Stochastic cooling of bunched beams from fluctuation and kinetic theory

Technical Report · Wed Sep 01 00:00:00 EDT 1982

DOI:https://doi.org/10.2172/6345296· OSTI ID:6345296

Chattopadhyay, S

A theoretical formalism for stochastic phase-space cooling of bunched beams in storage rings is developed on the dual basis of classical fluctuation theory and kinetic theory of many-body systems in phase-space. The physics is that of a collection of three-dimensional oscillators coupled via retarded nonconservative interactions determined by an electronic feedback loop. At the heart of the formulation is the existence of several disparate time-scales characterizing the cooling process. Both theoretical approaches describe the cooling process in the form of a Fokker-Planck transport equation in phase-space valid up to second order in the strength and first order in the auto-correlation of the cooling signal. With neglect of the collective correlations induced by the feedback loop, identical expressions are obtained in both cases for the coherent damping and Schottky noise diffusion coefficients. These are expressed in terms of Fourier coefficients in a harmonic decomposition in angle of the generalized nonconservative cooling force written in canonical action-angle variables of the particles in six-dimensional phase-space. Comparison of analytic results to a numerical simulation study with 90 pseudo-particles in a model cooling system is presented.

• Research Organization: Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 6345296
• Report Number(s): LBL-14826; ON: DE83012472
• Resource Relation: Other Information: Portions are illegible in microfiche products. Thesis
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
STOCHASTIC COOLING
BEAM DYNAMICS
BEAM BUNCHING
BOLTZMANN-VLASOV EQUATION
COMPUTERIZED SIMULATION
EQUATIONS OF MOTION
FOKKER-PLANCK EQUATION
NUMERICAL ANALYSIS
PHASE SPACE
SAMPLING
STORAGE RINGS
THEORETICAL DATA
BEAM COOLING
DATA
DIFFERENTIAL EQUATIONS
EQUATIONS
INFORMATION
MATHEMATICAL SPACE
MATHEMATICS
NUMERICAL DATA
PARTIAL DIFFERENTIAL EQUATIONS
SIMULATION
SPACE
430200* - Particle Accelerators- Beam Dynamics
Field Calculations
& Ion Optics