EP3668281A1 - Neutron source and method for locating a target material - Google Patents

Abstract

The invention relates to a neutron source and a method for locating a target material. According to the invention, a layer sequence for a target material is determined in an iterative process which uses Formula 1, nEiΔE = NAρM − 1 * δEiΔE * σEiΔEwobein (E <sub> i </ sub>, ΔE) the number of neutrons produced, i = index, which denotes the layer, namely 1,2,3 ..... nN _A the Avogadro constant, ρ (g cm < sup> -3 </sup>) the density of the selected element, M (g) the molar mass of the selected element, E _i the entry energy of the primary ion into layer i, ΔE the energy loss of the primary ion on passage the layer thickness δ, δ (E _i, ΔE) (cm) the layer thickness of the selected element for an energy loss of the ions ΔE with an entry energy of E _i, σ (E <sub> i < / sub>, ΔE) (cm ²) the integral cross section over the energy range ΔE for the emission probability of one or more neutrons from the interaction ng between ions and atomic nuclei of element i. The layers determined in this way are combined to form a target material.

Description

The invention relates to a neutron source and a method for finding a target material.

In ion accelerator-based neutron sources [1], neutrons are produced by the interaction of ions, such as protons and deuterons, with atomic nuclei of a target, the energy of the primary ions being below the energy required for the release of neutrons by fragmentation of the atomic nuclei of the target (process in the Neutrons in the spallation neutron source). To date, targets for ion accelerator-based neutron sources in the low MeV range consist of a single-layer system made of lithium [2] or beryllium [3], depending on the energy of the primary ions.

Targets made of lithium or beryllium are not designed for maximum neutron production while minimizing safety-relevant by-products, e.g. Tritium, optimized for this. Furthermore, lithium and beryllium are toxic elements and beryllium is classified as a critical raw material. Beryllium is considered a critical substance because it is important for nuclear weapons, for example, and access is therefore limited. In addition, beryllium contains impurities that decay after use as a target and represent hazardous waste that is difficult to dispose of.

It is therefore the object of the invention to provide a target which, when operating ion-accelerating neutron sources, has a higher neutron yield than single-element targets such as e.g. Beryllium provides and in a preferred embodiment, the use of which does not produce radioactive by-products. It is also the object of the invention to find substitutes for beryllium as target which do not have the problems associated with beryllium or have them to a reduced extent.

Starting from the preamble of claim 1, the object is achieved according to the invention with the features specified in the characterizing part.

With the method according to the invention and the target identified with it, it is now possible to achieve a higher neutron yield than with single-element targets and, in a preferred embodiment, to reduce or completely eliminate the production of radioactive by-products. Substitutes for eg beryllium can be found, which are more readily available and have fewer problems with disposal bring, especially because no or less radioactive decay of the target material is recorded after use of the target material. The problems associated with the use of beryllium are avoided. Beryllium can be completely replaced as a target material or used to a lesser extent.

Advantageous developments of the invention are specified in the subclaims.

The invention is explained in its general form below, without this being interpreted restrictively.

The primary ions lose energy due to deceleration in the target material. It was recognized that the production of neutrons and by-products depends on the energy of the ions, the number of nucleons in the nucleus and the density of the target material, the optimization of neutron production and the minimization of radioactive by-products by adapting the target material to the residual energy of the primary ions can, and that it can be used to provide targets that solve the tasks.

According to the invention, a method for selecting target materials from layers and a multi-layer system is provided which consists of at least two layers of preferably at least two elements which follow one another within the layer sequence and which produce neutrons when primary ions strike. In a special embodiment, two or more layers of the same element can also follow one another, so that these layers appear externally as one layer, although it is composed of the sequence of individual layers of the same element.

According to the invention, the target consists of a multilayer system with at least two layers, in which each layer consists of an element which delivers the greatest yield of neutrons with regard to the primary energy of the ion beam entering this layer. The layers can consist of 2, 3, 4, 5 ....... 10, for example 2-4 layers. The number of layers is basically not limited but depends on practical criteria.

berechnet, wobei

• n (E_i, ΔE) die Anzahl der produzierten Neutronen,
• i = Index, der die Schicht bezeichnet, nämlich 1,2,3 .....n
• N_A die Avogadro-Konstante,
• ρ (g cm^-3) die Dichte des ausgewählten Elements,
• M (g) die molare Masse des ausgewählten Elements,
• E_i die Eintrittsenergie des Primärions in die Schicht i,
• ΔE der Energieverlust des Primärions beim Durchtritt der Schichtdicke δ,
• δ (E_i, ΔE) (cm) die Schichtdicke des ausgewählten Elements für einen Energieverlust der Ionen ΔE bei einer Eintrittsenergie von E_i,
• σ (E_i, ΔE) (cm²) der integrale Wirkungsquerschnitt über den Energiebereich ΔE für die Emissionswahrscheinlichkeit von einem oder mehreren Neutronen aus der Wechselwirkung zwischen Ionen und Atomkernen des ausgewählten Elements ist.

The selection of the elements according to the invention and their layer thickness for optimal neutron production takes place arithmetically according to the invention using formula 1. The neutron production n (E _i , ΔE) (neutrons per ion) for the selected element, the energy E _{i of} the ions when entering the Element and the energy loss of the ions ΔE (MeV) is with $$\mathit{n}\left({\mathit{E}}_{\mathit{i}},\mathit{\Delta E}\right)={\mathit{N}}_{\mathit{A}}\mathit{\rho }{\mathit{M}}^{-\mathit{1}}*\mathit{\delta }\left({\mathit{E}}_{\mathit{i}},\mathit{\Delta E}\right)*\mathit{\sigma }\left({\mathit{E}}_{\mathit{i}},\mathit{\Delta E}\right)$$

calculated where

• n (E _i , ΔE ) the number of neutrons produced,
• i = index that denotes the layer, namely 1,2,3 ..... n
• N _A Avogadro's number,
• ρ (g cm ^-3 ) the density of the selected element,
• M (g) the molar mass of the selected element,
• E _i the entry energy of the primary ion into layer i,
• ΔE the energy loss of the primary ion when the layer thickness δ passes through ,
• δ (E _i , ΔE) (cm) the layer thickness of the selected element for an energy loss of the ions ΔE with an entry energy of E _i ,
• σ (E _i , ΔE) (cm ² ) is the integral cross section over the energy range ΔE for the emission probability of one or more neutrons from the interaction between ions and atomic nuclei of the selected element.

The values of δ (E _i , ΔE) can be calculated with the software SRIM (Stopping and Range of ions in Matter) [4], which is publicly available. The values of σ (E _i , ΔE) can be found in the database TENDL-2017 [5] or TENDL-2015 or ENDF / B-VII or any other database with tabulated cross-sections that are publicly accessible.

For a selected element , the neutron production is calculated using the parameters N _A , p, M specified in formula 1 by specifying values for E _i , ΔE as parameters.

ΔE can be chosen freely; for example, 5MeV or 1 MeV can be selected for ΔE .

For the selected element, the entry energy E _i and the energy loss ΔE , the value for the layer thickness δ (E _i , ΔE) is determined and used in formula 1.
The latter can be done using the SRIM software, which is freely available.
The values of σ (E _i , ΔE) for the selected element can be found in the database TENDL-2017 or TENDL-2015 or ENDF / B-VII or any other database with tabulated cross sections.

This calculates the neutron production according to Formula 1 for an element and a layer thickness.

For each selected element, with a defined starting energy E ₁ , where i = 1 and a defined energy loss, eg ΔE = 1 MeV, the neutron production up to the final energy E _n with i = n is calculated when the ions pass through the layers.
This is done as follows. You start at the starting energy E ₁ and calculate the neutron production according to formula 1. After passing through the layer, the ions have an energy of E ₂ = E ₁ - ΔE, or more generally, E _{i + 1} = E _i - ΔE. This energy is the entry energy into the next layer and one can calculate the neutron production of the other layers according to Formula 1 by iteratively varying the energies E ₁ , E ₂ , E ₃ up to the final energy E _n . The corresponding cross section σ (E _i , ΔE) is used for each E _i .

This iterative calculation is carried out for all selected elements and sensible energy parameters, but at least for two elements, for example 5, 10, 15 or 20 elements.

Preferably a selected chemical element is a solid.

At each iterative step for the i-th layer, the element with the corresponding layer thickness that has the highest neutron production can now be selected.

Hereby the successive layers are selected, which in their combination result in the highest value for the neutron production. Two successive layers can consist of the same material, so that they melt together to form one layer.

From the layer thicknesses determined in this way and the associated neutron production, layer sequences for targets can be put together, which result in maximum neutron production.

The maximum total neutron production of the multi-layer system is: $${\mathrm{N}}_{\mathrm{total}}={\mathrm{\Sigma }}_{\mathrm{i}}\mathrm{Max}\left\{\mathrm{n}\left({\mathrm{E}}_{\mathrm{i}},\mathit{\Delta E}\right)\right\}$$

berechnet, wobei

• a (E_i, ΔE) die Anzahl der radioaktiven Kerne,
• i = Index, der die Schicht bezeichnet, nämlich 1,2,3 .....n
• N_A die Avogadro-Konstante,
• ρ (g cm^-3) die Dichte des ausgewählten Elements,
• M (g) die molare Masse des ausgewählten Elements,
• E_i die Eintrittsenergie des Primärions in die Schicht i,
• ΔE der Energieverlust des Primärions beim Durchtritt der Schichtdicke δ,
• δ (E_i, ΔE) (cm) die Schichtdicke des ausgewählten Elements für einen Energieverlust der Ionen ΔE bei einer Eintrittsenergie von E_i,
• σ_a (E_i, ΔE) (cm²) der integrale Wirkungsquerschnitt über den Energiebereich ΔE für die Erzeugung von radioaktiven Kernen aus der Wechselwirkung zwischen Ionen und Atomkernen des ausgewählten Elements ist.

In a preferred embodiment, layers are selected according to formula 3 which are not very radioactive because they have the least activation, $$\mathit{a}\left({\mathit{E}}_{\mathit{i}},\mathit{\Delta E}\right)={\mathit{N}}_{\mathit{A}}\mathit{\rho }{\mathit{M}}^{-\mathit{1}}*\mathit{\delta }\left({\mathit{E}}_{\mathit{i}},\mathit{\Delta E}\right)*{\mathit{\sigma }}_{\mathit{a}}\left({\mathit{E}}_{\mathit{i}},\mathit{\Delta E}\right)$$

calculated where

• a (E _i , ΔE ) the number of radioactive nuclei,
• i = index that denotes the layer, namely 1,2,3 ..... n
• N _A Avogadro's number,
• ρ (g cm ^-3 ) the density of the selected element,
• M (g) the molar mass of the selected element,
• E _i the entry energy of the primary ion into layer i,
• ΔE the energy loss of the primary ion when the layer thickness δ passes through ,
• δ (E _i , ΔE) (cm) the layer thickness of the selected element for an energy loss of the ions ΔE with an entry energy of E _i ,
• σ _a (E _i , ΔE ) (cm ² ) is the integral cross section over the energy range ΔE for the generation of radioactive nuclei from the interaction between ions and atomic nuclei of the selected element.

As for the calculation of neutron production, the values of δ (E _i , ΔE) can be calculated with the software package SRIM (Stopping and Range of ions in Matter) [4], which is publicly available. The values of σ (E _i , ΔE) can be found in the database TENDL-2017 [5] or TENDL-2015 or ENDF / B-VII or any other database with tabulated cross-sections that are publicly accessible.

For a selected element , the production of radioactive nuclei is calculated using the parameters N _A , p, M specified in formula 3 by specifying values for E _i , ΔE as parameters. ΔE can be chosen freely; for example, 5MeV or 1 MeV can be selected for ΔE .
For the selected element, the entry energy E _i and the energy loss ΔE , the value for the layer thickness δ (E _i , ΔE) is determined and used in formula 3.
The latter can be done using the SRIM software, which is freely available.
The values of σ _a (E _i , ΔE) for the selected element can be found in the database TENDL-2017 or TENDL-2015 or ENDF / B-VII or any other database with tabulated cross sections.
This is used to calculate the production of radioactive nuclei according to Formula 3 for an element and a layer thickness.

The production of radioactive nuclei up to the final energy E _n with i = n when the ions pass through the layers is calculated for each selected element with a defined starting energy E ₁ , where i = 1, and a defined energy loss, for example ΔE = 1 MeV.
This is done as follows. You start at the starting energy E ₁ and calculate the production of radioactive nuclei according to formula 3. After passing through the layer, the ions have an energy of E ₂ = E ₁ - ΔE or more generally E _{i + 1} = E _i - ΔE. This energy is the entry energy into the next layer, and one can calculate the production of radioactive nuclei of the further layers according to formula 3 by varying the energies E ₁ , E ₂ , E ₃ , ..... iteratively up to the final energy E _n become. The corresponding cross section σ (E _i , ΔE) is used for each E _i .

This iterative calculation is carried out for all selected elements and meaningful energy parameters, but for at least two elements, for example 5, 10, 15 or 20 elements.

Preferably, a selected chemical element is a solid.

At each iterative step for the i-th layer, the element with the corresponding layer thickness that has the lowest production of radioactive nuclei can now be selected.

This selects the successive layers, which in their combination result in the lowest value for the production of radioactive nuclei. Two successive layers can consist of the same material, so that they melt together to form one layer. From the layer thicknesses determined in this way and the associated production of radioactive nuclei, layer sequences for targets can be put together, which result in minimal production of radioactive nuclei.

The minimum production of radioactive cores of the multi-layer system is: $${\mathrm{A}}_{\mathrm{total}}={\mathrm{\Sigma }}_{\mathrm{i}}\mathrm{Min}\left\{\mathrm{a}\left({\mathrm{E}}_{\mathrm{i}},\mathit{\Delta E}\right)\right\}$$

wobei

• G(E_i, ΔE) die Gewichtungsfunktion ist, nach der das Material für die Eintrittsenergie der Ionen von E_i und den Energieverlust von ΔE ausgewählt wird,
• n(E_i, ΔE) die Neutronenproduktion bei Eintrittsenergie der Ionen von E_i und Energieverlust von ΔE,
• a(E_i, ΔE) die Produktion von radioaktiven Nebenprodukten bei Eintrittsenergie der Ionen von E_i und Energieverlust von ΔE,
• x die Gewichtung der Neutronenproduktion und
• y die Gewichtung der Produktion der radioaktiven Nebenprodukte ist.

The choice of layers using these two methods can contradict each other. Here you can specify preferences as to whether higher neutron production is more important or one Minimization of the by-products that arise. You can do this with a weighting function. $$\mathrm{G}\left({\mathrm{E}}_{\mathrm{i}},\mathit{\Delta E}\right)={\left[\mathrm{n}\left({\mathrm{E}}_{\mathrm{i}},\mathit{\Delta E}\right)\right]}^{\mathrm{x}}/{\left[\mathrm{a}\left({\mathrm{E}}_{\mathrm{i}},\mathit{\Delta E}\right)\right]}^{\mathrm{y}}$$

in which

• G (E _i , ΔE ) is the weighting function according to which the material for the entry energy of the ions of E _i and the energy loss of ΔE is selected,
• n (E _i , ΔE ) the neutron production at the entry energy of the ions of E _i and energy loss of ΔE,
• a (E _i , ΔE ) the production of radioactive by-products at the entry energy of the ions of E _i and energy loss of ΔE,
• x the weight of neutron production and
• y is the weight of the production of radioactive by-products.

x and y can be chosen freely, depending on whether priority should be given to maximizing neutron production or minimizing radioactive by-products.
If only neutron production is to be considered, then x = 1 and y = 0 must be selected and Formula 5 is reduced to Formula 1.
If there is only a minimization of radioactive by-products, then choose x = 0 and y = 1. If the maximization of neutron production and the minimization of radioactive by-products are to be equivalent, choose x = 0.5 and y = 0.5. However, all other values are also permissible.

As for the determination of materials in neutron production or the production of radioactive by-products, formula (5) can now be used iteratively to make a selection of the materials.

For this purpose, the weighting for the respective entry energy E _i and the energy loss ΔE is determined for each element with defined weighting factors x and y , according to formula (5) with prior determination of the neutron production according to formula (1) and the production of radioactive by-products according to formula (3) calculated. This is calculated iteratively from the starting energy E ₁ , where i = 1, and a fixed energy loss, for example ΔE = 1 MeV, to the final energy E _n with i = n when the ions pass through the layers. You start at the starting energy E ₁ and calculate the value for the weighting function according to formula 5. After passing through the layer, the ions have an energy of E ₂ = E ₁ - ΔE, more generally E _{i + 1} = E _i - ΔE . This energy is the entry energy into the next layer and one can calculate the value of the weighting function of the other layers according to formula 5 by varying the energies E ₁ , E ₂ , E ₃ , ..... iteratively up to the final energy E _n .

This iterative calculation is carried out for all selected elements and sensible energy parameters, but at least for 2 elements.

Now, with every iterative step, the element with the corresponding layer thickness, which has the best ratio of neutron production and the production of radioactive by-products, can be selected with the i-th layer.

Hereby the successive layers are selected, which in their combination result in the best ratio of neutron production and the production of radioactive by-products. Two successive layers can consist of the same material, so that they melt together to form one layer.

Part of the invention is any target material from layers which can be determined using the method according to the invention.

At least two successive layers can consist of the same element.

The layers of the target according to the invention preferably consist of a solid.

Specific examples:

The following examples show examples of targets identified using the method according to the invention.
The examples are structured as follows:
The heading indicates the primary energy for which the targets are suitable. For each example, two tables are given, which have the following content:
The first table describes the target with its layer sequence.
The first column shows the energy range in MeV for each target material, with which the primary ions enter the material and the energy with which they exit. The second column denotes the material of the layer, the third column the layer thickness of the Material in mm. Column four indicates the ratio between neutrons generated per primary ion entering the sample. Column 5 shows the tritium ions generated per primary ion as a by-product.

In the second table, parameters for the target according to the invention are given. Column 1 lists the target according to the invention in the first line and beryllium as a comparison target in the second line. The next columns contain the neutrons generated per registered primary ion, the gain factor for neutrons and the number of tritium ions generated per registered primary ion in absolute numbers, in each case as a comparison between the target and beryllium as standard, which is to be replaced by the target according to the invention.
1) In the following, the optimization of a neutron source for neutron emission and the minimization of by-products (tritium) for protons with effective cross sections is taken from the TENDL-2017 database with a starting energy E _{1 of} the primary ions of 30, 50 and 70 MeV and one Final energy of the ions given by 0 MeV. For comparison, neutron or tritium production from a beryllium target is shown in the tables below. The neutron production is a function of the primary energy of the protons in Figure 6 shown. The tritium production is a function of the primary energy of the protons in Figure 7 shown. Above a proton energy of 30 MeV, the optimized target consists of a multi-layer system made of vanadium and tungsten.
• For protons with a primary energy of 30 MeV: Energy area (MeV) element Thickness (mm) Neutrons / ion Tritium / ion 0 - 20 Vanadium (V) 1.09 0.00735 2.00 10 ^-7 20-30 Tungsten (W) 0.5149 0.0124 1,076 10 ^-5 Target Neutrons / ion Profit factor neutrons Tritium / ion V + W 0.0198 2.19 1,096 10 ^-5 Be 0.00906 - 1.29 10 ^-3 • For protons with a primary energy of 50 MeV: Energy area (MeV) element Thickness (mm) Neutrons / ion Tritium / ion 0 - 20 Vanadium (V) 1.09 0.00735 2.00 10 ^-7 20-50 Tungsten (W) 1.9449 0.06576 1.17 10 ^-4 Target Neutrons / ion Profit factor neutrons Tritium / ion V + W 0.07311 2.71 1.17 10 ^-4 Be 0.02695 - 5.5610 ^-3 • For protons with a primary energy of 70 MeV: Energy area (MeV) element Thickness (mm) Neutrons / ion Tritium / ion 0 - 20 Vanadium (V) 1.09 0.00735 2.00 10 ^-7 20-70 Tungsten (W) 3,855 0.15388 3.44 10 ^-4 Target Neutrons / ion Profit factor neutrons Tritium / ion V + W 0.16123 3.01 3.48 10 ^-4 Be 0.05361 - 1.04 10 ^-2 2) The following is an example of the optimization of a neutron source for neutron emission and the minimization of by-products (tritium) for deuterons with cross sections taken from the TENDL-2017 database, given a starting energy E _{1 of} the primary ions of 30, 50 and 70 MeV and a final energy of the ions of 0 MeV. For comparison, neutron or tritium production from a beryllium target is shown in the tables below. The neutron production is a function of the primary energy of the deuterons in Figure 8 shown. The tritium production is a function of the primary energy of the deuterons in Figure 9 shown. Above a deuteron energy of 30 MeV, the optimized target consists of a multi-layer system made of boron, vanadium and tungsten.
• For deuterons with a primary energy of 30 MeV: Energy area (MeV) element Thickness (mm) Neutrons / ion Tritium / ion 0 - 20 Boron (B) 1.25 0.0116 4.16 10 ^-4 20-30 Vanadium (V) 0.6715 0.0138 7.33 10 ^-5 Target Total neutrons / ions Profit factor neutrons Tritium / ion total B + V 0.02545 1.10 4.89 10 ^-4 Be 0.02311 - 3.86 10 ^-3 • For deuterons with a primary energy of 50 MeV: Energy area (MeV) element Thickness (mm) Neutrons / ion Tritium / ion 0 - 20 Boron (B) 1.25 0.0116 4.16 10 ^-4 20-30 Vanadium (V) 0.6715 0.0138 7.33 10 ^-5 30-50 Tungsten (W) 0.8787 0.05142 1.77 10 ^-4 Target Total neutrons / ions Profit factor neutrons Tritium / ion total B + V + W 0.07687 1.30 6.66 10 ^-4 Be 0.05903 - 1.27 10 ^-2 • For deuterons with a primary energy of 70 MeV: Energy area (MeV) element Thickness (mm) Neutrons / ion Tritium / ion 0 - 20 Boron (B) 1.25 0.0116 4.16 10 ^-4 20-30 Vanadium (V) 0.6715 0.0138 7.33 10 ^-5 30-70 Tungsten (W) 2.0587 0.14915 4.95 10 ^-4 Target Total neutrons / ions Profit factor neutrons Tritium / ion total B + V + W 0.17460 1,608 9.83 10 ^-4 Be 0.10873 - 2.32 10 ^-2

The figures are explained below.

Fig. 1:

Das Prinzip des Mehrfachschichtsystems zur Maximierung der Neutro-nenproduktion bei Minimierung der Tritiumproduktion im Vergleich zu einem Einfachschichtsystem bestehend aus Beryllium

Fig. 2:

Die Neutronenproduktion (n/ion/MeV) als Funktion der Kernladungszahl des Targetatoms und der Protonenenergie (Energiebereich von 1 bis 70 MeV)

Fig. 3:

Die Neutronenproduktion (n/ion/MeV) als Funktion der Kernladungszahl des Targetatoms und der Deuteronenenergie (Energiebereich von 1 bis 70 MeV)

Fig. 4:

Die Tritiumproduktion (T/ion/MeV) als Funktion der Kernladungszahl des Targetatoms und der Protonenenergie (Energiebereich 1 bis 70 MeV)

Fig. 5:

Die Tritiumproduktion (T/ion/MeV) als Funktion der Kernladungszahl des Targetatoms und der Deuteronenenergie (Energiebereich 1 bis 70 MeV)

Fig. 6:

Die Neutronenproduktion eines optimierten Targets im Vergleich zur Neutronen-produktion eines Berylliumtargets als Funktion der Primärenergie der Protonen

Fig. 7:

Die Tritiumproduktion eines optimierten Targets im Vergleich zur Tritiumproduktion eines Berylliumtargets als Funktion der Primärenergie der Protonen

Fig. 8:

Die Neutronenproduktion eines optimierten Targets im Vergleich zur Neutronen-produktion eines Berylliumtargets als Funktion der Primärenergie der Deuteronen

Fig. 9:

Die Tritiumproduktion eines optimierten Targets im Vergleich zur Tritiumproduktion eines Berylliumtargets als Funktion der Primärenergie der Deuteronen.

It shows:

Fig. 1:

The principle of the multi-layer system to maximize neutron production while minimizing tritium production compared to a single-layer system consisting of beryllium

Fig. 2:

Neutron production (n / ion / MeV) as a function of the atomic number of the target atom and the proton energy (energy range from 1 to 70 MeV)

Fig. 3:

Neutron production (n / ion / MeV) as a function of the atomic number of the target atom and the deuteron energy (energy range from 1 to 70 MeV)

Fig. 4:

Tritium production (T / ion / MeV) as a function of the atomic number of the target atom and the proton energy (energy range 1 to 70 MeV)

Fig. 5:

Tritium production (T / ion / MeV) as a function of the atomic number of the target atom and the deuteron energy (energy range 1 to 70 MeV)

Fig. 6:

The neutron production of an optimized target compared to the neutron production of a beryllium target as a function of the primary energy of the protons

Fig. 7:

The tritium production of an optimized target compared to the tritium production of a beryllium target as a function of the primary energy of the protons

Fig. 8:

The neutron production of an optimized target compared to the neutron production of a beryllium target as a function of the primary energy of the deuterons

Fig. 9:

The tritium production of an optimized target compared to the tritium production of a beryllium target as a function of the primary energy of the deuterons.

In Figure 1 a single-layer system according to the prior art and an inventive layer system are shown as examples. The left embodiment consists of beryllium, the right, according to the invention, consists of a layer sequence with layers A, B, C and D. The formulas below the images illustrate that the multi-layer system has an increased neutron production, given by the sum of the individual neutron productions n _i in the layers i = A, B, C and D compared to a single layer, such as beryllium, given by n. The multi-layer system has a reduced production of radioactive by-products, given by the sum of the individual production of by-products a _i in layers i = A, B , C and D compared to a single layer, such as beryllium, given by a .

In the sub-figures too Figure 2 the shades of gray mean neutron production as a function of the atomic number of the target atom and the proton energy (primary energy).

In the sub-figures too Figure 3 the shades of gray mean neutron production as a function of the atomic number of the target atom and the deuteron energy (primary energy).

In the sub-figures 4, the gray tones mean the tritium production as a function of the atomic number of the target atom and the proton energy (primary energy).

In the sub-figures 5, the gray tones mean the tritium production as a function of the atomic number of the target atom and the deuteron energy (primary energy).

In Figure 6 the abscissa denotes the primary energy in MeV and the ordinate the neutron production n / primary ion, i.e. the profit factor.

In Figure 7 the abscissa denotes the primary energy in MeV and the ordinate the tritium production.

In Figure 8 the abscissa denotes the primary energy in MeV and the ordinate the neutron production n / primary ion, i.e. the profit factor.

In Figure 9 the abscissa denotes the primary energy in MeV and the ordinate the tritium production.

Literature:

1. [1] Use of accelerator based neutron sources, IAEA Vienna 2000, IAEA TECDOC 1153 ISSN 1011-4289
2. [2] Kamada, S et al. Development of target system for intense neutron source of p-Li reaction, Applied Radiation and isotopes 88 (2014) 195-197
3. [3] Rinckel T et al. Target performance at the low energy neutron source, Physica procedia 26 (2012) 168-177
4. [4] SRIM Stopping and Range of Ions in Matter, https://www.srim.org
5. [5] TALYS-based evaluated nuclear data library, TENDL-2017 (release date: December 30, 2017) https://tendl.web.psi.ch/tendl 2017 / tendl2017.html

Claims (15)

Method for finding a target material,
characterized,
that the neutron production n (E _i , ΔE) for a selected element, the energy E _{i of} the ions when entering the element and the energy loss of the ions ΔE (MeV) with Formula 1 $$\mathit{n}\left({\mathit{E}}_{\mathit{i}},\mathit{\Delta E}\right)={\mathit{N}}_{\mathit{A}}\mathit{\rho }{\mathit{M}}^{-\mathit{1}}*\mathit{\delta }\left({\mathit{E}}_{\mathit{i}},\mathit{\Delta E}\right)*\mathit{\sigma }\left({\mathit{E}}_{\mathit{i}},\mathit{\Delta E}\right)$$

is calculated, where n (E _i , ΔE ) the number of neutrons produced, i = index that denotes the layer, namely 1,2,3 ..... n N _A Avogadro's number, ρ (g cm ^-3 ) the density of the selected element, M (g) the molar mass of the selected element, E _i the entry energy of the primary ion into layer i, ΔE the energy loss of the primary ion when the layer thickness δ passes through , δ (E _i , ΔE) (cm) the layer thickness of the selected element for an energy loss of the ions ΔE with an entry energy of E _i , σ (E _i , ΔE) (cm ² ) is the integral cross section over the energy range ΔE for the emission probability of one or more neutrons from the interaction between ions and atomic nuclei of the selected element, wherein the neutron production for a selected item, using the parameters N _A p, M, is computed by values are specified as parameters for E _i and AE, for the selected element and the entry of energy E _i, and the energy loss AE, the value for the layer thickness δ (E _i , ΔE) is determined and used in formula 1, the neutron production through the layers being calculated for the selected element with a fixed starting energy E ₁ and a fixed energy loss ΔE when the ions pass, the exit energy E ₂ = E ₁ - ΔE of a layer is used as the entry energy into the subsequent layer and this step is carried out iteratively for E _{i + 1} = E _i - ΔE , with the corresponding cross section σ (E _i , ΔE ) used for each E _i , this iterative calculation for performed at least two selected elements and for each i-th layer the element is selected which has the highest neutron production and on top of each other the following Layers are determined which, in their combination, have the highest value for neutron production. Method according to one of claims 1,
characterized,
that a solid is chosen as the element. Method according to one of claims 1 to 2,
characterized,
that a value of 5 MeV or 1 MeV is used for the value ΔE . Method according to one of claims 1 to 3,
characterized,
that a further selection is carried out in order to optimize the layer sequence of the target material with regard to reduced radioactivity, by using formula 3 $$\mathit{a}\left({\mathit{E}}_{\mathit{i}},\mathit{\Delta E}\right)={\mathit{N}}_{\mathit{A}}\mathit{\rho }{\mathit{M}}^{-\mathit{1}}*\mathit{\delta }\left({\mathit{E}}_{\mathit{i}},\mathit{\Delta E}\right)*{\mathit{\sigma }}_{\mathit{a}}\left({\mathit{E}}_{\mathit{i}},\mathit{\Delta E}\right)$$

the lowest radioactivity is calculated, whereby a (E _i , ΔE ) the number of radioactive nuclei, i = index that denotes the layer, namely 1,2,3 ..... n N _A Avogadro's number, ρ (g cm ^-3 ) the density of the selected element, M (g) the molar mass of the selected element, E _i the entry energy of the primary ion into layer i, ΔE the energy loss of the primary ion when the layer thickness δ passes through , δ (E _i , ΔE) (cm) the layer thickness of the selected element for an energy loss of the ions ΔE with an entry energy of E _i , σ _a (E _i , ΔE) (cm ² ) is the integral cross section over the energy range ΔE for the generation of radioactive nuclei from the interaction between ions and atomic nuclei of the selected element, using the number of radioactive nuclei produced for a selected element the parameters N _A , p, M are calculated by specifying values for E _i and ΔE , and the value for the layer thickness δ (E _i , ΔE) for the selected element and the entry energy E _i and the energy loss ΔE determined and used in Formula 3,
the number of radioactive nuclei produced through the layers is calculated for the selected element with a defined starting energy E ₁ and a determined energy loss when the ions pass through, the exit energy E ₂ = E ₁ - ΔE of a layer being used as the entry energy into the subsequent layer, and this step is carried out iteratively for E _{i + 1} = E _i - ΔE , the corresponding cross section σ _a (E _i , ΔE) being used for each E _i , and this iterative calculation being carried out for at least two selected elements and for each i-th layer the element is selected which has the lowest production of radioactive nuclei and successive layers are determined which in their combination have the lowest production of radioactive nuclei Method according to one of claims 1 to 4,
characterized;
that a solid is chosen as the element. Method according to one of claims 1 to 5,
characterized,
that a balance is made between high neutron production and minimization of the formation of the radioactive nuclei. Method according to claim 6,
characterized,
that a weighting function according to Formula 5 $$\mathrm{G}\left({\mathrm{E}}_{\mathrm{i}},\mathit{\Delta E}\right)={\left[\mathrm{n}\left({\mathrm{E}}_{\mathrm{i}},\mathit{\Delta E}\right)\right]}^{\mathrm{x}}/{\left[\mathrm{a}\left({\mathrm{E}}_{\mathrm{i}},\mathit{\Delta E}\right)\right]}^{\mathrm{y}}$$

is used, whereby G (E _i , ΔE ) is the weighting function according to which the material for the entry energy of the ions of E _i and the energy loss of ΔE is selected, n (E _i , ΔE ) is the neutron production, with entry energy of the ions from E _i and energy loss from ΔE , a (E _i , ΔE ) is the production of by-products with entry energy of the ions from E _i and energy loss from ΔE, x the weight of neutron production and y is the weight of by-product production. Method according to one of claims 6 or 7,
characterized,
that for each element with defined weighting factors x and y , according to formula (5) with prior determination of the neutron production according to formula (1) and the production of by-products according to formula (3), the weighting for the respective entry energy E _i and the energy loss ΔE is calculated , which is iteratively calculated from the starting energy E ₁ , where i = 1, and a fixed energy loss ΔE up to a final energy E _n with i = n when the ions pass, the ions having an energy of E ₂ = after passing through a layer E ₁ - ΔE and this energy E _{2 is used} as the entry energy into an iteration according to formula 5, and this step is carried out iteratively for E _{i + 1} = E _i - ΔE . Method according to one of claims 6 to 8,
characterized,
that x and y can be chosen freely, depending on whether maximizing neuron production or minimizing radioactive by-products have priority. Method according to claim 9,
characterized,
that is used for x = 1 and y = 0. Method according to claim 9,
characterized,
that is used for y = 1 and x = 0. Method according to claim 9,
characterized,
that is used for x = 0.5 and y = 0.5. Target material,
characterized,
that it can be found by the method of one of claims 1 to 13. Target material according to claim 14,
characterized,
that it consists of at least two layers. Target material according to claim 14 or 15,
characterized,
that at least 2 successive layers consist of the same element.

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