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@unpublished{yuan:sap2023-tupb004,
% --- JACoW template Dec 2024 ---
author = {Y.S. Yuan},
title = {{Unified rms envelope model and the envelope instability family in high-intensity hadron synchrotrons}},
eventtitle = {14th Symp. Accel. Phys. (SAP'23)},
eventdate = {2023-07-10/2023-07-12},
language = {english},
intype = {presented at},
series = {Symposium on Accelerator Physics},
number = {14},
venue = {Xichang, China},
note = {presented at the 14th Symp. Accel. Phys. (SAP'23) in Xichang, China, unpublished},
abstract = {{High-intensity beam dynamics is usually described by the well-known rms envelope equations. For circular accelerators, the rms envelope equation set become inadequate, especially for characterizing high-intensity beams because of the missing of the coupling of space charge and dispersion. In this report we develop an unified rms envelope model, including all the second order beam moments existing in circular accelerators. Based on the unified approach, a separated phenomena of instability can be observed, and a new dispersion-coupling mode is identified. The well-known 90 envelope instability is generalized to a family of resonances of second-order eigenmodes, including all the possible envelope instabilities in circular accelerators. The unified approach has the implication for characterizing high-intensity beams in circular accelerators and for working point optimization and beam loss control.}},
}