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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]
The intensity field can in principle be solved from the integrodifferential radiative transfer equation (RTE), but an exact solution is usually impossible and even in the case of geometrically simple systems can contain unusual special functions such as the Chandrasekhar's H-function and Chandrasekhar's X- and Y-functions. [3]
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).
Defining equation SI units Dimension Number of atoms N = Number of atoms remaining at time t. N 0 = Initial number of atoms at time t = 0 N D = Number of atoms decayed at time t = + dimensionless dimensionless Decay rate, activity of a radioisotope: A = Bq = Hz = s −1 [T] −1: Decay constant: λ
Paul Frederick Zweifel (June 21, 1929 – February 12, 2017) was a mathematical physicist and a prominent leader in the mathematical theory of nuclear reactors and the mathematical development of linear transport theory, [1] a discipline that encompasses neutron transport in the core of a nuclear reactor as well as the propagation of photons in radiative transfer.
A continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when applied to a conserved quantity , but it can be generalized to apply to any extensive quantity .
Because the Boltzmann equation is practical in solving problems in rarefied or dilute gases, it has been used in many diverse areas of technology. It is used to calculate Space Shuttle re-entry in the upper atmosphere. [42] It is the basis for Neutron transport theory, and ion transport in Semiconductors. [43] [44]
The Boltzmann equation can be used to determine how physical quantities change, such as heat energy and momentum, when a fluid is in transport. One may also derive other properties characteristic to fluids such as viscosity , thermal conductivity , and electrical conductivity (by treating the charge carriers in a material as a gas). [ 2 ]