Study of Dynamic Aperture for PETRA III Ring K. Balewski, W. Brefeld, W. Decking, Y. Li DESY
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1 Stud of Dnamc Aprtur for PETRA III Rng K. Balws, W. Brfld, W. Dcng, Y. L DESY FLS6 Hamburg PETRA III Yong-Jun L t al.
2 Ovrvw Introducton Dnamcs of dampng wgglrs hoc of machn tuns, and optmzaton of stupol confguraton Smulaton rsults FLS6 Hamburg PETRA III Yong-Jun L t al.
3 Introducton Man paramtrs of PETRA III paramtrs valu Enrg (GV) 6 Numbr of nsrton dvcs 13 Ma. currnt (ma) >1 Horzontal mttanc (nm rad) 1. Vrtcal mttanc (nm rad).1 FLS6 Hamburg PETRA III Yong-Jun L t al.
4 Laout of storag rng S1 FLS6 Hamburg PETRA III Yong-Jun L t al.
5 Nw octant DBA optcs Dsgn rqurmnts (usrs): 5 & m long nsrton dvcs low and hgh b Dsgn constrans (machn): low ξ, low ε Dsgn consquncs: D small > no stupols FLS6 Hamburg PETRA III Yong-Jun L t al.
6 Old FODO octant FLS6 Hamburg PETRA III Yong-Jun L t al.
7 Dampng wgglr scton FLS6 Hamburg PETRA III Yong-Jun L t al.
8 Old Octant ll Optons 7 o FODO cll Lattc unchangd Dampng wgglr ndd to rach 1nmrad 9 o short FODO cll Lattc and hardwar nw Small dsprson, strong focusng lads to strong chromatc stupols TME cll Lattc nw Hardwar rusd Small dsprson, strong focusng lads to strong chromatc stupols FLS6 Hamburg PETRA III Yong-Jun L t al.
9 omparson of lattcs (1) FODO 7 Short FODO 9 TME FLS6 Hamburg PETRA III Yong-Jun L t al.
10 omparson of lattcs () Dnamc Aprtur for njcton: A [mm mrad] dg short FODO TME 7dg FODO phs. Aprtur A [mm mrad] FLS6 Hamburg PETRA III Yong-Jun L t al.
11 Dnamcs of dampng wgglrs Fttng wgglr fld map nto analtcal formula; onstructng transformaton matr for lnar optcs match; onstructng nonlnar map for smulaton (dnamc aprtur calculaton). FLS6 Hamburg PETRA III Yong-Jun L t al.
12 Wgglr Fld alculatons B B B z r B - n B B B 1,3,..., snh( cosh( cosh( )snh( )cosh( )snh( π + )cos( z) )cos( z) )sn( z) r Bn fn, n,, n, N (, n,, z) ( ), n +, n n B (Tsla) B (G) Halbach modl fld map z (cm) 15.5 fld map Halbach modl Longtudnal Fld profl Wgglr Dsgn (Novosbrs) L.m B1.5T Halbach Formula 15.5 FLS6 Hamburg PETRA III Yong-Jun L t al Transvrs Fld profl (cm)
13 Partcl Moton n Wgglr Fld ~ H ( z) Don t cancl aftr on prod 4 th ordr Hamltonan of planar Wgglr B sn z ' Ldpol p ' + ' B + sn p B p B + 6 p sn z sn + L( hghr z z 4 ordr) FLS6 Hamburg PETRA III Yong-Jun L t al. ' 4 Ldrft spac Lquadrupol Lstupol Loctupol ancl aftr on prod
14 Lnar map of wgglr M ( z, z + Δz) M M' M M' + Δz ' +Δz + Δz ' Δz ' Δz B (1 + δ ) ' + L (1 + δ ) ~ : ΔzH ( z): B B (1 + δ ) p p p ( z + ) ( z + ) ( z + ) + L + L + L FLS6 Hamburg PETRA III Yong-Jun L t al. sn sn sn
15 FLS6 Hamburg PETRA III Yong-Jun L t al. Lnar transformaton matr of wgglr + Δ Δ Δ Δ + Δ Δ ) sn( ) sn( 1 17 z p B z z K z z K m z p B z z sn( ) 17 + Δ z p z B m T z ),1, ',, ',, ( δ r ( ),, sn ) (1 δ + + z p B K
16 Dsprson of on prod FLS6 Hamburg PETRA III Yong-Jun L t al.
17 Nonlnar Map: Partcl Tracng Rung-Kutta Intgraton through fttd fld maps (nonsmplctc) Smplctc Intgraton through fttd fld maps (Y. Wu) Numrcal Gnratng Functon from numrcal R-K ntgraton (M. Schr) F(q,p f,q,p f ) a lmn q p fl q m p n f p f (mrad) p f (mrad) Rung Kutta Smplctc Intgraton Gnratong Functon (mm) (mm) FLS6 Hamburg PETRA III Yong-Jun L t al.
18 Th comparson of dffrnt tracng mthods Tracng mthod Rung-Kutta mthod Smplctc ntgraton Gnratng functon smplctct spd accurac no slow hgh s slow hgh s fast hgh FLS6 Hamburg PETRA III Yong-Jun L t al.
19 On-turn-map; Normal Form to optmz stupol confguraton oncatnaton of on-turn-map; Norm form tchnqu to construct 1 st ordr nonlnar coffcnts; Mnmzaton of thos coffcnts and tuns dpndnc of ampltuds. FLS6 Hamburg PETRA III Yong-Jun L t al.
20 FLS6 Hamburg PETRA III Yong-Jun L t al. 1 st ordr nonlnar coffcnts of stupol D -3 D 3 D 3 D 3 D 3 - D 3 - D 3 - D 3 D ( ) ( ) ( ) ( )
21 Optmzaton rsults Four famls of stupol ar usd for chromatct corrcton; Harmonc stupol at dsprson-fr scton dos NOT hlp mprov DA. FLS6 Hamburg PETRA III Yong-Jun L t al.
22 Smulaton Smulaton cod s modfd vrson SIXTRAK (W. Dcng and Y. L) Smulaton ncludng Dampng wgglrs (numrcal GF); 13 nsrton dvcs wth tpcal paramtrs (analtcal GF); Multpol rrors of all lmnts (1-1 th ordr thn-lngth cs, ~.5mm orbt dstorton and ~1% bta-bat); 7mm phscal aprtur lmts of undulators gap. FLS6 Hamburg PETRA III Yong-Jun L t al.
23 Idal machn wth Q36.95, Q Oct-5 11:1:4 19-Oct-5 11:1:4 [mm] [mm] A [mm mrad] A [mm mrad] FLS6 Hamburg PETRA III Yong-Jun L t al.
24 Frqunc map.4 19-Oct-5 11:1:4.35 ν ν FLS6 Hamburg PETRA III Yong-Jun L t al.
25 Dnamc aprtur of PETRA III rng FLS6 Hamburg PETRA III Yong-Jun L t al.
26 On random sd.4 19-Oct-5 17:35:59 19-Oct-5 17:35:59 ν A [mm mrad] ν A [mm mrad] FLS6 Hamburg PETRA III Yong-Jun L t al.
27 Than ou for our attnton! FLS6 Hamburg PETRA III Yong-Jun L t al.
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