ZGOUBI USERS' GUIDE - HEP

4.4 Optical Elements and related numerical procedures 99Ã6b 1 1Ö®Z4S 1 2 1 ×(4.4.14)FFAG-SPI: Spiral FFAG magnet, £ -upletFFAG-SPI works much like FFAG as to the field modelling, apart from the axial dependence of the field.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 £ q the to (maximum) dipoles of the £ -tuple, the 2 effective field boundaries (entrance and exitEFBs) 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, andNFig. 29)´ ² £: arbitrary inner angle, used for EFB’s positioning: azimuth of an EFB with respect to ACENT: spiral angleFigure 29: 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¡ b1 î }ð"$Å ¡ 4Qd b ´ b 1wherein 4Qd bis a reference field, at reference radius 1 2 bCalculation of ¡ b 1"$Å ´The fringe field coefficient ´ b 1including radial dependence of the gap size, whereas ´"$Å 1 is calculated as described below."$Å"/Å associated with a dipole is computed as in the procedure DIPOLES (eq. 4.4.11),so to simulate the effect of gap shaping of b 1(with normally - but not in practice - ¡ Ñ b). ñ®m 1 "$Å on field fall-off, over the all radial extent of a scaling FFAG dipoleFull field at arbitrary positionFor the rest, namely, calculation of the full field at arbitrary position, analytical calculation or numerical interpolationof the mid-plane field derivatives, extrapolation off median plane, etc., things are performed exactly as in the caseof the DIPOLES procedure (see page 86).