Laser cooling and crystalline beams in storage rings

Seurer, M.; Reinhard, P.‐G.; Toepffer, C.

doi:10.1016/s0168-9002(98)00426-4

Cited by 2 publications

(2 citation statements)

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“…( 21), we see that the Fokker-Planck related moments exactly agree with those appearing in Eq. ( 9) -provided that we restrict ourselves to Ornstein-Uhlenbeck processes, and the global temperature definition (22). Under these preconditions, the insertion of Eq.…”

Section: Entropy and Rms-emittancementioning

confidence: 99%

“…If we neglect the (reversible) changes of the rms-emittance due to changes of excess field energy, on the basis of Eqs. ( 16) we may easily establish a closed coupled set of generalized envelope and temperature change equations [4,22] which can be directly integrated. The results of an integration of this set of equations based on the geometry of the GSI experimental storage ring (ESR) are plotted in Fig.…”

Section: -D Beammentioning

confidence: 99%

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Concept of entropy in the realm of charged particle beams

Struckmeier¹

1996

Phys. Rev. E

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Stochastic phenomena occurring within charged particle beams can be handled using the Vlasov-Fokker-Planck generalization of the Vlasov equation. In particular, this non-deterministic approach can deal with effects due to Coulomb scattering between the beam particles. Moreover, stochastic phenomena also occur in computer simulations of charged particle beams. Both processes-although different in their physical nature-can be described by the Vlasov-Fokker-Planck equation, since in both cases the underlying stochastic process can be classified as a Markov process. This description is applied to beams in periodic focusing systems. We derive an equation relating the change of the µ-phase space entropy to the change of rms-emittance and "temperature weighted excess field energy". This equation enables us both to improve our capability to interpret the results of computer simulations, as well as to identify the conditions needed to minimize scattering induced degradation of the quality of beams circulating in storage rings.

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Section: Entropy and Rms-emittancementioning

confidence: 99%

Section: -D Beammentioning

confidence: 99%