Stability properties of the transverse envelope equations describing intense ion beam transport

The transverse evolution of the envelope of an intense, unbunched ion beam in a linear transport channel can be modeled for the approximation of linear self-fields by the Kapchinskij-Vladimirskij (KV) envelope equations. Here we employ the KV envelope equations to analyze the linear stability proper...

Full description

Bibliographic Details
Main Authors: Steven M. Lund, Boris Bukh
Format: Article
Language:English
Published: American Physical Society 2004-02-01
Series:Physical Review Special Topics. Accelerators and Beams
Online Access:http://doi.org/10.1103/PhysRevSTAB.7.024801
_version_ 1818307815254523904
author Steven M. Lund
Boris Bukh
author_facet Steven M. Lund
Boris Bukh
author_sort Steven M. Lund
collection DOAJ
description The transverse evolution of the envelope of an intense, unbunched ion beam in a linear transport channel can be modeled for the approximation of linear self-fields by the Kapchinskij-Vladimirskij (KV) envelope equations. Here we employ the KV envelope equations to analyze the linear stability properties of so-called mismatch perturbations about the matched (i.e., periodic) beam envelope in continuous focusing, periodic solenoidal, and periodic quadrupole transport lattices for a coasting beam. The formulation is analyzed and explicit self-consistent KV distributions are derived for an elliptical beam envelope in a periodic solenoidal transport channel. This derivation extends previous work to identify emittance measures and Larmor-frame transformations to allow application of standard form envelope equations to solenoidal focusing channels. Perturbed envelope equations are derived that include driving sources of mismatch excitation resulting from focusing errors, particle loss, and beam emittance growth. These equations are solved analytically for continuous focusing and demonstrate a factor of 2 increase in maximum mismatch excursions resulting from sudden driving perturbations relative to adiabatic driving perturbations. Numerical and analytical studies are carried out to explore properties of normal mode envelope oscillations without driving excitations in periodic solenoidal and quadrupole focusing lattices. Previous work on this topic by Struckmeier and Reiser [Part. Accel. 14, 227 (1984)] is extended and clarified. Regions of parametric instability are mapped, new classes of envelope instabilities are found, parametric sensitivities are explored, general limits and mode invariants are derived, and analytically accessible limits are checked. Important, and previously unexplored, launching conditions are described for pure envelope modes in periodic quadrupole focusing channels.
first_indexed 2024-12-13T07:04:22Z
format Article
id doaj.art-6539349d5b804756b4506c0cafcc9a80
institution Directory Open Access Journal
issn 1098-4402
language English
last_indexed 2024-12-13T07:04:22Z
publishDate 2004-02-01
publisher American Physical Society
record_format Article
series Physical Review Special Topics. Accelerators and Beams
spelling doaj.art-6539349d5b804756b4506c0cafcc9a802022-12-21T23:55:51ZengAmerican Physical SocietyPhysical Review Special Topics. Accelerators and Beams1098-44022004-02-017202480110.1103/PhysRevSTAB.7.024801Stability properties of the transverse envelope equations describing intense ion beam transportSteven M. LundBoris BukhThe transverse evolution of the envelope of an intense, unbunched ion beam in a linear transport channel can be modeled for the approximation of linear self-fields by the Kapchinskij-Vladimirskij (KV) envelope equations. Here we employ the KV envelope equations to analyze the linear stability properties of so-called mismatch perturbations about the matched (i.e., periodic) beam envelope in continuous focusing, periodic solenoidal, and periodic quadrupole transport lattices for a coasting beam. The formulation is analyzed and explicit self-consistent KV distributions are derived for an elliptical beam envelope in a periodic solenoidal transport channel. This derivation extends previous work to identify emittance measures and Larmor-frame transformations to allow application of standard form envelope equations to solenoidal focusing channels. Perturbed envelope equations are derived that include driving sources of mismatch excitation resulting from focusing errors, particle loss, and beam emittance growth. These equations are solved analytically for continuous focusing and demonstrate a factor of 2 increase in maximum mismatch excursions resulting from sudden driving perturbations relative to adiabatic driving perturbations. Numerical and analytical studies are carried out to explore properties of normal mode envelope oscillations without driving excitations in periodic solenoidal and quadrupole focusing lattices. Previous work on this topic by Struckmeier and Reiser [Part. Accel. 14, 227 (1984)] is extended and clarified. Regions of parametric instability are mapped, new classes of envelope instabilities are found, parametric sensitivities are explored, general limits and mode invariants are derived, and analytically accessible limits are checked. Important, and previously unexplored, launching conditions are described for pure envelope modes in periodic quadrupole focusing channels.http://doi.org/10.1103/PhysRevSTAB.7.024801
spellingShingle Steven M. Lund
Boris Bukh
Stability properties of the transverse envelope equations describing intense ion beam transport
Physical Review Special Topics. Accelerators and Beams
title Stability properties of the transverse envelope equations describing intense ion beam transport
title_full Stability properties of the transverse envelope equations describing intense ion beam transport
title_fullStr Stability properties of the transverse envelope equations describing intense ion beam transport
title_full_unstemmed Stability properties of the transverse envelope equations describing intense ion beam transport
title_short Stability properties of the transverse envelope equations describing intense ion beam transport
title_sort stability properties of the transverse envelope equations describing intense ion beam transport
url http://doi.org/10.1103/PhysRevSTAB.7.024801
work_keys_str_mv AT stevenmlund stabilitypropertiesofthetransverseenvelopeequationsdescribingintenseionbeamtransport
AT borisbukh stabilitypropertiesofthetransverseenvelopeequationsdescribingintenseionbeamtransport