Duderstadt J.J. and Hamilton L.J., Nuclear reactor analysis, J. Wiley and Sons, New York, 1976.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Optical Diffusion Tomography In a highly scattering medium, it is useful to look only at the intensity of the electromagnetic wave. Here, photons are treated as particles which elastically scatter through the random medium. The theoretical framework for this model is Boltzmann transport theory [29], which applies conservation of energy for the photon density scatter and source mechanisms. A common approximation to the Boltzmann transport equation is the diffusion equation [29] 30] which assumes that the flux has a weak angular dependence, that all photons travel at the same speed, that ....

....scatter through the random medium. The theoretical framework for this model is Boltzmann transport theory [29] which applies conservation of energy for the photon density scatter and source mechanisms. A common approximation to the Boltzmann transport equation is the diffusion equation [29], 30] which assumes that the flux has a weak angular dependence, that all photons travel at the same speed, that the sources are isotropic, and that the photon current density changes slowly with time, relative to the mean collision time [29] The diffusion approximation is accurate in soft ....

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J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis.New York: Wiley, 1976.

....the coherence of light is so quickly lost that it is useful to look only at the intensity of the electromagnetic wave. Here, photons are essentially treated as particles which elastically scatter through the random medium. The theoretical framework for this model is Boltzmann transport theory [29], which applies conservation of energy for the photon density scatter and source mechanisms. A common approximation to the Boltzmann transport equation is the di#usion approximation [29, 30] which assumes that the flux has a weak angular dependence, that all photons travel at the same speed, that ....

....scatter through the random medium. The theoretical framework for this model is Boltzmann transport theory [29] which applies conservation of energy for the photon density scatter and source mechanisms. A common approximation to the Boltzmann transport equation is the di#usion approximation [29, 30], which assumes that the flux has a weak angular dependence, that all photons travel at the same speed, that the sources are isotropic, and that the photon 5 current density changes slowly with time, relative to the mean collision time [29] The di#usion approximation is accurate in soft tissue ....

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J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis. New York: Wiley, 1976.

....absorbers, e.g. absorbtion rods, are used to absorb excess neutrons. The absorbers are gradually removed as the fuel is spent. At EOC there is just enough fuel to sustain the process with the absorbers completely removed, and the production and absorbtion terms are respectively given by (see [6, 2]) neutron production = P n j=1 p j = 1 neutron absorption = P n j=1 p j k j (T ) 5) The parameter k j can therefore be interpreted as the ratio of the neutron production and the neutron absorption in batch j. The value of k j is high when a batch contains a large amount of fuel and k ....

....(T ) O( ffik j (T ) 2 ) p j [1 ffik j (T ) p j [2 Gamma (1 Gamma ffik j (T ) p j [2 Gamma k j (T ) to obtain n X j=1 p j k j (T ) 1 L: 6) 3 2. 4 Coupling eigenvalue equation The last set of equations concern the (N Theta N) fast group coupling coefficient matrix G [6], where G rs (r; s = 1; N) is the probability that a neutron produced at fuel location (or node) s will be absorbed in node r. This leads to the following eigenvalue equation for the vector OE of fast neutron fluxes [6] OE i (i = 1; N) in the nodes: OE = 1 k eff GKOE (7) where ....

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J.J. Duderstadt, L.J. Hamilton. Nuclear Reactor Analysis. John Wiley and Sons (1976)

.... Parallel Solvers for the Two Group Neutron Diffusion Equations of Reactor Kinetics ROBERT SCHEICHL 1 INTRODUCTION We are concerned with the solution of the transient two group neutron diffusion equations arising in the simulation process of nuclear reactor cores [DH76] OE g t = r Delta (D g rOE g ) f g i OE 1 ; OE 2 ; C i ) i=1; 6 j ; g = 1; 2 (1) C i t = h i (OE 1 ; OE 2 ; C i ) i = 1; 6 (2) The unknowns in this system are the flux densities OE 1 and OE 2 of the fast (g = 1) and thermic (g = 2) neutrons, as well as the ....

Duderstadt J. J. and Hamilton L. J. (1976) Nuclear reactor analysis. J. Wiley & Sons, New York.

....way to describe the neutron flux in the reactor core is to consider the production, absorption and transport of neutrons as a diffusion process. This approach forms the basis of the model used in this paper, and will briefly be discussed here. More detailed descriptions can be found in e.g. [4, 10, 11]. 2.1 Diffusion equations The diffusion model describes how neutrons are produced, absorbed, and how they diffuse everywhere in the core. The diffusion coefficients and production and absorption rates depend on the material in the core, and also on the energy level of the neutrons. Neutrons ....

....cm Gamma2 s Gamma1 ) The neutron flux for the fast and thermal group. The neutron flux is defined as the total rate at which neutrons pass a sphere with unit cross section area. 2 Now, the set of time dependent diffusion equations for the fast and thermal group can be written as (see [4]) 1 v1 OE 1 (x;t) t Gamma r x Delta D 1 (x)r x OE 1 (x; t) Omega 1 a (x)OE 1 (x; t) Omega s (x)OE 1 (x; t) 1 Omega 1 f (x)OE 1 (x; t) 2 Omega 2 f (x)OE 2 (x; t) 1) 1 v2 OE 2 (x;t) t Gamma r x Delta D 2 (x)r x OE 2 (x; t) Omega 2 a ....

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J.J. Duderstadt and L.J. Hamilton. Nuclear Reactor Analysis. John Wiley & Sons, Inc., 1976.

....is induced by the capture of a free neutron, and results in a lot of energy, and some new free neutrons. The behaviour of the free neutrons, represented by the flux, plays a major role in models describing the fission process, and will be estimated by a neutron diffusion process. see e.g. 2] [4] and [7] We introduce the following parameters, where X is the space of the core and the surrounding water. ffl Omega f (x) Omega a (dim cm Gamma1 ) Fission resp. absorbtion cross section: the probability per unit path length that a neutron moving through the core will cause a fission ....

....production and absorbtion. ffl v (dim. cm s Gamma1 ) The average neutron speed. Define the neutron flux ffl OE(x; t) dim. cm Gamma2 s Gamma1 ) defined as the total rate at which neutrons pass through a unit area in any orientation. The time dependent diffusion equations then reads [4] 1 v OE(x; t) t Gamma Dr 2 x OE(x; t) Omega a OE(x; t) Omega f (x)OE(x; t) 1) In general, the shape of the flux will change with time. However, under certain conditions, we may assume that OE(x; t) can be separated into T (t)OE(x) When working this out, and dividing the result ....

J.J. Duderstadt and L.J. Hamilton. Nuclear Reactor Analysis. John Wiley & Sons, Inc., 1976.

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Duderstadt, James J., and Louis J. Hamilton, Nuclear Reactor Analysis, John Wiley and Sons, 1976.

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Duderstadt J.J. and Hamilton L.J., Nuclear reactor analysis, J. Wiley and Sons, New York, 1976.

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J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976).

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J. J. Duderstadt and L. J. Hamilton, Nuclear reactor analysis, J. Wiley & Sons, New York, 1976.

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Duderstadt, J.J ; Hamilton, L.J.: Nuclear Reactor Analysis. J. Wiley & Sons, New York 1976.

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J.J. Duderstadt and L.J. Hamilton. Nuclear Reactor Analysis. J. Wiley & Sons, Inc., 1976.

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