Liouville`s theorem and phase-space cooling

Conference · Tue Sep 28 04:00:00 EDT 1993

OSTI ID:10105677

Mills, R L ^[1]; Sessler, A M ^[2]

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1. Ohio State Univ., Columbus, OH (United States)
2. Lawrence Berkeley Lab., CA (United States)

A discussion is presented of Liouville`s theorem and its consequences for conservative dynamical systems. A formal proof of Liouville`s theorem is given. The Boltzmann equation is derived, and the collisionless Boltzmann equation is shown to be rigorously true for a continuous medium. The Fokker-Planck equation is derived. Discussion is given as to when the various equations are applicable and, in particular, under what circumstances phase space cooling may occur.

• Research Organization: Lawrence Berkeley Lab., CA (United States)
• Sponsoring Organization: USDOE, Washington, DC (United States)
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 10105677
• Report Number(s): LBL--34667; CONF-9310193--5; ON: DE94003412; IN: CBP-Note-039
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
430200
661300
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BEAM COOLING
BEAM DYNAMICS, FIELD CALCULATIONS, AND ION OPTICS
BOLTZMANN EQUATION
FOKKER-PLANCK EQUATION
LIOUVILLE THEOREM
OTHER ASPECTS OF PHYSICAL SCIENCE