## 1 Introduction  
Radioisotope sources of electricity form a very useful class of micro power sources of energy, while many of them are devices that use the intermediate conversion of ionizing radiation energy into heat [1; 2]. Alternative structures include isotope sources, which use the effect of ionization by corpuscular radiation of semiconductor converters to generate electricity [3; 4; 5; 6; 7; 8; 9; 10]. Such an approach promises high efficiency; however, radiation damage to the semiconductor material becomes an almost insurmountable obstacle, negating the potential advantage of such a source--long service life. The problem can be solved by utilizing indirect converters, in which the photovoltaic semiconductor element and the isotope source are separated by a layer of high light yield and radiation-hard scintillation material [11; 12; 13]. Such requirements are met by crystalline compounds of the garnet structural type, activated by rare-earth elements [14]. Their radiation resistance under a different kind of ionizing radiation was confirmed in [15; 16; 17; 18]. Tolerance to ionizing radiation occurs in garnets because the formed color centers have absorption bands primarily in the ultraviolet region and do not overlap the Ce3+ scintillation band of such materials, which is typically localized in the yellow-green region of the spectrum [19; 20; 21].  
Among the currently developed crystalline scintillators with a garnet structure [22], the (Gd,Y)\({}_{3}\)Al\({}_{2}\)Ga\({}_{3}\)O\({}_{12}\) materials activated by Ce and Tb ions have the highest scintillation yield. Activation with Ce ions leads to fast scintillation, which, however, is not a critical parameter for the considered application. Moreover, the scintillation of Ce ions experiences strong temperature quenching, which is not typical for scintillations of Tb ions in crystals of the same composition [23]. Luminescence bands of Tb ions located in the visible range originating from f-f transitions are parity and multiplicity forbidden. Their characteristic decay time is in the millisecond range. For such scintillators, upon intense excitation by ionizing radiation, an additional channel of luminescence quenching occurs by the Augermechanism [24]. Such a mechanism may lead to a significant decrease in the luminescence yield and, consequently, to a decrease in the efficiency of the converter immediately after the start of its operation.  
To elucidate the effects of saturation, we performed a direct measurement of the saturation of the scintillation yield in (Gd,Y)\({}_{3}\)Al\({}_{2}\)Ga\({}_{3}\)O\({}_{12}\) ceramic samples activated with Ce and Tb ions using a 150 keV electron accelerator with intensity varied over a wide range. We focused on the samples activated with Tb ions, which were optimized to achieve the optimal concentration of the activator and the composition of the matrix of the quaternary garnet. A model of luminescence saturation in the considered compounds as a function of ionization density was developed. It satisfactorily describes the experimental data. The data obtained led us to the conclusion that the saturation effect will not lead to a significant change in the efficiency of the converter when widely used isotope sources for betavoltaic are used.