Statistical analysis of multipole components in the magnetic field of the RHIC arc regions

The existence of multipolar components in the dipole and quadrupole magnets is one of the factors limiting the beam stability in the RHIC operations. Therefore, the statistical properties of the non-linear fields are crucial for understanding the beam behavior and for achieving the superior performance in RHIC. In an earlier work [1], the field quality analysis of the RHIC interaction regions (IR) was presented. Furthermore, a procedure for developing non-linear IR models constructed from measured multipolar data of RHIC IR magnets was described. However, the field quality in the regions outside of the RHIC IR had not yet been addressed. In this paper, we present the statistical analysis of multipolar components in the magnetic fields of the RHIC arc regions. The emphasis is on the lower order components, especially the sextupole in the arc dipole and the 12-pole in the quadrupole magnets, since they are shown to have the strongest effects on the beam stability. Finally, the inclusion of the measured multipolar components data of RHIC arc regions and their statistical properties into tracking models is discussed