Nonlinear accelerator lattices with one and two analytic invariants

PDF Version Also Available for Download.

Description

Integrable systems appeared in physics long ago at the onset of classical dynamics with examples being Kepler's and other famous problems. Unfortunately, the majority of nonlinear problems turned out to be nonintegrable. In accelerator terms, any 2D nonlinear nonintegrable mapping produces chaotic motion and a complex network of stable and unstable resonances. Nevertheless, in the proximity of an integrable system the full volume of such a chaotic network is small. Thus, the integrable nonlinear motion in accelerators has the potential to introduce a large betatron tune spread to suppress instabilities and to mitigate the effects of space charge and magnetic ... continued below

Physical Description

17 pages

Creation Information

Danilov, V.; /SNS Project, Oak Ridge; Nagaitsev, S. & /Fermilab February 1, 2010.

Context

This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. More information about this article can be viewed below.

Who

People and organizations associated with either the creation of this article or its content.

Publisher

Provided By

UNT Libraries Government Documents Department

Serving as both a federal and a state depository library, the UNT Libraries Government Documents Department maintains millions of items in a variety of formats. The department is a member of the FDLP Content Partnerships Program and an Affiliated Archive of the National Archives.

Contact Us

What

Descriptive information to help identify this article. Follow the links below to find similar items on the Digital Library.

Description

Integrable systems appeared in physics long ago at the onset of classical dynamics with examples being Kepler's and other famous problems. Unfortunately, the majority of nonlinear problems turned out to be nonintegrable. In accelerator terms, any 2D nonlinear nonintegrable mapping produces chaotic motion and a complex network of stable and unstable resonances. Nevertheless, in the proximity of an integrable system the full volume of such a chaotic network is small. Thus, the integrable nonlinear motion in accelerators has the potential to introduce a large betatron tune spread to suppress instabilities and to mitigate the effects of space charge and magnetic field errors. To create such an accelerator lattice one has to find magnetic and electric field combinations leading to a stable integrable motion. This paper presents families of lattices with one invariant where bounded motion can be easily created in large volumes of the phase space. In addition, it presents 3 families of integrable nonlinear accelerator lattices, realizable with longitudinal-coordinate-dependent magnetic or electric fields with the stable nonlinear motion, which can be solved in terms of separable variables.

Physical Description

17 pages

Source

  • Journal Name: Submitted to Phys.Rev.ST. Accel.Beams; Journal Volume: 13; Journal Issue: 8

Language

Item Type

Identifier

Unique identifying numbers for this article in the Digital Library or other systems.

  • Report No.: FERMILAB-PUB-10-030-AD
  • Grant Number: AC02-07CH11359
  • DOI: 10.1103/PhysRevSTAB.13.084002 | External Link
  • Office of Scientific & Technical Information Report Number: 973926
  • Archival Resource Key: ark:/67531/metadc928140

Collections

This article is part of the following collection of related materials.

Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

What responsibilities do I have when using this article?

When

Dates and time periods associated with this article.

Creation Date

  • February 1, 2010

Added to The UNT Digital Library

  • Nov. 13, 2016, 7:26 p.m.

Description Last Updated

  • Nov. 30, 2016, 1:07 p.m.

Usage Statistics

When was this article last used?

Yesterday: 0
Past 30 days: 1
Total Uses: 3

Interact With This Article

Here are some suggestions for what to do next.

Start Reading

PDF Version Also Available for Download.

International Image Interoperability Framework

IIF Logo

We support the IIIF Presentation API

Danilov, V.; /SNS Project, Oak Ridge; Nagaitsev, S. & /Fermilab. Nonlinear accelerator lattices with one and two analytic invariants, article, February 1, 2010; Batavia, Illinois. (digital.library.unt.edu/ark:/67531/metadc928140/: accessed October 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.