Monte-Carlo Study of the (102°,90°) Physics Optics for LEP

A new physics optics with phase advances Px 102 ° and Py 90 ° in the arc cells was recently tested in LEP. This note summarises the main results from the optics evaluation procedure that is now routinely applied to new LEP optics. This includes the study of the orbits, optics and dynamic apertures of an ensemble of imperfect machines with corrections similar to those applied in Introduction To evaluate the potential performance of a new optics for LEP, it is necessary to perform calculations of orbits, optics, beam parameters and dynamic apertures on an ensemble of imperfect machines. Over the last few years, a standard procedure has evolved for this purpose. For the present note, it has been applied to a "squeezed" (102°,90°) optics at 91.5 GeV. This optics is very similar to the optics that was subsequently tested in operation (the differences are discussed in Section 1.2). The procedure followed is briefly outlined in the following subsection. Full technical details of the methods and computations will be published elsewhere. Only a selection of the most relevant results is presented in this note. Many others can be extracted from the database generated by the evaluation procedure. 1.1 Outline of computational procedure In outline, the optics evaluation procedure consists of the following steps, using the program MAD [1] for the optical calculations: Ë The optics, nominal beam energy, detailed RF configuration and any other conditions or parameters defining the machine configuration are chosen. Ë The linear betatron coupling introduced by the solenoids is corrected using the usual tilted quadrupoles. Ë An ensemble of 30 imperfect machines are generated, with random field errors, tilts and misalignments applied to all magnetic elements. The experimental solenoids and the sliced-up quadrupoles embedded in their fields are given special treatment to ensure the proper correlations among their random displacements and tilts. The magnitudes of the random errors have been chosen to reflect the real tolerances in LEP; in previous studies they have produced a good statistical correspondence between the simulated machines and the well-optimised operational state of LEP Ë "Collimators" are inserted in many elements in order to simulate the vacuum chamber for tracking. Ë Electrostatic separators were not excited in this case. Ë The average orbit in each machine is corrected down to an RMS, as measured in the pickups, of 0.6 mm in the horizontal plane and 0.4 mm in the vertical plane. All correctors are used and various tricks are applied to find the closed orbit. This helps to ensure that the machine is not declared unstable in cases where the closed orbit is merely hard to find. However no attempt is made to simulate the operational procedure of finding a "golden orbit". Ë The vertical beta-functions Ey are corrected to their nominal values at each IP using a matching procedure similar to that applied in operation. Ë The tunes of the positron beam are corrected to their nominal values using the QF and QD strings. The tunes of the electrons are different. Ë Physically equivalent imperfect machines are constructed for the positrons and electrons (in MAD this step is not trivial). Optics and beam parameter calculations are carried out for each machine and the results are condensed into a database of Mathematica functions. Ë A 4-dimensional dynamic aperture scan (usually with fairly low resolution in the spherical polar angles in action space) is carried out for each machine. As usual for LEP, the initial phase of synchrotron oscillations has to be scanned. Tracking is done with the deterministic part of synchrotron radiation in every element (so radiation damping and other effects arise naturally). The dynamic aperture surfaces are also saved in the database. In the present study, the dynamic apertures were computed only for the positrons. MonteCarloStudySummary.nb 2