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Title: Envelope Hamiltonian for charged-particle dynamics in general linear coupled systems

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Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 23; Journal Issue: 7; Related Information: CHORUS Timestamp: 2016-12-27 20:30:58; Journal ID: ISSN 1070-664X
American Institute of Physics
Country of Publication:
United States

Citation Formats

Chung, Moses, Qin, Hong, and Davidson, Ronald C. Envelope Hamiltonian for charged-particle dynamics in general linear coupled systems. United States: N. p., 2016. Web. doi:10.1063/1.4959112.
Chung, Moses, Qin, Hong, & Davidson, Ronald C. Envelope Hamiltonian for charged-particle dynamics in general linear coupled systems. United States. doi:10.1063/1.4959112.
Chung, Moses, Qin, Hong, and Davidson, Ronald C. 2016. "Envelope Hamiltonian for charged-particle dynamics in general linear coupled systems". United States. doi:10.1063/1.4959112.
title = {Envelope Hamiltonian for charged-particle dynamics in general linear coupled systems},
author = {Chung, Moses and Qin, Hong and Davidson, Ronald C.},
abstractNote = {},
doi = {10.1063/1.4959112},
journal = {Physics of Plasmas},
number = 7,
volume = 23,
place = {United States},
year = 2016,
month = 7

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1063/1.4959112

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  • We report the discovery of an envelope Hamiltonian describing the charged-particle dynamics in general linear coupled lattices.
  • We introduce a Hamiltonian to describe the Kapchinskij-Vladimirskij envelope equation in the envelope phase space. The envelope Hamiltonian, in the presence of periodic focusing fields, can be decomposed into an unperturbed autonomous Hamiltonian and a time dependent perturbation generated by the remnant focusing field. This periodic perturbation produces families of parametric resonances, which form a tree of bifurcation branches. Each branch follows the tune of the unperturbed Hamiltonian. A prescription for selecting a proper unperturbed Hamiltonian will be discussed.
  • The envelope equations and Twiss parameters (β and α) provide important bases for uncoupled linear beam dynamics. For sophisticated beam manipulations, however, coupling elements between two transverse planes are intentionally introduced. The recently developed generalized Courant-Snyder theory offers an effective way of describing the linear beam dynamics in such coupled systems with a remarkably similar mathematical structure to the original Courant-Snyder theory. In this work, we present numerical solutions to the symmetrized matrix envelope equation for β which removes the gauge freedom in the matrix envelope equation for w. Furthermore, we construct the transfer and beam matrices in terms ofmore » the generalized Twiss parameters, which enables calculation of the beam envelopes in arbitrary linear coupled systems.« less
  • An envelope equation, which includes the effects of a solenoidal field, acceleration, self-induced forces, and scattering by a background medium, is derived for the rms radius of a relativistic beam. The system is assumed to be cylindrically symmetric with high enough energy that the paraxial approximation is applicable. The solenoidal field is taken to be uniform normal to the direction of propagation but the beam current profile is arbitrary. The well-known equations of propagation are recovered in their respective domains of applicability (i.e., vacuum transport in a solenoid, equilibrium conditions, the Nordsieck equation, free expansion, and the sausage-mode equation). Amore » treatment is also given of the matching conditions for a beam injected into gas through a foil in the presence of a solenoidal field. The derivation of the envelope equation differs from previous work in making use of the scalar virial moment of the single-particle equation of motion. The beam emittance appears in a natural way as a constant of integration and is shown to be proportional to the effective phase area occupied by the particles. No distribution function is specified for the transverse velocities, but the beam is assumed to pulsate in a self-similar fashion.« less