Alternating-Phase Focusing: A Model to Study Nonlinear Dynamics Page: 1 of 11
9 pagesView a full description of this article.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
The wbrrotred rmanurwnp has been authored
by a con la cor of the U S. Governm ent
under contract No w-3109ENG-38.
ACtoro Dly, the U. S Govermment retain a
nonexlubve, ryayty-fre" hcense to publtt
or reproduce the pubhshed form of th l
conibu tion. or allow chberl to do Wt, for
U. S. Government purposes.
Alternating-Phase Focusing: A Model to Study
Nonlinear Dynamics N/CP---76665
E92 019027
L Sagalovsky and J I Delayen
Argonne National Laboratory, 9700 S Cass Avenue. Argotine, l 60439, USA
Abstract. We discuss a new model to study alternating-phase focusing
(A PF). Our aIpproach is bared on representing the accelerating electric field
with i a continuous phase modulated traveling wave. The resulting nonlili-
ear equations of motion can he solved analytically to predict the regions of
stable APF motion. We also identify the key parameters which adequately
describe the physics of A P 1. Tihe model is believed to be applicable to low-3
ion linacs with short. independently-cont rolled superconducting cavit ies being
developed at ANL.
1. Introduction
The basic idea o. AF is to achieve stable beam transport in both axial and radial
planes of motion by alternating the sign of equiiibriun plase of tihe accelerating electric
field. The advantages of realizing a three-dimensional beam focusing without the isi of
solenoids or quadrupole magnets must be weighed against t he compromises in longitudi-
nal acceptance one is forced to make. Previous works in the field [I, 2, 3, 4. 51 addressed
APE in the context, of a linac with a discrete number of accelerating gaips spaced in a
predetermined master to achieve a particular value of the synchronous phase in ech1 gap
(such as the case in the 7-mode \Wideroe linac and the Alvarez DTL). In contrast. the
application we have in Illind is a linac with superconducting accelerating cavities of the
type described in [6], 'tiese low- i cavities are short, can be independent ly controlled in
adjusting hoth the phase and the amiplitude of the electric field, and wN-le shown to pro.
dure ver' high accelerating gradienits [7]. T'he mi o idel presented in this papir is thought
to be a good description of e'mential A PF physics for the superconducting limacs and a
starting point in trying to determine the practical limits of A P .
2. Beam dynamics it APF linacs C
2.1, Anabytrcal mode and assum;ptions
We assume that the electric field is descri berdI b a cylindrically synnet Iic traveling wave
,;Ith ta .:: Itlrtlclls ph.a:e m.oduk,,rt,,,n. ttare, ,,, h s t,,,,. e ,,.,.io ~,...,.. . b. ..... ........-,,:
E(r ) = E cos [wt - ok(')dz' + Q4- + ) sit (2r/ ) , (1)
DISTRIBUTION QF T HI DOCUMENT IS UNLIMITED
Upcoming Pages
Here’s what’s next.
Search Inside
This article can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Article.
Sagalovsky, L. & Delayen, J. R. Alternating-Phase Focusing: A Model to Study Nonlinear Dynamics, article, January 1, 1992; Illinois. (https://digital.library.unt.edu/ark:/67531/metadc1446407/m1/1/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.