Required Accuracy of the RHIC Circumference

The ideal RHIC design circumference is: CRHIC = 3833.845000 m. The RHIC accelerator complex consists of two rings, "Blue" and "Yellow" in which two counter-rotating beams of particles will collide head-on at up to six interaction regions. There will be 57 bunches of particles filling each of the two rings (or 114 bunches, in a possible future upgrade). The number 57 is derived from the design ratio of RHIC and AGS circumferences, CRHIC/CAGS=19/4, multiplied by the AGS number of 12 rotating bunches. The AGS circumference was obtained from the revolution frequency measurements at the AGS top energy. A report from the AGS experiments shows that the regular AGS circumference is CAGS = 807.10475 m. The extraction orbit was reported to be 807.12526 m. Each AGS cycle has twelve proton bunches or three heavy ion bunches. The RHIC circumference was obtained from the AGS circumference as: CRHIC = 19/4 * 807.1253 m = 3833.845 m. The actual RHIC central circumference propagates through the center of the quadrupoles and through the center of the curved bending magnet beam pipes. It will be different from the design circumference due to surveying errors in positioning the magnets. The ratio of RHIC and AGS central circumferences will not be exactly equal to 19/4. There are also unavoidable errors in defining and measuring the network of the ring surveying monuments. Error analysis of existing network monuments indicates that the average error in measurements of the distances between the twelve monuments is ΔSavg = 0.34 mm, which implies that an error of order 1.2 mm in the RHIC circumference may already exist. Any kind of beam transfer from the AGS to RHIC requires correction of the main bending buss, and/or of the rf frequency, in one or both accelerators. The actual synchronous reference orbit of an accelerator (the "closed orbit" in 6 phase space dimensions, including synchrotron oscillations) ideally has the same circumference as the central orbit, since the beam is then in the center of the aperture, where the magnetic field quality is highest. Any deviation from the center of the aperture puts the beam into a region of the magnetic field where the magnetic multipoles have higher values, lowering the beam dynamical aperture. In practice the synchronous orbit must be made to deviate from the central orbit, in order for injected bunches to be free from oscillations in the RHIC rf bucket. Studies of RHIC long term particle tracking at the injection energy, as well as at other energies, have been performed. The latest tracking results were performed with alignment errors of quadrupoles and dipoles, with random and systematic multipole errors within the magnets, and with the synchrotron oscillations. Results from ten different random seeds at injection were obtained after the orbit was corrected with the correction element system. The rms of the closed orbit errors of the ten seeds were ranging from Xrms = 0.124 to 0.204 mm and from Yrms = 0.139 to 0.189 mm. This implies that the length of the closed orbit during tracking was not the ideal central orbit (ΔCRHIC ≈ 1 mm).