Ring Injection/Extraction centroid/floor coordinates calculation

[nicholas_sereno]

Michael,

I am modelling extraction from a ring and am trying to make sure I get the beam centroid and floor coordinates correct. Here is the issue: when I model the kickers and septa as CSBENDs. Any quads between kickers and septa are assumed by elegant to be centered on the reference trajectory when they have offsets due to the upstream kickers. So, I model this by using MALIGN with FLOOR=0 to temporarily shift the reference trajectory back to the original ring axis so the quad kicks are computed correctly. Then I do another misalignment after the quad to center the trajectory on the new reference trajectory. There is a small difference due to the quad kick between the floor coordinates output and centroid trajectory when I do this. In the end, I want the floor coordinates of each element to be correct with the correct angle after extraction is complete.

Perhaps I am doing this incorrectly and should use HKICKs instead but they don't move the reference trajectory. Or, perhaps there is an example that shows how to do injection/extraction to/from a ring consitently between floor coordinates and centroid trajectory calculations.

Attached are the elegant input files and here is sddsplot command to plot floor coordinates and centroid trajectory. In this example I left the septa out and only have kickers and quads in the beamline.

sddsplot -topline="RCS Extraction Beamline Centroid Tracking Vs Floor Coordinates " \
-title="Kickers and Septa Defined as CSBENDs" \
-mode=y=offset \
-col=s,Profile RCS_EXT_PULSED.mag -overlay=xmode=normal,yfactor=0.2,yOffset=-0.10 \
-col=s,Cx "-leg=spec=Centroid" RCS_EXT_PULSED.cen -graph=symb,sca=2,conn,type=0,subtype=0 \
-col=s,X "-leg=spec=Floor Coords-X" RCS_EXT_PULSED.flr -graph=symb,sca=2,conn,type=2,subtype=2

Thanks,
Nick

[michael_borland]

Nick,

For injection modeling, what I typically do is to model the septum as a bending magnet, taking it to be the last element in the transport line. I then have a MALIGN element that offsets the beam centroids to put things into the ring coordinate system. This allows tracking the injected beam with the correct initial centroid. Once the beam is in the ring, the kickers are modeled with an EHKICK, EVKICK, BUMPER, etc.

In the ring model, the septum appears as a drift space. I compute the floor coordinates of the exit of the septum in the ring frame, then use the parameters of the MALIGN element to compute the floor coordinates of the end of the transport line. I then use elegant's floor-coordinate matching capability to adjust the transport line as needed to match those coordinates.

To check the result, one can insert the MALIGN element at the end of the transport line with FLOOR=1. You should recover the floor coordinates of the end of the septum in the ring coordinate system.

--Michael

[nicholas_sereno]

Thanks Michael,

Makes sense.

Nick

[nicholas_sereno]

Michael,

One important thing I left out of this discussion on injection/extraction modelling is dispersion when one misaligns the beamline. Your suggestion works very well as far as understanding centroid and floor coordinates calculations with the extracted or injected beam displaced in ring quads. Apply a single misalignment at the septum to transform from the ring to transport line reference system. However, the dispersion I think needs to be adjusted as well at least for the extraction case. The kicker generates a dispersion opposite in sign to the septa since the kicker is in the ring coordinate system and does not change the reference trajectory upstream of the septum. How does one fix the dispersion when using MALIGN at the septum?

Thanks,
Nick