This project involves using a Monte Carlo code to estimate the critical size of various objects with respect to the growth of thermal neutron density. The project is divided into 2 phases. In the first phase, The essential goal is to theoretically think of a strategy that strikes a balance between statistical fluctuations and transient effects to achieve optimal accuracy. Once an optimal strategy is devised, the project transitions to the second phase, which involves implementing a cylindrical geometry with a height equal to the radius (H = R) and utilizing the Monte Carlo code to estimate the critical length of this cylindrical geometry.
Methodology:
Phase 1:
Two approaches were explored to optimize the accuracy of the calculations:
- Manually adjusting queue length: This involved starting with a shorter queue to minimize transient effects and gradually increasing it until stable behavior was observed.
- Adaptive queue length: This involved dynamically modifying the queue length based on the behavior of the neutron population. A feedback loop was used to modify the queue length after a certain number of trajectories.
The effectiveness of the approach depended on the available computational budget, desired accuracy, and problem complexity.
Phase 2:
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The code was modified to accommodate a cylindrical geometry by creating a ‘cylinder’ object class inherited from the ‘shape’ class.
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An iterative technique was employed to determine the critical length for the cylinder.
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The critical length was initially estimated and the trajectory tracking process was initiated.
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The count of neutron particles in the queue was observed to determine whether the critical length estimate was too high or too low.
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The critical length estimate was adjusted based on the observed trend.
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The process was repeated until the critical length was accurately determined to a satisfactory level.
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The critical length for the cylindrical geometry was found to be 7.745868 cm.
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The critical length for a cylindrical geometry is greater than that of a slab geometry due to the curved trajectories taken by neutrons in a cylinder.
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Observing the growth rate of neutrons against the number of trajectories reveals an initial surge followed by a steady decline. This transient behavior is caused by the replacement of the initial set of neutrons by a new set, effectively flushing out the initial group. Once the new set of neutrons takes over, the growth rate stabilizes around zero, indicating an equilibrium state and confirmation of criticality.
