ZGOUBI USERS' GUIDE - HEP

104 4 DESCRIPTION OF THE AVAILABLE PROCEDURES7>^^2 >22¡q¡q ^^2¡ >q^^>^^>¡\q¡\q^¡ >\q7ÊMULTIPOL: Magnetic multipoleThe simulation of multipolar magnetic field( ¡ @ ), sextupolar ( ¡ U ), etc., up to 20-polar ( ¡ qby MULTIPOL proceeds by addition of the dipolar ( ¡ q ), quadrupolar\) components, and of their derivatives up to fourth order, following¡ @ ¡ U óBDBEB*¡ @¡ U BDBEBr ^^ §^ §^ §^ §^ §¡ @¡ UóBDBEBretc.^ § ^ ^ § ^ ^ § ^ ^ § ^ ^ § ^ in section 1.3.6.The independent components ¡ q , ¡ @ , ¡ U , ..., ¡ q\and their derivatives up to the fourth order are calculated as describedThe 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 · 7ˆ4) at exit, such that the extent is ³³ ³ ¢ >( ³ Š V¢ T, ..., ³ Š V¢ 7ˆ4)Š Vat entrance ¢ > and ( Œ V , ..., ³ Œ V· 7ˆ4) at exit.V³ ³ Œ· >· Tfield for the multipole component is considered as a sharp edge field. In sharp edge field model, the wedge angle vertical" qIf 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). If ¢ b³ (· b C\) ( @†\§ Œ is\), the entrance (exit) fringefirst order focusing effect (if ¡ q is non zero) is simulated at magnet entrance and exit by a kick ¥applied to each particle (¥, ¥at the EFB, the local horizontal bending radius and Êhorizontal angle T).,are the vertical angles upstream and downstream the EFB, the vertical particle positionthe wedge angle experienced by the particle ; depends on theÊ> ¥7 w, 7 f¡ )-Overlapping of fringe fields inside the optical element is treated separately for each component, in the way described inQUADRUPO.Any multipole component ¡ can be rotated independently by an angle 1 §# around the longitudinal § -axis, for thesimulation of positioning defects, as well as skewed lenses.Magnet (mis-)alignement is assured by KPOS. KPOS also allows some degrees of automatic alignement useful for periodicstructures (section 4.6.5).