Doppler effect, thermal

Experimental details for the cross-section measurements were presented in the literature. Briefly, after the irradiation by electron beam pulse for a few nanoseconds, the time-dependent absorption for the atomic line transition Rg Rg -i-/zv was measured to observe the time-dependent population of the excited rare gas atoms Rg. The population of excited Rg was determined using an absorption law for the atomic lines, where the broadening of the absorption profile due to the thermal Doppler effect and due to the attractive interatomic potentials was reasonably taken into consideration. The time-dependent optical emission from energy transfer products, such as ... 

The thermal motion of the atoms in the source volume leads to a broadening of the observed line, because the thermal velocity vth of the electron-emitting atom is added to the electron velocity v0. For an estimation of the resulting disturbance by this kinematical effect it is sufficient to select for the thermal velocity the two directions at which the Doppler effect becomes extreme, i.e.,... 

The situation is more complicated in the applications of the statistical method to radiation phenomena. Some of the older attempts have not as yet yielded clear results. Among these are the connection of the interference limit for large path differences with the average time between collisions undergone by the center of emission,2,6 or the remark that, on account of the corresponding Doppler effect, the thermal motion of the sources of emission creates a lower limit for the width of fine spectral lines.218... 

The thermal shift 6j of the Mdssbauer spectrum is the sum of a contribution due to the second-order Doppler effect (6sod) and a possible contribution due to an intrinsic dependence of the isomer shift (8j) on temperature. The second-order Doppler shift is proportional to the mean square velocity of the Mdssbauer nucleus. For the purpose of a comparison with thermodynamic data, the SOD shift may be described in terms of the Debye approximation,6... 

The Doppler broadening effect is caused by the thermal motion of the emitting or absorbing atoms. Under typical conditions the speeds of atoms are about 1000 ms . Although this is considerably smaller than the speed of light (r = 3 X 10 ms ), it is fast enough for the Doppler effect to become noticeable. 

At plant start up in the 4S, the system temperature is raised to 350°C by heat input from the electromagnetic pump before raising the reflector. This procedure greatly reduces the reactivity temperature swing. The reactivity to be inserted to increase the power is about 86 6, which causes the following reactivity effects thermal expansion of the fuel, structure, coolant, core support grid and doppler reactivity. Because metallic fuel is employed in the 4S, the reactivity is small compared with the 1500 for MOX (Mixed Oxide) fuel, mainly due to its small Doppler coefflcient. 

It was considered that the fuel thermal expansion, which is the major component of the power coefficient of JOYO, decreases at high bumup due to fuel restmcturing during irradiation. It was also observed that the power coefficients varied depending on the reactor power as shown in Fig. 6. This phenomenon appeared to be due to a combination of the core bowing effect, fuel thermal expansion and Doppler effects. These causes need further investigation. 

Brillouin scattering occurs as a result of an interaction between the propagating optical signal and thermally acoustic waves present in the silica fibre giving rise to frequency-shifted components, similar to a Doppler effect. The acoustic velocity is directly related to the medium density and depends on both temperature and strain. As a result, the so-called Brillouin frequency shift carries information about the local temperature and strain of the fibre. Furthermore, Briflouin-based sensing techniques rely on the measurement of a frequency as opposed to Raman-based techniques that are intensity based. 

The mass of the nucleus decreases by the mass lost with the 7-photon emission and for this reason the shifts will be different in the source and the absorber. A Doppler effect originating from the thermal motion of the nuclei must be supplied to the source and for 7 resonance we have,... 

Reactor power is chosen in the range of 1500-2KX) MW (thermal). Sodium void reactivity effect is (0 to -0.1) x l0 The number of the zones with different enrichment is 2 or 3. A multi-batch loading scheme is assumed. The following reactivity effects are taken into account sodium thermal expansion and void reactivity Doppler effect axial core expansion radial core expansion control rod drive expansion. IPPE provides reactivity worth tables and specifies correlations for calculations of structural feedback effects of reactivity (with reference data). The duration of the LOF scenario to be computed is taken as about KXX) s. 

C. Comparison of Doppler Effect for Fast and Thermal Reactor. 113... 

The Doppler effect in thermal reactors (13, 14) has been developed to the point where calculations are considered to be highly reliable. The reliability has not yet been established for fast reactors. Authors have typically attached uncertainties of 50% to their calculated Doppler temperature coefficients of reactivity (6, 12k, 121). However, we believe that, with improvements in the theory of recent years, the theoretical methods are actually substantially more accurate than 50%, and the main remaining errors lie in the experimental data for resonance parameters and calculation of the group fluxes and adjoints. It is the main purpose of this chapter to present a derivation and discussion of the currently available theoretical techniques for fast reactors. ... 

We do not give a complete review of the work done on Doppler effect over the past 10 years. This has been very well done in a recent paper by Nordheim (13), who reviews the Doppler effect in both thermal and fast reactors. Instead, we attempt to present a unified development of the... 

The J function of thermal reactor Doppler effect theory is also extremely useful to fast reactor theory. It is given in our notation by... 

The second-order Doppler shift, (5sod> which is often called temperature shift, is a peak shift related to the relativistic Doppler effect originating from the thermal motion of the nuclei. If the Mossbauer atom has a speed u, and moves in a direction making angle a with the direction of the y ray it emits, then the v frequency of the emitted y ray will differ from the Vo frequency it had if the atom had been at rest. The v frequency is related to Vo in the following way ... 

The second perturbation, namely the thermal motion of emitter nuclei, produce a Doppler-effect broadening of the emission line and causes it to extend in part beyond the energy Eq even though centered at Ey (= Eq—Er). The y-ray energy will be broadened into a distribution by the Doppler-effect energy, E = MvV, which is proportional to the initial velocity, Vx. from the random thermal motion of the atom, and v from the recoil of the nucleus. 

The thermal shift of Mossbauer lines arises from the second-order Doppler effect (Pound Rebka, 1959). If is the mean-square velocity of the Mossbauer nucleus in the crystal, then the relative shift in energy of the Mossbauer line will be given by AE/Eq= — /2c. In the Debye model approximation this leads to AE... 

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