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Cancer has become one of the important factors threatening human life and health, and methods for treating cancer are constantly being studied and explored. It is an urgent demand in the healthcare to treat cancer by rays. Boron Neutron Capture Therapy (BNCT) is given increasing amount of attention due to its ability of selective cancer cell killing. The BNCT neutron source based on the 18 MeV/1 mA cyclotron is researched. To improve the flux of the epithermal neutrons, simultaneously reducing fast neutron dose as much as possible, this paper studies the generation and transport of neutrons in the Beam Shaping Assembly (BSA) of the BNCT. By comparing reaction cross sections (including neutron multiplied reaction, neutron inelastic scattering and neutron elastic scattering) of different materials, the materials of neutron multiplier and neutron moderator are researched. In this study, Be is chosen as the target to produce neutron by 9Be(p,n)9B reaction. Pb is chosen as neutron multiplier. LiF or MgF2 is chosen as neutron moderator. Ni is chosen as fast neutron filtration material. The neutron yield can achieved 5.25×10^13 n/s. The epithermal neutron flux is 2.92×10^9 n/cm2/s, with the fast neutron dose of 5.87×10^-13 Gy·cm2 per epithermal neutron.