ZGOUBI USERS' GUIDE - HEP

94 4 DESCRIPTION OF THE AVAILABLE PROCEDURES¢ @q^^22ŠŠ¢2q¢q ^^¢ >qÑ^^>Á^Áq^>¢\q>^¢¡\q7 X^¢ >¢ \qqELMULT: Electric multipoleThe simulation of multipolar electric field( ¢ U ), etc., up to 20-polarproceeds by addition ofthe dipolar , quadrupolar ( ), sextupolarŠ ¢components, and of their derivatives up to fourth order, following@ \¢ @ ¢ U óBEBDBIŠ ¢ @¢ UóBEBDBI§ >Q2 ^^ §^ §^ §^ §¢ @¢ UóBDBEB*^ § ^ etc.^ § ^ ^ § ^ ^ § ^ ^ § ^ The independent components q to ¢ q\and their derivatives up to the second order are calculated by differentiating thegeneral multipole potential given in eq. 1.3.5 (page 20), followed by a ¢ X rotation about the § -axis, so that the so definedçright electric multipole of order , and of strength [19, 20]žX @ q> wX1˜ 4X˜ X = potential at the electrode, 1 4effect than the right magnetic multipole of order ž and strength Ñ X = radius at pole tip, Á = relativistic Lorentz factor of the particle) has the same focusing¡ = field at pole tip, = particle¡., Xrigidity, see MULTIPOL).4 ¡.,© @Ÿž Such rotation of the multipole components is obtained following the procedure described in section 1.5.4.1 X(¬The entrance and exit fringe fields are treated separately. They are characterized § Š by the integration zone at entranceand at exit, as for QUADRUPO, and by the Š extent at entrance, Œ at exit. The fringe field extents for the dipole§ Œcomponent ³ are and ³ . The fringe field for the quadrupolar (sextupolar, ..., 20-polar) component is given by aŠ Œcoefficient ( , ..., ¢ T ¢ 7ˆ4) at entrance, and · > (· , ..., T · 7¸4) at exit, such that the fringe field extent is ³³ ¢ >( ³³ ¢ T, ŠºV ŠºV¢ ¢ 7ˆ4..., ) at entrance and > ( ³ ŒLV , ..., ³ ŒíV· 7¸4) at exit.ŒíV³ ³ ŠìV· >· TIf Š —\( ³ Œ ý\) the multipole lens is considered to have a sharp edge field at entrance (exit), and then, § Šforced to zero (for the mere purpose of saving computing time).³§ Œ isfield." qIf ¢ b “\ (· b ý\) ( \), the entrance (exit) fringe field for multipole component is considered as a sharp edgeOverlapping of fringe fields inside the element is treated separately for each component, in the way described in QUADRUPO.Moreover, any multipole component ¢ can be rotated independently by an angle 1 §# around the longitudinal § -axis,for the simulation of positioning defects, as well as skewed lenses.Use PARTICUL prior to ELMULT, for the definition of particle mass and charge.