID: 1544458; OSTI ID: 1557568
- Report Number(s):
- SAND-2020-5533J
Journal ID: ISSN 1070-664X; 686364
- Grant/Contract Number:
- AC04-94AL85000; AC02-09CH11466; NA0003525; JP17H03514
- Resource Type:
- Journal Article: Accepted Manuscript
- Journal Name:
- Physics of Plasmas
- Additional Journal Information:
- Journal Volume: 26; Journal Issue: 7; 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; Electromagnetism; plasmas; geometrical optics
Citation Formats
Dodin, I. Y., Ruiz, D. E., Yanagihara, K., Zhou, Y., and Kubo, S. Quasioptical modeling of wave beams with and without mode conversion. I. Basic theory. United States: N. p., 2019.
Web. doi:10.1063/1.5095076.
Dodin, I. Y., Ruiz, D. E., Yanagihara, K., Zhou, Y., & Kubo, S. Quasioptical modeling of wave beams with and without mode conversion. I. Basic theory. United States. https://doi.org/10.1063/1.5095076
Dodin, I. Y., Ruiz, D. E., Yanagihara, K., Zhou, Y., and Kubo, S. Tue .
"Quasioptical modeling of wave beams with and without mode conversion. I. Basic theory". United States. https://doi.org/10.1063/1.5095076. https://www.osti.gov/servlets/purl/1634798.
@article{osti_1634798,
title = {Quasioptical modeling of wave beams with and without mode conversion. I. Basic theory},
author = {Dodin, I. Y. and Ruiz, D. E. and Yanagihara, K. and Zhou, Y. and Kubo, S.},
abstractNote = {This work opens a series of papers where we develop a general quasi-optical theory for mode-converting electromagnetic beams in plasma and implement it in a numerical algorithm. Here, the basic theory is introduced. We consider a general quasimonochromatic multicomponent wave in a weakly inhomogeneous linear medium with no sources. For any given dispersion operator that governs the wave field, we explicitly calculate the approximate operator that governs the wave envelope ψ to the second order in the geometrical-optics parameter. Then, we further simplify this envelope operator by assuming that the gradient of ψ transverse to the local group velocity is much larger than the corresponding parallel gradient. This leads to a parabolic differential equation for ψ (“quasioptical equation”) on the basis of the geometrical-optics polarization vectors. Scalar and mode-converting vector beams are described on the same footing. Here, we also explain how to apply this model to electromagnetic waves in general. In the next papers of this series, we report successful quasioptical modeling of radio frequency wave beams in magnetized plasma based on this theory.},
doi = {10.1063/1.5095076},
url = {https://www.osti.gov/biblio/1634798},
journal = {Physics of Plasmas},
issn = {1070-664X},
number = 7,
volume = 26,
place = {United States},
year = {2019},
month = {7}
}
Web of Science
Works referenced in this record:
Self-adjointness of momentum operators in generalized coordinates
journal, February 1984
- Domingos, J. M.; Caldeira, M. H.
- Foundations of Physics, Vol. 14, Issue 2
Spin Hall effect of photons in a static gravitational field
journal, April 2007
- Gosselin, Pierre; Bérard, Alain; Mohrbach, Hervé
- Physical Review D, Vol. 75, Issue 8
Geometric view on noneikonal waves
journal, April 2014
- Dodin, I. Y.
- Physics Letters A, Vol. 378, Issue 22-23
Quasioptical modeling of wave beams with and without mode conversion. III. Numerical simulations of mode-converting beams
journal, July 2019
- Yanagihara, K.; Dodin, I. Y.; Kubo, S.
- Physics of Plasmas, Vol. 26, Issue 7
Quasioptical modeling of wave beams with and without mode conversion. II. Numerical simulations of single-mode beams
journal, July 2019
- Yanagihara, K.; Dodin, I. Y.; Kubo, S.
- Physics of Plasmas, Vol. 26, Issue 7
Quantum phase-space representation for curved configuration spaces
journal, December 2013
- Gneiting, Clemens; Fischer, Timo; Hornberger, Klaus
- Physical Review A, Vol. 88, Issue 6
Development and application of a ray-tracing code integrating with 3D equilibrium mapping in LHD ECH experiments
journal, November 2015
- Ii Tsujimura, T.; Kubo, S.; Takahashi, H.
- Nuclear Fusion, Vol. 55, Issue 12
Ponderomotive dynamics of waves in quasiperiodically modulated media
journal, March 2017
- Ruiz, D. E.; Dodin, I. Y.
- Physical Review A, Vol. 95, Issue 3
Four-dimensional eikonal theory of linear mode conversion
journal, April 1987
- Friedland, Lazar; Goldner, Galya; Kaufman, Allan N.
- Physical Review Letters, Vol. 58, Issue 14
Quantum mechanics as a statistical theory
journal, January 1949
- Moyal, J. E.
- Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 45, Issue 1
Axiomatic geometrical optics, Abraham-Minkowski controversy, and photon properties derived classically
journal, November 2012
- Dodin, I. Y.; Fisch, N. J.
- Physical Review A, Vol. 86, Issue 5
On the Quantum Correction For Thermodynamic Equilibrium
journal, June 1932
- Wigner, E.
- Physical Review, Vol. 40, Issue 5
TORBEAM 2.0, a paraxial beam tracing code for electron-cyclotron beams in fusion plasmas for extended physics applications
journal, April 2018
- Poli, E.; Bock, A.; Lochbrunner, M.
- Computer Physics Communications, Vol. 225
Gyroresonant absorption from congruent reduction of an anisotropic pressure fluid model
journal, September 1988
- Friedland, Lazar
- Physics of Fluids, Vol. 31, Issue 9
Gravitational birefringence of light in Robertson-Walker cosmologies
journal, August 2017
- Duval, C.; Schücker, T.
- Physical Review D, Vol. 96, Issue 4
Relativistic ponderomotive Hamiltonian of a Dirac particle in a vacuum laser field
journal, December 2015
- Ruiz, D. E.; Ellison, C. L.; Dodin, I. Y.
- Physical Review A, Vol. 92, Issue 6
Quasi-optical description of wave beams in smoothly inhomogeneous anisotropic media
journal, June 2007
- Balakin, A. A.; Balakina, M. A.; Permitin, G. V.
- Journal of Physics D: Applied Physics, Vol. 40, Issue 14
Variational principles for dissipative (sub)systems, with applications to the theory of linear dispersion and geometrical optics
journal, April 2017
- Dodin, I. Y.; Zhmoginov, A. I.; Ruiz, D. E.
- Physics Letters A, Vol. 381, Issue 16
Lagrangian geometrical optics of nonadiabatic vector waves and spin particles
journal, October 2015
- Ruiz, D. E.; Dodin, I. Y.
- Physics Letters A, Vol. 379, Issue 38
Use of the multidimensional WKB method to describe propagation of lower hybrid waves in tokamak plasma
journal, July 1992
- Pereverzev, G. V.
- Nuclear Fusion, Vol. 32, Issue 7
The semiclassical evolution of wave packets
journal, May 1986
- Littlejohn, R.
- Physics Reports, Vol. 138, Issue 4-5
Propagation of a Gaussian beam in a nonhomogeneous plasma
journal, September 1989
- Mazzucato, E.
- Physics of Fluids B: Plasma Physics, Vol. 1, Issue 9
Point Transformations in Quantum Mechanics
journal, February 1952
- DeWitt, Bryce Seligman
- Physical Review, Vol. 85, Issue 4
Vlasov equation and collisionless hydrodynamics adapted to curved spacetime
journal, November 2010
- Dodin, I. Y.; Fisch, N. J.
- Physics of Plasmas, Vol. 17, Issue 11
Parabolic approximation method for fast magnetosonic wave propagation in tokamaks
journal, January 1986
- Phillips, C. K.; Perkins, F. W.; Hwang, D. Q.
- Physics of Fluids, Vol. 29, Issue 5
Ray-tracing code TRAVIS for ECR heating, EC current drive and ECE diagnostic
journal, January 2014
- Marushchenko, N. B.; Turkin, Y.; Maassberg, H.
- Computer Physics Communications, Vol. 185, Issue 1
Mode conversion in cold low-density plasma with a sheared magnetic field
journal, December 2017
- Dodin, I. Y.; Ruiz, D. E.; Kubo, S.
- Physics of Plasmas, Vol. 24, Issue 12
Scalar equation for wave beams in a magnetized plasma
journal, April 2007
- Balakin, A. A.; Balakina, M. A.; Permitin, G. V.
- Plasma Physics Reports, Vol. 33, Issue 4
TORBEAM, a beam tracing code for electron-cyclotron waves in tokamak plasmas
journal, May 2001
- Poli, E.; Peeters, A. G.; Pereverzev, G. V.
- Computer Physics Communications, Vol. 136, Issue 1-2
Penetration of high-frequency waves into a weakly inhomogeneous magnetized plasma at oblique incidence and their transformation to Bernstein modes
journal, August 1973
- Preinhaelter, J.; Kopecký, V.
- Journal of Plasma Physics, Vol. 10, Issue 1
Geometric phases in the asymptotic theory of coupled wave equations
journal, October 1991
- Littlejohn, Robert G.; Flynn, William G.
- Physical Review A, Vol. 44, Issue 8
ECRH power deposition from a quasi-optical point of view
journal, April 2008
- Balakin, A. A.; Balakina, M. A.; Westerhof, E.
- Nuclear Fusion, Vol. 48, Issue 6
Extending geometrical optics: A Lagrangian theory for vector waves
journal, May 2017
- Ruiz, D. E.; Dodin, I. Y.
- Physics of Plasmas, Vol. 24, Issue 5
Hall Effect of Light
journal, August 2004
- Onoda, Masaru; Murakami, Shuichi; Nagaosa, Naoto
- Physical Review Letters, Vol. 93, Issue 8
Wave power flux and ray-tracing in regions of resonant absorption
journal, January 2000
- Tokman, M. D.; Westerhof, E.; Gavrilova, M. A.
- Plasma Physics and Controlled Fusion, Vol. 42, Issue 2
Current Status of Large Helical Device and Its Prospect for Deuterium Experiment
journal, July 2017
- Osakabe, M.; Takeiri, Y.; Morisaki, T.
- Fusion Science and Technology
Overview of the Large Helical Device project
journal, September 1999
- Iiyoshi, A.; Komori, A.; Ejiri, A.
- Nuclear Fusion, Vol. 39, Issue 9Y
Congruent reduction in geometric optics and mode conversion
journal, January 1987
- Friedland, Lazar; Kaufman, Allan N.
- Physics of Fluids, Vol. 30, Issue 10
Spin–orbit interactions of light
journal, November 2015
- Bliokh, K. Y.; Rodríguez-Fortuño, F. J.; Nori, F.
- Nature Photonics, Vol. 9, Issue 12
Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity
journal, June 2001
- Bridges, Thomas J.; Reich, Sebastian
- Physics Letters A, Vol. 284, Issue 4-5
Phase-space representations of wave equations with applications to the eikonal approximation for short-wavelength waves
journal, February 1988
- McDonald, Steven W.
- Physics Reports, Vol. 158, Issue 6
A Quasi-Optical Beam-Tracing Code for Electron Cyclotron Absorption and Current Drive: GRAY
journal, August 2007
- Farina, Daniela
- Fusion Science and Technology, Vol. 52, Issue 2
WKB method for systems of integral equations
journal, August 1980
- Berk, H. L.; Pfirsch, D.
- Journal of Mathematical Physics, Vol. 21, Issue 8
Beam tracing in inhomogeneous anisotropic plasmas
journal, October 1998
- Pereverzev, G. V.
- Physics of Plasmas, Vol. 5, Issue 10
Plasma interface of the EC waves to the LHD peripheral region
conference, January 2015
- Kubo, S.; Igami, H.; Tsujimura, T. I.
- RADIO FREQUENCY POWER IN PLASMAS: Proceedings of the 21st Topical Conference, AIP Conference Proceedings
Effects of aberration on paraxial wave beams: beam tracing versus quasi-optical solutions
journal, June 2010
- Maj, O.; Balakin, A. A.; Poli, E.
- Plasma Physics and Controlled Fusion, Vol. 52, Issue 8
First-principles variational formulation of polarization effects in geometrical optics
journal, October 2015
- Ruiz, D. E.; Dodin, I. Y.
- Physical Review A, Vol. 92, Issue 4
Review of recent experimental and modeling progress in the lower hybrid range of frequencies at ITER relevant parameters
journal, June 2014
- Bonoli, Paul T.
- Physics of Plasmas, Vol. 21, Issue 6
Optimization of incident wave polarization for ECRH in LHD
journal, February 2005
- Notake, T.; Kubo, S.; Shimozuma, T.
- Plasma Physics and Controlled Fusion, Vol. 47, Issue 3
Geometrodynamics of spinning light
journal, November 2008
- Bliokh, Konstantin Y.; Niv, Avi; Kleiner, Vladimir
- Nature Photonics, Vol. 2, Issue 12
Geometric optics in space− and time−varying plasmas
journal, January 1975
- Bernstein, Ira B.
- Physics of Fluids, Vol. 18, Issue 3
Works referencing / citing this record:
Quasioptical modeling of wave beams with and without mode conversion. II. Numerical simulations of single-mode beams
journal, July 2019
- Yanagihara, K.; Dodin, I. Y.; Kubo, S.
- Physics of Plasmas, Vol. 26, Issue 7
Quasioptical modeling of wave beams with and without mode conversion. III. Numerical simulations of mode-converting beams
journal, July 2019
- Yanagihara, K.; Dodin, I. Y.; Kubo, S.
- Physics of Plasmas, Vol. 26, Issue 7
Pseudo-differential representation of the metaplectic transform and its application to fast algorithms
journal, January 2019
- Lopez, N. A.; Dodin, I. Y.
- Journal of the Optical Society of America A, Vol. 36, Issue 11