Skip to main content
U.S. Department of Energy
Office of Scientific and Technical Information

Quasioptical modeling of wave beams with and without mode conversion. I. Basic theory

Journal Article · · Physics of Plasmas
DOI:https://doi.org/10.1063/1.5095076· OSTI ID:1557568
 [1];  [2];  [3];  [1];  [4]
  1. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  3. Nagoya Univ., Aichi (Japan)
  4. National Inst. for Fusion Science, Gifu (Japan)

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.

Research Organization:
Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States); Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA); Japan Society for the Promotion of Science (JSPS)
Contributing Organization:
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.
Grant/Contract Number:
NA0003525; AC02-09CH11466; AC04-94AL85000
OSTI ID:
1557568
Alternate ID(s):
OSTI ID: 1544458
OSTI ID: 1634798
Journal Information:
Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 7 Vol. 26; ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English

References (64)

Geometrical Optics of Inhomogeneous Media book January 1990
Self-adjointness of momentum operators in generalized coordinates journal February 1984
The semiclassical evolution of wave packets journal May 1986
Phase-space representations of wave equations with applications to the eikonal approximation for short-wavelength waves journal February 1988
TORBEAM, a beam tracing code for electron-cyclotron waves in tokamak plasmas journal May 2001
Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity journal June 2001
Ray-tracing code TRAVIS for ECR heating, EC current drive and ECE diagnostic journal January 2014
TORBEAM 2.0, a paraxial beam tracing code for electron-cyclotron beams in fusion plasmas for extended physics applications journal April 2018
Geometric view on noneikonal waves journal April 2014
Lagrangian geometrical optics of nonadiabatic vector waves and spin particles journal October 2015
Variational principles for dissipative (sub)systems, with applications to the theory of linear dispersion and geometrical optics journal April 2017
Ray Tracing and Beyond book January 2014
Penetration of high-frequency waves into a weakly inhomogeneous magnetized plasma at oblique incidence and their transformation to Bernstein modes journal August 1973
Quantum mechanics as a statistical theory journal January 1949
Geometrodynamics of spinning light journal November 2008
Spin–orbit interactions of light journal November 2015
Vlasov equation and collisionless hydrodynamics adapted to curved spacetime journal November 2010
Review of recent experimental and modeling progress in the lower hybrid range of frequencies at ITER relevant parameters conference January 2014
Review of recent experimental and modeling progress in the lower hybrid range of frequencies at ITER relevant parameters journal June 2014
Plasma interface of the EC waves to the LHD peripheral region
  • Kubo, S.; Igami, H.; Tsujimura, T. I.
  • RADIO FREQUENCY POWER IN PLASMAS: Proceedings of the 21st Topical Conference, AIP Conference Proceedings https://doi.org/10.1063/1.4936543
conference January 2015
Extending geometrical optics: A Lagrangian theory for vector waves journal May 2017
Mode conversion in cold low-density plasma with a sheared magnetic field journal December 2017
Quasioptical modeling of wave beams with and without mode conversion. II. Numerical simulations of single-mode beams journal July 2019
Quasioptical modeling of wave beams with and without mode conversion. III. Numerical simulations of mode-converting beams journal July 2019
WKB method for systems of integral equations journal August 1980
Propagation of a Gaussian beam in a nonhomogeneous plasma journal September 1989
Geometric optics in space− and time−varying plasmas journal January 1975
Parabolic approximation method for fast magnetosonic wave propagation in tokamaks journal January 1986
Congruent reduction in geometric optics and mode conversion journal January 1987
Gyroresonant absorption from congruent reduction of an anisotropic pressure fluid model journal September 1988
Beam tracing in inhomogeneous anisotropic plasmas journal October 1998
Current Status of Large Helical Device and Its Prospect for Deuterium Experiment journal July 2017
Quasi-optical description of wave beams in smoothly inhomogeneous anisotropic media journal June 2007
Use of the multidimensional WKB method to describe propagation of lower hybrid waves in tokamak plasma journal July 1992
Overview of the Large Helical Device project journal September 1999
ECRH power deposition from a quasi-optical point of view journal April 2008
Development and application of a ray-tracing code integrating with 3D equilibrium mapping in LHD ECH experiments journal November 2015
Wave power flux and ray-tracing in regions of resonant absorption journal January 2000
Optimization of incident wave polarization for ECRH in LHD journal February 2005
Effects of aberration on paraxial wave beams: beam tracing versus quasi-optical solutions journal June 2010
On the Quantum Correction For Thermodynamic Equilibrium journal June 1932
Point Transformations in Quantum Mechanics journal February 1952
Geometric phases in the asymptotic theory of coupled wave equations journal October 1991
Axiomatic geometrical optics, Abraham-Minkowski controversy, and photon properties derived classically journal November 2012
Quantum phase-space representation for curved configuration spaces journal December 2013
First-principles variational formulation of polarization effects in geometrical optics journal October 2015
Relativistic ponderomotive Hamiltonian of a Dirac particle in a vacuum laser field journal December 2015
Ponderomotive dynamics of waves in quasiperiodically modulated media journal March 2017
Spin Hall effect of photons in a static gravitational field journal April 2007
Gravitational birefringence of light in Robertson-Walker cosmologies journal August 2017
Four-dimensional eikonal theory of linear mode conversion journal April 1987
Hall Effect of Light journal August 2004
Scalar equation for wave beams in a magnetized plasma journal April 2007
A Quasi-Optical Beam-Tracing Code for Electron Cyclotron Absorption and Current Drive: GRAY journal August 2007
Geometrodynamics of Spinning Light text January 2008
Vlasov equation and collisionless hydrodynamics adapted to curved spacetime text January 2010
Axiomatic geometrical optics, Abraham-Minkowski controversy, and photon properties derived classically text January 2012
Quantum phase-space representation for curved configuration spaces text January 2013
Spin-orbit interactions of light text January 2015
First-principle variational formulation of polarization effects in geometrical optics text January 2015
Relativistic ponderomotive Hamiltonian of a Dirac particle in a vacuum laser field text January 2015
Gravitational birefringence of light in Robertson-Walker cosmologies text January 2016
Variational principles for dissipative (sub)systems, with applications to the theory of linear dispersion and geometrical optics text January 2016
Spin Hall effect of Photons in a Static Gravitational Field text January 2006

Cited By (3)

Quasioptical modeling of wave beams with and without mode conversion. II. Numerical simulations of single-mode beams journal July 2019
Quasioptical modeling of wave beams with and without mode conversion. III. Numerical simulations of mode-converting beams journal July 2019
Pseudo-differential representation of the metaplectic transform and its application to fast algorithms journal January 2019