Design Details

The µLan Detector is being designed with 180 independent coincident timing elements, termed ``tiles''. Each tile consists of two plastic scintillators in the shapes of equilateral triangles with 10 cm sides. The inner and outer scintillators have thicknesses 6.35 mm and 3.175 mm, respectively. A gap of approximately 7 mm is maintained between each tile so that no positron from any edge of the target can cross from the inner scintillator of one tile into the outer scintillator of an adjacent tile. The light from the outer scintillator is transported to a PMT through a solid, UV-Absorbing (UVA) tapered lightguide whose length is sufficient to stop the most energetic decay positrons. The UVA plastic prevents unwanted Cherenkov light from introducing an energy-dependent additional light source to this counter. The length ensures that no positron enters the tube. The inner scintillator is coupled to its PMT through an adiabatic UVA lightguide attached at right angles to one of the 10 cm long triangular edges. The end of the lightguide has a $45^\circ$ bevel which is mirrored in order to reflect scintillator light into the PMT. These shapes are illustrated in figure 3.

Figure 3: A sketch of the individual elements which make up a timing tile. Note, actual shapes of lightguides nvolve adiabatic tapers.

Prototypes have been constructed and are currently being tested. Figure 4 shows the response of the inner scintillator to a MIP defined from a cosmic ray telescope. While the light collection of the outer scintillator is quite straightforward, that of the inner scintillator was expected to be more problematic. We used the lightguide Monte Carlo program GUIDEIT [20] to study the proposed right angle matched guide. The transmission was found to average approximately 36%. This simulation assumed flat surfaces wrapped with Al foil and an inclined edge at the scintillator-lightguide interface having a mirrored surface. We have tested the prototypes using a calibrated XP2020 PMT and have determined the number of photoelectrons per MIP to be N_MIP = 300 and N_MIP = 160 for the inner and outer scintillators, respectively. These specifications greatly exceed our design requirements.

Figure 4: Response of the inner and outer scintillator prototypes to minimum ionizing particles defined by an external cosmic ray telescope. The data are fitted to a Landau function (solid lines). The inner detector peaks at 300 pe/MIP and the outer detector peaks at 160 pe/MIP.

A measurement of the uniformity of response of the inner scintillator was made with a ¹⁰⁶Ru $\beta$ source. A plot of the relative light output is shown in figure 5. Over the whole triangular surface, the variance from the mean is 9%. Improvements can be expected as wrapping techniques are varied.

Figure 5: Relative light yield versus impact position for the inner scintillator. A $\beta$ source was used to simulate positrons entering at different positions.

Figures 6 and 7 show the overall icosahedral geometrical structure containing 20 SuperTriangles. Each SuperTriangle has nine tiles; in the figure, only the outer scintillator is shown, indicating the active area of the device. This structure is centered on the stopping target. This means that any line drawn through the target will connect two tiles with point-like symmetry. We call these matched tiles a ``tile pair'' and plan to do the analysis with special consideration of the performance of such pairs; for example, the sum and difference of counts versus time for a tile pair highlights any residual muon precession asymmetry. In practice we expect to instrument 174 out of the 180 tiles, leaving out 3 tile pairs approximately along the principle axes defined by the beam, the vertical and the horizontal. The overall structure will be rotated periodically in order to bring the beam in through these gaps. We have selected this type of triangular structure for other practical reasons. For example, every tile is identical in size and shape and can be readily interchanged with any other. This keeps the simplicity of the detector in line with the demands of a precision experiment. We also expect that the production and quality control, gain settings, and uniformity of the individual elements will be enhanced by choosing a geometrical structure with identical components. The structure permits modular construction of SuperTriangles. We expect to build and test a complete pair of SuperTriangles in the next year.

Figure 6: Final overall geometry of the detector representing an icosahedron of SuperTriangles. The individual tiles are shown without the lightguides.

Figure 7: Final overall geometry with the outer ightguides shown.

The area of each tile is 43.3 cm². The nine tiles occupy approximately 85% of the inside of a SuperTriangle. The gaps between SuperTriangle edges will be minimized, subject to mechanical constraints for tile positioning. We expect an overall geometrical coverage of more than 75% of $4\pi$ taking into account support structures and the 6 tile positions which will be purposely left open for the beam entrance. The average inside radius (calculated as if the detector where spherical) is approximately 28 cm. We anticipate that the overall mechanical support system will form a web around the outside and will fix the PMT/base housings to the frame and in position. The relative position of a tile inside a SuperTriangle will be maintained by spacers.

In two previous experiments we have used 300 ps wide light pulses from a nitrogen laser to excite directly the scintillator in the detector system. The 337 nm wavelength from the laser is absorbed and re-emitted in a manner which mimics charged-particle ionization of the plastic. For the muon lifetime measurement, we are particularly interested in obtaining accurate timing measurements during any time following muon injection. To make an early-to-late timing check, we intend to use the pulsed laser to pulse the tiles at a sequence of times following muon injection (and directly on top of the actual data). Each timing tile response can be compared to a reference detector located out of the beam. This procedure is only necessary for a small number of selected runs.

The laser light is distributed to the individual scintillator tiles through a splitter box. We own two splitter boxes with a $1 \rightarrow 160$ distribution and a third with one with a $1 \rightarrow 60$ distribution. Presently in use at 2 are 25 additional splitter boxes with a distribution of $1 \rightarrow 12$. A 50 or $100~\mu$m UV transmitting fiber connects the splitter box outputs to the scintillator tiles.