S N Brown 2nd order achromat ; ;example 1 from K.L. Brown, SLAC-PUB-2257 (1979) ;in GICOSY H. Weick, 05.01.2013 ; a focusing cell is defined with correctors ; after 4 such cells the system becomes a 2nd order achromat ; with a unity first order transfer matrix ; R P 9111.8 1 1 ; proton at 9.1 GeV adjusted to get correct Brho P X 0.03 0.003 ; initial phase space 30mm x 3 mrad in x P Y 0.03 0.003 ; initial phase space 30mm x 3 mrad in y D P 0.0 0.01 ; deviation in momentum is 1% for plots O C N M L N ; output mode momentum and path length ;F T H ; C M 1 ; calculation mode fixed equations ;C M 2 ; calculation mode differential algebra for fringe fields ;C M 3 ; calculation mode differential algebra for all ; C O 2 ; calculation order O O 2 ; output order ; S S ; start system ; ; original values from K.L. Brown 1979 ; MQX = 8.02262 /10 ; kG -> T ; MQY = -8.01363 /10 ; kG -> T ; MSX = 1.22642 /10 ; kG -> T ; MSY = -2.38768 /10 ; kG -> T ; ; refitted values in variables MQX = 8.014575556E-01 ; MQY = -8.021127910E-01 ; MSX = 1.226940521E-01 ; MSY = -2.390698123E-01 ; ; ; ;F B MQX MQY ; definition of a fit variables for 1st order fit F B MSX MSY ; definition of a fit variables for 2nd order fit F D ; disable fit ; ;----------------------- B B EINS ; block begin, named "EINS" ; M Q 0.4 MQX 0.1 ; magnetic quadrupole M H 0.2 MSX 0.1 ; magnetic hexapole D L 0.3 ; drift length ; M S 166.782 2.0 0.1 ; magnetic sector field ; D L 0.3 ; M H 0.2 MSY 0.1 ; M Q 0.8 MQY 0.1 ; M H 0.2 MSY 0.1 ; D L 0.3 ; ; M S 166.782 2.0 0.1 ; ; D L 0.3 ; M H 0.2 MSX 0.1 ; M Q 0.4 MQX 0.1 ; ; B E ; block end ;-------------------- ; B I EINS ; apply block defined before B I EINS ; B I EINS ; B I EINS ; ; F1 = ([X,X]-1.0)^2*9999 ; construct variables for 1st order fit F2 = ([Y,Y]-1.0)^2*9999 ; MIN1 = F1 + F2 ; variable to minimize in fit ;P S MIN1,'|',MQX,' ',MQY ; print output to screen ; F4 = ([Y,BD]-0.0)^2*999 ; construct variables for 2nd order fit F5 = ([X,AD]-0.0)^2*999 ; MIN2 = F4 + F5 ; ;P S F4,' ',F5,' - ',MSX,' ',MSY ; F V MIN2 ; define fit variable to minimize F E 1E-20 1000 6 ; fit ; D B 0.14 0.14 100 3 3 1 3 3 3 1 ; draw beams D S 0.14 10 100 3 3 1 3 1 1 ; draw system with beams (top view) D E 0.12 2.0 20 ([X,D]) ; draw expression D E 0.12 3000.0 20 ([X,AA]) ; D E 0.12 20.0 20 ([X,XA]) ; D E 0.12 20.0 20 ([X,AD]) ; D E 0.12 1.0 20 ([A,XD]) ; D E 0.12 200.0 20 ([Y,AY]) ; D E 0.12 50.0 20 ([Y,BD]) ; D E 0.12 1.0 20 ([B,YD]) ; END ; end of calculation ;