ZGOUBI USERS' GUIDE - HEP

4.4 Optical Elements and related numerical procedures 85Ãʼn7>bDIPOLES: Dipole magnet £ -uplet [23]DIPOLES works much like DIPOLE as to the field modelling, yet with the particularity that it allows positioning up to 5such dipoles within the angular sector with full aperture ŕ thus allowing accounting for overlapping fringe fields Thisis done in the following way 5The 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 dipoles of the £ -tuple, the 2 effective field boundaries (entrance and exit EFBs) fromwhich the dipole field is drawn (eq. 4.4.11) 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 page65, andNFig. 19)´ ² £: 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 EFBCalculation of the Field Due to a Single DipoleThe magnetic field is calculated in polar coordinates. At all1 in the median plane ( a\), the magnetic field due a"/Åsingle one (index ) of the dipoles of £ a -tuple magnet is written b 1"$Å ¡ 4 d b ´ b 1"$Å ¡q 7Öe 1w{1 2 b 1 2 b > Öe 1†w{1 2 b ¾wherein 4Qd bis a reference field, at reference radius 1 2 b 1¡1 2 >b>¿(4.4.10)KBDBDB, andfield model is proper to simulate for instance chicane dipoles, isochronous or superconducting FFAG magnets, etc.´"$Å is the fringe field coefficient, see below. ThisB2MB1ACN2ACN3B3ACN1ATFigure 19: Definition of a dipole triplet using the DIPOLES or FFAG procedures.Calculation of the Fringe Field Coefficient®In a dipole, with each EFB a realistic extent of the fringe field,