Rajesh Mohan

Steady-state fast neutron spectra in slabs on natural uranium-a comparison of diffusion and transport theories

Space-dependent fast neutron spectra have been calculated in slabs of natural uranium by solving the multigroup diffusion equation. It is shown that the eigenfunction expansion method can be used even in this case when the fission term is present, by using the biorthogonality property between the eigenfunctions of the actual matrix and those of the transpose matrix. These results have been compared with the corresponding results based on transport theory. Except close to the source and the free boundary, the authors find good agreement between the two sets of results.

An eigenvalue and eigenfunction study of space-dependent fast neutron spectra in /sup 232/Th

The multigroup space eigenvalues and eigenfunctions of a one-dimensional steady-state diffusion theory operator have been used to study the spatial behavior of a fast neutron field in certain thorium systems. The nuclear data used are from the 26-group ABBN data set. It has been shown that for a fast thorium system, unlike a fast uranium system, all the space eigenvalues lie in the continuum and no discrete space eigenvalue exists. A fast thorium system behaves more like a fast nonmultiplying system. The spectra shifts continuously to lower energies as one moves away from the source; however, pseudoasymptotic conditions are established in certain distance ranges. In order to test the validity of the diffusion theory and eigenfunction expansion method, results have also been obtained using transport theory. In all cases the two sets of results are in reasonably good agreement. To see the effect of geometry, the spectra at certain distances inside a 1-m-thick thorium slab are compared with the corresponding spectra inside a thorium sphere of 1-m radius. At all distances the normalized slab and sphere spectra are nearly the same.

An elgenvalue and eigenfunction study of time-dependent fast-neutron spectra in 232Th☆

The pulsed problem for fast neutrons in Th has been studied using the multigroup diffusion equation and eigenfunction expansion method. The time-dependent fast-neutron spectra have been obtained up to 8000 ns inside Th systems with buckling ranging from 0.0 to 0.015 cm−2. The results have been obtained using the 27-group BARC data set. It has been shown that for a fast Th system, unlike a fast U system, all the time eigenvalues lie in the continuum and no discrete time eigenvalue exists. A fast Th system behaves more like a non-multiplying system. The spectra shift continuously to lower energies with increasing time. However, pseudo-asymptotic conditions are established in certain time intervals. The start of pseudo-equilibrium conditions and the duration for which they persist is seen to increase with decreasing buckling. The reason for the establishment of pseudo-equilibrium conditions has been discussed. The theoretical results for the instantaneous decay constant inside a 40 cm cube of Th have been compared with the experimental results of Moo et al. (1973). The present results are in good agreement with the above experimental results based on the 239Pu detector.

The existence of equilibrium spectra in fast natural uranium assemblies. The effect of anisotropy in scattering

The calculated results of steady state, space- and angle-dependent fast neutron spectra inside various one dimensional slabs of natural uranium are reported. The effect of anisotropy in scattering on fast neutron spectra has been studied for three different orders of anisotropy, zero, first and third. It is shown that with a high energy, plane source of monoenergetic neutrons, spectral equilibrium is established in natural uranium slabs beyond 90 cm from the source plane, with an associated diffusion length of 19.9 cm. This is consistent with the lower bound for diffusion length in natural uranium. Further, the neutron flux is larger when anisotropy in scattering is included in the calculations.

Decay of fast neutron pulses in uranium assemblies

The multigroup diffusion equation is solved for the pulsed problem and the timedependent energy spectra are obtained using the eigenfunction expansion method. It is shown that complete spectral equilibrium can be obtained beyond 2000 ns in a 40-cm cube of natural uranium. This time is found to increase with increasing assembly size. The earlier exponential decays observed in a pulsed uranium system are traced to the establishment of the pseudo-equilibrium condition due to the trapping of neutrons in certain energy groups. It is shown that such a pseudo-decay corresponds to the establishment of the first higher mode of decay and the time range in which it is established is a function of B/sup 2/.

On the validity of simple theoretical relations used for analysing the intensity modulated photoresponse of a semiconductor

Abstract A material independent theoretical simulation of a modulated light experiment has been carried out. The space dependent study of amplitude A and phase-shift θ for a wide range of values of normalized absorption coefficient a′ ( = aL0) and normalized ω′ ( = ωτ) shows that for La/L(ω)⩽0.5 the phase-shift is accurately given by the relation θ = ξ(ω)x whereas θ is given by tan−1(ωτ) only if the condition La/L(ω)⩽15 is satisfied. The spatial behaviour of amplitude shows that log A varies linearly with x in both the cases. For La/L(ω)⩽0.5 the slope of the straight line is found equal to α(ω) (=1/L(ω)) whereas it is equal to a′ for Laa/L(ω)⩾2.

Theoretical study of photoresponse to pulsed radiation in n-InSb in the temperature range 77–300 K

The results of a theoretical simulation of a transient experiment in n-InSb in the temperature range 77–300 K, are reported. Minority carrier lifetimes for the three recombination processes, radiative, SRH and Auger, have been calculated at different temperatures using the temperature dependence of intrinsic carrier concentration,ni, and density of states effective mass of heavy holes,md. It was found that around room temperature the lifetimes for the three processes become comparable and at higher temperatures the Auger lifetime becomes dominant. This fact was ignored in previous work where only SRH and radiative processes were considered in the calculation of effective lifetime. The present results of effective lifetime in n-InSb are in reasonably good agreement with the results obtained previously. The effect of higher time modes on the decay of photoresponse to pulsed radiation is discussed. An instantaneous time constant has been defined and its variation with time at different temperatures has been studied.

Thermal neutron extrapolation distances for slabs of beryllium and water

Extrapolation distances for thermal neutrons have been obtained for slabs of beryllium and light water by minimising the difference between the steady-state leakage spectra calculated on the basis of diffusion and transport theories. Using the present values of extrapolation distance ensure that neutron spectra (both in beryllium and water) calculated on the basis of diffusion theory agree well with the corresponding transport theory spectra, even at distances close to the free surface. The authors find the extrapolation distance to be dependent of the thickness of the slab, increasing with increase in the thickness.