Light simulation in plastic scintillator strip with embedded wavelength shifting fiber

    Cosmic muons are the important contributors to background processes when search for the conversion of a muon to an electron[1, 2]. Cosmic ray veto geometry surrounding the detectors and stopping target should be carefully eliminated this background. Passive and active shielding should provide background of $\sim$0.1 events in signal window for 3 year run of experiments. Scintillator-based active shielding will consist of four layers. The scintillator strips will read out by multiclad wavelength shifting (WLS) fibers connected to photodetectors. Most promising devices based on new technologies used as photodetectors are the silicon photomultipliers (SiPM)[3]. Photon detection efficiency of SiPM is dependent on wavelength of the photon, temperature, dark count[4] etc., and very difficult to be measured and even more difficult to model[5]. For this reason, we are limited only to the study of the light propagation and collection. Even for this purpose, a Monte Carlo simulation can adequately predict the experimental results only if the detector parameters are sufficiently close to their true values. Some of parameter, e.g. surface boundaries descriptions, can be tuned by using measurements for particular scintillator strip configurations.

    The Monte Carlo simulation with all possible processes play a crucial role in the feasibility study of the proposed detector module and in identifying detector parameter values. Low-energy optical photons (photons with a wavelength much greater than the typical atomic spacing) undergo the following processes: bulk absorption, Rayleigh scattering, reflection and refraction at medium boundaries, and wavelength shifting.

The boundary processes on all scintillator play an important role in tracing photons in strips. Compared to them, photon self-absorption in scintillator is less significant[6]. In Geant4.10.06 [7] simulation we combined the polished scintillator surface finishes with the backpainted wrapping option which represents diffuse (Lambertian) reflection. In this simulation we use the UNIFIED model for the processes between two dielectric materials.

     The peak of emission light of a plastic scintillator (e.g., Saint Gobain BC400 series) does not matches the peak sensitivity of used photodetectors. To solve this problem it is necessary to use the WLS fiber to transfer light to the photodetector. In this simulation the fiber are multiclad consisting of a scintillating core surrounded by an acrylic inner cladding

For WLS fiber attenuation length of 500 cm for its own radiation, and for plastic scintillator attenuation length of 300 cm are assumed. The total diameter of fiber is 1.2 mm. The total thickness of cladding structure is 6% of the diameter of a fiber. In this simulation the strip contains one or two co-extruded grooves with 3 mm depth and 1.3 mm width for insertion of the WLS fiber. The selected strip and fiber parameters are close to those used in the test-beam measurements at JINR (Dubna, Russia).

This simulation was performed using Geant4 for plastic scintillator with the dimension 4*1*300 cm³ and co-extruded TiO₂ white diffuse reflective (R=98$\%$) coating. The strip contain one at the center or two grooves at a distance of 2 cm from each other along the entire length of scintillator strip. We collect photons from a WLS fiber at one of the strip ends (hereinafter referred to as photodetector side). On the photodetector side at the fiber end the photons are fully absorbed. The opposite ends of the fibers are blackened.

Cosmic muons were generated according to[9] in the range 0.3-5000 GeV. The zenith angle and energy distribution for simulated cosmic muons are displayed in Figure 2.

Figure 9 shows the relation between the mean number of optical photons detected at the photodetector side and the distance between point of impact of electrons from the radiation source and photodetector side. This graph is fitted by a function

$\qquad\qquad\quad N_{phot}(z)=A*e^{-z/\lambda_{1}}+B*e^{-z/\lambda_{2}}.$

Note that this formula was proposed by Kaiser et al.[10] for the case when light is collected from the ends of the scintillator using a photomultipliers. The first term is the transmission behavior for photons that travel directly to the photodetector side.

    To study the light attenuation when the strip surface is irradiated by cosmic muons we retreated on each side of the surface by 1 mm and divided it into 40 equal parts. Each sector has been uniformly irradiated by 500 muons with energies, azimuth and zenith angles modeled accordingly to[9]. In Figure 10, we demonstrate the light attenuation for this case. The points in the Figure are located in the center of each of the 40 sections. For the given points, the results of one exponential and double exponential fit are the same (blue curve in the Figure), $\lambda_{1}=\lambda_{2}$=5.88 m. The green curve in Figure corresponds to the fit by the formula

$\qquad\qquad\quad N_{phot}(z)=A*e^{-z/\lambda}+B,$

where $\lambda=$2.32 m.

     We are sincerely grateful to Z. Tsamalaidze and Yu. Davydov for initiating this work.