Misalignment of a tilted csbend
Posted: 29 Dec 2022, 22:33
Hi Michael,
In the latest version of elegant, If I set MALIGN_METHOD to 1 or 2, using M. Venturini's modeling approach, but setting the misalignment errors DX, DY, DZ, ETILT, EYAW, EPITCH all to zero, the tracking of initial zero orbit coordinate through a tilted csbend by design (ETILT is zero, while TILT is nonzero) leads to a large, nonzero orbit coordinate. However, tracking a zero orbit (relative to the design orbit) through an ideal tilted bend by design should yield zero orbit. So I think the result is unphysical.
An example:
lat.lte:
MAL: MALIGN
B0: CSBEND,L=1.6,ANGLE=0.08,E1=0.04,E2=0.04,N_SLICES=20, MALIGN_METHOD=1,TILT="pi 2 /" ! a vertical bend
W1: WATCH, MODE="coordinate", FILENAME="test.w1"
RING: LINE=( MAL, B0, W1 )
track.ele:
&run_setup
lattice=lat.lte
use_beamline=RING
p_central_mev=6e3
rootname=test
&end
&run_control &end
&bunched_beam &end
&track &end
The output of test.w1 is:
Printout for SDDS file test.w1
x xp y yp t p dt particleID
m m s m$be$nc s
----------------------------------------------------------------------------------------------------------------------
-6.417111e-02 8.017110e-02 -6.355474e-02 -8.042834e-02 5.319865e-09 1.174170e+04 -1.716077e-11 1
I traced this to the function "offsetParticlesForEntranceCenteredMisalignmentExact" in malign_mat.c, which includes cz=cos(az+tilt) and sz = sin(az + tilt), and couples the ETILT and the TILT in the calculation of the rotation matrix for the misalignment map.
However, I think a more reasonable approach is the following: let's denote the maps of the entrance & exit misalignment as Mm1 and Mm2, the map of the TILT rotation as Mt, the map of a normal csbend including fringe field as Mb, then the total map should be the concatenation of the following maps with the map at the right-hand-side acting on the coordinates first: Mm2, Inverse[Mt], Mb, Mt and Mm1. Care should be taken when concatenating Mt and Mm1, or Mm2 and Inverse[Mt].
Best,
Zhe
In the latest version of elegant, If I set MALIGN_METHOD to 1 or 2, using M. Venturini's modeling approach, but setting the misalignment errors DX, DY, DZ, ETILT, EYAW, EPITCH all to zero, the tracking of initial zero orbit coordinate through a tilted csbend by design (ETILT is zero, while TILT is nonzero) leads to a large, nonzero orbit coordinate. However, tracking a zero orbit (relative to the design orbit) through an ideal tilted bend by design should yield zero orbit. So I think the result is unphysical.
An example:
lat.lte:
MAL: MALIGN
B0: CSBEND,L=1.6,ANGLE=0.08,E1=0.04,E2=0.04,N_SLICES=20, MALIGN_METHOD=1,TILT="pi 2 /" ! a vertical bend
W1: WATCH, MODE="coordinate", FILENAME="test.w1"
RING: LINE=( MAL, B0, W1 )
track.ele:
&run_setup
lattice=lat.lte
use_beamline=RING
p_central_mev=6e3
rootname=test
&end
&run_control &end
&bunched_beam &end
&track &end
The output of test.w1 is:
Printout for SDDS file test.w1
x xp y yp t p dt particleID
m m s m$be$nc s
----------------------------------------------------------------------------------------------------------------------
-6.417111e-02 8.017110e-02 -6.355474e-02 -8.042834e-02 5.319865e-09 1.174170e+04 -1.716077e-11 1
I traced this to the function "offsetParticlesForEntranceCenteredMisalignmentExact" in malign_mat.c, which includes cz=cos(az+tilt) and sz = sin(az + tilt), and couples the ETILT and the TILT in the calculation of the rotation matrix for the misalignment map.
However, I think a more reasonable approach is the following: let's denote the maps of the entrance & exit misalignment as Mm1 and Mm2, the map of the TILT rotation as Mt, the map of a normal csbend including fringe field as Mb, then the total map should be the concatenation of the following maps with the map at the right-hand-side acting on the coordinates first: Mm2, Inverse[Mt], Mb, Mt and Mm1. Care should be taken when concatenating Mt and Mm1, or Mm2 and Inverse[Mt].
Best,
Zhe