# Using the diffusion approximation for reactor with cavities calculations

6/22/2018 2018 - #02 Physics and technology of nuclear reactors

https://doi.org/10.26583/npe.2018.2.07

### UDC: 621.039

The importance of the radiation calculations in the in-reactor cavities is associated with simulating of the emergency modes in fast breeder reactors (FBR), as well as states with different coolant levels in specially designed channels of passive feedback devices in lead-cooled fast reactors (LFR) or sodium cavities in sodium-cooled fast reactors (SFR).

The Last Flight (LF) method [1 – 8], or the method of the unscattered component is widely known and is commonly used in programs based on the method of spherical harmonics to obtain a solution in a gas medium at some distance from the calculated volume domain (DORT [6], TORT [4] and others [8]). The practice of using it [1] showed that acceptable results are achievable at a considerable distance from the surface between dense and gas media (more than two meters). A qualitative solution is not guaranteed for cavities within the calculation area.

In addition, it is desirable to implement the cavities calculation methodology in the framework of the approximations used in the reactor calculations, in particular, the diffusion approximation, which introduces certain features: the isotropy of the neutron flux density; forced introduction of a “conditional” calculation cell on the surface between dense and gas media.

If the LF method is oriented on the connection of the source point with the detection point, then in calculating the neutron field in the cavities it is necessary to determine the neutron yield from the surface area of the source and their arrival on a certain surface area of the cavity. To solve the problem, the authors suggested using the approximate solution presented in the paper.

Thus, the authors developed and implemented an algorithm for the in-reactor cavities calculations using the diffusion approximatio

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fast breeder reactor diffusion approximation cavities calculations