STOCHASTICITY

PDF Version Also Available for Download.

Description

Detailed examination of computed particle trajectories has revealed a complexity and disorder that is of increasing interest to accelerator specialists. To introduce this topic, the author would like you to consider for a moment the analysis of synchrotron oscillations for a particle in a coasting beam, regarded as a problem in one degree of freedom. A simple analysis replaces the electric field of the RF-v cavity system by a traveling wave, having the speed of a synchronous reference particle, and leads to a pair of differential equations of the form dy/dn = -K sin {pi}x, (1A) where y measures the ... continued below

Creation Information

Laslett, L. Jackson. May 1, 1974.

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

Detailed examination of computed particle trajectories has revealed a complexity and disorder that is of increasing interest to accelerator specialists. To introduce this topic, the author would like you to consider for a moment the analysis of synchrotron oscillations for a particle in a coasting beam, regarded as a problem in one degree of freedom. A simple analysis replaces the electric field of the RF-v cavity system by a traveling wave, having the speed of a synchronous reference particle, and leads to a pair of differential equations of the form dy/dn = -K sin {pi}x, (1A) where y measures the fractional departure of energy from the reference value {pi}x measures the electrical phase angle at which the particle traverses the cavity, and K is proportional to the cavity voltage; and dx/dn = {lambda}{prime}y, (1b) in which {lambda}{prime} is proportional to the change of revolution period with respect to particle energy. It will be recognized that these equations can be derived from a Hamiltonian function H = (1/2){lambda}{prime}y{sup 2}-(K/{pi})cos {pi}x. (2) Because this Hamiltonian function does not contain the independent variable explicitly, it will constitute a constant of the motion and possible trajectories in the x,y phase space will be just the curves defined by H = Constant, namely the familiar simple curves in phase space that are characteristic of a physical (non-linear) pendulum.

Source

  • IXth International Conference on High Energy Accelerators, Stanford, CA, 05/2-7/1974

Language

Item Type

Identifier

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

  • Report No.: LBL-3016
  • Grant Number: DE-AC03-76SF00098
  • Office of Scientific & Technical Information Report Number: 937058
  • Archival Resource Key: ark:/67531/metadc894813

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

  • May 1, 1974

Added to The UNT Digital Library

  • Sept. 27, 2016, 1:39 a.m.

Description Last Updated

  • Oct. 3, 2016, 4:47 p.m.

Usage Statistics

When was this article last used?

Yesterday: 0
Past 30 days: 0
Total Uses: 2

Interact With This Article

Here are some suggestions for what to do next.

Start Reading

PDF Version Also Available for Download.

Citations, Rights, Re-Use

Laslett, L. Jackson. STOCHASTICITY, article, May 1, 1974; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc894813/: accessed January 22, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.