Muon front end for the neutrino factory

In the neutrino factory, muons are produced by firing high-energy protons onto a target to produce pions. The pions decay to muons and pass through a capture channel known as the muon front end, before acceleration to 12.6 GeV. The muon front end comprises a variable frequency rf system for longitudinal capture and an ionization cooling channel. In this paper we detail recent improvements in the design of the muon front end.

Figure 1

(top) $x\mathrm{\text{−}}y$ projection and (bottom) fractional change in transverse amplitude of a shell of muons after transport through the chicane system for a variety of momenta. The muons were created on the surface of a hyperellipsoid in $(x,p_x,y,p_y)$ space at intervals of $25\mathrm{MeV}/c$ total momentum. The surface was chosen at each momentum to be constant in the 1.5 T field with 4D transverse amplitude of 50 mm. Simulation in MAUS 0.3.1 [5].

Figure 2

(top) Fractional power of protons and (bottom) good muon yield at the end of the cooling channel for different chicane bending angles and absorber thicknesses. Overlapping points have been laterally displaced for clarity. The bending angle per cell is shown; each arc of the chicane was simulated with ten two-coil cells, each of which was rotated in the simulation to provide a smoothly varying solenoid field. No dipole field was applied. A cylindrical beryllium absorber was placed after the chicane with thicknesses listed. The two points for 0 mm thickness and 0° bending angle in the bottom figure assume ($+$) ideal constant 1.5 T field and (*) 3D magnetic field maps. All chicane simulations use realistic magnet field maps. Simulation in G4Beamline 2.06 [6].

Figure 3

(top) Schematic of the muon front end, (middle) rotator lattice, and (bottom) cooling lattice.

Figure 4

Performance of the bunching and cooling channel as a function of distance along the channel, as simulated using the ICOOL 3.20 [7] and G4Beamline 2.06 [6]. (top) The evolution of the rms transverse emittance (computed over all bunches). (bottom) The evolution of the number of muons within a reference acceptance (muons within 201.25 MHz rf bunches with momentum in the range $100–300\mathrm{MeV}/c$, transverse amplitude squared less than 0.03 m and longitudinal amplitude squared less than 0.15 m). The cooling section starts at $s=155\mathrm{m}$, where the rms transverse emittance is 0.018 m and $0.08\mu$ per proton are in the reference acceptance. The capture performance is shown for a cooling channel extending to $s=270\mathrm{m}$ although in this design the cooling channel extends only to 230 m. Acceptance is maximal at $0.20\mu$ per initial 8 GeV proton at $s=240\mathrm{m}$ (85 m of cooling) and the rms transverse emittance is 7 mm. At $s=230\mathrm{m}$ (75 m of cooling) the number of $\mu \mathrm{s}$ per proton is 0.19 and the transverse emittance is 7.5 mm.

Figure 5

Distribution of particles in longitudinal phase space at the phase rotation end. $\mu +$ are shown in red and $\mu -$ are shown in blue.

Figure 6

The degradation in cooling performance with decreased rf voltage is shown. The baseline cooling lattice was simulated with lithium hydride thickness proportional to rf peak voltage to account for the reduction in energy gain and the number of muons within the accelerator acceptance was calculated before and after the cooling channel. The ratio of these two values was plotted against cooling channel rf field for a number of peak fields. The nominal cooling channel rf voltage is $16\mathrm{MV}/\mathrm{m}$.

Figure 7

Schematic of a bucked coil lattice in radially bucked coil (RBC) arrangement and simulated good muon yield with radially bucked coil and laterally bucked coil (LBC) lattices. The bucked coils were used also in the phase rotation section in these simulations.

Figure 8

Simulated good muon yield of $\mu +$ with capture optimized for higher energy and a cooling cell length of 3 m as opposed to 0.75 m in the baseline. The rf capture scheme was adjusted to capture at a central momentum of $273\mathrm{MeV}/c$ rather than the nominal $214\mathrm{MeV}/c$ of the baseline lattice. Two absorber materials were simulated, lithium hydride (LiH) and liquid hydrogen (${\mathrm{lH}}_2$).