Nonlinear Wave Number of an Electron Plasma Wave

Vidmar, Paul J.; Malmberg, J. H.; Starke, T. P.

doi:10.1103/physrevlett.34.646

Cited by 16 publications

(6 citation statements)

References 11 publications

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“…The wave frequency in this state is different from the linear value, the difference being proportional to o) B (Manheimer & Flynn 1971;Morales & O'Neil 1972;Dewar 1972;Lee & Pocobelli 1972. The foregoing characteristics are in general agreement with experiments (Malmberg & Wharton 1967;Franklin et al 1972a;Vidmar et al 1975), account being taken of the fact that the theories treat temporal rather than spatial variations, and with computer simulations (Armstrong 1967;Tsai 1974;Canosa & Gazdag 1974;Matsuda & Crawford 1975).…”

Section: Introductionsupporting

confidence: 79%

“…where / and A are identity and averaging operators. These equations are identical to those used in the renormalization procedure of plasma turbulence (Dupree 1966;Orszag & Kraichman 1967;Frisch 1968;Weinstock 1969;Rudakov & Tsytovich 1971;Tystovich 1972;Benford & Thomson 1972;Misguich & Balescu 1975). Following Tsytovich (1972), we introduce an average collision operator, v, such that (27) and rewrite 26) as^ (28This expression is then integrated to obtain…”

Section: Orbit Perturbationmentioning

confidence: 97%

“…However, this does not happen: since the distribution function increases rapidly with decreasing velocity, the number of trapped electrons increases rapidly with the wave amplitude. These electrons take more energy from the wave, and thus enhance the wave damping (Armstrong 1967;Dawson & Shanny 1968;Sato et al 1969;Nakamura & Ito 1971;Tsai 1974;Vidmar et al 1975;Sugihara & Yamanaka 1975;Canosa 1975). Consequently, a wave of amplitude larger than a certain value is damped, the precise value depending on the phase velocity.…”

Section: Introductionmentioning

confidence: 99%

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Approximate theory of large-amplitude wave propagation

Kim

1977

J. Plasma Phys.

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An orbit perturbation procedure is applied to the description of monochromatic, large-amplitude, electrostatic plasma wave propagation. In the lowest-order approximation, untrapped electrons are assumed to follow constant-velocity orbits and trapped electrons are assumed to execute simple harmonic motion. The deviations of these orbits from the actual orbits are regarded as perturbations. The nonlinear damping rate and frequency shift are then obtained in terms of simple functions. The results are in good agreement with previous less approximate analyses. A significant feature of the analysis is that it treats a single wave by techniques previously applied to turbulent spectra. The analysis can consequently be extended to the case of a large-amplitude wave interacting with a lower-amplitude spectrum of waves.

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Section: Introductionsupporting

confidence: 79%

Section: Orbit Perturbationmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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Approximate theory of large-amplitude wave propagation

Kim

1977

J. Plasma Phys.

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“…(6)(7)(8), the wave variables are not in their canonical form. For these we may choose either the complex wave amplitude representation (w, pw)' or we may transform these to action angle variables (9, J).…”

mentioning

confidence: 99%

Soluble theory of nonlinear beam-plasma interaction

Mynick

Kaufman

1978

The Physics of Fluids

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A soluble theory of the post-saturation portion of a beamplasma interaction is developed, concentrating on explaining the results of O'Neil, Winfrey, and Malmberg. Analytic progress is made possible by applying a certain constraint-procedure, characterized by the "rotating-bar" approximation, to a Hamiltonian formulation of the problem. The procedure yields, from the original N-particle Hamiltonian H, and new, reduced Hamiltonian H, which has only two particle-related degrees of freedom, and which maintains the conservation laws of energy and momentum possessed by H. The equations of motion coming from H still describe the selfconsistent interaction of a mode of the plasma with the beam particles, as opposed to previous work, and, because 'or the-great reduction in the number of degrees of freedom, explicit expressions for the nonlinear frequency shift, and growth rate, of the mode can be obtained which are in very good agreement with the simulation results of 0' Neil et al.

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“…Experimental observation of the spatial evolution of an electron plasma wave in a collisionless plasma was made by Wharton, Malmberg & O'Neil (1967), Franklin, Hamberger & Smith (1972) and Vidmar, Malmberg & Starke (1972). A larger bounce frequency and a smaller bounce amplitude than those observed by Franklin et al were obtained by Wharton et al Vidmar et al observed a variation in amplitude similar to that predicted by Malmberg & O'Neil; they also found qualitative agreement in phase variations.…”

Section: S-t Tsaimentioning

confidence: 99%

Spatial evolution of finite-amplitude plasma waves in collisionless plasmas

Tsai¹

1974

J. Plasma Phys.

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A numerical simulation concerning the spatial evolution of electron plasma waves and electron distributions in collisionless plasmas is performed. Only those particles in and around the resonant region are followed numerically, while the bulk plasma is treated analytically. Our results are in good agreement with existing theoretical results as well as experimental observations. The method introduced here is valid for waves with arbitrary amplitude. It does not depend on either a large-amplitude asymptotic expansion or a small-amplitude perturbation scheme.

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Nonlinear Wave Number of an Electron Plasma Wave

Cited by 16 publications

References 11 publications

Approximate theory of large-amplitude wave propagation

Approximate theory of large-amplitude wave propagation

Soluble theory of nonlinear beam-plasma interaction

Spatial evolution of finite-amplitude plasma waves in collisionless plasmas

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