Instability of nonlinear Trivelpiece-Gould waves. II. Weakly trapped particles

Dubin, Daniel H.  E.

doi:10.1063/1.5116376

Instability of nonlinear Trivelpiece-Gould waves. II. Weakly trapped particles

Journal Article · Wed Oct 16 00:00:00 EDT 2019 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.5116376· OSTI ID:1803319

Dubin, Daniel H. E. ^[1]

Univ. of California, San Diego, CA (United States); University of California at San Diego

This paper discusses a novel parametric instability mechanism caused by particles that are weakly trapped in the potential wells of a nonlinear “pump” wave. The pump wave is unstable to the growth of daughter waves with longer wavelength and nearly the same phase velocity as the pump. This induces adjacent potential peaks in the wave to slowly approach one-another, receding from other pairs of peaks. Particles that are weakly trapped between approaching peaks, with kinetic energies just below the potential maxima, are heated by compression and escape the well, and then become retrapped on the other side of the approaching peaks, where they amplify the compression by pushing the peaks together. The mechanism applies to low-collisionality plasmas supporting waves with near-acoustic dispersion relations such as ion sound waves, magnetized Langmuir waves, or Alfven waves. The theory is compared to particle in cell simulations of TrivelpieceGould (TG) traveling waves, as well as to experiments on pure ion plasmas that observe parametric instability in TG standing waves.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of California, San Diego, CA (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: SC0018236

OSTI ID:: 1803319

Alternate ID(s):: OSTI ID: 1570529

Journal Information:: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 10 Vol. 26; ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (28)

Computing spectra of linear operators using the Floquet–Fourier–Hill method Deconinck, Bernard; Nathan Kutz, J. Journal of Computational Physics, Vol. 219, Issue 1 https://doi.org/10.1016/j.jcp.2006.03.020	journal	November 2006
Numerical simulations of BGK modes Demeio, Lucio; Holloway, James Paul Journal of Plasma Physics, Vol. 46, Issue 1 https://doi.org/10.1017/S0022377800015956	journal	August 1991
Transition of the Dispersion Roots from Beam-Type to Landau-Type Solutions O'Neil, T. M. Physics of Fluids, Vol. 11, Issue 8 https://doi.org/10.1063/1.1692190	journal	January 1968
Nonlinear Effects of Large-Amplitude Plasma Waves Wharton, C. B. Physics of Fluids, Vol. 11, Issue 8 https://doi.org/10.1063/1.1692191	journal	January 1968
Nonlinear Development of an Electron Plasma Wave in a Cylindrical Waveguide Manheimer, Wallace M. Physics of Fluids, Vol. 12, Issue 11 https://doi.org/10.1063/1.1692362	journal	January 1969
Sideband Instability Kruer, W. L. Physics of Fluids, Vol. 13, Issue 11 https://doi.org/10.1063/1.1692859	journal	January 1970
Space Charge Waves in Cylindrical Plasma Columns Trivelpiece, A. W.; Gould, R. W. Journal of Applied Physics, Vol. 30, Issue 11 https://doi.org/10.1063/1.1735056	journal	November 1959
Transport optimization in stellarators Mynick, H. E. Physics of Plasmas, Vol. 13, Issue 5 https://doi.org/10.1063/1.2177643	journal	May 2006
Excitation of nonlinear electron acoustic waves Valentini, Francesco; O’Neil, Thomas M.; Dubin, Daniel H. E. Physics of Plasmas, Vol. 13, Issue 5 https://doi.org/10.1063/1.2198467	journal	May 2006
Experimental Investigation of Electron-Acoustic Waves in Electron Plasmas Kabantsev, Andrey A.; Valentini, F.; Driscoll, C. Fred NON-NEUTRAL PLASMA PHYSICS VI: Workshop on Non-Neutral Plasmas 2006, AIP Conference Proceedings https://doi.org/10.1063/1.2387902	conference	January 2006
Experimental realization of nearly steady-state toroidal electron plasmas Stoneking, M. R.; Marler, J. P.; Ha, B. N. Physics of Plasmas, Vol. 16, Issue 5 https://doi.org/10.1063/1.3118624	journal	May 2009
Enhanced superbanana transport caused by chaotic scattering across an asymmetric separatrix Dubin, Daniel H. E.; Kabantsev, A. A.; Driscoll, C. F. Physics of Plasmas, Vol. 19, Issue 5 https://doi.org/10.1063/1.3694053	journal	May 2012
Nonlinear Trivelpiece-Gould waves: Frequency, functional form, and stability Dubin, D. H. E.; Ashourvan, A. Physics of Plasmas, Vol. 22, Issue 10 https://doi.org/10.1063/1.4932001	journal	October 2015
Superbanana transport in the collisional heating of a plasma column forced across a squeeze potential Dubin, Daniel H. E. Physics of Plasmas, Vol. 24, Issue 11 https://doi.org/10.1063/1.5001062	journal	November 2017
Instability of nonlinear Trivelpiece-Gould waves I: Wave degeneracies Dubin, Daniel H. E. Physics of Plasmas, Vol. 26, Issue 10 https://doi.org/10.1063/1.5116375	journal	October 2019
Stability regions of dissipative trapped-ion instability Rosenbluth, M. N.; Ross, D. W.; Kostomarov, D. P. Nuclear Fusion, Vol. 12, Issue 1 https://doi.org/10.1088/0029-5515/12/1/001	journal	January 1972
The decay instability of Langmuir waves in the non-neutral electron plasma column Higaki, Hiroyuki Plasma Physics and Controlled Fusion, Vol. 39, Issue 11 https://doi.org/10.1088/0741-3335/39/11/003	journal	November 1997
Exact Nonlinear Plasma Oscillations Bernstein, Ira B.; Greene, John M.; Kruskal, Martin D. Physical Review, Vol. 108, Issue 3 https://doi.org/10.1103/PhysRev.108.546	journal	November 1957
Neoclassical Transport Caused by Collisionless Scattering across an Asymmetric Separatrix Dubin, Daniel H. E.; Driscoll, C. F.; Tsidulko, Yu. A. Physical Review Letters, Vol. 105, Issue 18 https://doi.org/10.1103/PhysRevLett.105.185003	journal	October 2010
Nonlinear Amplification and Decay of Phase-Mixed Waves in Compressing Plasma Schmit, P. F.; Dodin, I. Y.; Rocks, J. Physical Review Letters, Vol. 110, Issue 5 https://doi.org/10.1103/PhysRevLett.110.055001	journal	January 2013
Negative-Mass Instability in Nonlinear Plasma Waves Dodin, I. Y.; Schmit, P. F.; Rocks, J. Physical Review Letters, Vol. 110, Issue 21 https://doi.org/10.1103/PhysRevLett.110.215006	journal	May 2013
Parametric Instability Driven by Weakly Trapped Particles in Nonlinear Plasma Waves Dubin, Daniel H. E. Physical Review Letters, Vol. 121, Issue 1 https://doi.org/10.1103/PhysRevLett.121.015001	journal	July 2018
Trapped Particle Effects in the Parametric Instability of Near-Acoustic Plasma Waves Affolter, M.; Anderegg, F.; Dubin, D. H. E. Physical Review Letters, Vol. 121, Issue 23 https://doi.org/10.1103/PhysRevLett.121.235004	journal	December 2018
Dispersion of Electron Plasma Waves Malmberg, J. H.; Wharton, C. B. Physical Review Letters, Vol. 17, Issue 4 https://doi.org/10.1103/PhysRevLett.17.175	journal	July 1966
Plasma Diffusion in a Toroidal Stellarator Galeev, A. A.; Sagdeev, R. Z.; Furth, H. P. Physical Review Letters, Vol. 22, Issue 11 https://doi.org/10.1103/PhysRevLett.22.511	journal	March 1969
Trapped-Particle Instability Kruer, W. L.; Dawson, J. M.; Sudan, R. N. Physical Review Letters, Vol. 23, Issue 15 https://doi.org/10.1103/PhysRevLett.23.838	journal	October 1969
Trapped-Particle Asymmetry Modes in Single-Species Plasmas Kabantsev, A. A.; Driscoll, C. F.; Hilsabeck, T. J. Physical Review Letters, Vol. 87, Issue 22 https://doi.org/10.1103/PhysRevLett.87.225002	journal	November 2001
Measurement of Landau Damping and the Evolution to a BGK Equilibrium Danielson, J. R.; Anderegg, F.; Driscoll, C. F. Physical Review Letters, Vol. 92, Issue 24 https://doi.org/10.1103/PhysRevLett.92.245003	journal	June 2004

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Fluid and kinetic nonlinearities of near-acoustic plasma waves Affolter, M.; Anderegg, F.; Dubin, D. H. E. Physics of Plasmas, Vol. 26, Issue 12 https://doi.org/10.1063/1.5129529	journal	December 2019

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