Lagrangian geometrical optics of nonadiabatic vector waves and spin particles

Ruiz, D. E.; Dodin, I. Y.

doi:10.1016/j.physleta.2015.07.038

Cited by 24 publications

(60 citation statements)

References 51 publications

(94 reference statements)

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“…If D H2 is neglected, the envelope equation (119) becomes a Dirac-type equation similar to those considered in the context of XGO [24][25][26][27][28] and also, for instance, in Refs. [58,59].…”

Section: A Hilbert Space For Vector Wavesmentioning

confidence: 92%

“…In particular, this means that the Hermitian and anti-Hermitian parts [Eq. (26)] of an operator are determined by, respectively, the Hermitian and anti-Hermitian parts of its lower-index Weyl symbol. We summarize this as follows:…”

Section: A Hilbert Space For Vector Wavesmentioning

confidence: 99%

“…I), except here it is generalized to an arbitrary metric. This term causes polarization-driven bending of the ray trajectories, which is missed in traditional GO; also, it causes mode conversion, if more than one active mode is present [24][25][26][27][28]. These effects are is discussed in further detail in Sec.…”

Section: Equation For the Active Modesmentioning

confidence: 99%

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

et al. 2019

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This work opens a series of papers where we develop a general quasioptical theory for modeconverting electromagnetic beams in plasma and implement it in a numerical algorithm. Here, the basic theory is introduced. We consider a general quasimonochromatic multi-component 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") in the basis of the geometrical-optics polarization vectors. Scalar and mode-converting vector beams are described on the same footing. 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 radiofrequency wave beams in magnetized plasma based on this theory.

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Section: A Hilbert Space For Vector Wavesmentioning

confidence: 92%

Section: A Hilbert Space For Vector Wavesmentioning

confidence: 99%

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

et al. 2019

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“…(Sinceψ is a vector, this particle can be assigned a spin, as described in Ref. 38.) Here, H =Ĥ 0 +Ĥ int is a linear operator serving as a (non-Hermitian) Hamiltonian.…”

Section: The Modelmentioning

confidence: 99%

Structure formation in turbulence as an instability of effective quantum plasma

2020

Self Cite

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Structure formation in turbulence is effectively an instability of "plasma" formed by fluctuations serving as particles. These "particles" are quantumlike; namely, their wavelengths are non-negligible compared to the sizes of background coherent structures. The corresponding "kinetic equation" describes the Wigner matrix of the turbulent field, and the coherent structures serve as collective fields. This formalism is usually applied to manifestly quantumlike or scalar waves. Here, we extend it to compressible Navier-Stokes turbulence, where the fluctuation Hamiltonian is a five-dimensional matrix operator and diverse modulational modes are present. As an example, we calculate these modes for a sinusoidal shear flow and find two modulational instabilities. One of them is specific to supersonic flows, and the other one is a Kelvin-Helmholtz-type instability that is a generalization of the known zonostrophic instability. This work serves as a stepping stone toward improving the understanding of magnetohydrodynamic turbulence, which can be approached similarly.

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“…Equations (13)(14)(15)(16)(17)(18)(19)(20) comprise the general collisionless kinetic plasma model. Assuming E can be expressed uniquely in terms of D using Eq.…”

Section: The Hamiltonian Structure Of Collisionless Kinetic Theorymentioning

confidence: 99%

Finite-dimensional collisionless kinetic theory

Burby

2017

Physics of Plasmas

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A collisionless kinetic plasma model may often be cast as an infinite-dimensional noncanonical Hamiltonian system. I show that, when this is the case, the model can be discretized in space and particles while preserving its Hamiltonian structure, thereby producing a finite-dimensional Hamiltonian system that approximates the original kinetic model. I apply the general theory to two example systems: the relativistic Vlasov-Maxwell system with spin, and a gyrokinetic Vlasov-Maxwell system.

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Lagrangian geometrical optics of nonadiabatic vector waves and spin particles

Cited by 24 publications

References 51 publications

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

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

Structure formation in turbulence as an instability of effective quantum plasma

Finite-dimensional collisionless kinetic theory

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