Note on the Non-Linear Kinetics of Circulating-Fuel Reactors

Technical Report · Fri Aug 15 04:00:00 EDT 1952

DOI:https://doi.org/10.2172/4376518· OSTI ID:4376518

Tamor, S. ^[1]

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1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

The equations of motion for a somewhat idealized circulating-fuel reactor have been set up and discussed in several previous reports. The assumptions made are, in essence, that the instantaneous power density is constant along the length of the fuel tubes, that the excess reactivity depends only upon the average fuel temperature, and that the fuel temperature at the inlet is kept constant. The effect of delayed neutrons is ignored. It was suspected that its negative temperature coefficient makes this reactor inherently stable even without the damping provided by delayed neutrons. This was suggested in a crude way in reference 1 and subsequently proved in the linear approximation. Specifically, it was proved that for the linear case no antidamped solutions exist, while from equation 4 of reference 2 it follows that the only undamped solutions are periodic with period equal to, or a submultiple of, θ, the fuel transit time. It is the purpose of this note to prove the above statements in the non-linear case.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States); Oak Ridge Y-12 Plant (Y-12), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA), Nuclear Criticality Safety Program (NCSP); US Atomic Energy Commission (AEC)
• DOE Contract Number: W-7405-ENG-26
• NSA Number: NSA-10-004373
• OSTI ID: 4376518
• Report Number(s): AECD-4018; Y-F10-109
• Country of Publication: United States
• Language: English

Related Subjects

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Antidamped Solutions
Asymptotic Power
DELAYED NEUTRONS
DIFFERENTIAL EQUATIONS
Delayed Neutrons
FUELS
LIQUID FLOW
NEUTRON FLUX
NONLINEAR PROBLEMS
NUMERICALS
Nuclear Criticality Safety Program (NCSP)
POWER
REACTIVITY
REACTOR SAFETY
REACTORS
SOLUTIONS
STABILITY
TEMPERATURE
TUBES