8.1 Neutron Transport and Interactions

Neutron transport theory is crucial for understanding how neutrons move and interact in fusion reactors. It's all about tracking these tiny particles as they zip around, bounce off things, and sometimes get absorbed. This knowledge is key to designing safe and efficient fusion systems.

Applying neutron transport theory helps with important tasks in fusion reactor design. It's used to figure out how to breed tritium fuel, shield against radiation, and manage radioactive waste. These applications are vital for making fusion a practical energy source.

Neutron Transport Theory and Applications

Fundamentals of neutron transport theory

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• Describes movement and interactions of neutrons in matter
• Considers neutron sources, scattering, absorption, and leakage
• Boltzmann transport equation
  • Governing equation for neutron transport
  • Includes terms for neutron streaming, collision, and source
• Neutron flux $\phi(r,E,\Omega)$ represents number of neutrons per unit area per unit time at position $r$, energy $E$, and direction $\Omega$
• Neutron current $J(r,E,\Omega)$ represents net number of neutrons crossing a unit area per unit time

Applications in fusion reactor design

• Breeding tritium in lithium blankets
  • Neutrons interact with lithium to produce tritium fuel (Li-6, Li-7)
  • Ensures self-sufficiency in tritium supply
• Shielding and radiation protection
  • Designing materials (concrete, boron carbide) and geometries to attenuate neutron flux
  • Protecting reactor components and personnel from radiation damage
• Activation analysis and waste management
  • Predicting activation of reactor materials (steel, copper) by neutron irradiation
  • Assessing production and handling of radioactive waste

Types of neutron-matter interactions

• Elastic scattering
  • Neutron collides with nucleus and conserves kinetic energy
  • Important for moderating (slowing down) neutrons (water, graphite)
  • Described by scattering cross-section $\sigma_s(E)$
• Inelastic scattering
  • Neutron collides with nucleus and transfers energy to nucleus
  • Nucleus left in excited state and may emit gamma rays
  • Contributes to neutron moderation and energy deposition
• Radiative capture (absorption)
  • Neutron absorbed by nucleus, forming heavier isotope (boron-10, gadolinium)
  • Often followed by gamma ray emission
  • Described by absorption cross-section $\sigma_a(E)$
• Neutron-induced fission
  • Neutron causes heavy nucleus to split into two or more fragments (uranium-235, plutonium-239)
  • Releases additional neutrons and large amounts of energy
  • Important for breeding tritium in lithium blankets
• Transmutation reactions
  • Neutron absorption leads to formation of different element
  • Can produce radioactive isotopes and activate reactor materials (cobalt-60, nickel-63)
  • Relevant for assessing material damage and waste production

Computational Methods and Reactor Performance

Solving neutron transport equations

• Deterministic methods
  1. Discrete ordinates ($S_N$) method
     • Discretizes angular and spatial domains
     • Solves transport equation for each discrete direction and spatial cell
  2. Spherical harmonics ($P_N$) method
     • Expands angular dependence of neutron flux in spherical harmonics
     • Leads to set of coupled partial differential equations
  3. Finite difference and finite element methods for spatial discretization
• Monte Carlo methods
  • Stochastic approach based on random sampling
  • Simulates individual neutron histories from birth to absorption or escape
  • Provides detailed and accurate results but can be computationally intensive
• Computational tools and codes
  • MCNP (Monte Carlo N-Particle) code
    • Widely used for neutron, photon, and electron transport simulations
    • Supports complex geometries and various physics models
  • Other popular Monte Carlo codes (TRIPOLI, Serpent, OpenMC)
  • Deterministic transport codes (PARTISN, TORT, ATTILA)

Impact of neutron behavior on fusion reactors

• Tritium breeding ratio (TBR)
  • Ratio of tritium produced to tritium consumed in reactor
  • TBR > 1 required for self-sufficient tritium supply
  • Influenced by neutron transport in breeding blanket
• Neutron multiplication and energy multiplication
  • Neutron multiplication: Increase in neutron population due to fission or other multiplicative reactions
  • Energy multiplication: Ratio of total energy deposited to energy of incident neutrons
  • Affect overall energy balance and power output of reactor
• Radiation damage and material activation
  • Displacement per atom (DPA): Measure of radiation-induced material damage
  • Gas production (helium, hydrogen) can lead to swelling and embrittlement
  • Activation of reactor components affects maintenance and decommissioning
• Shielding effectiveness and occupational dose
  • Adequate shielding required to protect personnel and equipment
  • Occupational dose limits must be met for safe operation
  • Neutron transport calculations guide design of shielding materials and thicknesses (concrete, lead, water)