ZGOUBI USERS' GUIDE - HEP

114 4 DESCRIPTION OF THE AVAILABLE PROCEDURESG44>>4@G§FÓf› º ± ¡¬ ¡ ¨center º†¡ Ž iÄ >2i4qP4>SñB>G4SOLENOID: Solenoid (Fig. 36)44The solenoidal magnet § ¨ has an effective length , a mean radius and an £#¤L§ ¨ asymptotic field¡ ¡„Ž (i.e.,1 ¡ ï 1 4), wherein =longitudinal field component, ¡|Ž £#¤ = number of Ampere-Turns,± §#"$ £#¤"­¤m. ¬>ô \¬ ¡R q ©The distance of ray-tracing beyond the effective §„¨ length , § Š is at the entrance, § Œ and at the exit (Fig. 7/‘ >36).The field , , and its derivatives up to the second order with respect to § , or are obtained§#"/after the method proposed in ref. [25], that involves the three complete elliptic integrals , and ¢¡ . These are calculated õwith the algorithm proposed in the same reference. Their derivatives are calculated by means of recursive Ñ relations [26].This analytical model for the solenoidal field allows simulating an extended range of coil geometries (legnth and 4radius)provided that the coil thickness is small enough compared to the mean radius .1In particular the field on-axis writes (taking Ä C\ as solenoid center)§ G 1 >1 > 4'÷¡ Ž §„Ï @ w ÄÄ "$ †\ £#¤and yields the magnetic length4 §„Ï @ 5ħ„¨pö§ ¨ @ w Ä~§„Ï @ Ä~Ž Ä "$ ï 1 4 ¡R1 >¡ Ž §„¨Èø qwith in additionÄ C\ §„¨§ ¨Ä †\ G£#¤¡ Ž SÉ Žùµ µ§ ¨Figure 36: Solenoidal magnet.