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@inproceedings{mitchell:ipac2021-wepab248,
author = {C.E. Mitchell and K. Hwang and R.D. Ryne},
title = {{Kurth Vlasov-Poisson Solution for a Beam in the Presence of Time-Dependent Isotropic Focusing}},
booktitle = {Proc. IPAC'21},
pages = {3213--3216},
eid = {WEPAB248},
language = {english},
keywords = {focusing, emittance, space-charge, simulation, proton},
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-WEPAB248},
url = {https://jacow.org/ipac2021/papers/wepab248.pdf},
note = {https://doi.org/10.18429/JACoW-IPAC2021-WEPAB248},
abstract = {{The well-known K-V distribution provides an exact solution of the self-consistent Vlasov-Poisson system describing an unbunched charged particle beam with nonzero temperature in the presence of time-dependent linear transverse focusing. We describe a lesser-known exact solution of the Vlasov-Poisson system that is based on the work of Kurth in stellar dynamics. Unlike the K-V distribution, the Kurth distribution is a true function of the phase space variables, and the solution may be constructed on either the 4D or 6D phase space, for the special case of isotropic linear focusing. Numerical studies are performed for benchmarking simulation codes, and the stability properties of a 4D Kurth distribution are compared with those of a K-V distribution.}},
}