Doppler effect improves reactor stability. Broadened resonance (heating of a fuel) results in a higher probability of absorbtion, thus causes negative reactivity insertion (reduction of reactor power).
In general, Doppler broadening is the broadening of spectral lines due to the Doppler effect caused by a distribution of kinetic energies of molecules or atoms. In reactor physics a particular case of this phenomenon is the thermal Doppler broadening of the resonance capture cross sections of the fertile material (e.g. 238U or 240Pu) caused by thermal motion of target nuclei in the nuclear fuel.
See also: Nuclear Resonance
The Doppler broadening of resonances is very important phenomenon, which improves reactor stability, because it accounts for the dominant part of the fuel temperature coefficient (the change in reactivity per degree change in fuel temperature) in thermal reactors and makes a substantial contribution in fast reactors as well. This coefficient is also called the prompt temperature coefficient because it causes an immediate response on changes in fuel temperature. The prompt temperature coefficient of most thermal reactors is negative.
A negative fuel temperature coefficient is generally considered to be even more important than a negative moderator temperature coefficient. Especially in case of reactivity initiated accidents (RIA), the Doppler coefficient of reactivity would be the first and most important effect in the compensation of the inserted positive reactivity. The time for heat to be transferred to the moderator is usually measured in seconds, while the Doppler coefficient is effective almost instantaneously. Therefore the moderator temperature cannot turn the power rise for several seconds, whereas the fuel temperature coefficient starts adding negative reactivity immediately. The fuel temperature coefficient αf may be defined as:
The Doppler effect arises from the dependence of neutron cross sections on the relative velocity between neutron and nucleus. The probability of the radiative capture depends on the center-of-mass energy, therefore depends on the kinetic energy of the incident neutron and the velocity of target nucleus. Target nuclei are themselves in continual motion owing to their thermal energy. As a result of these thermal motions neutrons impinging on a target appears to the nuclei in the target to have a continuous spread in energy. This, in turn, has an effect on the observed shape of resonance. Raising the temperature causes the nuclei to vibrate more rapidly within their lattice structures, effectively broadening the energy range of neutrons that may be resonantly absorbed in the fuel. The resonance becomes shorter and wider than when the nuclei are at rest.
Although the shape of a resonance changes with temperature, the total area under the resonance remains essentially constant. But this does not imply constant neutron absorbtion. Despite the constant area under resonance, the resonance integral, which determines the absorbtion, increases with increasing target temperature. The broadened resonances result in a larger percentage of neutrons having energies that are susceptible to capture in the fuel pellets. On the other hand with colder fuel, only neutrons very close to the resonance energy are absorbed.
Moreover, there is a further phenomenon closely connected with Doppler broadening. The vicinity of the resonance causes an increase in the neutron absorption probability, when a neutron have an energy near a resonance. This results in a reduction of the effective absorption per nucleus due to the depression of the energy dependent flux Φ(E) near the resonance in comparison to a flat flux. At energies just below the resonance, where Σa(E) becomes small again, the neutron flux reaches almost to the same value just above the resonance. This reduction in the energy dependent neutron flux near the resonance energy is known as energy self-shielding. These two phenomena provides negative reactivity feedback against fuel temperature increase.
An increase in temperature from T1 to T2 causes the broadening of spectral lines of resonances. Although the area under the resonance remains the same, the broadening of spectral lines causes an increase in neutron flux in the fuel φf(E), which in turn increases the absorption as the temperature increases.