3 Non-linear Dynamics in Accelerators
95
use my_analysis
type(my_taylor) z(3)
type(normalform) NORMAL
type(my_map) M,id
real(dp) L,DL,k1,k3,fix(3)
! 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(2) =z(2)*k3*z(1)**3/1+z(3) ! add
octupole kick
z(1) =z(1)+LC*z(2)
z(1)
= z(1)+DL/2*z(2)
z(2)
= z(2)-kd*DL*z(1)/(1 + z(3))
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 ex2
(0,0,0) 0.9369211296691E-01
(0,0,1) -0.9649503806747E-01
(2,0,0) 0.5383744464902E+02
(0,2,0) 0.5383744464902E+02
(0,0,2) 0.1009289258270E+00
(2,0,1) 0.2116575633218E+02
..........
(1,0,0) 0.9083165810508E-01
(0,1,0) 0.1667704101367E+03
(1,0,1) 0.1238115392391E+01
(0,1,1)-0.3527698956093E+02
(3,0,0)-0.1578216232118E+01
(2,1,0)-0.1429958442579E+02
(1,2,0)-0.4318760015031E+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
(3,0,0)-0.1505298087837E-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
The added octupole kick results in a
detuning with amplitude of dQ/dJ = 53.837