Thermal Flux Spectrum

Since most of the reactions in a thermal reactor occur at thermal or near thermal energies a description of the exiergy spectrum for neutrons at these energies is of most inqportantance The simplest model assumes that the neutrons reach an energy distribution In egulllbrlum with the moderator atoms. That Is If the moderator has an absolute temperature T the thermal neutrons have a speed distribution which follows MBUcwell s gas law. 

2) It does not take into account the moderating effect of more than moderator, 

3) It Ignores the contribution from neutrons still slowing down. 

Bach of these practical aspects is discussed in turn. 

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SCHLOSSER, J. E., Spectrum V - Infinite Medium Thermal Flux Spectrum Program, HW-71953, (December 5, 1961). 

The Maxwe11-Boltzmann thermal flux spectrum in a reactor is described by the equation,... 

X-rays emitted from the reverse-shocked ejecta dominate those from the blast-shocked CSM because of much higher density in the ejecta3). The electron temperature of the shocked ejecta is raised to >lOfceV and then decreases with time to lOfceV at tmoi, at which the flux at lOfceV reaches its maximum. Free-free emission dominates the thermal spectrum except for a contribution of iron K-line emission around 7fceV. If CSM concerned is the remnant of a stellar wind, the mass loss rate can be estimated from the observed thermal flux at lOfceV as4),... 

The determination of sodium in pure aluminum by the reaction Na (7i,y)Na is complicated by the reaction Al (n, )Na brought about by the fast component of the neutron flux spectrum. Salmon (77) determined the contribution to the sodium content by this reaction in BEPO by irradiating identical samples and standards normally and in the thermal column. The difference in the sodium content determined by these two methods gives the apparent sodium content derived from the (n.,o) reaction. Salmon found this value to be 81 ppm under the conditions of the experiment. 

With these data it sedms reasonable to postulate that (a).the observed thermal flux at the surface of the graphite is proportional to the total flux there, and (b) the cadmium ratios at this location are proportional to the fraction of fast neutrons (of the iron-penetrating variety) in the spectrum. 

Harvey Amster and Roland Suarez, The calculation of thermal constants averaged over a Wigner-Wilkins flux spectrum, WAPD-TM-39, January, 1957. 

In Eq. (30.38), the term Qo(a)//in the factor (1 + Qo( )//) corrects for activation by epithermal neutrons. This factor is the heart of the ko method and was the key innovation that made the method possible. It was necessary to predict, with high accuracy, the relative reaction rates for two different (n,y) reactions in any reactor neutron spectrum. For each reaction, the Qo value, the ratio of the resonance integral to the thermal neutron activation cross section, and / the ratio of thermal flux to epithermal flux for the irradiation channel used, is needed. ... 

The neutron spectrum from a nuclear reactor is typically divided into two components a thermalized flux with a Maxwell energy distribution and an epithermal flux whose energy distribution is proportional to the reciprocal of the neutron energy, / ... 

H. Amster and Suarez, The Calculation of Thermal Constants Avenged Over a Wigner-Wilkens Flux Spectrum-Description of the SOFOCATE Code," WAPD-TM-39 (January 1997). 

H. Amster and R. Suarez, The Calculation of Thermal Constants Averaged over a Wlgner-iWlfcins Flux Spectrum Descrlptimi the SOFOCATE Code, WAPD-TM-39(1957). 

The subcadmium activation distributions were used in conjunction with cross sections computed by Westcott to calculate values of the thermal utilization f and the thermal migration area L in the usual way. A base value of V was calculated from Westcott values, assuming the neutron flux spectrum in the moderator to be Maxwellian at 2(PC. This value was then modified for flux hardening effects >y comparing the ratios of the 1/v activations (Cu and Mn) and the U-235 activations at various locations. Values of the fast fission factor < were obtained by comparing the fission product activities of natural and depleted uranium foils according to the technique described by Futch . The neutron age r was measured to indium resonance from isolated fuel assemblies in DjO. Corrections were calculated for the age to thermal energy and for lattice effects. 

The measured fission rates were input to the SAND-II code together with a starting spectrum calculated with the KENO Monte Carlo-code. The SAND-II code produced an adjusted dalcubted spectral shape which agreed vrith the measured data. Table I presents these SAND-II results for the thermal flux, flux of neutrons with energy. 1 and 1 MeV, total flux, and the mean neutron energy. A detailed error analysis was not made, but on the basis of similar Mrilyses, uncertainties in these spectral values are estimated to be 10 to 15% (1 o). 

Measurement of flux spectrum/flux variations (such as beam ports and thermal columns). 

She third defect mentioned in the previous section for the thermal flux distribution vas the omission of the contribution of the slowlng-dowi neutrons to the thermal spectrum. It must be recognised that the thermal and epithermal flux distributions overlap, it Is here vhere It, 1s most useful to coofblne the two distributions and again introduce the Westcott fhix formulation. Westcott defines a neutron-density distribution per unit speed interval as follows ... 

Prompt neutrons are moderated to thermal energies to produce the thermal spectrum shown in Figure 2.7, The peak thermal flux,. 0253 eV at room temperature of 20 C or 293 K, is approximately two decades greater than the peak fission flux, but the energy range of thermal neutrons is a small fraction of the fission energy range so that the total number of thermal neutrons in the core is less than the total number of fission neutrons. 

Figure .7 Thermal and Fission Neutron Flux Spectrum...

Different strategies exist to characterize a planet s atmosphere direct detection resolves the planet and star individually, and transmission as well as secondary eclipse measurements subtract the stellar light fi om a combined star-planet detection. For directly imaged planets, in the visible part of the spectrum, we observe the starlight, reflected off the planet in the thermal IR we observe the planet s own emitted thermal flux. An Earth-like, temperate planet is a very faint, small object close to a very bright and large object, its parent star. 

This distribution is the same as that obtained by multiplying the neutron distribution in the reactor by v. This then is the same distribution as the thermal-neutron flux spectrum in the reactor. 

Figure 5.24. Gamma-ray spectrum of preconcentrated river water after short irradiation. Irradiation time 5 min thermal-neutron flux 1 x 1013 n cm 3 s"1 decay time 3 d counting time 1000 s. Source [627]...

Fig. 1 Thermal spectrum (solid line) calculated with an energy resolution of 0.49(E/keV),/2keV (FWHM) is overlaid on the observed spectrum with Ginga0 (crosses). The residual flux over the thermal emission is represented by the histogram.

Some of the alternative TOF instrument designs involve replacing the beryllium filter with either a crystal or a mechanical chopper to monochromate the incident beam. With this change, the spectrometer can be used with a higher incident neutron energy (typically E 50 meV) so that a smaller momentum transfer Q is possible for 5 the same energy transfer (21,22). With a monochromatic incident beam, a beryllium filter is sometimes substituted for the chopper after the sample in order to increase the scattered intensity but with a sacrifice in the,minimum Q attainable. Energy transfers up to 100 meV (800 cm" ) can be achieved with TOF spectrometers at steady state reactors before the incident neutron flux is limited by the thermal spectrum of the reactor. (With hot moderators such as at the Institut Laue-... 

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