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The neutron transport equation is a balance statement that conserves neutrons. Each term represents a gain or a loss of a neutron, and the balance, in essence, claims that neutrons gained equals neutrons lost. It is formulated as follows: [1]
In 1947, John von Neumann sent a letter to Robert Richtmyer proposing the use of a statistical method to solve neutron diffusion and multiplication problems in fission devices. [5] His letter contained an 81-step pseudo code and was the first formulation of a Monte Carlo computation for an electronic computing machine.
In the case of time-independent monochromatic radiation in an elastically scattering medium, the RTE is [1] (,) = (,) + (,) (, ′) ′where the first term on the RHS is the contribution of emission, the second term the contribution of absorption and the last term is the contribution from scattering in the medium.
The mere fact that an assembly is supercritical does not guarantee that it contains any free neutrons at all. At least one neutron is required to "strike" a chain reaction, and if the spontaneous fission rate is sufficiently low it may take a long time (in 235 U reactors, as long as many minutes) before a chance neutron encounter starts a chain reaction even if the reactor is supercritical.
This involves computing exact or approximate solutions of the transport equation, and there are various forms of the transport equation that have been studied. Common varieties include steady-state vs time-dependent, scalar vs vector (the latter including polarization), and monoenergetic vs multi-energy (multi-group).
The convection–diffusion equation can be derived in a straightforward way [4] from the continuity equation, which states that the rate of change for a scalar quantity in a differential control volume is given by flow and diffusion into and out of that part of the system along with any generation or consumption inside the control volume: + =, where j is the total flux and R is a net ...
Indeed, neutron-rich isotopes such as 49 S, 52 Cl, and 53 Ar that were calculated to lie beyond the drip line have been reported as bound in 2017–2019, indicating that the neutron drip line may lie even farther away from the beta-stability line than predicted. [23] The table below lists the heaviest particle-bound isotope of the first ten ...
The inhour equation is initially derived from the point kinetics equations. The point reactor kinetics model assumes that the spatial flux shape does not change with time. This removes spatial dependencies and looks at only changes with times in the neutron population. [3] The point kinetics equation for neutron population is shown in Equation 4.