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.
