Inhour

The asymptotic period is one of the most commonly used methods for reactivity determination, whereby the measured asymptotic period is related to reactivity via the Inhour equation (7, 8). The definition of reactivity inferred from the Inhour equation depends on the definition of the reactor s effective kinetic parameters. 

The Inhour equation relating the asymptotic period to the static reactivity is... 

We shall refer to as the asymptotic-period reactivity. The Inhour equation for this reactivity can be obtained by multiplying Eq. (19) by 0q, integrating over phase space and rearranging ... 

The calculation of the effective kinetic parameters of the Inhour equation for the asymptotic-period reactivity requires only one distribution 0, for each subcritical configuration. The effective kinetic parameters for the... 

Inhour equation for the static reactivity [Eq. (13)] are functions of two such distributions, (f), and 4>. The asymptotic-period reactivity is, therefore, the natural reactivity to infer from the Inhour equation. 

An additional equation can be derived from (9) and (10) which is very important in experimental low power reactor physics. When a reactor undergoes a step-insertion of reactivity, which renders the reactor slightly supercritical, for example, and when transient disturbances die out, the neutron and delayed emitter populations will behave as e, where o) is the largest root of the inhour equation, obtained from (9) and (10) by taking fi(t) F(t) e ... 

For a definition of the unit of measurement called the inhour see Weinberg and Wigner [2]. 

Figure 2. Comparison of calculations from two-region and homogenized inhour...

The inhour equation for both approaches takes the form... 

Figure 2 shows the results of sample calculations utilizing the homogenized and two-region inhour equations. The examples are infinite slab reactors with uranium-233 as the core and uranium-235 as the blanket fuels. The choice of placing uranium-233 on the inside is because of a particular study under way at the time the calculations were made. Fuel concentrations... 

The problem of immediate concern is that of the calibration of a control rod in a thermal reactor. By control rod calibration is meant the determination of the reactivity worth of a control rod per unit distance of travel, usually in a vertical direction. Such a calibration, particularly in experimental critical facilities, is of great importance in connection with a variety of reactor experiments. It is rather easy to calibrate a control rod, particularly in a low power critical assembly. A rod is withdrawn a few centimeters in a just critical reactor. As soon as the flux takes off on an exponential ascent the reactor period can be measured with the aid of appropriate detectors and recording devices. A relationship between the reactor period and reactivity is afforded from the inhour equation. Thus, the reactivity worth of a control rod per unit length of travel in a certain area of the reactor is determined. The rod may be calibrated over its entire length of travel by the expedient of maintaining criticality by the opposing... 

The most recent and apparently also the most accurate experiments to date are those of G. J. Fischer et al. 12c, 21). They quote an accuracy of +0.02 inhours for all measurements. The reactivity changes in the U experiments varied from -0.156 to -0.327 inhours, depending upon the sample size and the reactor spectrum. The measurements for Pu and U are, of course, less accurate, as the magnitude of the reactivity changes were only 0.02 to 0.06 inhours, and the corrections for expansion are of the same magnitude. The corrected measurements for the fissionable isotopes correspond to small positive temperature coefficients of reactivity, as expected theoretically. ... 

The situation under discussion here is one where, over the period of time in which Eqs. (9.93) apply [and therefore (9.98)], the multiplication constant of the system (thus also the reactivity) is constant in time (and, in general, different from unity). The reactivity is actually a dimensionless number, but on the basis of (9.98) it is sometimes measured in inhours. An inhour (a unit specific to a given reactor) is defined as that amount of reactivity which will allow, as a solution to (9.98),... 

An alternative derivation is given by W. K. >gen, The Inhour Formula for a Circulating-fuel Nuclear Reactor with Slug Flow, Oak Ridge National Laboratory, ORNL CF 53-12-108, Dec. 22, 1953. 

Answer Since the Ix our describes a unit of excess reactivity as defined above, the inhour and k excess are related. 

Three Inhours of excess reactivity increase by 2,718 in 20 minutes. 

Answer Ihe effective concentration of iodine and xenon are stated in units of reactivity effect (not in atoms, grams, etc.) One inhour of iodine... 

Answer (a) 8OO inhours at zero time, (b) 13OO inhours at eight hours after... 

Answer (a) 25 hours, (b) about 725 inhours, (c) about, 15 inho Oi s five... 

The total or sum (679 inhours) represents the reactivity status of the operating pile with te.mperature and xenon effects at their eouilibri jm values all fut ore reactivity changes add to or subtract from this 679 inho ur base. 

Ar (long term gains discharged in metal) = -5 inhours... 

Answer The initial graphite coefficient was ass umed to be O.67 ih/MW. The metal discharge causes a change 0.67 - O.63 O.O - ih/MW. This corresponds to a loss of (1200) (0.04) 46 inhours of graphite contribution d oring equilibrium operation at 1200 MW follow ing startup. 

Answer From the table note that the xenon (L) value of 689 inhours at... 

Answer (a) About 3 0 Inhour gain in reactivity from xenon decay, (b) 3 0... 

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