[FFA_CEBAF_Collab] Lambertson simulations

[Jay Benesch]

Colleagues, 

This is what I was immersed in most of the day, not noticing the time.  

Six of the 18 fine-mesh models have solved.  Attached is a spreadsheet
with harmonics at 0.25 cm intervals along orbits starting 2.1 cm, 0 and
-2.1 cm with respect to linac height aka zero in this model.  I sum them
directly at the top and normalize to 1 cm radius as I had to use other
radii to keep the circles from touching the steel.  The vertical orbits
for A and C are interesting: they aren't flat, moving almost a mm
towards the B plate.

I arrived at the orbits as follows.  Use the ac9 sim, ~20 GeV, as it's
what I expect to be ultimate energy ceiling.  Adjust beam energy until angle
produced at large distance, z=[300,500] is 1.601 degrees vs 1.600
desired.  Resulting energy 2.008E10 V vs 1.992E10 desired.  Close
enough.  I then propagated 2.008E10 V electron through A, B and C holes
with Opera recording the orbit.  I took the 2499 (x,y,z) locations for
each beam and created a command file which ultimately resulted in the
values in the spreadsheet.  (Opera drops the starting value in the
location file  for reasons I don't understand. I could add 0.25 cm to
starting Z and ask for 2501 points but I don't bother.)

I was surprised when I compared the results when asking for 5 harmonics
to be fit vs 10.  They are identical for the first 5.  This suggests to
me that Opera is always computing 10 harmonics and simply displaying the
first N requested.  Fourier decomposition isn't supposed to work this
way.  I vaguely remember making the same discovery over a decade ago.  
I include ten harmonics only for the 22 GeV (ac10) simulation, five for all the others. 

Opera is taking an immense amount of time on the low pass simulations because the steel is in the curved region of the BH curve and the mesh generator did not do the best job.  3DS support provided some suggestions to improve meshing but I wanted to run all of these with the same mesh.  Check back at the end of the month. 

Nothing surprising to me: all the septa I've modeled have such ugly content.  https://iopscience.iop.org/article/10.1088/1748-0221/13/11/T11001/meta FEM models and Fourier decomposition of three thick septa J. Benesch Published 12 November 2018

Jay
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