Nuclear Reactor Physics and Design

2.

Neutron Transport and Diffusion Theory

2.1.

Neutron Population Description

2.1.1.

2.1.1.1.

2.1.1.2.

2.1.1.3.

Energy Dependence

2.1.1.4.

Spatial Distribution

2.1.2.

Neutron Current

2.1.2.1.

Current Density Vector

2.1.2.2.

2.1.2.3.

Partial Currents

2.1.3.

2.1.3.1.

Absorption Rate

2.1.3.2.

2.1.3.3.

Scattering Rate

2.1.3.4.

Production Rate

2.2.

The Neutron Transport Equation

2.2.1.

Derivation from First Principles

2.2.1.1.

Neutron Balance Equation

2.2.1.2.

Phase Space Variables

2.2.2.

The Boltzmann Transport Equation

2.2.2.1.

2.2.2.2.

2.2.2.3.

2.2.3.

Boundary Conditions

2.2.3.1.

Vacuum Boundary

2.2.3.2.

Reflective Boundary

2.2.3.3.

Periodic Boundary

2.2.4.

Integral Form of Transport Equation

2.2.4.1.

Collision Probability Method

2.2.4.2.

Method of Characteristics

2.3.

Neutron Diffusion Theory

2.3.1.

2.3.1.1.

2.3.1.2.

Limitations and Validity

2.3.2.

Derivation of Diffusion Equation

2.3.2.1.

P1 Approximation

2.3.2.2.

Diffusion Coefficient

2.3.2.3.

Steady-State Diffusion Equation

2.3.2.4.

Time-Dependent Diffusion Equation

2.3.3.

Boundary and Interface Conditions

2.3.3.1.

Vacuum Boundary Condition

2.3.3.2.

Extrapolated Boundary

2.3.3.3.

Interface Conditions

2.3.3.4.

Albedo Boundary Condition

2.3.4.

Solutions to Diffusion Equation

2.3.4.1.

Homogeneous Media

2.3.4.2.

Point Source Solutions

2.3.4.3.

Plane Source Solutions

2.4.

Neutron Slowing Down Theory

2.4.1.

Elastic Scattering Kinematics

2.4.1.1.

Laboratory and Center-of-Mass Systems

2.4.1.2.

Energy Transfer in Elastic Collisions

2.4.1.3.

Scattering Angle Distribution

2.4.2.

Slowing Down Parameters

2.4.2.1.

Average Logarithmic Energy Decrement

2.4.2.2.

Average Number of Collisions

2.4.2.3.

Slowing Down Power

2.4.3.

2.4.3.1.

Fermi Age Equation

2.4.3.2.

Age to Thermal Energy

2.4.3.3.

Slowing Down Density

2.4.4.

Resonance Escape

2.4.4.1.

Resonance Escape Probability

2.4.4.2.

Narrow Resonance Approximation

2.4.4.3.

Wide Resonance Approximation

2.5.

Thermal Neutron Physics

2.5.1.

Neutron Thermalization

2.5.1.1.

Thermalization Process

2.5.1.2.

Thermal Equilibrium

2.5.1.3.

Thermalization Length

2.5.2.

Maxwell-Boltzmann Distribution

2.5.2.1.

Thermal Neutron Spectrum

2.5.2.2.

Most Probable Energy

2.5.2.3.

2.5.3.

Neutron Temperature

2.5.3.1.

Effective Temperature

2.5.3.2.

Hardening of Spectrum

2.5.4.

Thermal Utilization

2.5.4.1.

Thermal Disadvantage Factor

2.5.4.2.

Resonance Disadvantage Factor

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1. Fundamentals of Nuclear and Neutron Physics

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3. Reactor Criticality and Neutron Balance