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Busch's theorem for mappings.

DE2001781160

Publication Date	2001
Personal Author	Burov, A.
Page Count	3
Abstract	For rotation-invariant Hamiltonian systems, canonical angular momentum is conserved. In beam optics, this statement is known as Busch's theorem. This theorem can be generalized to symplectic mappings; two generalizations are presented in this paper. The first one states that a group of rotation-invariant mappings is identical to a group of the angular-momentum preserving mappings, assuming both of them symplectic and linear. The second generalization of Busch's theorem claims that for any beam which rotation symmetry happened to be preserved, an absolute value of the angular momentum of any particle from this beam is preserved as well; the linear symplectic mapping does not have to be rotation-invariant here.
Keywords	Beam optics Angular momentum Hamiltonians Rotation Symmetry Particle beams
Source Agency	Technical Information Center Oak Ridge Tennessee
Corporate Authors	Fermi National Accelerator Lab., Batavia, IL.; Department of Energy, Washington, DC.
Document Type	Conference Proceedings
NTIS Issue Number	200125
Contract Number	AC02-76CH03000

Busch's theorem for mappings.

Busch's theorem for mappings.
DE2001781160

Publication Date	2001
Personal Author	Burov, A.
Page Count	3
Abstract	For rotation-invariant Hamiltonian systems, canonical angular momentum is conserved. In beam optics, this statement is known as Busch's theorem. This theorem can be generalized to symplectic mappings; two generalizations are presented in this paper. The first one states that a group of rotation-invariant mappings is identical to a group of the angular-momentum preserving mappings, assuming both of them symplectic and linear. The second generalization of Busch's theorem claims that for any beam which rotation symmetry happened to be preserved, an absolute value of the angular momentum of any particle from this beam is preserved as well; the linear symplectic mapping does not have to be rotation-invariant here.
Keywords	Beam optics Angular momentum Hamiltonians Rotation Symmetry Particle beams
Source Agency	Technical Information Center Oak Ridge Tennessee
Corporate Authors	Fermi National Accelerator Lab., Batavia, IL.; Department of Energy, Washington, DC.
Document Type	Conference Proceedings
NTIS Issue Number	200125
Contract Number	AC02-76CH03000