Filter and neutron beam source including the same

Abstract

Disclosed is a filter including a second layer disposed between a first layer and a third layer. The first layer is composed of iron. The second layer is composed of 1 part by volume of lithium fluoride, 20 to 50 parts by volume of aluminum, and 50 to 80 parts by volume of aluminum fluoride. The third layer is composed of 1 part by weight of lithium fluoride and 99 to 100 parts by weight of magnesium fluoride.

Claims

1. A neutron beam filter, comprising: a first layer composed of iron; a second layer composed of 1 part by volume of lithium fluoride, 20 to 50 parts by volume of aluminum, and 50 to 80 parts by volume of aluminum fluoride; and a third layer composed of 1 part by weight of lithium fluoride and 99 to 100 parts by weight of magnesium fluoride, wherein the lithium fluoride is dispersed in the magnesium fluoride, wherein the second layer is disposed between the first layer and the third layer, and wherein the neutron beam filter is configured to form a moderated neutron beam.

2. The neutron beam filter as claimed in claim 1, wherein the filter has a total thickness of 67.5 cm to 70 cm, and a circular cross-section with a radius of 40 cm to 60 cm.

3. The neutron beam filter as claimed in claim 1, wherein the first layer has a thickness of 25 cm to 40 cm, the second layer has a thickness of 10 cm to 37.5 cm, and the third layer has a thickness of 5 cm to 20 cm.

4. A neutron beam source, comprising: an accelerator; a beryllium target; and the filter as claimed in claim 1, wherein the beryllium target is disposed between the accelerator and the filter, and the first layer of the filter is disposed between the beryllium target and the third layer.

5. The neutron beam source as claimed in claim 4, wherein: the accelerator produces a proton beam of 30 MeV/1 mA, the first layer of the filter has a thickness of 25 cm to 40 cm, the second layer of the filter has a thickness of 10 cm to 37.5 cm, and the third layer of the filter has a thickness of 5 cm to 20 cm.

6. The neutron beam source as claimed in claim 4, wherein: the accelerator produces a proton beam of 29 MeV/1 mA, the first layer of the filter has a thickness of 25 cm to 37.5 cm, the second layer of the filter has a thickness of 12.5 cm to 37.5 cm, and the third layer of the filter has a thickness of 5 cm to 17.5 cm.

7. The neutron beam source as claimed in claim 4, wherein: the accelerator produces a proton beam of 31 MeV/1 mA, the first layer of the filter has a thickness of 27.5 cm to 40 cm, the second layer of the filter has a thickness of 10 cm to 35 cm, and the third layer of the filter has a thickness of 7.5 cm to 20 cm.

8. The neutron beam source as claimed in claim 4, wherein: the accelerator produces a proton beam of 30 MeV/1 mA for colliding the beryllium target to form neutrons; and the neutrons pass through the filter to form a moderated neutron beam, wherein the moderated neutron beam has an epithermal neutron flux of 1.7×10.sup.9 n cm.sup.−2s.sup.−1 to 1.9×10.sup.9 n cm.sup.−2s.sup.−1, and a fast neutron dose component of 2.9×10.sup.−11 cGy cm.sup.2 to 3.5×10.sup.−11 cGy cm.sup.2 per epithermal neutron.

9. The neutron beam source as claimed in claim 4, wherein: the accelerator produces a proton beam of 29 MeV/1 mA for colliding the beryllium target to form neutrons; and the neutrons pass through the filter to form a moderated neutron beam, wherein the moderated neutron beam has an epithermal neutron flux of 1.7×10.sup.9 n cm.sup.−2s.sup.−1 to 1.9×10.sup.9 n cm.sup.−2s.sup.−1, and a fast neutron dose component of 2.9×10.sup.−11 cGy cm.sup.2 to 3.5×10.sup.−11 cGy cm.sup.2 per epithermal neutron.

10. The neutron beam source as claimed in claim 4, wherein: the accelerator produces a proton beam of 31 MeV/1 mA for colliding the beryllium target to form neutrons; and the neutrons pass through the filter to form a moderated neutron beam, wherein the moderated neutron beam has an epithermal neutron flux of 1.7×10.sup.9 n cm.sup.−2s.sup.−1 to 1.9×10.sup.9 n cm.sup.−2s.sup.−1, and a fast neutron dose component of 2.9×10.sup.−11 cGy cm.sup.2 to 3.7×10.sup.−11 cGy cm.sup.2 per epithermal neutron.

11. The neutron beam source as claimed in claim 4, further comprising a collimator element, wherein the filter is disposed between the beryllium target and the collimator element.

12. The neutron beam source as claimed in claim 11, wherein: the accelerator produces a proton beam of 30 MeV/1 mA for colliding the beryllium target to form neutrons; and the neutrons pass through the filter and the collimator to form a moderated neutron beam, wherein the moderated neutron beam has an epithermal neutron flux of 1.7×10.sup.9 n cm.sup.2 s.sup.−1 to 2.0×10.sup.9 n cm.sup.−2s.sup.−1, and a fast neutron dose component of 2.0×10.sup.−11 cGy cm.sup.2 to 2.6×10.sup.−11 cGy cm.sup.2 per epithermal neutron.

13. The neutron beam source as claimed in claim 11, wherein: the accelerator produces a proton beam of 30 MeV/2 mA for colliding the beryllium target to form neutrons; and the neutrons pass through the filter and the collimator to form a moderated neutron beam, wherein the moderated neutron beam has an epithermal neutron flux of 3.4×10.sup.9 n cm.sup.−2s.sup.−1 to 4.0×10.sup.9 n cm.sup.−2s.sup.−1, and a fast neutron dose component of 2.0×10.sup.−11 cGy cm.sup.2 to 2.6×10.sup.−11 cGy cm.sup.2 per epithermal neutron.

14. The neutron beam source as claimed in claim 4, further comprising a lead wall surrounding sidewalls of the filter.

15. The neutron beam source as claimed in claim 14, wherein the lead wall has a thickness of greater than or equal to 15 cm.

16. The neutron beam source as claimed in claim 4 being applied to accelerator-based boron neutron capture therapy.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The disclosure can be more fully understood by reading the subsequent detailed description and examples with references made to the accompanying drawings, wherein:

(2) FIG. 1 shows a neutron beam source in one embodiment of the disclosure;

(3) FIG. 2 shows a filter in one embodiment of the disclosure; and

(4) FIG. 3 shows a neutron beam source containing a collimator element in one embodiment of the disclosure.

DETAILED DESCRIPTION

(5) In the following detailed description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the disclosed embodiments. It will be apparent, however, that one or more embodiments may be practiced without these specific details. In other instances, well-known structures and devices are schematically shown in order to simplify the drawing.

(6) As shown in FIG. 1, a neutron beam source 10 in one embodiment of the disclosure is constructed from three principal parts: an accelerator 11, a target 13, and a filter 15, wherein the target 13 is disposed between the accelerator 11 and the filter 15. For example, the accelerator 11 can be a cyclotron commercially available from Sumitomo Heavy Industries. The accelerator 11 is used to provide protons with energy of about 30 MeV and a current of greater than or equal to 1 mA to collide with the target 13, thereby producing fast neutrons. The fast neutrons pass through the filter 15 turning into an epithermal neutron beam. The International Atomic Energy Agency (IAEA) suggests that a desirable minimum epithermal neutron beam intensity for BNCT would be 10.sup.9 epithermal neutrons cm.sup.−2.Math.s.sup.−1, and the fast neutron dose component and the gamma ray dose component would be less than 2.0×10.sup.−11 cGy cm.sup.2 per epithermal neutron. Since the criterion for gamma ray dose component is easily achieved, the disclosure mainly discusses the epithermal neutron flux and the fast neutron dose component. An overly low epithermal neutron flux may prolong the irradiation time of the therapy for a patient 17. An overly high fast neutron flux may damage the normal tissues of the patient 17. The protons (produced by the accelerator 11) with overly high energy will increase the difficulty of shielding design without further increasing the neutron yield. The protons (produced by the accelerator 11) with overly low energy may produce neutrons of insufficient yield, and the current of the protons would need to be increased to compensate for the neutron yield.

(7) In one embodiment, the target 13 is composed of beryllium with a thickness of 0.55 cm to 0.58 cm. An overly thick target 13 cannot easily dissipate heat. An overly thin target 13 decreases the neutron yield.

(8) In one embodiment of the disclosure, the filter 15 has a total thickness of 67.5 cm to 70 cm, and a cross-section area of 0.5 m.sup.2 to 1.13 m.sup.2 (e.g. a circle with a radius of 40 cm to 60 cm). A filter 15 with an overly thin total thickness cannot efficiently reduce the fast neutron dose component. A filter 15 with an overly thick total thickness cannot produce sufficient epithermal neutron flux. A filter with an overly large cross-section area will increase the filter weight and cost, and reduce the average epithermal neutron flux without improving the neutron beam quality. A filter 15 (having the same thickness as a filter with a proper cross-section area) with an overly small cross-section area cannot efficiently reduce the fast neutron dose component.

(9) As shown in FIG. 2, the filter 15 is a tri-layered structure. The second layer 15B is disposed between a first layer 15A and a third layer 15C, and the first layer 15A is disposed between the target 13 and the third layer 15C. As the protons collide with the target 13 neutrons are produced, which sequentially pass through the first layer 15A, the second layer 15B, and the third layer 15C. The first layer 15A is composed of iron. The neutrons with energy higher than 1 MeV will be moderated to energy less than 1 MeV by inelastic scattering with iron. In one embodiment of the disclosure, the first layer 15A has a thickness of 25 cm to 40 cm. A first layer 15A with an overly thin thickness will cause too many neutrons having energy higher than 1 MeV. A first layer 15A with an overly thick thickness will reduce thicknesses of other layers for shaping the neutrons with energy less than 1 MeV, thereby affecting the neutron beam quality. The second layer 15B is composed of 1 part by volume of lithium fluoride, 20 to 50 parts by volume of aluminum, and 50 to 80 parts by volume of aluminum fluoride. For example, the second layer 15B can be referred to U.S. Pat. No. 5,703,918. In one embodiment, the second layer 15B has a thickness of 10 cm to 37.5 cm. When the total thickness of the filter 15 is fixed, a second layer 15B with an overly thick thickness will result in an overly thin third layer, thereby fail to sufficiently moderate the neutrons and results in an overly high fast neutron dose rate. A second layer 15B with an overly thin thickness will cause an overly thick third layer. The fast neutron dose rate of the neutron beam can be sufficiently reduced. However, the epithermal neutron flux will be overly low. The third layer 15C is composed of 1 part by weight of lithium fluoride and 99 to 100 parts by weight of magnesium fluoride. An overly low percentage of the lithium fluoride and an overly high percentage of the magnesium fluoride will produce a neutron beam with an overly high thermal neutron flux. An overly high percentage of the lithium fluoride and an overly low percentage of the magnesium fluoride will produce a neutron beam with an overly high fast neutron dose per epithermal neutron. In one embodiment, the third layer 15C has a thickness of 5 cm to 20 cm. A third layer 15C with an overly thick thickness will overly moderate the neutrons, thereby producing a neutron beam with an overly low epithermal neutron flux. A third layer 15C with an overly thin thickness will be insufficient to moderate the neutrons, thereby producing a neutron beam with an overly high fast neutron dose rate.

(10) In one embodiment, a lead wall 14 with a thickness of greater than 15 cm can be disposed outside the filter 15 to further increase the final epithermal neutron flux. An overly thick lead wall 14 will be over weighted. The filter 15 can be surrounded by a shield 20 to avoid radiation penetrating out of the filter 15. In one embodiment, the shield 20 can be concrete.

(11) In one embodiment, the accelerator 11 produces a proton beam of 30 MeV/1 mA, and the neutron beam source 10 correspondingly produces a neutron beam having an epithermal neutron flux of 1.7×10.sup.9 n cm.sup.−2s.sup.−1 to 1.9×10.sup.9 n cm.sup.−2s.sup.−1, and a fast neutron dose component of 2.9×10.sup.−11 cGy cm.sup.2 to 3.5×10.sup.−11 cGy cm.sup.2 per epithermal neutron.

(12) In one embodiment, a collimator element 16 can be added as shown in FIG. 3. The collimator element is located between the patient 17 and the filter 15, and the filter 15 is located between the collimator element 16 and the target 13. The design of the collimator element 16 can be referred in Y-W H. Liu, T. T. Huang, S. H. Jiang, H. M. Liu, (2004) “Renovation of Epithermal Neutron Beam for BNCT at THOR,” Appl. Radiat. Isot. 61, 1039-1043. The collimator element 16 may focus and maintain the epithermal neutron flux intensity, and simultaneously reduce the fast neutron dose rate. For example, the accelerator 11 produces a proton beam of 30 MeV/1 mA, and the neutron beam source 10 with the collimator element 16 correspondingly produces a neutron beam having an epithermal neutron flux of 1.7×10.sup.9 n cm.sup.−2s.sup.−1 to 2.0×10.sup.9 n cm.sup.−2s.sup.−1, and a fast neutron dose component of 2.0×10.sup.−11 cGy cm.sup.2 to 2.6×10.sup.−11 cGy cm.sup.2 per epithermal neutron. When the accelerator 11 produces a proton beam of 30 MeV/2 mA, the neutron beam source 10 with the collimator element 16 correspondingly produces a neutron beam having a double epithermal neutron flux (e.g. 3.4×10.sup.9 n cm.sup.−2s.sup.−1 to 4.0×10.sup.9 n cm.sup.−2s.sup.−1), a double fast neutron dose rate, compared to that from a proton beam of 30 MeV/1 mA. The fast neutron dose component remains the same (2.0×10.sup.−11 cGy cm.sup.2 to 2.6×10.sup.−11 cGy cm.sup.2 per epithermal neutron). Because the neutron beam source 10 can produce sufficient epithermal neutron flux and a low fast neutron dose rate, the neutron beam source 10 is suitable for use in accelerator-based BNCT.

(13) If the proton energy produced by the accelerator changes, the thickness ranges of the three layers in the filter for producing ideal epithermal neutrons will change slightly.

(14) When the energy of the protons produced by the accelerator increases to 31 MeV/1 mA, the filter for producing ideal epithermal neutrons has a tri-layered structure as follows: a first layer with a thickness of 27.5 cm to 40 cm, a second layer with a thickness of 10 cm to 35 cm, and a third layer with a thickness of 7.5 cm to 20 cm. In one embodiment, the neutron beam source 10 produces a neutron beam having an epithermal neutron flux of 1.7×10.sup.9 n cm.sup.−2s.sup.−1 to 1.9×10.sup.9 n cm.sup.−2s.sup.−1, and a fast neutron dose component of 2.9×10.sup.−11 cGy cm.sup.2 to 3.7×10.sup.−11 cGy cm.sup.2 per epithermal neutron.

(15) When the energy of protons produced by the accelerator decreases to 29 MeV/1 mA, the filter for producing ideal epithermal neutrons has a tri-layered structure as below: a first layer with a thickness of 25 cm to 37.5 cm, a second layer with a thickness of 12.5 cm to 37.5 cm, and a third layer with a thickness of 5 cm to 17.5 cm. In one embodiment, the neutron beam source 10 produces a neutron beam having an epithermal neutron flux of 1.7×10.sup.9 n cm.sup.−2s.sup.−1 to 1.9×10.sup.9 n cm.sup.−2s.sup.−1, and a fast neutron dose component of 2.9×10.sup.−11 cGy cm.sup.2 to 3.5×10.sup.−11 cGy cm.sup.2 per epithermal neutron.

(16) Below, exemplary embodiments will be described in detail with reference to accompanying drawings for easy understanding. The inventive concept may be embodied in various forms without being limited to the exemplary embodiments set forth herein. Descriptions of well-known parts are omitted for clarity, and like reference numerals refer to like elements throughout.

EXAMPLES

(17) In the experiments described below, the simulation calculation software used MCNPX, developed by Los Alamos National Laboratory, and the cross-section library was ENDF/B-7.

(18) In Examples 1 to 4, the accelerator produced protons of 30 MeV/1 mA, and the target was beryllium with a thickness of 0.55 cm. The first layer of the filter was composed of iron. The second layer of the filter was composed of 1 part by weight of lithium fluoride, 30 parts by weight of aluminum, and 69 parts by weight of aluminum fluoride (equal to 1 part by volume of lithium fluoride, 31 parts by volume of aluminum, and 68 parts by volume of aluminum fluoride). The third layer of the filter was composed of 1 part by weight of lithium fluoride and 99 parts by weight of magnesium fluoride.

Example 1

(19) The first layer, the second layer, and the third layer, each with a different thickness, were selected to construct filters having a circular cross-section with a radius of 50 cm. The epithermal neutron flux, the fast neutron dose rate, and the fast neutron dose per epithermal neutron of the neutron beams produced by neutron beam sources containing the filters are tabulated in Table 1.

(20) TABLE-US-00001 TABLE 1 Example 1-1 Example 1-2 Example 1-3 Example 1-4 Example 1-5 Filter structure First layer First layer First layer First layer First layer (30 cm) + (30 cm) + (30 cm) + (30 cm) + (30 cm) + second layer second layer second layer Third layer second layer (35 cm) (40 cm) (42.5 cm) (35 cm) (25 cm) + third layer (12.5 cm) Epithermal 2.33 × 10.sup.9  2.02 × 10.sup.9  1.86 × 10.sup.9  1.55 × 10.sup.9  1.89 × 10.sup.9  neutron flux (0.08%) (0.09%) (0.09%) (0.10%) (0.09%) (n cm.sup.−2 .Math. s.sup.−1) (1 standard deviation) Fast neutron 0.146 0.083 0.063 0.052 0.065 dose rate  (0.4%) (0.51%) (0.61%) (0.83%) (0.67%) (cGy .Math. s.sup.−1) (1 standard deviation) Fast neutron 6.27 × 10.sup.−11 4.13 × 10.sup.−11 3.40 × 10.sup.−11 3.39 × 10.sup.−11 3.46 × 10.sup.−11 dose per epithermal neutron (cGy .Math. cm.sup.2/n)

(21) As shown in Table 1, the atomic mass of the aluminum in the second layer was large, therefore, it could not effectively slow down the fast neutrons. As such, the second layer should be thickened to reduce the fast neutron dose rate. But the thicker second layer also reduced the epithermal neutron flux. The atomic mass of the magnesium in the third layer was smaller, therefore, it could slow down the fast neutrons effectively. However, it also reduced the epithermal neutron flux. When the total thickness of the first layer and the second layer (e.g. Example 1-1) was the same as the total thickness of the first layer and the third layer (e.g. Example 1-4), the epithermal neutron flux in Example 1-4 was less than the epithermal neutron flux in Example 1-1. As shown in the comparison between Examples 1-3 and 1-4, the second layer in the filter composed of the first layer and the second layer should be 7.5 cm thicker than the third layer in the filter composed of the first layer and the third layer in order to achieve approximately the same fast neutron dose rate. By comparing Examples 1-3, 1-4, and 1-5, it is shown that for achieving an approximately the same and reasonably low value of fast neutron dose per epithermal neutron, the tri-layered filter in Example 1-5 not only produced a higher epithermal neutron flux, but also had a total thickness being 5 cm thinner than the bi-layered filter in Example 1-3.

Example 2

(22) Example 2-1 was similar to Example 1-5, and the difference in Example 2-1 was that the positions of the second layer and the third layer were exchanged. Although the epithermal neutron flux in Example 2-1 was higher than that in Example 1-5, the fast neutron dose in Example 2-1 was also higher than that in Example 1-5. For reducing the fast neutron dose rate in Example 2-1, the thickness of the third layer was increased in Example 2-2. Although the fast neutron dose rate in Example 2-2 is similar to that in Example 1-5, the epithermal neutron flux in Example 2-2 is also reduced. Accordingly, the position arrangement of the first layer, the second layer, and the third layer in Example 1-5 is better than the position arrangement of the first layer, the third layer, and the second layer in Examples 2-1 and 2-2.

(23) TABLE-US-00002 TABLE 2 Example 1-5 Example 2-1 Example 2-2 Filter structure First layer First layer First layer (30 cm) + (30 cm) + (30 cm) + second layer third layer third layer (25 cm) + (12.5 cm) + (14 cm) + third layer second layer second layer (12.5 cm) (25 cm) (25 cm) Epithermal neutron 1.89 × 10.sup.9 1.96 × 10.sup.9 1.82 × 10.sup.9 flux (n cm.sup.−2 .Math. s.sup.−1) (0.09%) (0.09%) (0.09%) (1 standard deviation) Fast neutron dose rate 0.065 0.077 0.063 (cGy .Math. s.sup.−1) (0.67%) (0.59%) (0.62%) (1 standard deviation) Fast neutron dose per 3.46 × 10.sup.−11 3.91 × 10.sup.−11 3.44 × 10.sup.−11 epithermal neutron (cGy .Math. cm.sup.2/n)

Example 3

(24) The first layer of fixed thickness (30 cm) was followed by different thickness of second layer and third layer to construct a circular filter with a radius of 50 cm. The filter was further added with a collimator element disclosed in Y-W H. Liu, T. T. Huang, S. H. Jiang, H. M. Liu, (2004) “Renovation of Epithermal Neutron Beam for BNCT at THOR,” Appl. Radiat. Isot. 61, 1039-1043. The epithermal neutron flux, the fast neutron dose rate, and the fast neutron dose per epithermal neutron of the neutron beams produced by neutron beam sources containing the filters and the collimator element are tabulated in Table 3.

(25) TABLE-US-00003 TABLE 3 Example 3-1 Example 3-2 Example 3-3 Example 3-4 Filter structure First layer First layer First layer First layer (30 cm) + (30 cm) + (30 cm) + (30 cm) + second layer third layer third layer second layer (42.5 cm) (35 cm) (14 cm) + (25 cm) + second layer third layer (25 cm) (12.5 cm) Epithermal 1.92 × 10.sup.9  1.58 × 10.sup.9  1.86 × 10.sup.9  1.99 × 10.sup.9  neutron flux (0.18%) (0.20%) (0.19%) (0.18%) (n cm.sup.−2 .Math. s.sup.−1) (1 standard deviation) Fast neutron 0.043 0.043 0.046 0.050 dose rate (1.41%) (1.80%) (1.46%) (1.50%) (cGy .Math. s.sup.−1) (1 standard deviation) Fast neutron 2.25 × 10.sup.−11 2.70 × 10.sup.−11 2.45 × 10.sup.−11 2.51 × 10.sup.−11 dose per epithermal neutron) (cGy .Math. cm.sup.2/n)

(26) By comparing the results in Table 3 with Table 1 and Table 2, it is seen that the collimator element can maintain the epithermal neutron flux intensity and reduce the fast neutron dose rate to a value close to that suggested by IAEA.

Example 4

(27) Different thicknesses of the first layer, the second layer, and the third layer were selected to construct filters having a circular cross-section with a radius of 50 cm. No collimator element was adopted in this Example. The epithermal neutron flux, the fast neutron dose rate, and the fast neutron dose per epithermal neutron of the neutron beams produced by neutron beam sources containing the filters are tabulated in Table 4.

(28) TABLE-US-00004 TABLE 4 Epithermal Fast neutron Fast neutron Filter structure neutron flux dose rate dose per First Second Third (n cm.sup.−2 .Math. s.sup.−1) (cGy .Math. s.sup.−1) epithermal Proton layer layer layer (1 standard (1 standard neutron 30 MeV/1 mA (cm) (cm) (cm) deviation) deviation) (cGy .Math. cm.sup.2/n) Example 30 35 5 1.89 × 10.sup.9 0.064 3.41 × 10.sup.−11 4-1 (0.09%) (0.63%) Example 30 25 12.5 1.89 × 10.sup.9 0.065 3.46 × 10.sup.−11 4-2 (0.09%) (0.67%) Example 25 37.5 7.5 1.84 × 10.sup.9 0.058 3.15 × 10.sup.−11 4-3 (0.07%) (0.52%) Example 35 25 10 1.80 × 10.sup.9 0.060 3.30 × 10.sup.−11 4-4 (0.09%) (0.61%) Example 35 15 17.5 1.80 × 10.sup.99 0.062 3.43 × 10.sup.−11 4-5 (0.09%) (0.61%) Example 37.5 10 20 1.79 × 10.sup.9 0.062 3.44 × 10.sup.−11 4-6 (0.07%) (0.41%) Example 30 30 10 1.78 × 10.sup.9 0.054 3.03 × 10.sup.−11 4-7 (0.09%) (0.74%) Example 30 20 17.5 1.76 × 10.sup.9 0.056 3.17 × 10.sup.−11 4-8 (0.10%) (0.73%) Example 40 15 15 1.75 × 10.sup.9 0.060 3.43 × 10.sup.−11 4-9 (0.07%) (0.39%) Example 35 12.5 20 1.74 × 10.sup.9 0.057 3.29 × 10.sup.−11 4-10 (0.10%) (0.68%) Example 30 27.5 12.5 1.72 × 10.sup.9 0.050 2.90 × 10.sup.−11 4-11 (0.10%) (0.77%) Example 35 20 15 1.70 × 10.sup.9 0.050 2.94 × 10.sup.−11 4-12 (0.10%) (0.69%) Example 30 17.5 20 1.70 × 10.sup.9 0.054 3.17 × 10.sup.−11 4-13 (0.10%) (0.80%)

(29) As shown in Table 4, the neutron beam source with the filter (having the first layer, the second layer, and the third layer with proper thicknesses) provided sufficient epithermal neutron flux and low fast neutron dose rate.

Example 5

(30) For accelerator producing protons of 31 MeV/1 mA, different thicknesses of the first layer, the second layer, and the third layer were selected to construct filters having a circular cross-section with a radius of 50 cm. No collimator element was adopted in this Example. The epithermal neutron flux, the fast neutron dose rate, and the fast neutron dose per epithermal neutron of the neutron beams produced by neutron beam sources containing the filters are tabulated in Table 5.

(31) TABLE-US-00005 TABLE 5 Epithermal Fast neutron Fast neutron Filter structure neutron flux dose rate dose per First Second Third (n cm.sup.−2 .Math. s.sup.−1) (cGy .Math. s.sup.−1) epithermal Proton layer layer layer (1 standard (1 standard neutron 31 MeV/1 mA (cm) (cm) (cm) deviation) deviation) (cGy .Math. cm.sup.2/n) Example 27.5 35 7.5 1.86 × 10.sup.9 0.062 3.35 × 10.sup.−11 5-1 (0.12%) (0.90%) Example 37.5 10 20 1.79 × 10.sup.9 0.065 3.64 × 10.sup.−11 5-2 (0.12%) (0.77%) Example 40 15 15 1.74 × 10.sup.9 0.062 3.56 × 10.sup.−11 5-3 (0.12%) (0.72%)

Example 6

(32) For accelerator producing protons of 29 MeV, 1 mA, different thicknesses of the first layer, the second layer, and the third layer were selected to construct filters having a circular cross-section with a radius of 50 cm. No collimator element was adopted in this Example. The epithermal neutron flux, the fast neutron dose rate, and the fast neutron dose per epithermal neutron of the neutron beams produced by neutron beam sources containing the filters are tabulated in Table 6.

(33) TABLE-US-00006 TABLE 6 Epithermal Fast neutron Fast neutron Filter structure neutron flux dose rate dose per First Second Third (n cm.sup.−2 .Math. s.sup.−1) (cGy .Math. s.sup.−1) epithermal Proton layer layer layer (1 standard (1 standard neutron 29 MeV/1 mA (cm) (cm) (cm) deviation) deviation) (cGy .Math. cm.sup.2/n) Example 25 37.5 7.5 1.71 × 10.sup.9 0.050 2.91 × 10.sup.−11 6-1 (0.12%) (1.04%) Example 30 35 5 1.81 × 10.sup.9 0.056 3.09 × 10.sup.−11 6-2 (0.12%) (0.88%) Example 37.5 12.5 17.5 1.72 × 10.sup.9 0.060 3.47 × 10.sup.−11 6-3 (0.12%) (0.73%)

Example 7

(34) For accelerator producing protons of 30 MeV/1 mA, different thicknesses of the first layer, the second layer, and the third layer were selected to construct filters having a circular cross-section with a radius of 50 cm. The collimator element in Example 3 was adopted in this Example. The epithermal neutron flux, the fast neutron dose rate, and the fast neutron dose per epithermal neutron of the neutron beams produced by neutron beam sources containing the filters after passing through the collimator are tabulated in Table 7.

(35) TABLE-US-00007 TABLE 7 Epithermal Fast neutron Fast neutron Filter structure neutron flux dose rate dose per First Second Third (n cm.sup.−2 .Math. s.sup.−1) (cGy .Math. s.sup.−1) epithermal Proton layer layer layer (1 standard (1 standard neutron 30 MeV/1 mA (cm) (cm) (cm) deviation) deviation) (cGy .Math. cm.sup.2/n) Example 25 37.5 7.5 1.79 × 10.sup.9 0.046 2.55 × 10.sup.−11 7-1 (0.08%) (0.77%) Example 30 35 5 2.01 × 10.sup.9 0.047 2.34 × 10.sup.−11 7-2 (0.07%) (0.69%) Example 40 15 15 1.87 × 10.sup.9 0.038 2.03 × 10.sup.−11 7-3 (0.07%) (0.65%) Example 37.5 10 20 1.90 × 10.sup.9 0.042 2.21 × 10.sup.−11 7-4 (0.07%) (0.69%)

(36) It will be apparent to those skilled in the art that various modifications and variations can be made to the disclosed methods and materials. It is intended that the specification and examples be considered as exemplary only, with a true scope of the disclosure being indicated by the following claims and their equivalents.