Simulation of Proposed On-Line Third Order Resonance Correction Schemes Page: 2 of 13
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December 20, 2006
Simulation of proposed on-line
third order resonance correction schemes
Y. Luo, J. Bengtsson, W. Fischer, and D. Trbojevic
Brookhaven National Laboratory, Upton, NY 11973, USA
The preparation for the next polarized proton run in the Relativistic Heavy Ion Collider (RHIC) includes
on-line third order resonance correction schemes. This is a report on simulations to evaluate several proposed
schemes. The nonlinear chromaticities and the first order resonance driving terms are calculated before and
after each correction. Each correction scheme use different sextupole families with corresponding parameter
optimization. The use of the are sextupole families versus interaction region sextupoles is discussed.
To increase the tune space available for beam-beam generated tune spread, in RHIC polarized proton opera-
tion, both the nonlinear chromaticity and the third order resonance corrections at the current working point
are desirable . At the current working point the fractional tunes are constraint by resonances at tunes of
0.666 and 0.7. The resonance at 0.7 affects both the luminosity lifetime and the polarization.
There are a total of 144 sextupole magnets in the 6 arcs of each RHIC ring. In previous runs, only
two families, one focusing and one defocussing, were used for the first order chromaticity correction. In an
attempt to correct the third order resonance driving term h30000 in Run-6, we split the are sextupoles into
12 sub-families since as there are a total of 12 are sextupole power supplies in each ring . This correction
scheme allowed us to control the 2 first order chromaticities, and 5 complex first order resonance driving
terms (5*2) from sextupoles. This attempt was hampered by the unsuccessful measurement of the h30000
driving term using AC dipole.
In the next RHIC run, the number of are sextupole power supplies is doubled from 12 to 24 to correct
the nonlinear chromaticity. There are 4 sextupole power supplies in each arc. In Ref. , the nonlinear
chromaticity correction scheme with six families was recommended. Later on, S. Tepikian proposed a 8-
family scheme for the nonlinear chromaticity correction . In this scheme, each outer or inner are has
4 sextupole families, and all outer or inner arcs have the same sextupole strength patterns. An on-line
nonlinear chromaticity correction scheme with these 8 families, based on the off-momentum tune response
matrix, was proposed and will be implemented for the next run . This scheme does not take into account
any resonance driving term correction.
It is also possible to use the sextupole correctors in the interaction regions (IRs) to reduce the third order
resonance driving terms . These IR correctors were designed to locally correct the multipole field errors
from the triplets and separation dipoles [7, 8]. Currently, only the 4 sextupole correctors in IR6 and IR8
have power supplies. During the RHIC Run-6, these 4 sextupole correctors were paired into two families, and
adjusted to minimize the beam decay as the horizontal tune of the non-colliding beam was approaching the
third order resonance line. However, after bringing the beams into collisions with the found best corrector
strengths, no clear lifetime improvement was established. This scheme does not consider the compensation
of other driving terms and chromaticities. To be able to better control the sextupole's first order driving
terms and first order chromaticities, additional sextupole correctors in the IRs other than IR6 and IR8 are
So far, only the resonance driving term h30000 could be measured with coherent turn-by-turn (TBT)
beam position monitor (BPM) data. The technique to measure h30000 with AC dipole excitation is being
established at RHIC. The term h30000 can be corrected on line by choosing an appropriate correction scheme
using are sextupole families or IR sextupole correctors. Other systematical driving terms contributed by the
are sextupoles can also be corrected.
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Y., Luo; Bengtsson, J.; Fischer, W. & Trbojevic, D. Simulation of Proposed On-Line Third Order Resonance Correction Schemes, report, January 1, 2007; United States. (digital.library.unt.edu/ark:/67531/metadc841340/m1/2/: accessed January 19, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.