On the motion of charged particles in a slightly damped sinusoidal potential wave

Best, R.W.B.

doi:10.1016/0031-8914(68)90016-5

Cited by 44 publications

(19 citation statements)

References 4 publications

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“…(Here K and E are the complete elliptic integrals of the first and second kind, respectively; cf., e.g., Ref. [19].) Since the generating function of the canonical transformation ðx; pÞ !…”

Section: (A)]mentioning

confidence: 99%

Nonlinear Dispersion of Stationary Waves in Collisionless Plasmas

Dodin

Fisch

2011

Phys. Rev. Lett.

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A nonlinear dispersion of a general stationary wave in collisionless plasma is obtained in a nondifferential form expressed in terms of a single-particle oscillation-center Hamiltonian. For electrostatic oscillations in nonmagnetized plasma, considered as a paradigmatic example, the linear dielectric function is generalized, and the trapped particle contribution to the wave frequency shift Δω is found analytically as a function of the wave amplitude a. Smooth distributions yield Δω ∼ a(1/2), as usual. However, beamlike distributions of trapped electrons result in different power laws, or even a logarithmic nonlinearity, which are derived as asymptotic limits of the same dispersion relation.

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Section: (A)]mentioning

confidence: 99%

Nonlinear Dispersion of Stationary Waves in Collisionless Plasmas

Dodin

Fisch

2011

Phys. Rev. Lett.

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“…This action integral can be expressed in terms of complete elliptic integrals (see, e.g., Ref. [10] or p. 65 of Ref.…”

Section: The Amplitude Is Assumed To Have the Form A(q/l) ^Aofiq/l)mentioning

confidence: 99%

Particle dynamics in a large-amplitude wave packet

Bruhwiler

Cary

1992

Phys. Rev. Lett.

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A new adiabatic theory permits the understanding of one-dimensional dynamics of particles interacting with a large-amplitude wave packet for bounce time short compared with the transit time. This theory differs from previous ones in that the Hamiltonian varies slowly not with the time, but with the coordinate. The resulting adiabatic invariant is not equal, even in lowest order, to the usual action. This theory predicts the basic features of the interaction observed in previous numerical studies.

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“…Since then, the adiabatic invariant has proved itself to be a very versatile tool especially in the study of the motion of a charged particle in an electromagnetic field (Best, 1968;Aamodt, 1971Aamodt, , 1972Tennyson 1979;Littlejohn, 1983;Caryet al, 1984;Menyuk, 1985) with applications to plasma physics and high energy accelerators.…”

Section: Introductionmentioning

confidence: 99%

“…It was soon realized (Best, 1968) that, except for the obvious discontinuity forced by the definition of the adiabatic invariant, thisinvariant does not change "much" for "most" of the trajectories crossing the critical curve. This "not much" was apparently estimated as c:(log C 1 )2 for the pendulum in an unpublished work of Gardner quoted by Aamodt (1971Aamodt ( -1972.…”

Section: Introductionmentioning

confidence: 99%

Dynamics Reported

1993

Dynamics Reported

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Dynamical Systems are a rapidly developing field with a strong impact on applications. Dynamics Reported is a series of books of a new type. Its principal goal is to make available current topics, new ideas and techniques. Each volume contains about four or five articles of up to 60 pages. Great emphasis is put on an excellent presentation, well suited for advanced courses, seminars etc. such that the material becomes accessible to beginning graduate students. To explain the core of a new method contributions will treat examples rather than general theories, they will describe typical results rather than the most sophisticated ones. Theorems are accompanied by carefully written proofs. The presentation is as self-contained as possible.Authors will receive 5 copies of the volume containing their contributions. These will be split among multiple authors.Authors are encouraged to prepare their manuscripts in Plain TEX or LA TEX. Detailed information and macro packages are available via the Managing Editors.

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On the motion of charged particles in a slightly damped sinusoidal potential wave

Cited by 44 publications

References 4 publications

Nonlinear Dispersion of Stationary Waves in Collisionless Plasmas

Nonlinear Dispersion of Stationary Waves in Collisionless Plasmas

Particle dynamics in a large-amplitude wave packet

Dynamics Reported

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