A Lattice for a Hybrid Fast-Ramping Muon Accelerator to 750 GeV

We describe a lattice for accelerating muons from 375 GeV to 750 GeV. The lattice is a fast-ramping synchrotron with a mixture of fixed-field superconducting dipoles and warm dipoles, so as to have a high average bending field while still being able to rapidly change the average bending field as the beam momentum increases. For a 1.5 TeV center of mass muon collider, muons must be rapidly accelerated to 750 GeV. To accomplish this efficiently, we wish to make as many passes through the RF cavities as possible, while keeping the average RF gradients sufficiently high to avoid excess muon decays. A synchrotron where the magnets are very rapidly ramped has been envisioned as one option to accomplish this. The entire acceleration cycle takes place in less than 1 ms, presenting a technological challenge for the magnets. Clearly superconducting magnets cannot be ramped on this time scale, so instead room-temperature magnets will be ramped. To keep losses low, dipoles can use grain-oriented silicon steel, but quadrupoles will probably need to use more conventional steel, giving a lower maximum field for these high ramping rates. If we want to have a large average RF gradient and simultaneously make a large number of passes through the RF cavities, the average bending field must be high. To achieve such a large bending field while rapidly ramping magnets, it has been proposed to use a hybrid lattice consisting of interleaved superconducting dipoles and bipolar ramped dipoles. Due to the large single-bunch current and the relatively small apertures we desire (both because we would like to use high-frequency RF, and because power requirements and heating will be more reasonable for smaller aperture ramped magnets), collective effects are expected to be very significant. To reduce their effects, we propose to have strong synchrotron oscillations (a synchrotron tune of over 1). To have such a high synchrotron tune, a large number of superperiods are needed. Putting together all of these requirements, a set of requirements for a final acceleration stage for a muon collider has been proposed in Table 1. These basic requirements and some basics of the lattice structure for such a machine were decided upon at a workshop in April 2011 at the University of Mississippi, Oxford. Each superperiod consists of 6 arc cells, two sets of 2-cell dispersion suppressors, and three straight cells, for a total of 13 cells. Every cell has a FODO lattice structure. Each cell has a phase advance of {pi}/2 in both the horizontal and vertical planes. The magnets will have their fields ramped with time so as to keep the cell tunes constant. All dipole magnets are rectangular. The quadrupoles are split into two pieces to allow the eventual insertion of sextupoles for chromaticity correction. The arc cell is described, and its lattice functions are plotted. In the arc cells, the fields will be set to keep the on-energy closed orbit centered in the quadrupoles and in the drift at the center of each half cell. The behavior of the off-energy orbits is shown. At the energy extremes, the ramped fields take on the values given in Table 3