A Model for Radiolysis in a Flowing-Water Target during High-Intensity Proton Irradiation

Abstract

At the Facility for Rare Isotope Beams (FRIB), interactions between heavy-ion beams and beam-dump water will create a wide variety of radionuclides which can be accessed by a technique known as “isotope harvesting”. However, irradiation of water is always accompanied by the creation of numerous radical, ionic, and molecular radiolysis products. Some of the radiolysis products have sufficiently long lifetimes to accumulate in the irradiated water and affect the harvesting chemistry. Here we investigate the formation of hydrogen peroxide, molecular hydrogen, and molecular oxygen during a high-intensity proton irradiation of a flowing-water isotope-harvesting target and compare the experimental results to simulations. The simulations kinetically model the chemical reactions occurring in the homogeneous phase of radiolysis in flowing water and establish an “effective yield”. In both the experiment and simulations, the bulk quantities of H₂, H₂O₂, and O₂ are considerably lower than predicted by primary radiolysis yields (escape yields), meaning that in the high beam intensity regime the homogeneous phase reactions have a considerable impact on the overall chemical composition of the water. Further, it could be shown that for radiation which is characterized by a limited linear energy transfer, such as the here applied protons, the bulk outcome of the microscopic kinetic modeling could be estimated by a simplified steady-state model.

1. Introduction

The Facility for Rare Isotope Beams (FRIB) will create beams of radionuclides that have previously only existed in extreme cosmic environments. With its commissioning in 2022, FRIB will allow researchers to address forefront scientific questions in nuclear science. In the background of FRIB’s fundamental science efforts, there is an opportunity to use the high-energy ion beams to create additional radionuclides in the FRIB beam dump. The FRIB beam dump is a spinning drum of Ti64 alloy (6% Al, 4% V, balance Ti) which is continuously traversed by a stream of cooling water.^1,2 With a heavy-ion beam impinging on the nuclei of water molecules, nuclear reactions are induced, resulting in the formation of a variety of different radionuclides. In this way, a yet unexploited source of rare radionuclides becomes accessible and contributes to meeting the increasing demands of medicine, astrophysics, materials science, and stockpile stewardship science. So far exploratory research with the heavy-ion beams from the National Superconducting Cyclotron Laboratory (NSCL) has been conducted and facilitated the collection of various radioactive species, such as ²⁴Na, ⁴⁷Ca, ⁴⁸V, ⁶²Zn, ⁶⁷Cu, ^76/77Kr, and ⁸⁸Zr.²⁻¹¹

The slowing down of heavy ions when passing through water is mediated by inelastic collisions with bound electrons. The energy loss per unit distance, expressed as stopping power, determines the structure of ionization tracks and their relatively short ranges.^12,13 Following the initial energy deposition and ionization events, HO–H bond breaking occurs, and the decomposition of water molecules is initiated. The resulting species (OH, H, H₃O⁺ and e^–_aq) are nonhomogeneously distributed in separated regions, also known as “spurs”, along the radiation track. The track expands as these initial species react within the spur, forming the primary radiolysis species e^–_aq, OH, H, HO₂, H₃O⁺, OH^–, H₂O₂, and H₂. All recombination and spur expansion processes are completed ∼1 μs after the initial energy deposition. The molecular and radical species present at that time are defined by the primary radiolytic yield (also known as G value or escape yield) and are usually expressed as the number of molecules created per 100 eV of deposited energy.¹⁴⁻¹⁶ Escape yields in a medium are determined by the prevailing track structure which is heavily dependent on the radiation type and energy. The heavy ions’ linear energy transfer (LET), which is assumed to be equivalent to the stopping power in liquid water, is commonly used to describe the spatial distribution of the tracks.^17,18 The formation of the spurs is followed by diffusion of the species into the bulk solution, where they react with each other and with the surrounding molecules in the solvent. Within this chemistry stage, the system evolves via homogeneous kinetics where secondary products, among them O₂, are formed. The homogeneous reactions determine the temporal development of the concentrations of primary radiolysis species.^16,19,20 In closed systems exposed to low-LET irradiations over extended time periods, a chemical equilibrium will be established between the formation and removal processes. Such steady-state conditions stabilize the concentrations of radiolytic species on a moderate level, prevailing as long as the irradiation conditions are stable.^20,21 However, with high-LET radiation, water molecules will be decomposed continuously, and the establishment of a steady state is not expected.^13,22

For the irradiation of more complex systems, mass transport to nonirradiated volumes needs to be taken into consideration. Radicals generally react away quickly once they leave the irradiated zone, while the lifetimes of molecular products are sufficiently long to allow an accumulation and to affect the radiolysis environment of the water.^21,23 The most recent exploratory isotope harvesting studies at the NSCL were performed with a water-traversed beam blocker manufactured from Ti64-alloy, which mimics the conditions expected at FRIB. The radionuclides were created in the water matrix and transported to the collection sites by the continuous circulation of a large water volume (∼40 L). Depending on the volatility of the respective species, the collection is accomplished either from the aqueous phase on ion exchange resins or on gas traps after a carrier gas stream transferred the gaseous radionuclides into the headspace.⁴ In addition to acquiring the necessary technical and chemical knowledge about the isotope harvesting process, the suitability of the Ti64-alloy shell material was assessed. This was realized by high-intensity proton irradiation at the University of Wisconsin-Madison Cyclotron Laboratory (UW).²⁴

In consideration of our isotope harvesting efforts, additional importance is attached to understanding water conditions and the effects of radiolysis. A prediction of the expected concentrations of H₂, H₂O₂, and O₂ with an escape yield-based model was regarded as valid when taking the large volume of irradiated water into account. However, increasing discrepancies between the predicted and observed levels were recognized at elevated beam currents. The escape yields reported in the literature suggest a beam current independent behavior in the intensity range of a few nanoampere.¹⁹ Given that the focus of our experiments is directed toward the generation of radionuclides, the applied beam intensities were several orders of magnitude higher. Based on our observations, substantial interactions of all radiolytic species inside the irradiated volume are presumed.

In this work, an in-house written Python code was used to simulate the radiolysis reactions inside the flowing-water target during the proton irradiation. The computations suggest a dependence of the observed yields on the applied beam currents as well as on the prevailing concentrations of molecular hydrogen, hydrogen peroxide, and oxygen. However, the significance of the effective yield estimation was demonstrated to be less important once the concentrations within the entire system’s water approach steady-state conditions. While the establishment of a steady state is known to occur when low-LET radiation is applied onto unified water volumes, the contrast to our system is that our system consists of a small, beam-irradiated chamber, connected to a large, nonirradiated volume. However, at FRIB, predominantly heavy-ion beams of high LET will be studied. Under such conditions, the formation of molecular products is believed to follow an effective yield-based model, rather than transitioning toward a steady state. This radiolysis model establishes the groundwork for a later translation toward the conditions at FRIB and will aid in estimating the levels of radiolysis products generated during isotope harvesting.

2. Materials and Methods

2.1. Isotope Harvesting System and Experimental Setup

The proton irradiation was conducted at the UW (University of Wisconsin) Medical Physics Department’s GE PETtrace cyclotron and focused on the assessment of the durability of the flowing-water isotope harvesting target. An exhaustive description of the experimental design as well as the results of the study are published in a separate publication.²⁴ While the preliminary results on radiolysis are described there as well, the underlying radiolysis mechanisms were not discussed, and no in-depth explanations about the observed phenomena were provided. To move ahead, simulation was viewed as a useful tool for unraveling the details of the bulk radiolysis yields.

Here, a brief overview of the experimental setup is given to enhance the understanding of the simulation. The proton beam was extracted from the cyclotron with an energy of 16 MeV and was directed toward the water-filled beam blocker. Due to geometrical constraints, it was not possible to measure a suppressed beam current. Therefore, the beam intensity was inferred by combining information from calibrated and suppressed Faraday cups upstream of the beam blocker with the unsuppressed current. In addition, the beam current was benchmarked against the induced radioactivity in the beam blocker window. The entire irradiation (∼3.3 h) was divided into four irradiation periods, where the beam current was ramped up steadily, resulting in intensities of 1–33.7 μA.

The beam blocker is manufactured from 3D-printed titanium alloy (Ti64, 90% Ti, 6% Al, 4% V, Stratasys, Minneapolis MN, USA) and encompasses integrated channels to establish water flow. After passing through the 590 μm thick Ti64 front face, the proton energy was degraded to 9.7 MeV. A detailed description of the beam blocker is given elsewhere.⁴ An overview of the isotope harvesting system is provided by the schematic diagram in the Supporting Information, Figure S1, while the passage of the proton beam through the target is depicted in the Supporting Information, Figure S2.

With the low-energy proton beam impinging on the water-filled beam blocker, the induced nuclear reactions are limited to fusion-evaporation in the water and the target shell. The created radionuclides, such as ¹³N, ¹⁸F, ⁴⁸V, and ⁵¹Cr, were transported away from the production site by the fast water flow (13.2 L/min) through the target, also referred to as the “main loop”. This main loop is interfaced with the harvesting system, consisting of a reservoir of around 36 L of water. To facilitate the circulation of water, the pump operated in a constant pressure mode, set to 45 psi. Radionuclides were extracted from the water with ion exchange resins, while volatile species were captured from the gas phase on a variety of traps. These processes are organized in several subunits off the main loop.²⁴

The concentrations of radiolytic hydrogen, hydrogen peroxide, and oxygen were monitored throughout the irradiation. An online assessment of the H₂ and O₂ levels was achieved with one hydrogen sensor and two dissolved oxygen sensors (referred to later as “sensor 1” and “sensor 2”). A stream of He purge gas passing through the water reservoir facilitated the transportation of gaseous radionuclides from the system’s water to their collection sites, as well as the removal of dissolved oxygen and hydrogen. During temporary suspensions of the irradiation, water samples of ∼50 mL were withdrawn and analyzed for the hydrogen peroxide content. The quantification was accomplished by a semiquantitative strip test immediately after removal of the sample and by a precise spectrophotometric analysis, done within 7 days after the experiment.⁴ To prevent an accumulation of H₂O₂ to levels which could adversely affect the equipment, a subunit accommodated a H₂O₂ disintegration system. The catalytic reaction, which is mediated by the noble metals Pt and Pd, follows the overall reaction: H₂O₂ → H₂O + ¹/₂O₂.²⁵ Additionally, a heat exchanger connected to a chiller was employed to maintain the water temperature at ∼25 ^◦C. Considering the low levels of generated radioactive species and the low observed conductivity, the pH of neutral water was estimated for this experiment.

2.2. Radiolysis Measurements and System Conditions

The concentrations of radiolytically formed H₂, H₂O₂, and O₂ were predicted by mass transport calculations that are based upon production rates of the molecules in water and their simultaneous decomposition and volatilization rates. The dissolved gas equilibria were presumed to follow Henry’s law. The extremely low concentrations of radioactive and stable components in the water render any solution composition effects negligible, and thus, Henry’s law was considered as an adequate approximation. Further, Henry’s law was applied in a previous study to describe the behavior of gaseous radionuclides in our isotope harvesting system, and the approximation was corroborated by the simultaneous measurement of the volatile species in the gas and water phase.¹¹

The equations for estimating the levels of H₂, H₂O₂, and O₂ were published previously;²⁴ however, a brief overview of the computation is given in the Supporting Information, “Estimation of the H₂, H₂O₂, and O₂ levels”. In brief, the levels of H₂ are predicted by assuming a beam power-dependent production rate and a concurrent exchange of H₂ between the water and its headspace. To determine the H₂ levels at the end of the gas loop, the H₂ produced in the water passes through the headspace and the traps before it is analyzed by the sensor (%H₂ at sensor). The equations for all the steps are outlined in the Supporting Information, eqs S1–S4. Similarly, the net balance of H₂O₂ is governed by a beam-induced formation and a continuous peroxide decomposition by the catalytic converter after the third irradiation period (Supporting Information, eq S5). The amount of dissolved oxygen in the system’s water is approximated by a beam power-dependent production, a constant deaeration from the water, and additional O₂ input from the H₂O₂ decomposition when water is passed through the catalytic converter (Supporting Information, eq S6).²⁴

The production rates are also known as escape yields or G values and are expressed in units of molecules/100 eV. Previously, a model developed by La Verne, in which the escape yield is expressed as a function of the parameter MZ²/E, was used to predict the G values for H₂, H₂O₂, and O₂.^17,24 However, for light and low energetic ions the difference to the conventional LET model is negligible and in order to be consistent with all other literature data, the G values specified by Pastina et al. were used for computing the radiolysis product formation rates.¹⁹

2.3. Model Definition

The radiolysis model was developed in Python and refers to the homogeneous stage of radiolysis, which starts about 10^–7 s after the deposition of ionizing radiation. At this time, the radiolytic products have already diffused away from the tracks and are uniformly distributed in the bulk solution. The radiolysis kinetics of this phase can be accurately described by the set of elementary chemical reactions given in Table 2.^19,26

Table 2. Reactions and Rate Constants Used in the Simulation Models for the Closed Container and the Flowing-Water Target^a.

reaction no.	reaction	rate constant (M–1 s–1 or s–1)b
Acid–Base Reactions
0	H+ + OH– → H2O	1.18 × 1011 *
1	H2O → H+ + OH–	2.12 × 10–5 *
2	H2O2 → H+ + HO2–	9.43 × 10–2 *
3	H+ + HO2– → H2O2	5.02 × 1010 *
4	H2O2 + OH– → HO2– + H2O	1.33 × 1010 *
5	HO2– + H2O → H2O2 + OH–	1.27 × 106 *
6	e–aq + H2O → H + OH–	15.75 *
7	H + OH– → e–aq + H2O	2.44 × 107 *
8	H → e–aq + H+	5.83 *
9	e–aq + H+ → H	2.09 × 1010 *
10	OH + OH– → O– + H2O	1.33 × 1010 *
11	O– + H2O → OH + OH–	1.27 × 106 *
12	OH → O– + H+	9.43 × 10–2 *
13	O– + H+ → OH	5.02 × 1010 *
14	HO2 → O2– + H+	7.73 × 105 *
15	O2– + H+ → HO2	5.02 × 1010 *
16	HO2 + OH– → O2– + H2O	1.33 × 1010 *
17	O2– + H2O → HO2 + OH–	1.55 × 10–1 *
Chemical Reactions
18	e–aq + OH → OH-	3.55 × 1010 *
19	e–aq + H2O2 → OH + OH–	1.36 × 1010 *
20	e–aq + O2– + H2O → HO2– + OH–	1.30 × 1010
21	e–aq + HO2 → HO2–	1.30 × 1010 *
22	e–aq + O2 → O2–	2.29 × 1010 *
23	2e–aq + 2H2O → H2 + 2OH–	7.26 × 109 *
24	e–aq + H + H2O → H2 + OH–	2.76 × 1010 *
25	e–aq + HO2– → O– + OH–	3.50 × 109
26	e–aq + O– + H2O → 2OH–	2.20 × 1010
27	e–aq + O3– + H2O → O2 + 2OH–	1.60 × 1010
28	e–aq + O3 → O3–	3.60 × 1010
29	H + H2O → H2 + OH	4.58 × 10–5 *
30	H + O– → OH–	1.00 × 1010
31	H + HO2– → OH + OH–	9.00 × 107
32	H + O3– → OH– + O2	1.00 × 1010
33	H + H → H2	5.14 × 109 *
34	H + OH → H2O	1.09 × 1010 *
35	H + H2O2 → OH + H2O	3.65 × 107 *
36	H + O2 → HO2	1.31 × 1010 *
37	H + HO2 → H2O2	1.14 × 1010 *
38	H + O2– → HO2–	1.14 × 1010 *
39	H + O3 → HO3	3.80 × 1010
40	OH + OH → H2O2	4.81 × 109 *
41	OH + HO2 → H2O + O2	8.84 × 109 *
42	OH + O2– → OH– + O2	1.10 × 1010 *
43	OH + H2 → H + H2O	3.95 × 107 *
44	OH + H2O2 → HO2 + H2O	2.92 × 107 *
45	OH + O– → HO2–	2.50 × 1010
46	OH + HO2– → HO2 + OH–	7.50 × 109
47	OH + O3– → O3 + OH–	2.60 × 109
48	OH + O3– → 2O2– + H+	6.00 × 109
49	OH + O3 → HO2 + O2	1.10 × 108
50	HO2 + O2– → HO2– + O2	8.00 × 107
51	HO2 + HO2 → H2O2 + O2	8.40 × 105 *
52	HO2 + O– → O2 + OH–	6.00 × 109
53	HO2 + H2O2 → OH + O2 + H2O	0.50
54	HO2 + HO2– → OH + O2 + OH–	0.50
55	HO2 + O3– → 2O2 + OH–	6.00 × 109
56	HO2 + O3 → HO3 + O2	5.00 × 108
57	2O2– + 2H2O → H2O2 + O2 + 2OH–	0.3 *
58	O2– + O– + H2O → O2 + 2OH–	6.00 × 108
59	O2– + H2O2 → OH + O2 + OH–	0.13
60	O2– + HO2– → O– + O2 + OH–	0.13
61	O2– + O3– + H2O → 2O2 + 2OH–	1.00 × 104
62	O2– + O3 → O3– + O2	1.50 × 109
63	2O– + H2O → HO2– + OH–	1.00 × 109
64	O– + O2 → O3–	3.75 × 109 *
65	O– + H2 → H + OH–	1.28 × 108 *
66	O– + H2O2 → O2– + H2O	5.00 × 108
67	O– + HO2– → O2– + OH–	7.86 × 108 *
68	O– + O3– → 2O2–	7.00 × 108
69	O– + O3 → O2– + O2	5.00 × 109
70	O3– → O2 + O–	2.62 × 103 *
71	O3– + H+ → O2 + OH	9.00 × 1010
72	HO3 → O2 + OH	1.10 × 105

^aThe reactions and rate constants were taken from Pastina et al.¹⁹ For the reactions where water is a reactant, Pastina et al. considered the concentration of water in the expression of the rate constant. However, in the present system pure water is the main component, while the concentrations of H₂, H₂O₂, and O₂ are in the μM range. Therefore, this term was considered negligible, and only the numerical expressions of the rate constants are given in the following table.

^bFor several reactions updated rate constant data were available from Elliott & Bartels.²⁹ The data from this compilation were used to compute the reaction rate constants for a water temperature of 25 °C. Updated rate constants are labeled by an asterisk (*).

Simulation Model for a Closed Container

The first scenario for simulation involved numerically computing the saturation concentrations of radiolytic compounds during prolonged irradiation of water in a closed container. The model was designed to reproduce the conditions that would be reached when a 20 mL closed volume of water was uniformly exposed to either proton or γ radiation. For the ¹H⁺ irradiation model, a particle energy of 9.7 MeV was used, and an initial LET of 12.8 eV/nm was estimated with the Stopping and Range of Ions in Matter compilation code (SRIM 2013).²⁷ The simulations were performed with varying beam currents, ranging from 0.1 to 50 μA. The dose rates were calculated by considering the beam power deposited into the water volume. For the γ-radiolysis model, the dose rate was set to 0.25 Gy/s. Both scenarios ignored surface interactions and were treated as being perpetually homogeneous.

Inside the water volume the formation of the radiolytic species e_aq^–, H, H₂, OH, H₂O₂, HO₂, H⁺, and OH^– is assumed to occur with the respective escape yields, given in Table 1. The escape yields were published by Pastina et al. for γ-rays and 10 MeV ¹H⁺, where the latter is assumed to be a close approximation for the 9.7 MeV protons of the current experiment. With each delivered beam particle, the formation of primary radiolytic species is induced, and they are allowed to react homogeneously according to a set of 73 chemical reactions (Table 2). The reaction system was previously developed by Elliot et al. and successfully applied by Pastina et al. and Iwamatsu et al.^19,23,28 The simulation considers a constant temperature of 25 °C, and the pH of neutral water is accepted as an initial condition. During the chemistry phase numerous secondary species, such as HO₂^–, O₂^–, O₂, O^–, O₃^–, O₃, and HO₃ are created, and all begin to interact. Most of the elementary reactions are binary and have the general form

representing the reaction of species A and B to form species C and D with a rate constant k_AB→CD. When following any given species C, it is consumed in reactions with the same form, for example,

representing the reaction of species C and E to form species F and G with a rate constant k_CE→FG.

Table 1. G Values Used in the Model Calculations (Units in Molecules/100 eV)¹⁹.

species	G (10 MeV 1H+)	G (γ-rays)
e–aq	0.90	2.60
H	0.57	0.66
H2	0.64	0.45
OH	1.18	2.70
H2O2	0.74	0.70
HO2	0.03	0.02
H+	1.10	3.10
OH–	0.20	0.50

In the Python code, differential equations were used to describe this system of interactions and to compute the time-dependent concentrations. For example, the differential equation following the concentration of any radiolytic species, [C], in the water is expressed generically by eq 1:

1

where the first term, G_C·I(t), represents the beam-induced generation of species, and the following two terms account for the chemical reactions leading to the formation and destruction of species C as shown in reactions 1 and 2, respectively. Finally, the concentrations of all species were calculated through simultaneous numerical integration of the differential equations using one-nanosecond time steps.

A time resolution of one nanosecond was considered adequate to accurately estimate the levels of all radicals, ions, and molecules resulting from the complex interactions. However, the fast reaction rates of the interconversion between the protonated and deprotonated species, such as H₂O ↔ H⁺ + OH^– (pK_a = 13.999), H₂O₂ ↔ H⁺ + HO₂^– (pK_a = 11.65), OH ↔ H⁺ + O^– (pK_a = 11.9), and HO₂ ↔ H⁺ + O₂^– (pK_a = 4.57),¹⁹ required additional consideration. The quantities of all protonated and deprotonated species formed in chemical reactions with their specific rate constants (i.e., for H₂O: rxn 0 and 1, for H₂O₂: rxn 2 and 3, for OH: rxn 12 and 13, for HO₂: rxn 14 and 15 in Table 2) were compared with the quantities resulting from an adjusted acid–base equilibrium. The smaller values were used to approximate the levels at the end of the respective time step.

Simulation Model for the Flowing-Water Target

In a further development, the model was adapted to recreate the conditions during the 9.7 MeV proton irradiation of the flowing water as closely as possible. Given that the entire beam power is deposited in the first water-traversed channel in the experimental beam blocker, the formation of all radiolytic species occurs in this region. Based on previous observations, the directly irradiated area is estimated to be 0.7 cm². The irradiated water volume (in the following referred to as “beam strike volume”) is defined by the 2 mm distance between the two Ti64 sheets and amounts to 0.14 mL. The number of protons delivered by the applied beam currents, ranging from 1 to 33.7 μA, occurred at a frequency of 27.2 MHz and resulted in the transmission of 2.23 × 10¹²–7.50 × 10¹³ eV per pulse. With each delivered beam pulse the formation of primary species is induced. Their formation and subsequent reactions are based on the same set of escape yields and chemical reactions as described previously for the closed container model.

The flowing-water target was traversed by a fast water flow of 220.8 mL/s, which resulted in a flow of 41.7 mL/s through the beam strike volume. Thus, all the produced radiolytic species are continuously transported away from the irradiation site. This scenario is considered in the model by introducing a constant supply of fresh solution into the beam spot volume (Figure 1) with the removal of an equivalent amount of irradiated solution. The water in the beam spot was assumed to be instantaneously, and perfectly mixed. The evolution of all molecular and radical species was followed until equilibrium was attained, which occurred after ∼20 ms in all evaluated conditions. The steady-state concentrations of H₂, H₂O₂, and O₂ were used to compute their effective production yields, also denoted as effective G values (G_eff). Over the entire irradiation time of the experiment (∼3.3 h), the extended lifetimes of the molecular species enabled an accumulation in the system’s water. To recreate this behavior in the simulations, the solution inside the beam strike volume (in the following designated as “baseline” concentration), as well as the supplying solution, were assumed to encompass varying concentrations of H₂, H₂O₂, and O₂. This allowed us to assess the influence of different hydrogen, peroxide, and oxygen concentrations on the respective effective yields.

Figure 1.

A 16 MeV proton beam passes through the first layer of Ti64, uniformly dispersed over an area of about 0.7 cm². At the interface of the water, the protons encompass an energy of 9.7 MeV which they dissipate entirely in the volume between the two Ti64 sheets. This “beam strike volume” amounts to 0.14 mL, and the locally generated radiolytic and nuclear species are continuously transported away by the fast water flow (41.7 mL/s).

2.4. Radiolysis Reactions in the Proton-Irradiated Flowing-Water Target

The extent of the H₂ and H₂O₂ yield suppression within the flowing-water target was evaluated by introducing the “percentage metric for total yield suppression”, S_total (eq 2):

2

where G_eff represents the unsuppressed effective yield and G_lit is the published literature G value. In this representation, a positive value indicates the percentage suppression of the computed effective yield in comparison to the literature escape yield, whereas an enhanced yield is illustrated by a negative value.

The chemical reactions influencing the levels of H₂ and H₂O₂ in the flowing-water target were identified by consecutively suppressing individual reactions and comparing the resulting effective yields with the unsuppressed ones. The “percentage metric for yield suppression by Allen cycle rxn”, S_Allen, was computed by eq 3:

3

where G_Allen=0 represents the effective yield computed with suppressed Allen cycle reactions (Table 2, rxn 35 and 43). A close approximation of this value to S_total can be considered as a qualitative measure for the contribution of the Allen cycle reactions toward the observed suppression of H₂ and H₂O₂, respectively.

The “percentage metric for yield suppression by H₂O₂-mediating rxn”, S_H2O2 rxn, is given by eq 4:

4

For the calculation of G_H2O2,rxn, not only the Allen cycle reactions but also other H₂O₂ pathways, such as the reactions with hydrated electrons and hydroxyl radicals (Table 2, rxn 19, 35, 40, 43, 44), were suppressed. A value close to S_total underlines the significance of all before-mentioned reactions toward the observed suppressed H₂O₂ yield.

2.5. Quantification of Proton Beam-Induced Radiolysis in the System’s Water

The “Design of Experiments” feature of the statistical software “Minitab” (Minitab LCC, product version 20.1.2) was used to determine the functional dependencies of the effective G values of H₂, H₂O₂, and O₂ on their respective concentrations as well as on the beam current. This approach encompassed the software-supported proposal of a set of experimental conditions, used as input parameters for simulating the effective yields. This was followed by a functional analysis to establish an empirical model. To enhance the descriptive ability of the model, the beam current range was divided into four segments (0.5–7.5, 7.5–15.0, 15.0–24.5, and 24.5–34.0 μA) where the levels of H₂, H₂O₂, and O₂ were varied over a reasonable concentration range. The concentration ranges were chosen with respect to the observed levels during the irradiation experiment. After computing the effective G values with the suggested inputs of H₂, H₂O₂, and O₂ concentrations and beam currents, the functional dependencies were found with the “Response Surface” method. Next to linear, possible quadratic correlations could also be considered with this method. The recommended model was improved by consecutively removing the terms identified as statistically insignificant at a significance level α of 0.05. With the optimized regression equations for the effective H₂, H₂O₂, and O₂ yields, their levels could be mapped for the entire irradiation experiment. For the effective yield-based model the literature escape yields (G) in eqs S1, S5, and S6, outlined in the Supporting Information, were replaced by the values of the respective effective yields (G_eff).

In the simulations, when the water flow rate is set to zero (i.e., irradiation of a closed small-volume system), the concentrations of H₂ and H₂O₂ inside the target approach steady states. In the flowing-water system, given the small target volume and high-power deposition, it is feasible that during the time a small volume of water is passing through the beam strike area, it could approach a local steady state. The G_eff model can be augmented to respect the steady-state limit by introducing a throttle on the rate of change in concentration of H₂ and H₂O₂. In this model, called the G_eff + SS model, an introduced constraint limits the changes in H₂ and H₂O₂ concentrations (Δ[H₂O_2,Geff] or Δ[H_2,Geff]) during any time step to being no larger in magnitude that could be achieved when approaching the zero-flow steady-state limit. Thereby, the concentration of H₂O₂ at time t_i ([H₂O₂]_ti) is obtained by numerical integration of the following piecewise equation (eq 5):

5

To estimate the H₂ concentration at time t_i ([H₂]_ti), all H₂O₂ related expressions in eq 5 are replaced by the equivalent H₂ expressions. The individual components of eq 5, that is, the difference in H₂O₂ and H₂ levels for the steady-state approximation (Δ[H₂O_2,SS] or Δ[H_2,SS]) and the G_eff model (Δ[H₂O_2,Geff or Δ[H_2,Geff]) are illustrated by eqs 6–8.

The difference in H₂O₂ levels for the steady-state approximation (Δ[H₂O_2,SS]) within a 100 s time interval is given by eq 6:

6

where [H₂O₂]_SS,segment represents the steady-state concentration of H₂O₂ in the respective irradiation segment. This value was computed by employing the approximating power functions together with the calculated average dose rate of each irradiation segment (Supporting Information, Table S1 and Table S2). [H₂O₂]_ti−1 is the H₂O₂ concentration at the previous time t_i-1, Δt is the time interval between t_i and t_i–1 (100 s) and k_SS represents the time constant in Hz (a more in-depth description is given below). The difference in H₂ levels for the steady-state approximation (Δ[H_2,SS]) is computed by the same equation after replacing [H₂O₂]_SS,segment with the steady-state concentration of H₂ for the respective irradiation segment, that is, [H₂]_SS,segment (Supporting Information, Table S2), and using the preceding H₂ concentration [H₂]_ti−1.

The time constant, k_SS, was introduced as a free variable to consider the limited residence time in the beam strike volume and the consequential time delay in the approximation of steady-state concentrations within the system’s water. The Microsoft Excel Solver plug-in was used to find a value for k_SS that minimizes the χ² difference between the measured values of H₂ and H₂O₂ and the values produced by eq 5 at these times.

For the G_eff model the difference in H₂O₂ levels (Δ[H₂O_2,Geff]) in one time step is estimated by eq 7:

7

where P(t_i) represents the power of the ¹H⁺ beam at time t_i (eV/s), G_eff is the effective H₂O₂ yield (molecules/100 eV), and N_A is the Avogadro constant (6.022 × 10²³ particles/mol). [H₂O₂]_t−1 represents the hydrogen peroxide concentration at the preceding time t_i–1, and Δt is the time interval between t_i and t_i–1 where 100 s was used. The total water volume (V_water) is 36 L and k_KLC is the hydrogen peroxide decomposition rate of the catalytic converter (3.34 × 10^–5 s^–1).²⁴

Equation 8 was used to approximate the difference in H₂ levels for the G_eff model (Δ[H_2,Geff]):

8

The amount of H₂ in the headspace is represented by [H₂]_headspace, and the factor β₁ describes the kinetics of the exchange process (β₁ ∼ 0.05 L/s). R is the ideal gas constant (8.21 × 10^–3 L·atm/K·mol), K_H is Henry’s law constant for H₂ (780 μM/atm), and T is the bulk water temperature (∼298 K). A volume of ∼10 L was used for the headspace (V_headspace).

3. Results and Discussion

To demonstrate the validity of the developed model, the γ-radiolysis simulation with a closed 20 mL water container, which was previously described by Pastina et al., was repeated, and the results were compared.¹⁹ Following the development of the relevant water decomposition products over the irradiation time, the computed concentration levels are largely in agreement with the previously published data (see Figure 1 in Pastina et al.¹⁹). However, the computed steady-state concentrations are moderately lower, which could be due to the updated rate constant data used in our simulation (Table 2). In this way, the suitability of the fundamental code setup was confirmed and formed the basis for performing further experiments with protons.

3.1. Proton Irradiation of a Closed Container

In analogy to the gamma-ray irradiation of a closed 20 mL water container, similar computations were performed with 9.7 MeV protons. In Figure 2 a the development of relevant molecular, ionic, and radical species during the irradiation with a beam current of 1 μA is displayed. Initial levels of H₂, H₂O₂, OH, H, and e^-_aq range between 10^–9 and 10^–8 M, whereas the levels of O₂ and O₂^– are considerably lower. The formation of HO₂ is observed with some time delay and exceeds 10^–11 M only after ∼6 ms. Throughout the irradiation, the concentrations of H₂, H₂O₂, O₂, O₂^–, and HO₂ show an increasing trend, while the levels of OH, H, and e^-_aq are decreasing. H⁺ ions are a primary water radiolysis product and their generation by the incoming proton beam results in a local decrease of the pH during the irradiation.³⁰ To appropriately approximate the radiolysis chemistry in our simulation, the ratio between protonated and deprotonated species of all conjugate acid–base pairs is allowed to adjust with the prevailing pH. Further, the simulation considers a complete dissolution of all radiolytically produced gases. This is because the pressure within the closed container increases relative to the formed H₂ and O₂ and, in agreement with Henry’s law, the solubility of a gas is directly proportional to its partial pressure above the liquid.

Figure 2.

(a) Temporal development of relevant water decomposition products in 20 mL of pure water during the irradiation (600 s), simulated with 9.7 MeV ¹H⁺ at a beam current of 1 μA. The pH of the irradiated water is displayed on the secondary y-axes. (b) The computed steady-state concentrations of several molecular, radical, and ionic radiolysis products (H₂, H₂O₂, O₂, O₂^–, HO₂, OH, H, e^-_aq) as a function of dose rate in pure water. The dashed lines are the power function fits to the data. The measured steady-state concentration of H₂O₂ for 10 MeV ¹H⁺, published by Pastina et al.¹⁹ (pink data point), is in line with the simulated data points (red data points).

After an irradiation time of ∼100 s, the concentrations of all radiolytic products remain essentially unchanged. Such a scenario is referred to as a steady state and is defined by an equal rate of formation and decomposition. For most species the main production path is the primary radiolysis process, while the removal is typically mediated by reactions between molecules with radicals and ions.^20,21Equation 9 describes the steady-state concentration of the primary radiolysis product A ([A]_SS), where the production is determined by the dose rate (D_R) and the respective G value (G_A), and the decomposition is given by the rate constant (k_A+B) for the reaction of A with chemical species B.

9

The concentrations of other radiolysis products, which also depend on the dose rate, are included in the denominator, resulting in an approximate square-root dependency of the steady-state concentration on the dose rate (Supporting Information, Table S1). The exponents for the molecular species are slightly lower than 0.5, while the ones of radical species are marginally higher. The computed steady-state concentrations of several radiolysis products as a function of the dose rate are visualized in Figure 2b. The steady-state concentrations of hydrogen peroxide, estimated with this approximation, are in line with the experimentally obtained data from Pastina et al.¹⁹ (Figure 2b, pink data point). A similar behavior for the steady-state concentrations of γ-radiolysis products was described experimentally as well as by model calculations.^20,21,26,30 In comparison to γ-rays, the absolute steady-state concentrations of the molecular species are considerably higher for protons, while the radical quantities are diminished. Such behavior is expected from the absolute values of the radiolytic yields for protons and gamma-rays and can be explained by the different LETs of the radiation (a more in-depth explanation is given in the following section). Equilibrium conditions are approached rapidly for low-LET radiation, while at increased LET the concentrations of molecular species increase nearly linearly with time, and steady-state conditions are reached much more slowly.^19,21,30 However, with high-LET radiation, water molecules will be decomposed continuously, and the approximation of a steady state is not expected.^13,22

3.2. Radiolysis Reactions in the Proton-Irradiated Flowing-Water Target

The temporal development of relevant radical, ionic, and molecular products (H₂, H₂O₂, O₂, OH, e^–_aq, O₂^–, HO₂, H) inside the beam strike volume of the flowing-water target was computed for four different scenarios and is exemplified in Figure 3. The simulations were set up in a way that the entire volume was either filled with pure water or a solution of 50 μM H₂ and H₂O₂ prior to the onset of irradiation, and was also supplied with the same fluid throughout the beam irradiation (in the following referred to as “baseline” and “in-flowing solution” concentrations). The concentration levels of the radiolytic species were followed for 100 ms; however, a steady-state concentration was already approximated after an irradiation time of ∼6 ms. This is unlike the observations for the closed container (Figure 2a), where an equilibrium was achieved only after prolonged irradiation times. In the dynamics of the flowing-water target, the establishment of a dynamic equilibrium is determined by the removal rate, which depends on the outgoing water flow. At the set flow rate of 41.7 mL/s, the entire beam strike volume is replaced by fresh water after ∼3.4 ms which can be considered as the onset of the dynamic equilibrium.

Figure 3.

Temporal development of relevant water decomposition products in the beam strike volume of the flowing-water target, irradiated with proton beam intensities of (a, b) 1 μA and (c, d) 20 μA . The water that is initially present as well as the in-flowing water contained (a, c) 0 μM of the stable molecular species H₂, H₂O₂, and O₂ and (b, d) 50 μM H₂ and H₂O₂, respectively.

After an irradiation time of ∼20 ms, an apparent steady state was established, and the resulting levels of H₂, H₂O₂, and O₂ were used to compute the effective yields, also denoted as effective G values, G_eff. The escape yields (or “G values”) of radiolytic products are defined as the yield at the end of the nonhomogeneous track expansion before any homogeneous reactions occur. The calculated effective G values for H₂ and H₂O₂ for pure water and solutions encompassing 50 μM H₂ and H₂O₂ (scenarios represented in Figure 3) are displayed in the first two columns of Table 3. In comparison to the published escape yields for H₂ and H₂O₂, amounting to 0.64 and 0.74 molecules/100 eV,¹⁹ the G_eff values were noticeably diminished. A similar trend could be identified for the effective yields which were computed for a wide range of beam currents and H₂, H₂O₂, and O₂ concentrations (Supporting Information, Table S3a–d). However, throughout all these different scenarios, the material balance between the number of H and O atoms of all created radiolytic species equals the net water decomposition. (A more in-depth explanation is given in the Supporting Information, “Net water decomposition”.) Similar discrepancies between the measured H₂ and H₂O₂ levels and the escape yield-based predictions were observed earlier.^19,23,31 Following the end of the nonhomogeneous phase, the system transitions toward a homogeneous regime. There the regulatory effect of the chemical reactions is of increasing significance, particularly at elevated radical concentrations. The radiation’s LET determines the structure of the tracks and thereby directly impacts the quantity of radicals. Dispersed ionization events at low LET result in few intratrack reactions and a significant number of radicals can escape into the bulk solution. At high-LET conditions, single ionization events coalesce, leading to increased radical densities which enhances the probability to react with each other, and consequently, more molecular products are disseminated.^{16,19,23,32,33} Pastina et al. demonstrated that homogeneous reactions play a significant role for 10 MeV protons, which are characterized by a moderate LET value, and influence the observed levels of H₂ and H₂O₂.¹⁹ (A more in-depth explanation of this observation is given in the next paragraph.) A similar suppressive effect on the H₂ and H₂O₂ concentrations can be assumed for the irradiations of our flowing-water target with 9.7 MeV protons.

Table 3. Effective Yields, G_eff, the Percentage Metric for Total Yield Suppression, S_total, the Percentage Metric for Yield Suppression by Allen Cycle rxn, S_Allen, and the Percentage Metric for Yield Suppression by H₂O₂-Mediating rxn, S_H2O2rxn, of Different Solutions Computed for Low and High (1 and 20 μA) Beam Intensity Irradiations of the Flowing-Water Target.

	Geff (molecules/100 eV)		Stotal (%)		SAllen (%)		SH2O2rxn (%)
	1 μA	20 μA	1 μA	20 μA	1 μA	20 μA	1 μA	20 μA
for 0 μM H2, H2O2
H2	0.63	0.48	0.2	25	2	26
H2O2	0.57	0.33	23	56	3	12	26	58
for 50 μM H2
H2	0.52	0.45	19	29	20	30
H2O2	0.49	0.32	34	57	17	14	37	59
for 50 μM H2O2
H2	0.60	0.49	7	24	9	25
H2O2	0.22	0.29	70	61	10	13	71	63
for 50 μM H2, H2O2
H2	0.42	0.46	34	28	35	29
H2O2	0.19	0.28	75	62	23	15	75	64

By consecutively suppressing individual chemical reactions, it became possible to identify the ones which strongly influence the levels of H₂ and H₂O₂. A mechanism known as the “Allen cycle” is an important mediator for the concentrations of H₂ and H₂O₂ and starts with the reaction of hydrogen with hydroxyl radicals. Subsequently, the formed hydrogen atoms react with hydrogen peroxide, forming hydroxyl radicals and water.³⁴ The relevant reactions are given in Table 2, rxn 35 and 43. Within this chain mechanism, an effective elimination of H₂ and H₂O₂ is facilitated. A crucial precondition for the Allen cycle is the presence of radicals, particularly of OH and H. A LET of about 20 eV/nm is considered as a threshold below which adequate levels of radicals can escape from the ionization tracks to support the recombination reactions. With a LET of 12 eV/nm, the 9.7 MeV protons of the current experiment are below this threshold LET and can therefore contribute toward an effective annihilation of H₂ and H₂O₂.^19,23,26,35 An inhibiting effect was seen at excessive O₂ concentrations, which was also reported in previous studies.¹⁹

In our flowing-water target, the quantity of hydrogen is mainly regulated by the Allen cycle. However, a continuous reaction cycle can only be established when H₂ and H₂O₂ are present in sufficient amounts. This is the case at increased concentration levels or at enhanced beam intensities, which in turn generate higher levels of radiolytic species. When none of these conditions are given, as in the case of pure water irradiated with a low beam current (Table 3), the effective hydrogen yield (0.63 molecules H₂/100 eV) is similar to the literature escape yield (0.64 molecules H₂/100 eV).¹⁹ However, when exposing the same solution to higher beam intensities, suppression of the effective H₂ yield by 25% was achieved. (A more in-depth explanation about the metrics used to characterize the yield suppression is given in the Material and Methods section.) The irradiation of solutions containing either 50 μM H₂ or 50 μM H₂O₂ yielded similar results, whereas a beam current-independent suppression of 34 and 28% was observed when both components were present. The good agreement for all different solutions between S_total and S_Allen for the H₂ data supports an almost exclusive Allen cycle-mediated H₂ regulation.

In the case of hydrogen peroxide, the discrepancies between S_total in comparison to S_Allen suggest a considerable influence of other decomposition reactions. The interactions of peroxide with OH radicals (rxn 44) and hydrated electrons (rxn 19) were identified as the main alternative annihilation pathways. Similar radiolytic reaction channels for hydrogen peroxide were reported by previous studies.^19,23,26,31 The increased complexity of the hydrogen peroxide reaction scheme is reflected by the larger extent of total H₂O₂ suppression in comparison to the effects observed for hydrogen. For pure H₂O₂ solutions or mixtures of H₂O₂ and H₂, a decrease of 61–75% was seen, whereas a lower, and beam current-sensitive effect was observed for pure water and solutions containing only H₂. When the latter solution compositions were irradiated with low beam currents, the reaction of hydrogen peroxide with OH radicals (rxn 44) was shown to be hampered, which could be due to limited interactions between radicals and molecules. The efficiency of the H₂O₂ decomposition with hydrated electrons (rxn 19) was not affected by different beam intensities. With S_H2O2 rxn the influence of the main peroxide decomposition (rxn 19, 35, 43, 44) and formation reactions (rxn 40) are considered. The good agreement with the total H₂O₂ yield suppression underlines the importance of all these reactions in the H₂O₂ reaction pathway. For gamma-ray and proton irradiations with LETs below the 20 eV/nm threshold, similar reductions of the H₂O₂ concentration, also in the absence of additional H₂, were reported.^19,23

The formation of H₂ and H₂O₂ occurs mainly within the track, which is usually followed by an outward diffusion into the bulk water. Within the homogeneous regime, the chemistry is mainly determined by secondary reactions of radicals with stable molecular species.^23,31 The resulting yield attenuation of molecular products is described in detail above. Interactions between radicals play an inferior role, and as such, only a slight increase in the quantities of molecular products is observed.¹⁹ In the case of hydrogen, the combination of H atoms (rxn 33), as well as the reaction of H atoms with hydrated electrons (rxn 24), has a moderately enhancing effect on the H₂ levels. The latter reaction plays a limited role and is only relevant at elevated molecular hydrogen concentrations. The combination of OH radicals (rxn 40) is known to be the main intratrack process leading to the formation of hydrogen peroxide.^23,31,32 However, in the homogeneous domain rxn 40 is only of minor significance and limited to low H₂O₂ concentrations, particularly at low beam currents.

The observations of the hydrogen and hydrogen peroxide yields suggest that at elevated beam currents, the attenuation of both species depends only marginally on the solution composition. At FRIB, heavy-ion beams of high intensity will be stopped in the water-traversed beam blocker drum.¹ From the studies with our flowing-water target, suppressed effective H₂ and H₂O₂ yields, in comparison to the literature escape yields, can be expected at FRIB.

3.3. Proton Beam-Induced Radiolysis of the System’s Water

The “Design of Experiments” feature of the statistical software Minitab was employed to minimize the computational effort to determine the functional dependencies of the effective G values of H₂, H₂O₂, and O₂ on their respective concentrations as well as on the beam current. Such a systematic approach allows finding the cause-and-effect relationships by performing the least possible number of experimental runs. To approximate the dependency of the four input variables (H₂, H₂O₂, and O₂ concentration, beam current) and the computed G_eff values of the corresponding molecular species by an empirical model, a careful selection of the input ranges is required. Here the beam current was adopted as the decisive parameter and the entire range was divided into four segments. In comparison to other input factors, the beam current was regulated, and was therefore less susceptible to variations. The so-obtained polynomial equations, including the coefficients and terms of the functional dependency analysis, are given in the Supporting Information, Table S5a–d.

By applying the determined regression equations for G_eff(H₂, H₂O₂, O₂), the concentration levels of all molecular species could be mapped over the entire irradiation time, and the results are displayed in Figures 4a, 5, and 6. In the case of hydrogen (Figure 4a), the effective yield prediction suggests about 1.4-times higher H₂ concentration than observed throughout the entire irradiation. However, with the escape yield-based calculation (assuming a constant G value of 0.64 molecules H₂/100 eV¹⁹), the percentage of H₂ was estimated to be about 2-times higher. The H₂ data acquired within the first irradiation segment was not included in these considerations, since the sensor was not yet adequately equilibrated to the measurement conditions.

Figure 4.

(a) The measured % H₂ at the sensor (black line) is approximated by different estimations: The escape yield- and the G_eff-based models (green and blue line) predict higher H₂ levels, while the G_eff + SS-model suggests a reasonable approximation (orange line). (b) The steady-state concentrations of H₂ in the system’s water are calculated for each irradiation segment (red dashed lines) and are an integral part of the G_eff + SS-based calculation (orange line). The corresponding beam current (gray line) is outlined on the secondary y-axes for both panels a and b.

Figure 5.

Escape yield- and the G_eff-based prediction (green and blue line) overestimate the measured H₂O₂ concentrations (black squares). However, with the G_eff + SS-based estimation (orange line) an adequate approximation could be realized. The steady-state concentrations of H₂O₂ for each irradiation segment are outlined by the red dashed lines.

Figure 6.

Dissolved oxygen levels were assessed before (sensor 1) and after (sensor 2) the water was passed over the catalytic converter unit (black and purple lines). The O₂ levels of the system’s water, which were assessed by sensor 1, were approximated with the G_eff-based estimation (blue line).

At elevated beam currents, the discrepancies between the measured and G_eff-predicted hydrogen peroxide levels increased (Figure 5). For the end of the first irradiation period, the prediction suggests 1.1-times higher H₂O₂ levels than observed, which developed to a 1.9-fold increase after 6.4 h. However, with the escape yield model (assuming a constant G value of 0.74 H₂O₂ molecules/100 eV¹⁹), a maximum of 4.5 mM H₂O₂ was estimated, which is 7.5-times greater than the measured concentrations.

The dissolved oxygen content in the water was assessed with two sensors (sensors 1 and 2), placed before and after the catalytic hydrogen peroxide decomposition unit. The initially comparable sensor readings diverged when the water was passed over the catalytic unit with the onset of the third irradiation period (Figure 6). The exact stoichiometric relationship between H₂O₂ decomposition and O₂ discharge was already discussed by Abel et al. and is also considered in the here performed G_eff-based calculation.²⁴ Similar to the estimated hydrogen peroxide levels, increasing discrepancies between the oxygen levels measured by sensor 1 and the computed predictions became discernible. For the end of the last irradiation period, the computed values were 1.5-times higher than observed; however, only a maximum 1.2-fold increase was noticeable in all previous irradiation segments. Since molecular oxygen is not a primary water decomposition product, no escape yield-based prediction was performed. The G_eff-based calculation considers the oxygen formation by secondary reactions within the homogeneous phase. It needs to be mentioned that additional O₂ was generated by the catalytic H₂O₂ decomposition, which renders the relatively low oxygen levels susceptible to external influences, such as small variations in the converter’s decomposition rate or the deaeration rate. With this experimental setup it is not possible to clearly evaluate any deviations between the estimated and measured oxygen levels, thus no further analytical estimations were attempted.

In general, the G_eff-based calculation allowed a reasonable approximation of the H₂ and H₂O₂ trends, however, the predictions overestimated the observed concentrations. The effective yield computation takes into account the influence on the literature escape yields by the homogeneous chemical reactions, the geometry of the beam strike volume, and the continuous water flow. The latter determines the removal rate of radiolytic species and facilitates the rapid establishment of an apparent steady state inside the beam strike volume. Even though radiolysis phenomena have been extensively described in the literature, most experiments involved the irradiation of an enclosed volume of less than 100 mL. Under such conditions, a homogeneous distribution of the formed radiolysis products and the water molecules can be assumed. By exposing a definite volume to constant low-LET radiation over prolonged time periods, a steady state will establish and determine the concentrations of all radiolytic species.^{19−21,23,26} In our case, the setup encompassed a small, beam irradiated chamber (0.14 mL) connected to a nonirradiated, large water volume (∼36 L). While steady-state conditions are approximated rapidly in limited volumes, extensive irradiation times would be necessary to deliver the required dose to the entire system’s water. However, since the total amount of radiation was deposited only into the beam strike volume, a considerably lower dose and shorter irradiation time would be necessary to approach a local steady state. Based on these assumptions, the steady-state concentrations of H₂ and H₂O₂ were estimated for each irradiation segment by applying the previously outlined equations, which characterize the steady-state concentrations as a function of dose rate (Supporting Information, Table S1). With the slight beam current variations in each irradiation segment, the calculation with the average dose rate was regarded as adequate (Supporting Information, Table S2). Under uniform irradiation conditions, the necessary time to approach steady-state conditions is determined by the applied dose rate. However, in our system the time structure is additionally affected by the limited residence time inside the beam strike volume. Based on these conditions, a model was developed that considers the G_eff-mediated formation as well as the attenuating effect of the established steady state. To estimate the rate of the steady-state approximation, a time constant, k_SS, was introduced. This is a free variable, which was fitted to 2.64 × 10^–4 s^–1 at the minimized χ² difference between the measured and estimated H₂ and H₂O₂ concentrations. With the G_eff + SS-based calculation, the amount of H₂ in the system’s water was calculated (Figure 4b) and converted to the percentage H₂ at the sensor to allow a comparison with the measured data (Figure 4a). In this way, a reasonable approximation became possible, though the levels after the third irradiation segment are moderately overestimated. The observed discrepancies might be due to the removal of H₂ from the water and slight variations in the flow of the purge gas stream. The G_eff + SS-model also allowed an adequate estimation of the measured H₂O₂ levels over the entire irradiation time (Figure 5). It needs to be emphasized, that this model requires a fitted time constant k_SS, which, so far, is not confirmed by experimental measurements. The time constant is primarily influenced by the conditions of the system, such as the flow rate. However, since k_SS allows the extrapolation of a scenario where the water flow rate is set to zero (i.e., irradiation of a closed small-volume container) toward a flowing-water system with a connected large, nonirradiated volume, it includes any deviations related to such an estimation. Even though the establishment of a steady state in the entire system’s water is only based on simulations, the resulting model can explain our observations during the ¹H⁺ beam experiment. In the anticipated experimental confirmation, prolonged irradiation times at a constant dose rate are foreseen.

In this study we propose the establishment of a steady state for particle radiation with limited LET, such as 9.7 MeV protons, for an open, large-size system. This can be seen as an extension of previous studies, in which the approximation of a steady state has only been described for irradiations of small water volumes with low to moderate LET radiation.^{19−21,23,26,30} The here described steady state-based calculation can be directly translated toward FRIB conditions and aid in estimating the expected molecular product levels generated by ion beams of limited LET. However, at FRIB predominantly high-intensity, heavy-ion beams will be stopped in the beam dump, inducing various nuclear reactions that result in a range of diverse secondary, and sometimes even tertiary, beam fragments. Next to the generation of beam products, high-energy neutrons and γ-rays are expected as well,^36,37 which will contribute to the radiolysis of water molecules. The resulting radiation field will be determined by the ratio of the different radiation types, however, for most primary heavy-ion beams a strong high-LET component can be expected. Radiation characterized by a high LET contributes to a continuous decomposition of water molecules, while the convergence to steady-state concentrations of molecular products is not expected.^13,22 The comparable setup of the FRIB beam dump to our flowing-water target would suggest an effective yield-based H₂, H₂O₂, and O₂ formation, which is still considerably diminished in comparison to an escape yield-mediated production.

Even when considering an effective yield-based formation of radiolytic species in FRIB’s isotope harvesting beam dump, elevated molecular products can be expected in the system’s water. Such levels can render modest equipment wear possible, and influence the chemical behavior of radionuclides with sensitive trace-level aqueous chemistry, which could complicate the anticipated isotope harvesting efforts. A catalytic recombination unit is foreseen to keep the amount of radiolytic hydrogen and oxygen within limits. The large surface area of the water system’s stainless-steel pipes was previously assumed to effectively decompose hydrogen peroxide. However, the exposure of stainless-steel surfaces to large quantities of H₂O₂ has been shown to reduce the rate of degradation, resulting in increased H₂O₂ concentrations within the system’s water.⁴

The addition of H₂ to the primary coolant water of pressurized water reactors has been effective in preventing the buildup of oxidizing species. In these systems, ¹⁰B is added to the water as moderator and represents a source of high- LET ⁴He and ⁷Li particles, while the water is also exposed to γ-radiation and fast neutrons. With low-LET radiation excessive amounts of radicals are generated, which support the recombination of hydrogen peroxide in a hydrogen-rich environment.³⁸ However, the extent of water decomposition is strongly dependent on the local ratio between high- and low-LET radiation. In pure alpha beam irradiations, a decrease of the steady-state concentrations could only be observed when alpha particles of limited LET were applied, while high-LET alpha beams created an unchanged, almost linear increase of hydrogen peroxide levels.^19,39 The radiation field created by FRIB’s primary heavy-ion beams, when impinging onto the beam dump, is expected to entail a considerable amount of high-LET radiation. For every beam type and energy, it is necessary to determine whether the low-LET component can maintain a sufficient level of radical species to realize an effective recombination at elevated hydrogen levels. An alternative option to reduce the levels of hydrogen peroxide could be based on catalytic decomposition, like the catalytic converter unit in our harvesting system. This method would allow an effective peroxide decomposition independent from the prevalent radical concentrations. However, to allow a more confident prediction, a translation of the simulation model to include the dimensions and flow dynamics of the rotating FRIB beam dump would be necessary. The here established kinetic modeling of the homogeneous radiolysis phase of the flowing-water target will contribute toward the development of an adequate simulation for the conditions at FRIB.

4. Conclusions

In the high-intensity proton irradiation of our isotope harvesting system, lower levels of radiolytic hydrogen and hydrogen peroxide were observed than expected. While a suppression of the escape yield-based formation is assumed for closed, limited volumes, fewer interactions between radiolytic species are expected to occur in open, large-size systems like ours. With the developed simulation model, the noticeable influence of homogeneous interactions within the dynamics of the flowing-water target could be estimated. The decreased effective yields showed a dependency on the prevailing concentrations of molecular hydrogen, oxygen, and hydrogen peroxide as well as on the applied beam current. However, the experimental measurements could only be approximated by a model that additionally considers the establishment of a steady state. Such an effect, previously only described for enclosed systems subjected to low-LET radiation, is made possible by the small beam strike volume connected to the large water tank via mass transfer. However, for the heavy-ion beams at FRIB an effective yield-based formation is expected. The here developed simulation model provides a reasonable basis for a translation toward the conditions at FRIB and thereby aid in estimating the levels of generated molecular products.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.2c03540.

• Additional details about the computation of the H₂, H₂O₂, and O₂ levels in the isotope harvesting system, power functions for estimating the steady-state concentrations, tables of computed effective G values and steady-state concentrations of H₂ and H₂O₂, schematics of the isotope harvesting setup and the flowing-water target (PDF)

The authors declare no competing financial interest.