Target studies for surface muon production

Meson factories are powerful drivers of diverse physics programs. With beam powers already in the MW-regime attention has to be turned to target and beam line design to further significantly increase surface muon rates available for experiments. For this reason we have explored the possibility of using a neutron spallation target as a source of surface muons by performing detailed Geant4 simulations with pion production cross sections based on a parametrization of existing data. While the spallation target outperforms standard targets in the backward direction by more than a factor 7 it is not more efficient than standard targets viewed under 90°. Not surprisingly, the geometry of the target plays a large role in the generation of surface muons. Through careful optimization, a gain in surface muon rate of between 30% and 60% over the standard “box-like” target used at the Paul Scherrer Institute could be achieved by employing a rotated slab target. An additional 10% gain could also be possible by utilizing novel target materials such as, e.g., boron carbide.

Figure 1

Simulated double-differential cross sections for ${\pi }^{+}$ production on carbon at a proton energy of 585 MeV and a scattering angle of (a) 22.5, (b) 90 and (c) 135 degrees for several hadronic models used in Geant4 4.9.6 (BERT, BIC, INCLXX) and 4.9.5 (INCL_ABLA) in comparison to data from [12, 13]. The parametrization is described in the text.

Figure 2

Cross section of the SINQ spallation target as implemented in our Geant4 simulations. Visible are the outer and inner safety vessels made of ${\mathrm{AlMg}}_3$ (grey), the zircaloy (green) rods filled with lead (black) and the lead reflector surrounding the zircaloy rods. Protons enter the target from below.

Figure 3

Production vertices for (a) pions and (b) muons from pion decay at rest in a central vertical slice of 10 mm thickness through the spallation target. The lowest position of the safety vessel is at $z\approx -160\mathrm{mm}$ with the concave window extending up to $z\approx -125\mathrm{mm}$.

Figure 4

Initial position (a) and kinetic energy (b) of pions that generate detected surface muons. Please note the changed scale of the $y$-axis in (a) compared to Fig. 3.

Figure 5

(a) Momentum spectrum of all positive muons leaving the spallation target in the downward direction. Clearly visible is the peak at $30\mathrm{MeV}/c$ from surface muons and the broad distribution peaking at around $85\mathrm{MeV}/c$ from pions decaying in flight. (b) Size and divergence distribution $x$ and $x^{\prime }$. The $y$-components look similar.

Figure 6

Picture of the target E wheel used for surface muon production at PSI. The proton beam impinges on the outer rim as shown by the arrow. In order to radiatively cool the target, the wheel rotates with a frequency of 1 Hz.

Figure 7

Size and divergence distribution for the backward face (a) and side face (b) of target E.

Figure 8

Distribution of pion energies that generate surface muons in target E.

Figure 9

Different geometries studied in our target optimization. From left to right: grooved target, trapezoidal target, fork target, rotated slab target. The red line marks the proton beam.

Figure 10

Initial positions of accepted muons from the grooved target zoomed in to one groove. Instead of the expected half circular shape the distribution takes on a crescent form thereby reducing the surface volume gain from the grooves.

Figure 11

Pion stop density through the PSI standard target E in arbitrary units from one side to the other and integrated along its length. While the pion stop density is lowest at the sides where surface muons can actually escape the target it is approximately 70% higher in the center.

Figure 12

Enhancement factors in the three directions studied as a function of the rotation angle of the slab target. The length of the slab is fixed at 150 mm. Rotation angles between 5 and 10 degrees yield roughly equal gains in all three directions.

Figure 13

Size and divergence distribution along the backward face of the rotated slab target.

Figure 14

Distribution of emitted surface muons along the side face of the standard target and the backward face of the rotated slab target for the same number of protons on target. The overall increase in surface muons for the rotated slab target stems from a somewhat higher peak density and an effectively increased size of the target.

Figure 15

The relative surface muon yield and absolute pion yield at a proton energy of 585 MeV as a function of atomic number $Z$. Liquid densities are assumed for elements that are gaseous at normal temperature and pressure.