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TY - CONF AU - Li, Y. AU - Yu, L. ED - Schaa, Volker RW ED - Arduini, Gianluigi ED - Pranke, Juliana ED - Seidel, Mike ED - Lindroos, Mats TI - Applying Square Matrix to Optimize Storage Ring Nonlinear Lattice J2 - Proc. of IPAC2017, Copenhagen, Denmark, 14â19 May, 2017 C1 - Copenhagen, Denmark T2 - International Particle Accelerator Conference T3 - 8 LA - english AB - A new method of using linear algebra technique to analyze periodical nonlinear beam dynamics is presented. For a given dynamical system, a square upper triangular transfer matrix is constructed out of a one turn Taylor transfer map. First we separate the matrix into different low dimensional invariant subspaces according to their eigenvalues. Then a stable Jordan transformation can be obtained on each subspace. The transformation provides an excellent action-angle approximation to the solution of the nonlinear dynamics. And the deviation of the new action from constancy provides a measure of the nonlinearity of the motions, which provides a novel method to optimize the nonlinear dynamic system. We applied this method to optimize various rings, such as NSLS-II, SPEAR3, and APS-U lattice, the promising dynamic aperture have been achieved from both tracking simulation and experimental measurements. PB - JACoW CP - Geneva, Switzerland SP - 3241 EP - 3243 KW - lattice KW - resonance KW - dynamic-aperture KW - sextupole KW - storage-ring DA - 2017/05 PY - 2017 SN - 978-3-95450-182-3 DO - 10.18429/JACoW-IPAC2017-WEPIK122 UR - http://jacow.org/ipac2017/papers/wepik122.pdf ER -