## 2 Materials and Methods  
Numerical simulations were performed using the hybrid method, described in detail elsewhere [14] and schematically illustrated in Scheme 1. The concept of the hybrid method is to combine diffusion-kinetic calculation for the radiolytic species initially clustered in radiation tracks and kinetic calculation of reactants homogenously distributed in the bulk solvent. Numerical integration of a set of diffusion-kinetic equations up to 0.1 us provided the primary yields (or G values) of the primary species (e\({}_{\text{aq}}\)\({}^{-}\), \({}^{\bullet}\)OH, H\({}^{\bullet}\), H\({}^{+}\), OH\({}^{-}\), H\({}_{2}\)\(\rm H_{2}O_{2}\), \(\rm HO_{2}{{}^{\bullet}}\)). The primary yields, still often expressed in molecules per 100 eV of absorbed energy, were then recalculated to production rates \(P_{\rm i}\) according to the required dose rate. Simulations were performed for the dose rates of 1 and 10 kGy\(\cdot\)s\({}^{-1}\), which are similar to the in-core dose rates of gamma and fast neutron radiation. Table 1 presents production rates \(P_{\rm i(g)}\) and \(P_{\rm i(n)}\), obtained for gamma and fast neutron radiolysis of water at 300 \({}^{\circ}\)C. For mixed radiation, production rates were calculated using the equation \(P_{\rm i(mix)}=f_{\rm g}P_{\rm i(g)}+f_{\rm n}P_{\rm i(n)}\), where \(f_{\rm g}+f_{\rm n}=1\). The advantage of employing the hybrid method is that the production of primary radiolytic species satisfies both the material balance and the charge balance. At the concentration of additives [OH\({}^{-}\)] = 2\(\cdot\)10\({}^{-4}\) mol\(\cdot\)kg\({}^{-1}\) and [H\({}_{2}\)] \(\leq\) 1.5\(\cdot\)10\({}^{-4}\) mol\(\cdot\)kg\({}^{-1}\), considered in this study, the production rates for alkaline and hydrogenated solutions can be assumed the same as for neutral water at 300 \({}^{\circ}\)C [24]. The production rates specified in Table 1 were used as zeroth-order terms in a system of differential kinetic equations, which was defined with respect to 13 species (i.e., \(\rm e_{aq}{{}^{\bullet}}\)-, \(\rm{}^{\bullet}OH\), H\({}^{\bullet}\), OH\({}^{-}\), H\({}_{2}\)O, H\({}_{2}\), H\({}_{2}\)O\({}_{2}\), O\({}_{2}\), O\({}_{2}\)\({}^{\bullet-}\), \(\rm HO_{2}{{}^{\bullet}}\), \(\rm HO_{2}{{}^{-}}\), H\({}_{2}\), \(\rm H_{2}O_{2}\), O\({{}^{\bullet-}}\), O\({{}_{3}}\)\({{}^{\bullet-}}\), O\({}^{\bullet}\)) involved in the 1 st and 2 nd order reactions listed in Table 2. The reaction set and the associated high-temperature rate constants were compiled based on the data reported from different laboratories. \begin{table}
\begin{tabular}{c c c} \hline
**Species \(i\)** & \(P_{\rm i(g)}\)**, \(\bf M\cdot s^{-1}\)** & \(P_{\rm i(n)}\), \(\bf M\cdot s^{-1}\) \\ \hline \(\rm e_{aq}{{}^{\bullet}}\) & 2.385\(\cdot\)10\({}^{-4}\) & 1.062\(\cdot\)10\({}^{-4}\) \\ \(\rm H^{\bullet}\) & 5.970\(\cdot\)10\({}^{-5}\) & 5.455\(\cdot\)10\({}^{-05}\) \\ \(\rm H^{+}\) & 2.837\(\cdot\)10\({}^{-4}\) & 1.453\(\cdot\)10\({}^{-4}\) \\ \(\rm{}^{\bullet}OH\) & 3.564\(\cdot\)10\({}^{-4}\) & 2.730\(\cdot\)10\({}^{-4}\) \\ \(\rm H_{2}O_{2}\) & 1.866\(\cdot\)10\({}^{-5}\) & 3.201\(\cdot\)10\({}^{-5}\) \\ \(\rm H_{2}\) & 4.776\(\cdot\)10\({}^{-5}\) & 8.895\(\cdot\)10\({}^{-5}\) \\ \(\rm HO_{2}{{}^{\bullet}}\) & 0 & 5.584\(\cdot\)10\({}^{-7}\) \\ \(\rm OH^{-}\) & 4.522\(\cdot\)10\({}^{-5}\) & 3.910\(\cdot\)10\({}^{-5}\) \\ -\(\rm H_{2}O\) & 3.937\(\cdot\)10\({}^{-4}\) & 3.387\(\cdot\)10\({}^{-4}\) \\ \hline \end{tabular}
\end{table} 
Table 1: Production rates \(P_{\rm i(g)}\) and \(P_{\rm i(n)}\), of the primary species obtained assuming the dose rate value of 1 kGy\(\cdot\)s\({}^{-1}\) and using the G values for gamma and fast neutron radiolysis of water at 300 \({}^{\circ}\)C from ref. [14]. Last row describes loss of water molecules resulting from irradiation. In order to obtain steady-state concentrations, the system of differential equations was numerically integrated up to the time limit \(t_{\text{max}}\) = 100 s using the FACSIMILE 4 (ver. 4.2.50, MCPA Software, Harwell, UK) package.