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Direct Coupling of Energy Groups, Multigroup Neutron Diffusion

  1. Aug 28, 2012 #1
    This one comes from Duderstadt and Hamilton, Problem 7-3.

    In multi-group diffusion theory What percentage of neutrons slowing down in hydrogen will tend to skip energy groups if the group structure is chosen such that [itex]\frac{E_{g-1}}{E_{g}}[/itex]=100= 1/[itex]\alpha_{approx}[/itex].

    I know that the probability of a neutron scattering to a lower energy in hydrogen is uniformly distributed as: [itex]\frac{1}{E_{i}}[/itex] (because [itex]\alpha[/itex] = 0 in this case).

    My approach was to integrate the probability distribution from 0 to the bottom of the (approximated) energy group which should give me the probability that the final energy is less than [itex]\alpha E_{i}[/itex]:

    [itex]\int^{E_{i} \alpha_{approx}}_{0} \frac{1}{E_{i}} dE_{f}[/itex] which lead to a value of [itex]\alpha_{approx}=\frac{1}{100}=1[/itex]%.

    Am I doing this right?


    It is worth noting that for neutron moderators with A> 1 (anything heavier than hydrogen) the s-wave downscattering PDF is given by:
    [itex]P(E_{i}\rightarrow E_{f})=\frac{1}{(1-\alpha)*E_{i}}[/itex]

    where:
    [itex]\alpha=(\frac{A-1}{A+1})^{2}[/itex]

    and [itex]\alpha E_{i}[/itex] is the minimum energy a neutron can scatter to from [itex]E_{i}[/itex] in a collision with a nucleus of mass A.

    from this it is clear that if A=1 (as in hydrogen) α = 0 and thus the distribution goes as 1/E.


    Thanks!
     
  2. jcsd
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