Nuclear Fission Simulation

This project simulates neutron transport and nuclear fission processes using a Monte Carlo method. The simulation tracks neutron movements, interactions, and fission events within a defined geometry and material.

Table of Contents

• Installation
• Usage
• Classes and Functions
• Simulation Parameters
• Plotting and Analysis
• Contributing
• License

Installation

To run this project, you need Python 3 and the following packages:

• numpy
• matplotlib
• scipy
• pandas
• seaborn
• scikit-learn

You can install the required packages using pip:

pip install numpy matplotlib scipy pandas seaborn scikit-learn

Usage

To run the simulation, execute the nuclear_fission_simulation.py file:

python nuclear_fission_simulation.py

Mathematical Explanation of Nuclear Fission Simulation

This document provides a mathematical explanation of the nuclear fission simulation using Monte Carlo methods.

Watt Spectrum

The Watt spectrum describes the distribution of neutron energies emitted during fission:

$$ f(E) = a \sinh\left(\sqrt{bE}\right) e^{-aE - bE} $$

Cross-section Interpolation

The cross-section data for each isotope is interpolated using cubic splines:

$$ σ(E) = interp1d(energy_data, cross_section_data, kind='cubic') $$

Neutron Scattering

Neutrons scatter isotropically according to Maxwell-Boltzmann distribution:

$$ f(v) = \sqrt{\frac{2}{\pi}} \left(\frac{v^3}{kT}\right)^{3/2} e^{-\frac{v^2}{2kT}} $$

Simulation Process

The Monte Carlo simulation progresses through several steps:

1. Initialization of neutrons and materials.
2. Transport simulation using random walk.
3. Interaction determination (fission, absorption, or scattering).
4. Temperature evolution and energy deposition calculations.
5. Criticality analysis based on neutron flux and reaction rates.

Classes and Functions

generate_realistic_cross_section_data()

Generates synthetic cross-section data for different isotopes.

Isotope

Represents an isotope with its properties and cross-section data.

Neutron

Represents a neutron with its position, direction, and energy.

Material

Represents a material composed of different isotopes and manages its temperature and density.

SphericalShellGeometry

Defines a spherical shell geometry for the simulation space.

NuclearFissionModel

Handles the neutron transport, interactions, and fission processes.

• initialize_neutrons(num_neutrons): Initializes neutrons in the geometry.
• simulate_transport(time_step): Simulates neutron transport and interactions for a given time step.
• criticality_analysis(total_time, initial_time_step): Analyzes the system for criticality over a given total time.
• spatial_reaction_distribution(): Returns the spatial distribution of fission events.
• plot_results(model): Plots the results of the simulation, including reaction rates, fission event locations, neutron energy distribution, and temperature evolution.
• analyze_results(model): Analyzes the results of the simulation, including clustering of fission events, neutron lifecycle analysis, and reactivity calculation.
• monte_carlo_simulation(num_neutrons, material, geometry, total_time, initial_time_step): Runs the Monte Carlo simulation with the specified parameters.

Simulation Parameters

• num_neutrons: Initial number of neutrons.
• material: Material object containing isotopes and temperature.
• geometry: Geometry object defining the simulation space.
• total_time: Total time for the simulation.
• initial_time_step: Initial time step for the simulation.

Plotting and Analysis

The simulation results are visualized and analyzed through various plots and statistical methods:

• Reaction Rate Plot: Shows the reaction rate over time.
• 3D Fission Events Plot: Displays the locations and temperatures of fission events.
• Neutron Energy Distribution: Histogram of neutron energies.
• Temperature Evolution: Tracks the temperature changes over time.

Contributing

Contributions are welcome! Please fork the repository and submit a pull request.

License

This project is licensed under the MIT License. See the LICENSE file for details.