Doppler temperature

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. ... 

The development of the theory for calculation of Doppler temperature coefficients of reactivity involves many physical quantities and thus requires the introduction of many mathematical symbols and formulas. We present first the basic physical formulas and then a summary of the definition of the symbols utilized throughout. 

III. DEFINITION OF THE DOPPLER TEMPERATURE COEFFICIENT OF REACTIVITY FOR ONE ISOTOPE... 

We define the Doppler temperature coefficient of reactivity for a single isotope to be the fractional temperature derivative of the multiplication constant when the temperature of that isotope is changed and all other temperatures held constant. With this definition for a single isotope, the total reactivity change when all temperatures change an infinitesimal amount is... 

Operational features of the core stabilized by feedback coefficients (Doppler, temperature, etc.) were confirmed. This neutronic stability together Avith important thermal inertia make reactor control trouble-free. Particularly at low power uncoupling followed by recoupling of a turbogenerator set is performed without affecting the reactor. 

The value of the temperature in eqn (5.3) is nowadays referred to as the Doppler temperature or Doppler cooling limit. At a typical value of the natural hnewidth of an allowed transition 2y = 27t X 10 MHz, the temperature To is of the order of 100 pK. Because of the great promise that laser cooling and subsequent laser trapping of atoms held for laser spectroscopy, researchers at the Institute of Spectroscopy in Troitsk, Russia, launched experiments in this field. By the time the first successful experiment was conducted (Andreyev et al. 1981, 1982), the first theoretical work, summarized in a review of the manipulation of atoms by the light pressure force of a resonant laser (Letokhov and Minogin 1981a), had already been completed. 

Volume 4 of this report concludes that a pure plutonium fuel type is not desirable in LWRs because of the low mass loading per fuel rod (yielding short fuel cycles), relatively small prompt Doppler temperature coefficients, and strong positive isothermal temperature coefficients. Any workable fuel composition must have a negative prompt temperature coefficient (reactor power decreases as temperature increases) for safety and control purposes. 

The subsequent dynamic calculations were based upon point kinetic equations, which is certainly justified in the hot condition of the core. Furthermore it was assumed that the above mentioned parameters always uniquely define the state of the core that is to say, transients in the thermohydraulic behavior within the core were thought to be much faster than the variations of the parameters. Only a time lag between the Doppler temperature of the fuel and the power given to the coolant had to be considered also the time lag due to circulation in the primary loop was taken into account. For the latter reason changes of subcooling were studied independently of the power level. 

An assumption is made that the reactivity feedback for the reactor is divided evenly between the fuel Doppler effect and feedback from the core structural materials. Doppler temperature feedback is a function of the square root of the volume average temperature of the volume to which the feedback is being applied. The overall temperature feedback is divided between two heat structures the fuel pin structure for Doppler feedback and the core block structure for geometric feedback. Axial feedback coefficients are based on power squared weighting of the Doppler term calculated from the tabular input, and a geometric coefficient assumed to be half of the total temperature feedback. The... 

Figure B2.5.12 shows the energy-level scheme of the fine structure and hyperfme structure levels of iodine. The corresponding absorption spectrum shows six sharp hyperfme structure transitions. The experimental resolution is sufficient to detennine the Doppler line shape associated with the velocity distribution of the I atoms produced in the reaction. In this way, one can detennine either the temperature in an oven—as shown in Figure B2.5.12 —or the primary translational energy distribution of I atoms produced in photolysis, equation B2.5.35.

A remarkable feature of these spectra is the resolution of individual rotational lines in such large molecules. [Note that the expanded specttum in, for example. Figure 9.47(a) covers only 5000 MFIz (0.17 cm )]. This is due partly to the very low rotational temperature (3.0 K for aniline and 2.2 K for aniline Ar), partly to the reduction of the Doppler broadening and partly to the very high resolution of the ring dye laser used. 

The laser-Doppler anemometer measures local fluid velocity from the change in frequency of radiation, between a stationary source and a receiver, due to scattering by particles along the wave path. A laser is commonly used as the source of incident illumination. The measurements are essentially independent of local temperature and pressure. This technique can be used in many different flow systems with transparent fluids containing particles whose velocity is actually measured. For a brief review or the laser-Doppler technique see Goldstein, Appl. Mech. Rev., 27, 753-760 (1974). For additional details see Durst, MeUing, and Whitelaw, Principles and Practice of Laser-Doppler Anemometry, Academic, New York, 1976. 

It would appear that measurement of the integrated absorption coefficient should furnish an ideal method of quantitative analysis. In practice, however, the absolute measurement of the absorption coefficients of atomic spectral lines is extremely difficult. The natural line width of an atomic spectral line is about 10 5 nm, but owing to the influence of Doppler and pressure effects, the line is broadened to about 0.002 nm at flame temperatures of2000-3000 K. To measure the absorption coefficient of a line thus broadened would require a spectrometer with a resolving power of 500000. This difficulty was overcome by Walsh,41 who used a source of sharp emission lines with a much smaller half width than the absorption line, and the radiation frequency of which is centred on the absorption frequency. In this way, the absorption coefficient at the centre of the line, Kmax, may be measured. If the profile of the absorption line is assumed to be due only to Doppler broadening, then there is a relationship between Kmax and N0. Thus the only requirement of the spectrometer is that it shall be capable of isolating the required resonance line from all other lines emitted by the source. 

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