Abstract
The nonlinear 1-D plasma electrostatic oscillation is formulated in an analytic framework that allows closed-form analytic solutions along the characteristics, and solved numerically in configuration space. Additionally, a novel iterative analytical form for the finite-amplitude oscillation solution is derived, which compares favourably with the other two techniques. A fresh insight into the evolution of the oscillation is gained, including defining the least achievable density in the nonlinear oscillation as half of the equilibrium value, and relating the associated maximum density achievable in terms of that minimum.
Highlights
The electrostatic plasma oscillation is arguably the defining characteristic of that medium: the unique balance between conduction and particle currents that produces the distinctive “ring” that can only happen in a plasma
Such a central feature has attracted significant attention from both theorists and experimentalists, since the oscillation plays a key role in laser-plasma interactions: mathematical descriptions of its nonlinear evolution are vital to understanding wave breaking and energy transport in energetic processes
The main motivation for revisiting this classic problem is the unique context of cold plasma oscillations in pulsar crusts, where the magnetic field strength is so high that the associated material compression ensures that the positive ions can truly be considered to be stationary, while the abundant free electrons are constrained by the Landau levels to have momenta entirely aligned with the internal field direction
Summary
The electrostatic plasma oscillation is arguably the defining characteristic of that medium: the unique balance between conduction and particle currents that produces the distinctive “ring” that can only happen in a plasma. Such a central feature has attracted significant attention from both theorists and experimentalists, since the oscillation plays a key role in laser-plasma interactions: mathematical descriptions of its nonlinear evolution are vital to understanding wave breaking and energy transport in energetic processes.. The wave-breaking of such oscillations is alleged to eject electrons from the metallic crust into the pulsar atmosphere immediately above it, populating the environment with energetic electrons, the radiation from which can create the electron-positron pairs, which are the defining characteristic of the pulsar envelope The main motivation for revisiting this classic problem is the unique context of cold plasma oscillations in pulsar crusts, where the magnetic field strength is so high that the associated material compression ensures that the positive ions can truly be considered to be stationary, while the abundant free electrons are constrained by the Landau levels to have momenta entirely aligned with the internal field direction. The wave-breaking of such oscillations is alleged to eject electrons from the metallic crust into the pulsar atmosphere immediately above it, populating the environment with energetic electrons, the radiation from which can create the electron-positron pairs, which are the defining characteristic of the pulsar envelope
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