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94 4 DESCRIPTION OF THE AVAILABLE PROCEDURES¢ @q^^22ŠŠ¢2q¢q ^^¢ >qÑ^^>Á^Áq^>¢\q>^¢¡\q7 X^¢ >¢ \qqELMULT: Electric multipoleThe simulation of multipolar electric field( ¢ U ), etc., up to 20-polarproceeds by addition ofthe dipolar , quadrupolar ( ), sextupolarŠ ¢components, and of their derivatives up to fourth order, following@ \¢ @ ¢ U óBEBDBIŠ ¢ @¢ UóBEBDBI§ >Q2 ^^ §^ §^ §^ §¢ @¢ UóBDBEB*^ § ^ etc.^ § ^ ^ § ^ ^ § ^ ^ § ^ The independent components q to ¢ q\and their derivatives up to the second order are calculated by differentiating thegeneral multipole potential given in eq. 1.3.5 (page 20), followed by a ¢ X rotation about the § -axis, so that the so definedçright electric multipole of order , and of strength [19, 20]žX @ q> wX1˜ 4X˜ X = potential at the electrode, 1 4effect than the right magnetic multipole of order ž and strength Ñ X = radius at pole tip, Á = relativistic Lorentz factor of the particle) has the same focusing¡ = field at pole tip, = particle¡., Xrigidity, see MULTIPOL).4 ¡.,© @Ÿž Such rotation of the multipole components is obtained following the procedure described in section 1.5.4.1 X(¬The 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 · 7¸4) at exit, such that the fringe field extent is ³³ ¢ >( ³³ ¢ T, ŠºV ŠºV¢ ¢ 7ˆ4..., ) at entrance and > ( ³ ŒLV , ..., ³ ŒíV· 7¸4) at exit.ŒíV³ ³ ŠìV· >· TIf 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).³§ Œ isfield." qIf ¢ b “\ (· b ý\) ( \), the entrance (exit) fringe field for multipole component is considered as a sharp edgeOverlapping of fringe fields inside the element is treated separately for each component, in the way described in QUADRUPO.Moreover, any multipole component ¢ can be rotated independently by an angle 1 §# around the longitudinal § -axis,for the simulation of positioning defects, as well as skewed lenses.Use PARTICUL prior to ELMULT, for the definition of particle mass and charge.
4.4 Optical Elements and related numerical procedures 95©¢q©Figure 27: An electric multipole combining skew-quadrupoleR and skew-octupole¢ @ ‡” 1 @ ¢}R ‡1„R " \components ( q¢\ "\) [20].¢ U ¢ N BEBDB \}
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CEA DSM DAPNIA-02-395 (2002)ZGOUBI
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Table of contentsPART A Description
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PART ADescription of software conte
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8¤¥ PARTICUL Particle characteris
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10ELECTROMAGNETIC ELEMENTSDecapoleD
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!!%" && 131 NUMERICAL CALCULATION
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1.2 Integration of the Lorentz Equa
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1.2 Integration of the Lorentz Equa
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4Ž ^ ˜ ¡§ ^"- ^ ˜ ¡ ^¡wTGT
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in fourth order. The coefficients
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4 ´ ´""4§> ´4 >4>1.4 Calculati
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A cylindrically symmetric field can
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Introducing also ¡The derivatives
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30 3 SYNCHROTRON RADIATION¾ÍôVT
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32 3 SYNCHROTRON RADIATIONÉ Éwher
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354 DESCRIPTION OF THE AVAILABLE PR
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4.2 Definition of an Object 37where
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4.2 Definition of an Object 39\Pqî
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4.2 Definition of an Object 41¹q
Page 43 and 44: 4.3 Declaration of options 43\P4.3
Page 45 and 46: 4.3 Declaration of options 45END or
Page 47 and 48: 4.3 Declaration of options 47· £
Page 49 and 50: 4.3 Declaration of options 49{ww{{q
Page 51 and 52: 4.3 Declaration of options 51GASCAT
Page 53 and 54: 4.3 Declaration of options 53·{N$
Page 55 and 56: 4.3 Declaration of options 55PARTIC
Page 57 and 58: 4.3 Declaration of options 57RESET:
Page 59 and 60: 4.3 Declaration of options 59if qî
Page 61 and 62: 4.3 Declaration of options 61P4©@4
Page 63 and 64: 4.3 Declaration of options 63:£¨
Page 65 and 66: u2 >04.4 Optical Elements and relat
Page 67 and 68: 4.4 Optical Elements and related nu
Page 93: 4.4 Optical Elements and related nu
Page 123 and 124: 4.5 Output Procedures 123¨ ¢ < ¤
Page 125 and 126: 4.5 Output Procedures 1254·444"4HI
Page 127 and 128: 4.5 Output Procedures 127PICKUPS: B
Page 129 and 130: 4.5 Output Procedures 129wSPNPRNL,
Page 131 and 132: 4.5 Output Procedures 131TWISS: Cal
Page 133 and 134: 4.6 Complementary Features 133U@©@
Page 135: 4.6 Complementary Features 135¢ww@
Page 139 and 140: Keywords and input data formatting
Page 141 and 142: Keywords and input data formatting
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146 Keywords and input data formatt
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Examples 231oÑwü¦INTRODUCTIONSev
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2331 MONTE CARLO IMAGES IN SPES 2Fi
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235********************************
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237zgoubi data file.800 MeV/c KAON
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2393 IN-FLIGHT DECAY IN SPES 3Figur
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241Excerpt of zgoubi output : histo
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243Excerpt of zgoubi output : first
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245zgoubi data file (begining and e
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247zgoubi data file.MICROBEAM LINE,
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2499 HISTO HISTOGRAHISTOGRAMME DE L
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253INTRODUCTIONThe basic zgoubi FOR
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REFERENCES 255References[1] F. Méo
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Indexacceleration, 56, 58, 74, 155,
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