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首页> 美国政府科技报告 >Feasibility of tracking with differential-algebra maps in long-term stability studies for large hadron colliders
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Feasibility of tracking with differential-algebra maps in long-term stability studies for large hadron colliders

机译：在大型强子对撞机的长期稳定性研究中使用微分代数图进行跟踪的可行性

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A time-saving alternative to conventional element-by-element tracking in long-term stability studies is the use of truncated Taylor maps. This report discusses how the non-symplecticity of a moderately high-order truncated Taylor map affects its reliability when the map is used for tracking over several thousand turns. Various machines and two different map-constructing programs are compared. It is found that the discrepancies between the Taylor map results and those obtained by direct tracking grow with amplitude. Thus, such maps are not guaranteed to be sufficient for long-term tracking over millions of turns without suitable symplectification.

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