Total track length

Neutron fluxes, defined as the total track length per unit volume, are calculated in every region of the system in the full energy spectrum, but are finally condensed to 16 energy groups. Reaction rates may also be obtained... 

The quantities n x,v t) and 0(r,y,<), therefore, are given as functions per unit speed around v and per unit volume around x. By the expression around v we mean speeds which differ from v ever so slightly so that, if the deviation is dy, then as dv — 0, the speeds in question approach v. It is customary to call the total track length per unit volume per unit time. The basis for this terminology is evident from the definition (3.35). We write this relation in an expanded form... 

This definition is frequently abbreviated to total track length per unit volume per unit speed. Whenever this form is used, the complete statement (3.40) is implied. 

This equation corresponds to the relation (3.42) and states that the total track length per unit volume per unit time around r at time t is conserved in going from speed space to energy space. If we introduce the Jacobian dv/dE, it is easily shown that (again omitting r and /)... 

The concepts introduced above may be extended to describe integral characteristics of the neutron population. The function 0(r, ,O, which gives a detailed description, can be used to construct a quantity which refers to the bulk properties of the system. Thus, if we wish to determine the total track length of neutrons in a system of volume V which have energies in dE about we perform the following integration ... 

Likewise we can compute the total track length of neutrons of all energies in volume V from the relation... 

The calculation of the total track length took into account the contributions of all neutrons of speed irrespective of their direction of motion,... 

That conditions (2) and (3) cannot be satisfied by the function 0(r) is entirely clear (r) gives the total track length, whereas what is needed is the track length (or density) of neutrons which are traveling in a par-... 

By the arguments given above for the discrete distribution of sources, we can compute the total track length per unit volume per unit time at r due to all sources in the medium by integrating (5.96) over all space. 

Thus 4>(T,v Qft) is the total track length traveled per unit time by the neutrons described in (7.1). In most of the analysis presented in this chapter it will be convenient to work with this function rather than with the neutron density. 

This result may be used to compute the total track length 0(r), which is defined by Eq. (7.59). The substitution of (7.190) into (7.59) yields... 

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