Phase-space description of plasma waves. Part 1. Linear theory

1992 ◽  
Vol 47 (3) ◽  
pp. 465-477 ◽  
Author(s):  
T. Biro ◽  
K. Rönnmark
Keyword(s):  
Phase Space ◽  
Continuity Equation ◽  
Particle Distribution ◽  
Plasma Waves ◽  
Current Response ◽  
Time Varying ◽  
Plasma Parameters ◽  
Proper Form ◽  
Window Functions ◽  
Space Description

We develop an (r, k) phase-space description of waves in plasmas by introducing Gaussian window functions to separate short-scale oscillations from long-scale modulations of the wave fields and variations in the plasma parameters. To obtain a wave equation that unambiguously separates conservative dynamics from dissipation in an inhomogeneous and time-varying background plasma, we first discuss the proper form of the current response function. In analogy with the particle distribution function f(v, r, t), we introduce a wave density N(k, r, t) on phase space. This function is proved to satisfy a simple continuity equation. Dissipation is also included, and this allows us to describe the damping or growth of wave density along rays. Problems involving geometric optics of continuous media often appear simpler when viewed in phase space, since the flow of N in phase space is incompressible.

Phase-space description of plasma waves. Part 2. Nonlinear theory

1992 ◽  
Vol 47 (3) ◽  
pp. 479-489 ◽  
Author(s):  
K. Rönnmark ◽  
T. Biro
Keyword(s):  
Phase Space ◽  
General Formula ◽  
Nonlinear Theory ◽  
Vector Potential ◽  
Fourier Transforms ◽  
Kinetic Equations ◽  
Plasma Waves ◽  
Starting Point ◽  
Physical Fields ◽  
Space Description

A representation of the physical fields as functions on (k, ω, r, t) phase space can be based on Gaussian windows and Fourier transforms. Within this representation, we obtain a very general formula for the second-order nonlinear current J(k, ω, r, t) in terms of the vector potential A(k, ω, r, t). This formula is a convenient starting point for studies of coherent as well as turbulent nonlinear processes. We derive kinetic equations for weakly inhomogeneous and turbulent plasmas, including the effects of inhomogeneous turbulence, wave convection and refraction.

scholarly journals Emergent phase space description of unitary matrix model

2017 ◽  
Vol 2017 (11) ◽  
Author(s):  
Arghya Chattopadhyay ◽  
Parikshit Dutta ◽  
Suvankar Dutta
Keyword(s):  
Phase Space ◽  
Matrix Model ◽  
Unitary Matrix ◽  
Space Description

scholarly journals Dirac’s Method for the Two-Dimensional Damped Harmonic Oscillator in the Extended Phase Space

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 180 ◽  
Author(s):  
Laure Gouba
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Canonical Quantization ◽  
Extended Phase Space ◽  
Two Dimensional ◽  
Class Constraint ◽  
Extended Phase ◽  
Damped Harmonic Oscillator ◽  
Points Of View ◽  
Space Description

The system of a two-dimensional damped harmonic oscillator is revisited in the extended phase space. It is an old problem that has already been addressed by many authors that we present here with some fresh points of view and carry on a whole discussion. We show that the system is singular. The classical Hamiltonian is proportional to the first-class constraint. We pursue with the Dirac’s canonical quantization procedure by fixing the gauge and provide a reduced phase space description of the system. As a result, the quantum system is simply modeled by the original quantum Hamiltonian.

scholarly journals Collective absorption of laser radiation in plasma at sub-relativistic intensities

2019 ◽  
Vol 7 ◽  
Author(s):  
Y. J. Gu ◽  
O. Klimo ◽  
Ph. Nicolaï ◽  
S. Shekhanov ◽  
S. Weber ◽  
...  
Keyword(s):  
Inertial Confinement Fusion ◽  
Stimulated Raman Scattering ◽  
Laser Energy ◽  
Brillouin Scattering ◽  
Critical Density ◽  
Plasma Waves ◽  
High Amplitude ◽  
Inertial Confinement ◽  
Hot Electron ◽  
Plasma Parameters

Processes of laser energy absorption and electron heating in an expanding plasma in the range of irradiances $I\unicode[STIX]{x1D706}^{2}=10^{15}{-}10^{16}~\text{W}\,\cdot \,\unicode[STIX]{x03BC}\text{m}^{2}/\text{cm}^{2}$ are studied with the aid of kinetic simulations. The results show a strong reflection due to stimulated Brillouin scattering and a significant collisionless absorption related to stimulated Raman scattering near and below the quarter critical density. Also presented are parametric decay instability and resonant excitation of plasma waves near the critical density. All these processes result in the excitation of high-amplitude electron plasma waves and electron acceleration. The spectrum of scattered radiation is significantly modified by secondary parametric processes, which provide information on the spatial localization of nonlinear absorption and hot electron characteristics. The considered domain of laser and plasma parameters is relevant for the shock ignition scheme of inertial confinement fusion.

scholarly journals Coherent representation of fields and deformation quantization

2020 ◽  
Vol 17 (11) ◽  
pp. 2050166 ◽  
Author(s):  
Jasel Berra-Montiel ◽  
Alberto Molgado
Keyword(s):  
Phase Space ◽  
Deformation Quantization ◽  
Probability Distributions ◽  
Series Representation ◽  
Quantum Field ◽  
Husimi Distribution ◽  
Normal Star ◽  
Holomorphic Representation ◽  
Functional Distribution ◽  
Space Description

Motivated by some well-known results in the phase space description of quantum optics and quantum information theory, we aim to describe the formalism of quantum field theory by explicitly considering the holomorphic representation for a scalar field within the deformation quantization program. Notably, the symbol of a symmetric ordered operator in terms of holomorphic variables may be straightforwardly obtained by the quantum field analogue of the Husimi distribution associated with a normal ordered operator. This relation also allows to establish a [Formula: see text]-equivalence between the Moyal and the normal star-products. In addition, by writing the density operator in terms of coherent states we are able to directly introduce a series representation of the Wigner functional distribution, which may be convenient in order to calculate probability distributions of quantum field observables without performing formal phase space integrals at all.

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