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Extracting dynamical frequencies from invariants of motion in finite-dimensional nonlinear integrable systems

Journal Article · · Physical Review E
 [1];  [1];  [1];  [2];  [3]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  2. Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States); Univ. of Chicago, IL (United States)
  3. Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
+ Show Author Affiliations

Integrable dynamical systems play an important role in many areas of science, including accelerator and plasma physics. An integrable dynamical system with n degrees of freedom possesses n nontrivial integrals of motion, and can be solved, in principle, by covering the phase space with one or more charts in which the dynamics can be described using action-angle coordinates. To obtain the frequencies of motion, both the transformation to action-angle coordinates and its inverse must be known in explicit form. However, no general algorithm exists for constructing this transformation explicitly from a set of n known (and generally coupled) integrals of motion. In this study we describe how one can determine the dynamical frequencies of the motion as functions of these n integrals in the absence of explicitly known action-angle variables, and we provide several examples.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP)
Grant/Contract Number:
AC02-05CH11231; AC02-07CH11359
OSTI ID:
1821148
Alternate ID(s):
OSTI ID: 1827112
Journal Information:
Physical Review E, Journal Name: Physical Review E Journal Issue: 6 Vol. 103; ISSN 2470-0045
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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Betatron frequency and the Poincaré rotation number journal May 2020
Machine Learning Conservation Laws from Trajectories journal May 2021
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Accelerator-feasible N -body nonlinear integrable system journal December 2014
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Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Classical mechanics
Nonlinear beam dynamics
Single-particle dynamics