Map Computation from Magnetic Field Data and Application to the Lhc High-gradient Quadrupoles

In many cases the most accurate information about fields in a magnet comes either from direct measurement or from a numerical computation done with a 3D electromagnetic code. In this paper we show how this information can be used to compute transfer maps with high accuracy. The resulting transfer maps take into account all effects of real beamline elements including fringe-field and multipole error effects. The method we employ automatically incorporates the smoothing properties of the Laplace Green function. Consequently, it is robust against both measurement and electromagnetic code errors. As an example, we apply the method to a study of end effects in the High-Gradient quadrupoles for the low-beta insertion in the Large Hadron Collider (LHC). The map computation for the quadrupoles has been carried out using MARYLIE’s GENMAP routine and a newly written MARYLIE user-defined routine. For long-term tracking we used Cremona symplectification techniques as implemented in CTRACK.