Formula & Calculator
Conversion Ratio (Breeding)
Measures how efficiently a reactor converts fertile material into new fissile material relative to the fissile fuel it consumes.
Interpretation
CR = Fissile Atoms Produced / Fissile Atoms Consumed. Measures how many fissile atoms are generated per fissile atom burned. Important for breeding (CR>1). Used in advanced fuel cycles.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| CR | Conversion ratio | |
| Fissile Atoms Produced | New fissile atoms produced via conversion | |
| Fissile Atoms Consumed | Fissile atoms consumed by fission and capture |
What it means
The conversion ratio (CR) is the ratio of fissile atoms produced (by neutron capture on fertile materials like ²³⁸U or ²³²Th) to fissile atoms consumed (by fission) in a nuclear reactor. If CR > 1, the reactor is a breeder (produces more fissile material than it consumes). If CR < 1, it is a converter. Breeding is important for extending nuclear fuel resources, as it enables the use of abundant fertile isotopes. Sodium‑cooled fast reactors can achieve breeding ratios above 1.0. The CR is a key parameter in reactor design and fuel cycle analysis, influencing the sustainability and economics of nuclear power. Understanding CR is essential for nuclear engineers and policy makers evaluating long‑term fuel strategies and waste management.
Worked example
Conversion Ratio (Breeding) – Two Examples
Real‑World| Parameter | Value |
|---|---|
| Fissile produced | 850 |
| Fissile consumed | 1,000 |
| Parameter | Value |
|---|---|
| Fissile produced | 1,050 |
| Fissile consumed | 1,000 |
Common mistakes
- Conversion ratio CR: The ratio of fissile atoms produced to fissile atoms consumed – used in breeder reactors.
- CR > 1: Means more fissile material is produced than consumed (breeding).
- CR < 1: Converter (consumes more than it produces).
- Fissile atoms produced: Includes plutonium‑239 from uranium‑238 capture, or uranium‑233 from thorium.
- Consumed: Fissile atoms that undergo fission or capture.
- Units: Dimensionless.
Applications
The conversion ratio (or breeding ratio) is the number of fissile atoms produced per fissile atom consumed in a nuclear reactor. A conversion ratio greater than 1 indicates a breeder reactor, which produces more fuel than it consumes. This is a critical parameter for the sustainability of nuclear energy, as it enables the use of abundant fertile materials like uranium‑238 and thorium‑232. Reactor engineers use the conversion ratio to design breeder reactors (e.g., fast breeder reactors) and to assess the potential for fuel self‑sufficiency. It also influences the fuel cycle strategy, waste management, and resource utilisation. By maximising the conversion ratio, nuclear energy can become a long‑term, sustainable energy source.
- Design of fast breeder reactors and advanced fuel cycles
- Evaluation of fuel utilisation and resource sustainability
- Assessment of nuclear waste reduction through breeding
- Development of thorium‑based fuel cycles
- Economic analysis of nuclear fuel supply and demand
Frequently Asked Questions
The conversion ratio is the ratio of fissile atoms produced to fissile atoms consumed in a reactor: CR = (Fissile Atoms Produced) / (Fissile Atoms Consumed). If CR > 1, the reactor is a breeder, producing more fissile material than it consumes.
The term conversion ratio is often used for reactors where CR < 1 (typical thermal reactors). Breeding ratio is used when CR ≥ 1 (breeder reactors). In some contexts, they are interchangeable.
Confusing conversion ratio (CR) with breeding ratio, or thinking that a thermal reactor can have a high CR. Thermal reactors typically have CR < 0.8, while fast reactors can achieve CR > 1.
A higher CR means the reactor produces more fissile material from fertile material (U‑238 or Th‑232), extending the fuel cycle and improving resource utilisation. Breeders can multiply the energy extracted from uranium by a factor of ~60.
- Thermal reactors (PWR, BWR): CR ≈ 0.6‑0.8.
- Fast breeder reactors (LMFBR): CR > 1 (typically 1.2‑1.3).
- Heavy‑water reactors (CANDU): CR ≈ 0.8‑0.9.
Fertile materials (U‑238, Th‑232) absorb a neutron and become fissile (Pu‑239 or U‑233). The conversion ratio depends on how efficiently this transformation occurs.
Fast neutrons have a higher ratio of (n,γ) to fission cross sections in fertile materials, making fast reactors more efficient breeders. Thermal reactors have lower conversion ratios because of parasitic absorption.
If CR > 1, the reactor can breed more fuel than it consumes, potentially providing a self‑sustaining fuel cycle using abundant fertile material, thereby extending nuclear fuel resources indefinitely.
It is determined from the reactor physics calculations by tracking the production and consumption of fissile isotopes over the fuel cycle. Burnup and reprocessing data can also be used.
High CR requires a fast neutron spectrum, which increases the complexity of cooling and materials (liquid metal coolants). It also requires reprocessing to separate the bred fissile material from the spent fuel.