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104 4 DESCRIPTION OF THE AVAILABLE PROCEDURES7>^^2 >22¡q¡q ^^2¡ >q^^>^^>¡\q¡\q^¡ >\q7ÊMULTIPOL: Magnetic multipoleThe simulation of multipolar magnetic field( ¡ @ ), sextupolar ( ¡ U ), etc., up to 20-polar ( ¡ qby MULTIPOL proceeds by addition of the dipolar ( ¡ q ), quadrupolar\) components, and of their derivatives up to fourth order, following¡ @ ¡ U óBDBEB*¡ @¡ U BDBEBr ^^ §^ §^ §^ §^ §¡ @¡ UóBDBEBretc.^ § ^ ^ § ^ ^ § ^ ^ § ^ ^ § ^ in section 1.3.6.The independent components ¡ q , ¡ @ , ¡ U , ..., ¡ q\and their derivatives up to the fourth order are calculated as describedThe 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 · 7ˆ4) at exit, such that the extent is ³³ ³ ¢ >( ³ Š V¢ T, ..., ³ Š V¢ 7ˆ4)Š Vat entrance ¢ > and ( Œ V , ..., ³ Œ V· 7ˆ4) at exit.V³ ³ Œ· >· Tfield for the multipole component is considered as a sharp edge field. In sharp edge field model, the wedge angle vertical" qIf 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). If ¢ b³ (· b C\) ( @†\§ Œ is\), the entrance (exit) fringefirst order focusing effect (if ¡ q is non zero) is simulated at magnet entrance and exit by a kick ¥applied to each particle (¥, ¥at the EFB, the local horizontal bending radius and Êhorizontal angle T).,are the vertical angles upstream and downstream the EFB, the vertical particle positionthe wedge angle experienced by the particle ; depends on theÊ> ¥7 w, 7 f¡ )-Overlapping of fringe fields inside the optical element is treated separately for each component, in the way described inQUADRUPO.Any multipole component ¡ can be rotated independently by an angle 1 §# around the longitudinal § -axis, for thesimulation of positioning defects, as well as skewed lenses.Magnet (mis-)alignement is assured by KPOS. KPOS also allows some degrees of automatic alignement useful for periodicstructures (section 4.6.5).
4.4 Optical Elements and related numerical procedures 105˜4 ¡T 4 1£w£>Ž ¡ C\£ 4¦ U ¡|–>£>wT U wT>>>>sTwTOCTUPOLE: Octupole magnet (Fig. 30)The meaning of parameters for OCTUPOLE is the same as for QUADRUPO. In fringe field regions the magnetic¡ fieldand its derivatives up to fourth order are derived from the scalar potential approximated to the 8-th order in§©"$Œ"[ and §©"$Œ"[ uo n) )\ @) ) ) )\ §G.with£ 4Outside fringe field regions, or everywhere in sharp edge dodecapole ( ³ Š ³byC\) , ¡ §#"kS"e in the magnet is givenŒ£ 4¦¡|• ›Figure 30: Octupole magnet
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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
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4.3 Declaration of options 43\P4.3
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4.3 Declaration of options 45END or
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4.3 Declaration of options 47· £
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4.3 Declaration of options 49{ww{{q
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4.3 Declaration of options 51GASCAT
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Page 57 and 58: 4.3 Declaration of options 57RESET:
Page 59 and 60: 4.3 Declaration of options 59if qî
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Page 65 and 66: u2 >04.4 Optical Elements and relat
Page 67 and 68: 4.4 Optical Elements and related nu
Page 103: 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
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154 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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