94
W. Herr and E. Forest
! set up initial parameters
my_order=4 ! maximum order
4
fix=0.0 ! fixed point
id=1
z=fix+id
! set up lattice parameters
LC=62.5 ! half cell length
DL=3.0 ! quadrupole length
kf= 0.00295278 ! strength
kd=-0.00295278 ! strength
z(1)
= z(1)+DL/2*z(2)
z(1)
=z(1)+LC*z(2)
enddo
call print(z(1),6)
call print(z(2),6)
M=z ! overloads coefficient with the map
normal=m ! overloads map with normal
form
write(6,*) normal%tune, normal%dtune_da
end program ex1
(0,0,0) 0.9369211296691E-01
(0,0,1) -0.9649503806747E-01
(1,0,0) 0.9083165810508E-01
(0,1,0) 0.1667704101367E+03
(1,0,1) 0.1238115392391E+01
(0,1,1) -0.3527698956093E+02
(1,0,2) -0.1567062442887E+01
(0,1,2) 0.3478356898518E+02
(1,0,3) 0.1896009493384E+01
(0,1,3) -0.3429014840944E+02
(1,0,0) -0.5139797664004E-02
(0,1,0) 0.1572511594903E+01
(1,0,1) 0.1027959532801E-01
(0,1,1) -0.5648018984066E+00
(1,0,2) -0.1541939299201E-01
(0,1,2) 0.5570922019106E+00
(1,0,3) 0.2055919065602E-01
(0,1,3) -0.5493825054146E+01
From the elements in the Taylor expansion,
the result for the matrix per cell:
x f = 0.09083x i + 166.77p i
p f = −0.00514x i + 1.5725p i
The output from the normal form analysis
are (per cell!):
Tune = (0,0,0) = 0.093692
Chromaticity = (0,0,1) = -0.096495
program ex2
use my_own_da
do j = 1,8
z(1) = z(1)+DL/2*z(2)
z(2) = z(2)-kf*DL*z(1)/(1 + z(3))
z(1) = z(1)+DL/2*z(2)