Demonstration of Muon-Beam Transverse Phase-Space Compression

We demonstrate efficient transverse compression of a $12.5\mathrm{MeV}/\mathrm{c}$ muon beam stopped in a helium gas target featuring a vertical density gradient and crossed electric and magnetic fields. The muon stop distribution extending vertically over 14 mm was reduced to a 0.25 mm size (rms) within $3.5\mu \mathrm{s}$. The simulation including cross sections for low-energy ${\mu }^{+}$-He elastic and charge exchange (${\mu }^{+}\leftrightarrow$ muonium) collisions describes the measurements well. By combining the transverse compression stage with a previously demonstrated longitudinal compression stage, we can improve the phase space density of a ${\mu }^{+}$ beam by a factor of ${10}^{10}$ with ${10}^{-3}$ efficiency.

Figure 1

Left: schematic diagram of the muCool device. A standard muon beam is stopped in a cryogenic helium gas target with a vertical temperature gradient inside a 5 T field. The extent of the stopped muons is reduced first in the transverse ($y$), then in the longitudinal ($z$) direction. The now sub-mm muon beam is extracted through an orifice into vacuum and reaccelerated along the $z$ axis. The electrodes used to define the required electric field in the transverse compression stage are also sketched (gray and red rectangles), along with the values of applied high voltage. Right: schematic of ${\mu }^{+}$ trajectories in various gas densities and in crossed electric and magnetic fields.

Figure 2

Projection of the detection efficiency of the A1 and A2L positron detectors in the $xy$ plane, simulated with geant4 [18]. Color scale represents positron detection efficiency.

Figure 3

Muon trajectories in $xy$ plane simulated with geant4 for top-hole and bottom-hole injection and for compression (left) and pure-drift (right) density conditions. Small amount of compression visible in pure-drift simulation is caused by residual temperature gradient.

Figure 4

Measured (points) A1 and A2L time spectra for top- and bottom-hole injection and for compression (red) and pure-drift (black) conditions from Fig. 3, along with corresponding simulated time spectra with (solid curves) and without (dashed curves) a small angular target misalignment. The error bars are given by the statistical errors of the measured counts (before the lifetime compensation) scaled by $e^{t/2.2\mu \mathrm{s}}$. Each simulated time spectrum was fitted to the measured spectra using two fit parameters (normalization and flat background). Reduced chi squareds of each fit are also indicated ($\mathrm{ndf}=75$).

Figure 5

Product ${\sigma }_{MT}{v}_r$ vs muon c.m. energy, using energy-scaled proton-He cross sections of Ref. [21].

Figure 6

Muon trajectories in $xy$ plane for top-hole and compression conditions (6–19 K at 8.6 mbar), for various HV. The target axis was assumed to point in the (0.007,0.018,0.9998) direction, as determined previously by minimizing the chi squared for the 5.0 kV measurements.

Figure 7

Measured (points) A1 and A2L time spectra for top-hole and compression configuration and for various HV, scaled to have the same number of injected muons. The error bars are purely statistical, as in Fig. 4. The simulated time spectra (curves), corresponding to the trajectories of Fig. 6, were fitted to corresponding measured time spectra using two free parameters per spectrum (normalization and flat background). Chi squareds are indicated in parentheses ($\mathrm{ndf}=75$).