ZGOUBI USERS' GUIDE - HEP

4.4 Optical Elements and related numerical procedures 97Ãʼn7>b 1 1ÖFFAG: FFAG magnet, £ -uplet [23]FFAG works much like DIPOLES as to the field modelling, apart from the (so-called “scaling”) radial dependence of thefield.The FFAG procedure allows overlapping of fringe fields of neighboring dipoles, thus simulating in some sort the field ina dipole £ -tuple - as for instance in an FFAG doublet or triplet. This is done in the way described below.The dimensionning of the magnet is defined byAT : total angular apertureRM : mean radius used for the positioning of field boundariesFor each one of £ theEFBs) from which the dipole field is drawn are defined from geometric boundaries, the shape and position of which aredetermined by the following parameters (in the same manner as in DIPOLE, DIPOLE-M) (see Fig. 10-A page 65, andFig. 28)´ ² £q to (maximum) N dipoles of the £ -tuple, the 2 effective field boundaries (entrance and exit: arbitrary inner angle, used for EFB’s positioning: azimuth of an EFB with respect to ACENT: angle of an EFB with respect to its azimuth (wedge angle)7, : radius of curvature of an EFB> 1 1, ‰: extent of the linear part of an EFBB2MB1ACN2ACN3B3ACN1ATFigure 28: Definition of a dipole triplet using the DIPOLES or FFAG procedures.Calculation of the Field Due to a Single DipoleThe magnetic field is calculated in polar coordinates.1"/Å At all in the ( a\median plane ), the magnetic field due asingle one (index ) of the dipoles £ of a -tuple FFAG magnet is written¡ b1ïî }ð"$Å ¡ 4Qd b ´ b 1"$Å wherein 4Qd bis a reference field, at reference radius 1 2 bCalculation of ¡ b 1"$Å ´The fringe field coefficient ´ b 1including radial dependence of the gap size, whereas ´1 is calculated as described below."$Å"/Å associated with a dipole is computed as in the procedure DIPOLES (eq. 4.4.11),