skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Nonlinear behavior of weakly unstable linear modes in plasmas with aligned equilibrium mass flow

Abstract

The nonlinear evolution of weakly unstable linear magnetohydrodynamic waves in plasma configurations characterized by equilibrium mass flow aligned parallel to the magnetic field is investigated. The analysis is based on field representations expressed as expansions in Fourier harmonics and computation of modifications to the linear theory (first harmonic) arising from the nonlinear coupling between the zeroth and second harmonics. It is found that Landau's equation governs the nonlinear evolution of the system. A correction to the linearized theory appears at third order in the mode amplitude and is proportional to the linear growth rate. Furthermore, the conditions under which the nonlinearities provide a saturation mechanism to limit the growth of the linear instabilities is explored. Finally, this saturation phenomenon for a specific configuration consisting of a Z pinch with a small axial magnetic field is illustrated.

Authors:
;  [1]
  1. Department of Electrical and Computer Engineering, University of Wisconsin-Madison, Madison, WI (USA)
Publication Date:
OSTI Identifier:
6412246
Resource Type:
Journal Article
Journal Name:
Physics of Fluids B; (USA)
Additional Journal Information:
Journal Volume: 2:9; Journal ID: ISSN 0899-8221
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; PLASMA; NONLINEAR PROBLEMS; PLASMA DRIFT; EQUILIBRIUM; CORRECTIONS; COUPLING; FOURIER ANALYSIS; HARMONICS; INSTABILITY GROWTH RATES; LINEAR Z PINCH DEVICES; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; MASS TRANSFER; MODIFICATIONS; OSCILLATION MODES; SATURATION; FLUID MECHANICS; HYDRODYNAMICS; LINEAR PINCH DEVICES; MECHANICS; OPEN PLASMA DEVICES; OSCILLATIONS; PINCH DEVICES; THERMONUCLEAR DEVICES; 700107* - Fusion Energy- Plasma Research- Instabilities; 700103 - Fusion Energy- Plasma Research- Kinetics

Citation Formats

Peredo, M, and Tataronis, J A. Nonlinear behavior of weakly unstable linear modes in plasmas with aligned equilibrium mass flow. United States: N. p., 1990. Web. doi:10.1063/1.859427.
Peredo, M, & Tataronis, J A. Nonlinear behavior of weakly unstable linear modes in plasmas with aligned equilibrium mass flow. United States. https://doi.org/10.1063/1.859427
Peredo, M, and Tataronis, J A. 1990. "Nonlinear behavior of weakly unstable linear modes in plasmas with aligned equilibrium mass flow". United States. https://doi.org/10.1063/1.859427.
@article{osti_6412246,
title = {Nonlinear behavior of weakly unstable linear modes in plasmas with aligned equilibrium mass flow},
author = {Peredo, M and Tataronis, J A},
abstractNote = {The nonlinear evolution of weakly unstable linear magnetohydrodynamic waves in plasma configurations characterized by equilibrium mass flow aligned parallel to the magnetic field is investigated. The analysis is based on field representations expressed as expansions in Fourier harmonics and computation of modifications to the linear theory (first harmonic) arising from the nonlinear coupling between the zeroth and second harmonics. It is found that Landau's equation governs the nonlinear evolution of the system. A correction to the linearized theory appears at third order in the mode amplitude and is proportional to the linear growth rate. Furthermore, the conditions under which the nonlinearities provide a saturation mechanism to limit the growth of the linear instabilities is explored. Finally, this saturation phenomenon for a specific configuration consisting of a Z pinch with a small axial magnetic field is illustrated.},
doi = {10.1063/1.859427},
url = {https://www.osti.gov/biblio/6412246}, journal = {Physics of Fluids B; (USA)},
issn = {0899-8221},
number = ,
volume = 2:9,
place = {United States},
year = {Sat Sep 01 00:00:00 EDT 1990},
month = {Sat Sep 01 00:00:00 EDT 1990}
}