Diffusion in Hamiltonian systems with applications to twist maps and the two-beam accelerator

Thesis/Dissertation · Wed Jan 01 00:00:00 EST 1986

OSTI ID:7231654

Murray, N W

Two problems are studied that involve chaotic motion in Hamiltonian systems. First the evolution of a distribution of particles in phase space is examined. The motion of the particles is given by a near-integrable Hamiltonian mapping and the variables used to describe the motion are the action-angle variables of the integrable part of the Hamiltonian. The evolution of the distribution of angles is observed to be much faster than the evolution of the distribution of actions. This separation of time scales allows averaging over the angle variables and model the evolution of the action distribution function as a diffusive process. Using the Fermi map as an example, the Fokker-Planck equation is integrated for the action and the resulting distribution function is compared with direct solutions of the mapping equations. The second problem involves the motion of electrons in free-electron lasers (FELs). Using a variational principle, a self-consistent three-dimensional model is derived for tapered FELs. This model is then used to study the extent of stochastic motion in a particle accelerator. A high-current, low-energy (20 MeV) beam drives the FELs, producing 1-cm microwaves. These microwaves are used to accelerate a low current beam to energies of 1 TeV.

• Research Organization: California Univ., Berkeley (USA)
• OSTI ID: 7231654
• Resource Relation: Other Information: Thesis (Ph. D.)
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
43 PARTICLE ACCELERATORS
ACCELERATORS
BEAM DYNAMICS
FREE ELECTRON LASERS
ELECTRON MOBILITY
HAMILTONIANS
PARTICLE KINEMATICS
DISTRIBUTION FUNCTIONS
PHASE SPACE
FOKKER-PLANCK EQUATION
STOCHASTIC PROCESSES
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
LASERS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MOBILITY
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE MOBILITY
QUANTUM OPERATORS
SPACE
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics
430200 - Particle Accelerators- Beam Dynamics
Field Calculations
& Ion Optics