Simulation of large photomultipliers for experiments in astroparticle physics

Abstract

We have developed an accurate simulation model of the large 9 inch photomultiplier tubes (PMT) used in water-Cherenkov detectors of cosmic-ray induced extensive air-showers. This work was carried out as part of the development of the Off line simulation software for the Pierre Auger Observatory surface array, but our findings may be relevant also for other astrophysics experiments that employ similar large PMTs.The implementation is realistic in terms of geometrical dimensions, optical processes at various surfaces, thinfilm treatment of the photocathode, and photon reflections on the inner structure of the PMT. With the quantum efficiency obtained for this advanced model we have calibrated a much simpler and a more rudimentary model of the PMT which is more practical for massive simulation productions. We show that the quantum efficiency declared by manufactures of the PMTs is usually determined under conditions substantially different from those relevant for the particular experiment and thus requires careful (re)interpretation when applied to the experimental data or when used in simulations. In principle, the effective quantum efficiency could vary depending on the optical characteristics of individual events.

GEANT4 simulation of optical modules in neutrino telescopes

“…In the work by Motta and Schönert a detailed optical model for thin layers is presented that well describes the experimental measurements of absorption, reflection and refraction probabilities in photocathodes layers [7,8] that allow to deduce the complex index of the photocathode.…”

Enhanced model of quantum efficiency for the optical simulation of photodetectors

“…Summarizing contributions of multiple reflected photons, we get a geometrical series. The measured reflectance Rm can be expressed as R =�= R +I ( 1-R )2 R I-1 R 1 = R + (1 -R J R p • (4) In <l> 0 g 1 = 1 g g P g 1 -R g R p From (4), the photocathode reflectance for normal incidence can be calculated as (5) C. Analytical calculation of the internal quantum e f ficiency In the following, we will refer to PMTs as photodetectors and photocathodes as photo-sensitive surfaces, but the method can be applied similarly to solid state photomultipliers.…”

“…We handle these non-reflected photons similarly, from which one part produces photoelectrons while the other part is lost, assuming that the probability that a transmitted photon is reflected back by the electronic parts and passes the photocathode again is negligible. More precise photocathode model can be built according to [5]. (1-RJ1-R p ) <l> nr = <l> 0 • 1-R g R p (6) Now, one can calculate QEin from the QEex values:…”

“…We measured the reflectance of a Hamamatsu R2083 PMT and calculated Rp using (5). Measurement results are shown in …”

Spectral Characterization and Modeling of Wavelength-shifting Fibers

“…Several models of photon transport and fiber simulation have been introduced in various frameworks including dynamic programming [21], Monte Carlo [22,6,23], finite element analysis [24], and sensitivity analysis [25,26]. Others have considered simulations of electronic readout systems [27] and photomultiplier tubes [28]. Moreover, the literature on multimode optical fiber for use in data transmission is vast [29].…”