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Title: Normal-mode-based analysis of electron plasma waves with second-order Hermitian formalism

The classic problem of the dynamic evolution and Landau damping of linear Langmuir electron waves in a collisionless plasma with Maxwellian background is cast as a second-order, self-adjoint problem with a continuum spectrum of real and positive squared frequencies. The corresponding complete basis of singular normal modes is obtained, along with their orthogonality relation. This yields easily the general expression of the time-reversal-invariant solution for any initial-value problem. Examples are then given for specific initial conditions that illustrate different behaviors of the Landau-damped macroscopic moments of the perturbations.
Authors:
 [1] ; ORCiD logo [1]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Plasma Science and Fusion Center
Publication Date:
Grant/Contract Number:
FG02-91ER54109; SC0014664
Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 25; Journal Issue: 3; Journal ID: ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)
Research Org:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org:
USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24); Oak Ridge Inst. for Science and Education (ORISE), Oak Ridge, TN (United States); Oak Ridge Associated Universities (ORAU)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Linear acoustics; Maxwell equations; Classical field theory; Linear algebra; Hilbert space; Algebras; Acoustic waves; Computational methods; Classical electromagnetism; Plasma simulation
OSTI Identifier:
1423935
Alternate Identifier(s):
OSTI ID: 1423914

Ramos, J. J., and White, R. L.. Normal-mode-based analysis of electron plasma waves with second-order Hermitian formalism. United States: N. p., Web. doi:10.1063/1.5020794.
Ramos, J. J., & White, R. L.. Normal-mode-based analysis of electron plasma waves with second-order Hermitian formalism. United States. doi:10.1063/1.5020794.
Ramos, J. J., and White, R. L.. 2018. "Normal-mode-based analysis of electron plasma waves with second-order Hermitian formalism". United States. doi:10.1063/1.5020794.
@article{osti_1423935,
title = {Normal-mode-based analysis of electron plasma waves with second-order Hermitian formalism},
author = {Ramos, J. J. and White, R. L.},
abstractNote = {The classic problem of the dynamic evolution and Landau damping of linear Langmuir electron waves in a collisionless plasma with Maxwellian background is cast as a second-order, self-adjoint problem with a continuum spectrum of real and positive squared frequencies. The corresponding complete basis of singular normal modes is obtained, along with their orthogonality relation. This yields easily the general expression of the time-reversal-invariant solution for any initial-value problem. Examples are then given for specific initial conditions that illustrate different behaviors of the Landau-damped macroscopic moments of the perturbations.},
doi = {10.1063/1.5020794},
journal = {Physics of Plasmas},
number = 3,
volume = 25,
place = {United States},
year = {2018},
month = {3}
}