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Title: Nonlinear Trivelpiece-Gould waves: Frequency, functional form, and stability

Journal Article · · Physics of Plasmas
DOI:https://doi.org/10.1063/1.4932001· OSTI ID:1469375
 [1];  [1]
  1. Univ. of California San Diego, La Jolla, CA (United States)

Here, this paper considers the frequency, spatial form, and stability of nonlinear Trivelpiece-Gould (TG) waves on a cylindrical plasma column of length L and radius rp, treating both traveling waves and standing waves, and focussing on the regime of experimental interest in which L/rp >> 1. In this regime, TG waves are weakly dispersive, allowing strong mode-coupling between Fourier harmonics. The mode coupling implies that linear theory for such waves is a poor approximation even at fairly small amplitude, and nonlinear theories that include a small number of harmonics, such as three-wave parametric resonance theory, also fail to fully capture the stability properties of the system. It is found that nonlinear standing waves suffer jumps in their functional form as their amplitude is varied continuously. The jumps are caused by nonlinear resonances between the standing wave and nearly linear waves whose frequencies and wave numbers are harmonics of the standing wave. Also, the standing waves are found to be unstable to a multi-wave version of three-wave parametric resonance, with an amplitude required for instability onset that is much larger than expected from three wave theory. It is found that traveling waves are linearly stable for all amplitudes that could be studied, in contradiction to three-wave theory.

Research Organization:
Univ. of California, San Diego, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
SC0002451; SC0008693
OSTI ID:
1469375
Alternate ID(s):
OSTI ID: 1223037
Journal Information:
Physics of Plasmas, Vol. 22, Issue 10; ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 9 works
Citation information provided by
Web of Science

References (14)

Electron Plasma Waves and Free-Streaming Electron Bursts journal January 1971
Stability of Nonlinear Ion Sound Waves and Solitons in Plasmas journal July 1979
Finite length thermal equilibria of a pure electron plasma column journal January 1979
Plasma and trap-based techniques for science with positrons journal March 2015
Numerical calculation of axisymmetric electrostatic modes for cold finite‐length non‐neutral plasmas journal August 1995
Space Charge Waves in Cylindrical Plasma Columns journal November 1959
Dispersion of Electron Plasma Waves journal July 1966
Nonlinear Development of an Electron Plasma Wave in a Cylindrical Waveguide journal January 1969
The decay instability of Langmuir waves in the non-neutral electron plasma column journal November 1997
Parametric Excitation of Coupled Waves I. General Formulation journal April 1968
Radiation-Induced Instability of Electron Plasma Oscillations journal April 1965
Theory of Electron Holes journal September 1979
Observations of Solitary Structures in a Magnetized, Plasma Loaded Waveguide journal September 1979
Dynamics of nonlinear ion-acoustic waves in an external magnetic field journal December 1985

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Fluid and kinetic nonlinearities of near-acoustic plasma waves journal December 2019

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