Periodic solutions of the Hamilton-Jacobi equation by the shooting method: A technique for beam dynamics
Conference
·
OSTI ID:7002225
Periodic solutions of the Hamilton-Jacobi equation determine invariant tori in phase space. The Fourier spectrum of a torus with respect to angular coordinates gives useful information about nonlinear resonances and their potential for causing instabilities. We describe a method to solve the Hamilton-Jacobi equation for an arbitrary accelerator lattice. The method works with Fourier modes of the generating functions, and imposes periodicity in the machine azimuth by a shooting method. We give examples leading to three-dimensional plots in a surface of section. It is expected that the technique will be useful in lattice optimization. 14 refs., 6 figs., 1 tab.
- Research Organization:
- Colorado Univ., Boulder (USA); Stanford Linear Accelerator Center, Menlo Park, CA (USA)
- DOE Contract Number:
- AC03-76SF00515; FG02-86ER40302
- OSTI ID:
- 7002225
- Report Number(s):
- SLAC-PUB-4626; CONF-8804111-3; ON: DE88012733
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
43 PARTICLE ACCELERATORS
430200* -- Particle Accelerators-- Beam Dynamics
Field Calculations
& Ion Optics
99 GENERAL AND MISCELLANEOUS
990230 -- Mathematics & Mathematical Models-- (1987-1989)
ACCELERATORS
ALGORITHMS
BEAM DYNAMICS
COORDINATES
DIFFERENTIAL EQUATIONS
EQUATIONS
FOURIER ANALYSIS
HAMILTON-JACOBI EQUATIONS
HAMILTONIANS
ITERATIVE METHODS
MATHEMATICAL LOGIC
MATHEMATICAL OPERATORS
NUMERICAL SOLUTION
OPTIMIZATION
PARTIAL DIFFERENTIAL EQUATIONS
PERIODIC SYSTEM
QUANTUM OPERATORS
430200* -- Particle Accelerators-- Beam Dynamics
Field Calculations
& Ion Optics
99 GENERAL AND MISCELLANEOUS
990230 -- Mathematics & Mathematical Models-- (1987-1989)
ACCELERATORS
ALGORITHMS
BEAM DYNAMICS
COORDINATES
DIFFERENTIAL EQUATIONS
EQUATIONS
FOURIER ANALYSIS
HAMILTON-JACOBI EQUATIONS
HAMILTONIANS
ITERATIVE METHODS
MATHEMATICAL LOGIC
MATHEMATICAL OPERATORS
NUMERICAL SOLUTION
OPTIMIZATION
PARTIAL DIFFERENTIAL EQUATIONS
PERIODIC SYSTEM
QUANTUM OPERATORS