ZGOUBI USERS' GUIDE - HEP

4.4 Optical Elements and related numerical procedures 115@""qTOSCA: 2-D and 3-D Cartesian or cylindrical mesh field mapTOSCA is dedicated to the reading and treatment of 2-D or 3-D Cartesian or cylindrical mesh field maps as delivered bythe TOSCA magnet computer code standard output.The total number of field data files to be read is given by the parameter ¤that appears in the data list following thekeyword. Each file contains the field components , , on an , ) mesh at ¤a given coordinate. (§for 2-D maps, and in this case and are assumed zero all over the map 7 . For 3-D maps with mid-plane symmetry,– ¡ Ž ¡¡|• – ¡ Ž ¡, and thus, the first data file whose name follows in the data list is supposed to contain the median plane field¤dŽ “\(assuming and Ž ¡ – ý\), while the next file(s) contain the next maps in increasing Z order. For arbitrary3-D maps (and in particular, contrary to what precedes without mid-plane symmetry assumption), following MOD value,see below, the total number of maps (whose names follow in the data list) is ¡ , and map number ? ¤Œ @ A?¤(one.q is the †\The field map data files should be formatted following the FORTRAN reading sequence below.DO 1 K = 1, KZOPEN (UNIT = NL, FILE = FNAME, STATUS = ‘OLD’ [,FORM=’UNFORMATTED’])DO 1 J = 1, JYDO1 I = 1, IXIF (BINARY) THENREAD(NL) Y(J), Z(K), X(I), BY(J,K,I), BZ(J,K,I), BX(J,K,I)ELSEREAD(NL,100) Y(J), Z(K), X(I), BY(J,K,I), BZ(J,K,I), BX(J,K,I)100 FORMAT(1X,6E11.2)ENDIF1 CONTINUE{where, ¤§ (binary files, FNAME must begin with ‘B ’ or ‘b ’, a flag ‘BINARY’ will thus be set to ‘.TRUE.’.A flag MOD determines wether Cartesian or Z-axis cylindrical mesh is used. MOD can take various valuesdepending also on the map data file formatting. (To be documented - see FORTRAN subroutine FMAPW and its entriesFMAPR, FMAPR2.) , Ñ ) is the number of longitudinal (transverse horizontal, vertical) nodes of the 3-D uniform mesh. ForThe field¡|– ¡ • is normalized by means of BNORM in a similar way as in CARTEMES. As well thecoordinates X (and Y, Z with 3-D field maps) is normalized with a X-[Y-,Z-]NORM coefficient (usefull to convert tocentimeters, the working units in zgoubi .¡ ¡ ŽAt each step of the trajectory of a particle inside the map, the field and its derivatives are calculated- in the case of 2-D map, by means of a second or fourth order polynomial interpolation, depending on IORDRE(IORDRE = 2, 25 or 4), as for CARTEMES,- in the case of 3-D map, by means of a second order polynomial interpolation with a U U-point parallelipipedicgrid, as described in section 1.4.4.UEntrance and/or exit integration boundaries between which the trajectories are integrated in the field may be defined, inthe same way as in CARTEMES.7 Use MAP2D in case non-zero úüû , úËý are to be taken into account in a 2-D map.