Woods, BJQ orcid.org/0000-0003-2628-3873 (2019) Analytical solutions for nonlinear plasma waves with time-varying complex frequency. Plasma Research Express, 1 (4). ISSN 2516-1067
Abstract
Bernstein-Kruskal-Greene (or BGK) modes are ubiquitous nonlinear solutions for the 1D electrostatic Vlasov equation, with the particle distribution function f given as a function of the particle energy. Here, we consider other solutions f = f[ ] where the particle energy is equal to the second-order velocity space Taylor expansion of the function (x, v, t) near the wave-particle resonance. This formalism allows us to analytically examine the time evolution of plasma waves with time-varying complex frequency ω(t) + iγ(t) in the linear and nonlinear phases. Using a Laplace-like decomposition of the electric potential, we give allowed solutions for the time-varying complex frequencies. Then, we show that f can be represented analytically via a family of basis decompositions in such a system. Using a Gaussian decomposition, we give approximate solutions for contours of constant f for a single stationary frequency mode, and derive the evolution equation for the nonlinear growth of a frequency sweeping mode. For this family of modes, highly nonlinear orbits are found with the effective width in velocity of the island roughly a factor of √ 2 larger than the width of a BGK island.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2019 IOP Publishing Ltd. This is the Accepted Manuscript version of an article accepted for publication in Plasma Research Express. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/2516-1067/ab5052 |
Keywords: | plasma; kinetic theory; holes and clumps; frequency chirping; bifurcation; theoretical physics |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 24 Oct 2019 13:33 |
Last Modified: | 06 Nov 2020 01:39 |
Status: | Published |
Publisher: | IOP |
Identification Number: | 10.1088/2516-1067/ab5052 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:152557 |