We propose a novel scheme for final muon ionization cooling with quadrupole doublets followed by emittance exchange in vacuum to achieve the small beam sizes needed by a muon collider. A flat muon beam with a series of quadrupole doublet half cells a
ppears to provide the strong focusing required for final cooling. Each quadrupole doublet has a low beta region occupied by a dense, low Z absorber. After final cooling, normalized transverse, longitudinal, and angular momentum emittances of 0.100, 2.5, and 0.200 mm-rad are exchanged into 0.025, 70, and 0.0 mm-rad. A skew quadrupole triplet transforms a round muon bunch with modest angular momentum into a flat bunch with no angular momentum. Thin electrostatic septa efficiently slice the flat bunch into 17 parts. The 17 bunches are interleaved into a 3.7 meter long train with RF deflector cavities. Snap bunch coalescence combines the muon bunch train longitudinally in a 21 GeV ring in 55 microseconds, one quarter of a synchrotron oscillation period. A linear long wavelength RF bucket gives each bunch a different energy causing the bunches to drift in the ring until they merge into one bunch and can be captured in a short wavelength RF bucket with a 13% muon decay loss and a packing fraction as high as 87%.
A 1.8 T dipole magnet using thin grain oriented silicon steel laminations has been constructed as a prototype for a muon synchrotron ramping at 400 Hz. Following the practice in large 3 phase transformers and our own Opera-2d simulations, joints are
mitred to take advantage of the magnetic properties of the steel which are much better in the direction in which the steel was rolled. Measurements with a Hysteresigraph 5500 and Epstein frame show a high magnetic permeability which minimizes stored energy in the yoke allowing the magnet to ramp quickly with modest voltage. Coercivity is low which minimizes hysteresis losses. A power supply with a fast Insulated Gate Bipolar Transistor (IGBT) switch and a capacitor was constructed. Coils are wound with 12 gauge copper wire. Thin wire and laminations minimize eddy current losses. The magnetic field was measured with a peak sensing Hall probe.
Muon acceleration from 30 to 750 GeV in 72 orbits using two rings in the 1000m radius Tevatron tunnel is explored. The first ring ramps at 400 Hz and accelerates muons from 30 to 400 GeV in 28 orbits using 14 GV of 1.3 GHz superconducting RF. The rin
g duplicates the Fermilab 400 GeV main ring FODO lattice, which had a 61m cell length. Muon survival is 80%. The second ring accelerates muons from 400 to 750 GeV in 44 orbits using 8 GV of 1.3 GHz superconducting RF. The 30 T/m main ring quadrupoles are lengthened 87% to 3.3m. The four main ring dipoles in each half cell are replaced by three dipoles which ramp at 550 Hz from -1.8T to +1.8T interleaved with two 8T fixed superconducting dipoles. The ramping and superconducting dipoles oppose each other at 400 GeV and act in unison at 750 GeV. Muon survival is 92%. Two mm copper wire, 0.28mm grain oriented silicon steel laminations, and a low duty cycle mitigate eddy current losses. Low emittance muon bunches allow small aperatures and permit magnets to ramp with a few thousand volts. Little civil construction is required. The tunnel exists.
