# Characterisation of the muon beams for the Muon Ionization Cooling Experiment¶

## Abstract¶

A novel single-particle technique to measure emittance has been developed and used to characterise seventeen different muon beams for the Muon Ionisation Cooling Experiment (MICE). The muon beams, whose mean momenta vary from 171 to 281 MeV/c, have emittances of approximately 1.5--2.3 \pi mm-rad horizontally and 0.6--1.0 \pi mm-rad vertically, a horizontal dispersion of 90--190 mm and momentum spreads of about 25 MeV/c. There is reasonable agreement between the measured parameters of the beams and the results of simulations. The beams are found to meet the requirements of MICE.

## Paper¶

Published in European Journal of Physics C, Volume 73, Number 10

arXiv: 1306.1509

DOI: 10.1140/epjc/s10052-013-2582-8

## Figures¶

Figure 2. The time-of-flight system and beam line section used to characterise the beam. (PDF, jpg)

Figure 3. Quadrupole gradients for the (6\pi.mm-rad, 200 MeV/c) baseline muon beam (PDF, jpg)

Figure 4. The reconstruction coefficients A(pz) (a) and B(pz) (b) for the (6,200) baseline muon beam. The solid (blue) lines are for x' (horizontal); the dashed (red) lines are for y' (vertical).

(a: PDF, jpg)

(b: PDF, jpg)

Figure 5. Difference between reconstructed and true momenta for a simulated 200 MeV/c muon beam. (PDF, jpg)

Figure 6. Reconstructed trace space angles versus true simulated values. (PDF, jpg)

Figure 7. Reconstructed longitudinal momentum distributions at TOF1 for six MICE beams compared with simulations. The dotted (red), dash-dotted (blue) and shaded distributions are simulation, reconstructed simulation and data respectively. Distributions are normalised to contain equal numbers of events. (PDF, jpg)

Figure 8. Spatial distributions in the transverse plane at TOF1 for simulation (left), reconstructed simulation (centre), and data (right) for a (6,,200)\mu- beam, normalised to the same total contents. Simulated muons in the shaded area cross uncalibrated regions of TOF1 and are excluded from further analysis. (PDF, jpg)

Figure 9. Root mean square beam widths, \sigma_x, \sigma_y, at TOF1 versus pz. Solid black circles: \mu- data, open black circles: \mu+ data, solid red triangles: \mu- simulation, open red triangles: \mu+ simulation. The nominal "pz = 140" MeV/c beams correspond to momenta in the range 170--190 MeV/c, "pz = 200" to 220--250 MeV/c, and "pz = 240" to 250--290 MeV/c.

(\sigma_x: PDF, jpg)

(\sigma_y: PDF, jpg)

Figure 10. Horizontal (x) and vertical (y) trace space distributions at TOF1 for simulation (top), reconstructed simulation (centre) and data (bottom) for a (6, 200)\,\mu- beam. The ellipses correspond to \chi^2 = 6 (see text).

(PDF, jpg)

Figure 11. Distributions of \chi^2 for data (solid, shaded, black) and reconstructed simulation (dash-dot, blue) for the (6, 200), \mu- beam. Left: horizontal \chi^2; right: vertical \chi^2 at TOF1. (PDF, jpg)

Figure 12. RMS emittance ellipses in (x,x') trace-space for data without correction for the measurement resolution (black dotted line), corrected data (black solid line) and true simulation (red dashed line). (PDF, jpg)

Figure 13. Horizontal emittance after correction for measurement resolution and multiple scattering versus mean pz of the seventeen measured beams. Solid black circles: \mu- data, open black circles: \mu+ data, solid red triangles: \mu- simulation, open red triangles: \mu+ simulation. The nominal "pz = 140" MeV/c beams correspond to momenta in the range 170--190 MeV/c, "pz = 200" to 220--250 MeV/c, and "pz = 240" to 250--290 MeV/c. (PDF, jpg)

Figure 14. Vertical emittance after correction for measurement resolution and multiple scattering versus mean pz of the

seventeen measured beams. Solid black circles: \mu- data, open black circles: \mu+ data, solid red triangles: \mu- simulation, open red triangles: \mu+ simulation. The nominal "pz = 140" MeV/c beams correspond to momenta in the range 170--190 MeV/c, "pz = 200" to 220--250 MeV/c, and "pz = 240" to 250--290 MeV/c. (PDF, jpg)

Figure 15. The horizontal dispersion coefficient, \eta, versus mean pz of the seventeen measured beams. Solid black circles: \mu- data, open black circles: \mu+ data, solid red triangles: \mu- simulation, open red triangles: \mu+ simulation. The nominal "pz = 140" MeV/c beams correspond to momenta in the range 170--190 MeV/c, "pz = 200" to 220--250 MeV/c, and "pz = 240" to 250--290 MeV/c.(PDF, jpg)

## Tables¶

Table 1. Mean and RMS widths of the longitudinal momentum distributions for six beams compared with the corresponding simulations. (TeX, PDF, jpg)

Table 2. Contributions to the errors on the emittance measurements as percentage relative error. (TeX, PDF, jpg)

Table 4. Horizontal dispersion and the intrinsic emittances of the Step I beams. (TeX, PDF, jpg)