Designing a Fission Reactor for Long-Term Operation

[nuclear]

another question.

consider the possibility of designing a fission reactor that will operate for decades or even centuries without refueling. limit the investigation to thermal reactors with reaction rates = 2200 m/s cross section. Consider 3 fissile/fertile combinations:

1) Fissile= U-233 Fertile= Th-232
2) Fissile= U-235 Fertile= U-234
3) Fissile= Pu-239 Fertile= U-238

show that the necessary condition for continuos steady state operation of this reactor is that the macroscopic absorption cross section for the fertile nuclides equals that for the fissile spesies.

any hint how to approach this problem? where shall I start?

then, i was asked to compute the ratio of natural abundances but the natural abundances of U-233 is 0, then what should I do?

 

[Nate810]

The first step in solving this problem is to understand the fundamentals of reactor operation. A fission reactor works by maintaining a controlled chain reaction, in which a fissile material (such as uranium-235 or plutonium-239) is bombarded with neutrons to cause it to fission, releasing energy and more neutrons. These neutrons can then be absorbed by other fissile material to cause more fissions, creating a sustained chain reaction. To maintain a steady-state operation, the number of neutrons produced must match the number of neutrons absorbed. The absorption cross section of a material is the probability of a neutron being absorbed, and so for a steady-state reactor, the macroscopic absorption cross section for the fertile nuclide must equal that for the fissile species. To calculate the ratio of natural abundances, you will need to determine the relative concentrations of each of the fissile and fertile nuclides present in the reactor. This can be done by taking into account the natural abundances of each isotope, as well as their decay rates. For U-233, since its natural abundance is 0, you will need to consider the rate at which this isotope is produced in the reactor.

 

[M98Ranger]

To approach this problem, you can start by understanding the concept of a thermal reactor and its operation. A thermal reactor uses slow-moving neutrons to induce fission in the fuel material. The reaction rate is a measure of how many fission reactions occur per unit time and is determined by the cross section of the fuel material.

For continuous steady state operation, the rate of fission reactions must be equal to the rate of absorption reactions. This means that for every fission reaction, there must be an absorption reaction to maintain a constant reaction rate. In other words, the macroscopic absorption cross section for the fertile nuclides (Th-232, U-234, and U-238) must be equal to the macroscopic cross section for the fissile species (U-233, U-235, and Pu-239).

To compute the ratio of natural abundances, you can use the equation:

Natural Abundance = (Cross Section of Isotope/Total Cross Section of All Isotopes) * 100%

Since the natural abundance of U-233 is 0, you can exclude it from the calculation and focus on the other two combinations. For example, for the first combination of U-233 and Th-232, the natural abundance of Th-232 would be:

Natural Abundance of Th-232 = (Cross Section of Th-232 / (Cross Section of Th-232 + Cross Section of U-233)) * 100%

You can use this equation to calculate the natural abundances for the other two combinations and compare them to see which one has a higher natural abundance. This can give you an idea of which combination would be more suitable for long-term operation of a fission reactor.

Overall, this problem requires a good understanding of reactor design and cross sections of different isotopes. I suggest consulting with your instructor or a subject expert for further guidance and assistance.