ZGOUBI USERS' GUIDE - HEP

110 4 DESCRIPTION OF THE AVAILABLE PROCEDURES£¥'£4˜7 ¨w'« ² >|¨³o£w'« ³£q£@>w>q5¯ °± ¥'« ³£ î>T£££'« ³Ž ¡ C\£4 – ¡£ŒP>wq>§>'« ³£M£4 ¡4 1¥@>V4>T7 ¨'« ² > ¨³'« ³QUADRUPO: Quadrupole magnet (Fig. 32)4The length of §„¨ the magnet is the distance between the effective field boundaries (EFB). The field at the pole¡ 4tip 1.The extent of the entrance (exit) fringe field is characterized Š³Œ by . The distance of ray-tracing on both sides of theEFB’s, in the field fall off regions, will ³ Š be at the entrance, o—§ Œ and at the exit (Fig. 33), by prior and furtheroa§automatic changes of frame.In the fringe field ? regionsŠ Š Aand ? § Œ "$§ Œ Aon both sides of the EFB’s, ¡ §#"kS"e and its derivatives up to§ "/§fourth order are calculated at each step of the trajectory from the analytical expressions of the three components , ,¡|– ¡ •obtained by differentiation of the scalar potential (see section 1.3.6) approximated to the 8th order in ¡ and Ž . is) )) ) ) )§©"$Œ"[ U” Rs ›.> w) ) ) ) ) )\ R \ @ZU £ £ > £) whereis the gradient on axis [17]:§#") ) " BDBDB with£ 3'£ 4£ 43' and,;';'where,When fringe fields overlap inside the magnetis the distance to the field boundary and stands for ³ Š or ³ Œ (normally, ³ ]³Š § Œ , the gradient§).is expressed as1 4 ² ² ² T„¨ ² P ¨ ² M ¨ C² ²§ ¨where,If Š †\( ³ Œ \), the field at entrance (exit) is considered as sharp edged, and then § Šmere purpose of saving computing time).Outside of the fringe field regions (or everywhere when ³ Š ³Œ K\) ¡ ³Š is the entrance gradient andŒ is the exit gradient.§ Œ is forced to zero (for the§#"$Œ"[ in the magnet is given byŠ £ 4¡|•