Modifications to TEAPOT for Studies of Local Decoupling in the RHIC Arcs Page: 2 of 5
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the positions at the two adjacent HBPM's the interpolated coordinate is computed as
If we call the horizontal position and angle at the VBPM in question x1 and xi, and -
the horizontal positions and angles at the previous and following HBPM's xo, xo, x2,
and 2, we can write the following expressions for the positions at the BPM' s involving
transfer matrix elements:
x1 = Ril~xo + R(2)xo
xi = R 0 zo +RZ"2) o
X= R1) + R122)X.
When we solve these equations for xi as a function of x and x2, the result is
R R12 + 12 11 2 - O2_.
12 R22)Ra2 + R121Ri)2 )2 R1 2)R22(o1) + R(21Rii
The ideal twiss functions (for the machine with no errors) are used to compute the
transfer matrix elements. We use the expression above inside TEAPOT to compute the
interpolated coordinates x1 and, similarly, y1 (at HBPM's).
In order to use this interpolation the user must invoke the command CPLTRK as de-
scribed in the TEAPOT manual, which we now quote:
CPLTRK, KICKX = <value>, KICKY = <value>, THRESHOLD = <value>
This command computes interpolated coordinates at BPM's which measure beam po-
sition in only one plane for use in decoupling. To accomplish this two particles are
tracked, one with initial kick px=kickx and one with py=kicky (in mrad) at the ori-
gin. At each detector of type chcd or cvcd, the coordinates of the tracked particles
and the ideal twiss parameters are recorded. At each detector, the missing coordinate
(in the plane of the tracked particle for greatest accuracy) is obtained by interpolation,
using the ideal twiss parameters and the coordinates of the tracked particle at the adja-
cent detectors on either side. Output files of the ideal-interpolated and error-present ac-
tual coordinates at each chcd and cvcd are written (see the description of the fort.50,
fort.51, fort.60 and fort.61 in Appendix A). These can be used to study the accuracy of
the interpolation in detail. The RMS of the difference between the interpolated and ac-
tual coordinates is computed as a figure-of-merit for the interpolation in each plane. A
warning message is printed whenever the fractional deviation of the interpolated from
the actual coordinate is greater than the user-specified threshold at a detector.
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L., Scachinger & Talman, R. Modifications to TEAPOT for Studies of Local Decoupling in the RHIC Arcs, report, April 2, 1996; United States. (digital.library.unt.edu/ark:/67531/metadc869416/m1/2/: accessed February 21, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.