Nuclear reactor reactivity

The reactivity of a nuclear reactor is a dimensionless quantity characterizing the behavior of the fission chain reaction in the core of a nuclear reactor and expressed by the ratio:

\rho ={{k_{ef}-1} \over k_{ef}}

{\ displaystyle \ rho = {{k_ {ef} -1} \ over k_ {ef}}}

\ rho = {{k _ {{ef}} - 1} \ over k _ {{ef}}}

,

wherein $k_{ef}$ ${\ displaystyle k_ {ef}}$ $k _ {{ef}}$ means effective neutron multiplication factor . Reactivity depends on the shape of the reactor, the location of the materials in it and the neutron-physical properties of these materials. It is an integral parameter of a nuclear reactor, that is, it characterizes the entire reactor as a whole.

In different cases, for convenience, the magnitude of the reactivity can be expressed in percent, effective fractions of delayed neutrons , etc.

Content

Power Linkage

Depending on the sign of reactivity, the neutron power of the reactor behaves differently. For example, in the absence of an additional internal source of neutrons and feedback in a nuclear reactor, three different states are distinguished.

If a $\rho =0,k_{ef}=1$ ${\ displaystyle \ rho = 0, k_ {ef} = 1}$ , then the neutron power does not change. This state of the reactor is called critical .
If a $\rho >0,k_{ef}>1$ ${\ displaystyle \ rho> 0, k_ {ef}> 1}$ , then the neutron power after attenuation of transients will increase. This state of the reactor is called supercritical .
If a $\rho <0,k_{ef}<1$ ${\ displaystyle \ rho <0, k_ {ef} <1}$ , then the neutron power after attenuation of transients will decrease. This state of the reactor is called subcritical .

More precisely, reactivity $\rho$ ${\ displaystyle \ rho}$ is included as a parameter in the simplest approximate model of a nuclear reactor recorded in the point approximation :

N'(t)={\frac {\rho -\beta }{\Lambda }}N(t)+\lambda C(t)+S(t),

{\ displaystyle N '(t) = {\ frac {\ rho - \ beta} {\ Lambda}} N (t) + \ lambda C (t) + S (t),}

C'(t)={\frac {\beta }{\Lambda }}N(t)-\lambda C(t).

{\ displaystyle C '(t) = {\ frac {\ beta} {\ Lambda}} N (t) - \ lambda C (t).}

Here N (t) is the total number of neutrons in the reactor, $C(t)$ ${\ displaystyle C (t)}$ - the number of delayed neutron emitters, $\beta$ ${\ displaystyle \ beta}$ - effective fraction of delayed neutrons, $\lambda ,s^{-1}$ ${\ displaystyle \ lambda, s ^ {- 1}}$ Is the decay time constant of delayed neutron emitters, $\Lambda (\rho )\,,s$ ${\ displaystyle \ Lambda (\ rho) \ ,, s}$ - the average lifetime of instantaneous neutrons in a reactor (depends on reactivity), $S(t)$ ${\ displaystyle S (t)}$ - the intensity of other neutron sources (spontaneous decay, starting neutron source, etc.).

It should be noted that the behavior of the neutron field in nuclear power reactors is much more complex than in the model presented above. The neutron field depends on the spatial, angular and energy variables, on the influence of various types of feedbacks , effects of poisoning , burnout , etc. Taking these factors into account leads to a nonlinear integro-differential equation of the neutron field, from which it follows that there is no unambiguous relationship between the reactivity of the reactor and a change in its neutron power at the current time.

For example, if neutrons were initially located in places where they are more likely to be lost, then until the relative rate of change in the number of neutrons is the same at all points of the reactor, a tendency to decrease in power will be observed. The converse is also true, the initial distribution of the neutron flux density can be such that at the beginning of the process the neutron power will increase with negative reactivity.

Practical use

Reactivity is widely used in practice, since using this parameter it is convenient to characterize the degree of deviation of the reactor from its critical state. For example, by constructing the dependence of reactivity on the immersion depth of the absorbing rod in the core, it is possible to determine the position of the rod at which the reactor power will be constant.

In addition, for small deviations from the zero value (near-critical state of the reactor), the reactivity has the property of additivity, which allows attributing to the regulators the corresponding efficiency values (for example, the weight of the rod ).

Using reactivity, concepts are introduced that characterize, to a first approximation, the stability and safety of a reactor installation: effects and reactivity coefficients .

In the practice of operating nuclear power plants, effects and reactivity factors are used as

control parameters used to evaluate the level of safety of a nuclear reactor;
benchmarks, which are used for verification of reactor calculation software.

For these reasons, periodic measurements of effects and reactivity coefficients are carried out at existing reactor facilities.

In general, despite the widespread use of the term reactivity and its derivatives, their use in practice for predicting the actual behavior of a nuclear reactor is greatly limited by the conditions for performing the point approximation : a physically small size of the reactor or uniform, small perturbations.

Reactivity Units

Reactivity is a dimensionless quantity , it's just a number, and no special units are needed to measure reactivity. However, in practice, various relative and arbitrary units are used to measure it. First, reactivity can be measured as a percentage , that is, in units equal to one hundredth of a unit resulting from the definition of reactivity. Secondly, reactivity is measured in reverse hours . This unit is used for small reactivities when measuring reactor periods. The return hour is such reactivity, which corresponds to a steady - state reactor period of 1 hour. Finally, reactivity is measured in units of β (fraction of delayed neutrons ), or dollars and cents . For one dollar, reactivity equal to β is taken, and cents are hundredths of this reactivity.

Since p = β is the limit value of the reactivity of a reactor controlled by delayed neutrons, it is clear why such a reactivity value is taken as a unit, especially since the absolute value of this unit depends on the type of nuclear fuel. So, β ²³⁹ Pu (0.0021 or 0.21%) is three times less than β ²³⁵ U (0.0065 or 0.65%), and the reactivity expressed in absolute units does not always indicate how much it is close to the limit value. Reactivity in cents is always expressed in fractions of its limit value, and this representation of reactivity is universal.

Reactivity Management

The reactivity of a nuclear reactor is changed by moving in the active zone control elements of a chain reaction - a cylindrical or other form of control rods, the material of which contains substances that strongly absorb neutrons ( boron , cadmium , etc.). One such rod, when completely immersed in the active zone, introduces negative reactivity or, as they say, binds the reactivity of the reactor to several thousandths. The magnitude of the associated reactivity depends both on the material and the size of the surface of the rod, and on the place of immersion in the active zone, since the number of absorbed neutrons in the material of the rod depends on the neutron flux , which is minimal in the peripheral parts of the active zone. The removal of the core from the core is accompanied by the release of reactivity, and since the core always moves along its axis, the increment of reactivity is characterized by a change in position in the core of the core. When the rod is completely immersed, the maximum possible reactivity is associated, however, moving the rod to a predetermined fraction of its full length, for example, one hundredth, causes the smallest change in the reactivity of the reactor, because the end of the rod moves in the region with the lowest neutron flux.

If the rod is half immersed, it binds half of the possible reactivity, but now moving the rod to the same fraction of the length up is accompanied by the maximum release of reactivity. In this latter case, the released reactivity is twice as high as the average reactivity associated with the same fraction of the length of the rod. If for definiteness we assume that the total reactivity associated with the rod is 5 равна10 ⁻³ , then the release of reactivity when the rod is moved one hundredth of its length does not exceed 10 ⁻⁴ . The height of the reactor core is usually more than a meter, and the position of the end of the control rod is fixed with an accuracy much greater than a centimeter. As a result, it turns out that in the reactivity range from zero to maximum, the reactivity of the reactor can be controlled with an accuracy of 10 ⁻⁵ , and the steady-state periods corresponding to such small reactivities are measured in hours. In the absence of delayed neutrons , reactivity control accurate to 10 ⁻⁵ would be clearly insufficient.

Literature

A. N. Klimov. Nuclear physics and nuclear reactors. - M .: Atomizdat , 1971. - 384 p.
V.E. Levin. Nuclear physics and nuclear reactors. 4th ed. - M.: Atomizdat , 1979.- 288 p.
B.V. Petunin. Thermal energy of nuclear installations. - M.: Atomizdat , 1960 .-- 232 p.
V. E. Zhitarev, V. M. Kachanov, G. V. Lebedev, A. Yu. Sergeevnin. Issues of atomic science and technology, series - Physics of Nuclear Reactors, Issue 4, Kurchatov Institute National Research Center, 2013. - 46 p.