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@inproceedings{batygin:ipac2021-tupab206,
author = {Y.K. Batygin},
title = {{Matching of Intense Beam in Six-Dimensional Phase Space}},
booktitle = {Proc. IPAC'21},
pages = {1897--1900},
eid = {TUPAB206},
language = {english},
keywords = {space-charge, emittance, focusing, framework, quadrupole},
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-TUPAB206},
url = {https://jacow.org/ipac2021/papers/tupab206.pdf},
note = {https://doi.org/10.18429/JACoW-IPAC2021-TUPAB206},
abstract = {{Beam matching is a common technique that is routinely employed in accelerator design to minimize beam losses. Despite being widely used, a full theoretical understanding of beam matching in 6D phase space remains elusive. Here, we present an analytical treatment of 6D beam matching of a high-intensity beam onto an RF structure. We begin our analysis within the framework of a linear model, and apply the averaging method to attain a matched solution for a set of 3D beam envelope equations. We then consider the nonlinear regime, where the beam size is comparable with the separatrix size. Starting with a Hamiltonian analysis in 6D phase space, we attain a self-consistent beam profile and show that it is significantly different from the commonly used ellipsoidal shape. Subsequently, we analyze the special case of equilibrium with equal space charge depression between all degrees of freedom. A comparison of beam dynamics for equipartitioned, equal space charge depression, and equal emittances beams is given.}},
}