Computer modelling of the Hamamatsu R11410-20 PMT

Abstract

Abstract. A computer model of operation of Hamamatsu R11410-20 photomultiplier based on SPICE software package has been developed. The PMT amplification process is simulated with the use of voltage and current controlled sources of current. Boundaries of linear zone were obtained for high anode current (with respect to the base current) operation regime. The results of simulation are in reasonable agreement with the experimentally measured PMT characteristics. The model can be used for simulation of any type of PMT. IntroductionThere are various specific photomultiplier tube (PMT) applications when the anode current is relatively high in compare to the base current. The one of those is the use of PMTs for the scintillation and electroluminescent light detection in cryogenic noble gas filled two-phase emission detectors widely used nowadays to search for WIMP particles of dark matter in the Universe [1]. The RED-100 is a two-phase emission detector built for the experiment on coherent elastic neutrino-nucleus scattering (CEvNS) observation [2], another challenging experiment that is carried in a vicinity of a nuclear power plant reactor. There are 38 Hamamatsu R11410-20 3"-diameter PMTs in the RED-100 detector divided into two arrays, the top and bottom ones, with 19 PMTs in each array. The PTS of the RED-100 detector operates in the liquid xenon environment. The PMT bases are directly connected to the photomultiplier pins. The specific of the RED-100 detector operation requires the very wide dynamic range of PMT: from the single photoelectron signals of small scintillation to the very intense electroluminescent signals having several millions of photoelectrons; see for details [3] paper. Moreover, the rate of appearance of scintillation signal is substantially high, and the significant average anode current may result in nonlinearity of the PMT gain. This problem can be solved by the increase of the PMT base current or by designing a special divider circuit having individual power suppliers for the last dynodes. We selected the first option because of the restriction of cabling inside the detector cryostat. On the other hand, the value of the PMT base current must be restricted in order to avoid liquid xenon boiling on the divider circuit resistors.The main task when designing the PMT divider circuit was to understand the limitation on the average anode current of the PMT when the base current is set to a certain value. The common practice is to do this experimentally. However, computer modeling with the use of standard electrical circuit simulation packages may economize efforts significantly. Surprisingly, we have found only one paper [5] dedicated to computer modeling of a PMT with the use of SPICE package.

Comments on “SPICE Model of Photomultiplier Tube Under Different Bias Conditions”

“…which corresponds to [12,Eq 6] when all η i∈[1,N +1] = 1. For the first dynode (i = 1), the corresponding equation is:…”

“…Presumably, this discrepancy of the optimized parameters might have been caused by an oversight when transcribing the equations of [1] into the SPICE fields, which the optimizer compensates for by returning fairly different parameters so that the gain curve is still matched. For example, the GVALUE of the anode current source (12) might have been written with N = 9 in place of N = 8. In this hypothetical case, the incorrect (N = 9) analytical equation ( 4) predicts with the optimized parameters gains of G 1 ≈ 4.9 • 10 5 and G 2 ≈ 2.4 • 10 6 , that match well with the manufacturer gain curve.…”

Modeling and simulation of the R5912 photomultiplier for the LAGO project

“…To simplify the model, we can assume that k i values are equal for all dynodes due it depends on the dynode material [12]. Equation 4 is transformed in…”

A photomultiplier tube model for the water Cherenkov detectors of the LAGO

“…where is the inter-dynode resistance, and is the total resistance of the voltage divider. We assume values are equal for all dynodes due its dependence on the dynode material [10], equation Eq. 4 results in…”

“…Akimov et al propose a computer model of the Hamamatsu R11410-20 photomultiplier based on Spice using current-controlled sources. The authors insert a variable inter-dynode bias fraction and evaluate the limits of the anode current caused by the PMT gain [10]. Hueso-Gonzalez et al verify Krihely's model compensating some ambiguities and inconsistencies [11].…”