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@inproceedings{amstutz:ipac2021-wepab226,
author = {Ph. Amstutz and M. Vogt},
title = {{Investigation of Vlasov Systems with a Certain Class of Linearly-Collective Hamiltonians}},
booktitle = {Proc. IPAC'21},
pages = {3157--3160},
eid = {WEPAB226},
language = {english},
keywords = {bunching, simulation, collective-effects, linear-dynamics, distributed},
venue = {Campinas, SP, Brazil},
series = {International Particle Accelerator Conference},
number = {12},
publisher = {JACoW Publishing, Geneva, Switzerland},
month = {08},
year = {2021},
issn = {2673-5490},
isbn = {978-3-95450-214-1},
doi = {10.18429/JACoW-IPAC2021-WEPAB226},
url = {https://jacow.org/ipac2021/papers/wepab226.pdf},
note = {https://doi.org/10.18429/JACoW-IPAC2021-WEPAB226},
abstract = {{In many cases the Vlasov equation cannot be solved exactly due its inherent non-linearity arising from collective terms in the Hamiltonian. Based on the analysis of the Hamiltonian’s dependence on the phase-space density and the requirement for self-consistency in this contribution a class of Hamiltonians is defined and characterized. For members of this class the corresponding expansion of the Vlasov equation terminates. The new, potentially non-autonomous, Hamiltonian of the resulting Liouville equation depends only on the initial condition of the phase-space density. Prominent members of this class are Poisson-type kick-Hamiltonians, which we show as an example. We expect these investigations to be a potential starting point for the analysis and conception of operator-splitting schemes or splitting-free methods for beam-dynamics simulation codes.}},
}