Instability of nonlinear Trivelpiece-Gould waves I: Wave degeneracies

Dubin, D. H. E.

doi:10.1063/1.5116375

Cited by 6 publications

(1 citation statement)

References 33 publications

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“…We have also used a continuum version of this method in calculations involving the normal modes of a non-canonical conservative system of fluid equations. 29,30 A linearized Hamiltonian system is a dynamical system with N coordinates q = (q 1 , ..., q N ) and associated canonical momenta p = (p 1 , ..., p N ) whose Hamiltonian has the quadratic form…”

Section: Normal Modes Of a Linearized Hamiltonian Systemmentioning

confidence: 99%

Normal Modes, Rotational Inertia, and Thermal Fluctuations of Trapped Ion Crystals

Dubin

2020

Preprint

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The normal modes of a trapped ion crystal are derived using an approach based on the Hermitian properties of the system's dynamical matrix. This method is equivalent to the standard Bogoliubov method, but for classical systems it is arguably simpler and more general in that canonical coordinates are not necessary. The theory is developed for stable, unstable, and neutrally-stable systems. The method is then applied to ion crystals in a Penning trap. Reduced eigenvalue problems for the case of large applied magnetic field are developed, for which the spectrum breaks into ExB drift modes, axial modes, and cyclotron modes. Thermal fluctuation levels in these modes are analyzed and shown to be consistent with the Bohr-van-Leeuwen theorem, provided that neutrally-stable modes associated with crystal rotations are included in the analysis. An expression for the rotational inertia of the crystal is derived, and a magnetic contribution to this inertia, which dominates in large magnetic fields, is described. An unusual limit is discovered for the special case of spherically-symmetric confinement, in which the rotational inertia does not exist and changes in angular momentum leave the rotation frequency unaffected.

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Section: Normal Modes Of a Linearized Hamiltonian Systemmentioning

confidence: 99%

Normal Modes, Rotational Inertia, and Thermal Fluctuations of Trapped Ion Crystals

Dubin

2020

Preprint

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

Dubin

2019

Physics of Plasmas

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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 Alfvén waves. The theory is compared to particle in cell simulations of Trivelpiece-Gould (TG) traveling waves, as well as to experiments on pure ion plasmas that observe parametric instability in TG standing waves.

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Fluid and kinetic nonlinearities of near-acoustic plasma waves

et al. 2019

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Large amplitude, near-acoustic plasma waves have a temperature-dependent harmonic content and nonlinear frequency shifts. On cold plasmas, experiments show that fluid nonlinearities dominate, and the observed harmonic content is well predicted by a recent fluid analysis. In contrast, the measured nonlinear frequency shift is smaller than this theory prediction, suggesting the presence of other nonlinear effects neglected in this analysis. When the plasma is heated, kinetic effects become important, and we observe an increase in both the harmonic content and nonlinear frequency shift. Quantitative experiments on the stability of these large amplitude, near-acoustic plasma waves strongly support the idea that trapped particles reduce the amplitude threshold for instability below fluid models. At low temperatures, the broad characteristics of the parametric instability are determined by the frequency detuning of the pump and daughter wave and the wave-wave coupling strength, surprisingly consistent with simple cold fluid, three-wave theories. However, at higher temperatures, the pump wave becomes unstable at half the threshold pump wave amplitude, with similar exponential growth rates as for a cold plasma.

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Instability of nonlinear Trivelpiece-Gould waves I: Wave degeneracies

Cited by 6 publications

References 33 publications

Normal Modes, Rotational Inertia, and Thermal Fluctuations of Trapped Ion Crystals

Normal Modes, Rotational Inertia, and Thermal Fluctuations of Trapped Ion Crystals

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

Fluid and kinetic nonlinearities of near-acoustic plasma waves

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