In-core neutron sensors are most important because of the direct relation between the neutron-flux distribution and the thermal-power distribution in the reactor core.

Systems for determining neutron-flux distribution fall into two broad categories: systems using fixed sensors at a large number of fixed locations to provide data for generating one-, two-, or three-dimensional power — distribution information, and systems using traveling (mobile) neutron-sensing devices to provide a large number of neutron-flux scans of the core from which the desired power-distribution information can be derived. There are advantages and disadvantages to each system.

Fixed sensors can provide the operator with neutron — flux data at all times during reactor operation. They can also be adapted to sound an alarm or to control or protect against anv power-distribution anomaly that develops during the time interval between successive scans of a traveling sensor. Because the sensors are fixed in position, they must be made so they require no maintenance; in fact, generally, no maintenance or replacement can be performed on a fixed in-core sensor without shutting down the reactor. However, because fixed sensors are continuously exposed to the in-core environment during plant operation, they suffer radiation degradation or damage and must be replaced at planned intervals during refueling periods. Fixed sensors distributed throughout the reactor volume provide data at discrete points; data at all other points must be obtained by interpolation through curve fitting, usually with a computer (either on-line or off-line). The errors in the interpolated data depend on the sensor spacing and the precision of the computer curve-fitting routines.

Traveling or mapping flux-sensor systems, although unable to provide flux-distribution information at all times for alarm, control, or protection, can provide a spatially continuous flux plot along the entire path over which they travel. Traveling sensors thus can detect flux perturbations not picked up by fixed sensors, such as the flux distur­bances at fuel spacer grids and at the ends of control rods. Although these perturbations are seldom of great signifi­cance in reactor operation, since there is not much one can

do about them, the ability to sense them can lend confidence that the entire neutron-flux distribution is being observed, і e, an accurate one-dimensional picture of the real flux distribution is being observed The other two dimensions must still be filled in by interpolation through computer calculations unless, of course, there are traveling flux sensors in the other dimensions as well (which is not the case in present-day power reactors)

Although traveling or mapping neutron flux sensing systems incorporate motors and gear boxes that may require periodic maintenance, they are located where maintenance can be performed with minimum difficulty The flux sensors themselves may last the life of the reactor since flux maps are run only at relatively infrequent intervals and since the sensors are withdrawn from the core when not in use

All neutron-flux sensing systems measure the properties of the products of interactions between neutrons and the sensor materials (see Chap 2) When a neutron sensor is exposed for a long time to a neutron flux, its neutron sensitivity (output signal per unit neutron flux) usually decreases and its gamma sensitivity (output signal per unit gamma flux) remains unchanged This results in a steady decrease in the signal-to noise ratio with neutron exposure When the signal to-noise ratio decreases below a specified value, the lifetime of the neutron sensor is ended (by definition) For a given neutron sensor exposed to a mixed neutron and gamma flux, it follows that any design action that increases the initial value of the neutron to gamma signal ratio also increases the lifetime of the sensor

A block diagram of a logarithmic amplifier (log N) is shown in Fig. 5.17. The log N amplifier has two essential circuits for signal conditioning. The first is the log section, which converts the detector signal to a logarithmic output The second circuit is the period differentiator circuit

The input signal is biased to range over nine decades. So that this signal can be continuously monitored, it is converted to a log signal in the log amplifier circuit The circuit consists of an operational amplifier with an active feedback element, namely, the grounded-base transistor. The circuit can be described by the following equation

e = Eg log ~- (5 3)

lo

where e = output voltage

E0 = offset voltage of the operational amplifier і = input current from the CIC I0 = offset current of the operational amplifier

The output voltage then changes by a factor of 9 for an input current change of nine decades

The log N amplifier circuit is followed by an amplifier that conditions the signal for the meter and recorder outputs and provides a signal for the period differentiator.

The operation of the period differentiator circuit is the same as that for the circuit described in Sec 5-2.4(c) The output of the period differentiator circuit drives a meter and recorder and provides a signal for the period trip circuit. The period trip circuit alarms when the preset time value is exceeded. The trip circuit is described in Sec 5-2.4(e).

5- 3.5 Calibration and Checkout

The log N amplifier shown in Fig 5.17 has two built-in calibrators for checking out the system. The first is a current source with several fixed ranges used to calibrate the log N circuits, meters, and recorder. The second calibration device is a ramp generator for checking the period-differentiator circuit, meter trip, set point, and recorder The period calibrator is described in Sec 5-2 7 These two calibrators provide a means for checking the entire system.

5- 3.6 Control and Safety Circuits

The log N period amplifier provides an alarm (trip) when the period exceeds the set-point value The trip module and shutdown circuit are described in Sec. 5-2 8.

I CONTROL I NUCLEAR PANEL—- 4*—C0NS0LE “Л

INSTRUMENT I CONTROL CENTER NO 2——— *4*——- CABLE ROUTING ROOM

LEGEND A TO ANNUNCIATOR, CONTROL CONSOLE В TO ANNUNCIATOR, NUCLEAR PANEL 1 RELAY TRIP, OPERATING SHUTDOWN CIRCUIT (FLUX LEVEL, HIGH) 2 RELAY TRIP, OPERATING SHUTDOWN CIRCUIT (ION-CHAMBER VOLTAGE LOW)

Fig. 5.18—Block diagram of high-flux channels 9, 10, and 11

When a power reactor is operating in a steady state (constant coolant flow, constant temperatures, etc.), the effective multiplication factor is 1 and the reactivity is zero. If any of the basic parameters, such as coolant flow or temperature, are changed (e. g., to increase or decrease the power level or to compensate for changes in fuel reactivity), then reactivity must be added or subtracted. The most common situations are those in which the reactivity is inserted at a steady rate or as a step function.

Equations 1.7 and 1.8 can be solved for the case where the reactor is taken from delayed critical (p = 5k/k = 0) to prompt critical (p = 5k/k = (3) by inserting reactivity at a constant rate (ramp insertion). Figure 1.5 shows how the relative neutron density, n/n0 = n(t)/n(0), increases with time for several reactivity insertion rates and for several values of the neutron lifetime. Table 1.4 presents similar data in tabular form.

In Fig. 1.6 the effect of inserting a step change in к is shown. The reactor is at delayed critical at t = 0.

1-3.6 Reactivity Changes

For curves, tables, and equations presented in the pre­ceding sections, we assumed that the reactivity was only being altered by some control mechanism that “inserts reac­tivity.” There are other ways that reactivity is altered in an operating power reactor. The most important are: (1) varia­tion of fission-product concentrations, (2) burnup or deple­tion of fuel, and (3) variations in reactor temperatures, pressures, and densities.

An increase in the concentration of fission products reduces reactivity because the fission products absorb some of the neutrons that carry on the chain reaction. The

•The terminology “reactivity insertion," adding or subtracting reactivity, is used here because it is commonly considered proper language of the trade. More exactly, reactivity can be negative, positive, or zero at any operating instant, and adding reactivity could mean, for example, decreasing the negative reactivity toward zero as in startup or in going critical. If, during reactor operation, power is falling and we do not want it to, we say that we add reactivity. If the power is steady but low and we want to increase it, we again say that we add reactivity. If the power is high and we want to lower it, we say that we decrease reactivity, which more exactly means inserting negative reactivity to cause the power to fall. To level the power at a lower point, however, we again say that we add reactivity to compensate or return to a condition of zero reactivity.

The M 1 T Press, Cambridge, Mass, 1964 )

products of fission comprise a large variety of radioactive and stable nuclei whose relative concentrations m a reactor vary with time, power level, and prior operating history Two thermal-neutron absorbing fission products have strong effects on the reactivity of thermal reactors (the pressurized water reactors, the boiling-water reactors, and the gas-cooled reactors of Chaps 15, 16, and 18, respec­tively), namely, 1 3 5 Xe (a 9 2 hr beta cmittci) and l44Sm (a stable nuclide) Because both these nuclides are strong
absorbers of thermal neutrons, they are referred to as fission-product poisons or simply poisons The absorption of thermal neutrons by 135Xe is about 5000 times more probable, on an atom-for-atom basis, than the absorption of thermal neutrons by 2 3 5 U Similarly, 149Sm absorbs thermal neutrons nearly 90 times as easily as 2 3 5 U In almost all present-day power reactors, the chain reaction is propagated almost entirely by thermal-neutron fission processes Consequently, the presence of thermal-neutron

REACTIVITY 0

absorbers in the fuel reduces the rcactnitv of these reactors b absorbing neutrons that otherwise would be available to carry on the chain reaction

In the following paragraphs the basic effects of these two fission products are briefly summarised for details see Rets 3,5, and 7

(a) Xenon-135 [1] In 6 1% of the fissions of 2 3 5 U (or 5 1% of 23 3 U fissions, or 5 5% of 23 9Pu fissions), one of the fission fragments has a mass number of 135 It decays to stable 1 3 5 Ba in the following chain

fission -> 1 35Te(0 5 min)-^ 1 351(6 7 hr)
-|^13sXe(15 3 min)

О 7 1

3 5 Xe(9 2 hr)-£- 1 3 5 Cs(2 6 X 106 yr)

-£• 135Ba(stable)

Because of the short half life of 1 3 51 e, the above decay scheme tan be simplified for most purposes to

fission 1 351(6 7 hr)^- 1 3SXe(9 2 hr) — Д — 135Cs

In addition to being produced via the above chain, 1 35Xe is produced directly in 0 3% of the fissions of 2 3 5 U

The rate of change in the concentration of 1 5Xc is the difference between its production rate (per cm3) and its loss (per cm3) It is produced from the decay of 1 3I and directly from the fission process It is lost b decay to 135Cs and by neutron absorption to 136Xe(stable) The equation is thus

^=(XII+Yx2f0)-XxX-SxX0 (114)

where X = 135Xe concentration (nuclei/em3)

I = 1 3 5 I concentration (nuclei/cm3 )

Xx = l35Xe decay constant (fractional change in concentration attr’butable to beta decay) = 0 693/9 2 hr = 2 1 X 10 5/see

Xj = 1 3 5 I decay constant (fractional change in con­centration attributable to beta decay) = 0.693/6.7 hr = 2.9 X 10 s /sec ф = thermal-neutron flux (neutrons cm 2 sec 1 )

Ox = microscopic thermal-neutron-capture cross sec­tion of 1 3 5Xe = 3.5 X 10“‘ 8 cm2 Zf = macroscopic thermal-neutron-fission cross sec­tion of fuel = concentration of fuel (nuclei/cm3) times the microscopic thermal-neutron-fission cross section

Yx = fractional yield of 135Xe directly from fission

The quantity X] I can be determined by considering the rate of change in the 135I concentration. The 135I is produced from the decay of 13sTe, which, in turn, is produced directly from the fission process. Since the 135Te is so short-lived, it is valid to consider the 135i as produced directly from fission. In this case the equation for the 1 3 51 concentration is

YTe2f0 — X[I — CTjI ф (1.15)

where YTc is the yield of 135Te (6.1% for 2 3 5 U fission, etc.). The final term is the loss of 1 35I because of neutron capture (O] <g ax).

Equations 1.14 and 1.15 can be solved for various initial (t = 0) conditions and for various values of the thermal-neutron flux. One important solution is the equi­librium concentration of 13SXe. The last term of Eq. 1.15 can be neglected; so X|I= Y-pcZf0 at equilibrium condi­tions, and — 0 = YTeZf0 + Yx^f0 — XxX — 0Хф

Solving for X yields

YZf ф

4 + ОхФ where Y is Yx + Y-pe, the total fractional yield of 13sXe per fission (i. e., the yield via the 1 3 5Te chain and the direct yield). Equation 1.16 shows that, as the thermal-neutron flux is reduced, the equilibrium concentration of l3SXe becomes proportional to the flux-, for high thermal-neu-

tron-flux values, the equilibrium concentration of 135Xe becomes independent of the flux

Xcq = Y2f/ax (for ф>Хх/ах)

(1 17)

Xcq s (Y2f/х)ф (for Ф < AX/dX)

The effect of the I35Xe concentration on the control and operation of a nuclear power reactor is determined by how large the absorption of neutrons by 1 5Xe is relative to the absorption of neutrons by the nuclear fuel This determines the degree that the 135Xe interferes with the chain reaction 1 he ratio of macroscopic thermal neutron — absorption cross sections is defined

Poisoning = P(t)

_ macroscopic neut abs cross section of 1 3 5 Xe macroscopic neut abs cross section of the fuel

Xdx

Nuaa

Y(at/aa)0

P(teq)=Xx+ax0

Equation 1 19 is plotted in Pig 1.7 for 23SU fuel Values of Ax and (7X are given following Eq 1.14. The total yield is Y = 0 064 and df/da = 580 barns/685 barns = 0 85 The figure shows the equilibrium poisoning to be linear with the neutron flux when 0^1O12 neutrons cm 2 sec1 (see Pq 1 17) and to approach a constant for high flux values It can be shown (e g, Ref 3, p 334) that the poisoning defined in Eq 1 18 is approximately equal to the reduction in reactivity in a thermal reactor attributable to fission — product poisoning

Change in reactivity = 5k/k s —P(t) (1.20)

To keep a reactor operating at steady state (k = 1), sufficient reactivity must be added, e g, by withdrawing control rods, to compensate for (or override) the reduction in reactivity caused by the fission products in the fuel Thus, for example, in a 23sU-fueled thermal power reactor that is operating at к = 1 with a thermal-neutron flux at the fuel position of 5 X 1013 neutrons cm 2 sec"1, the reac­tivity that must be added to compensate for the effect of the equilibrium concentration of l3SXe is about ak/k = 0 049 (see Fig 1 7)

The effect of 135Xe poisoning is most pronounced when a reactor is shut down after it has been operating at full power for a time sufficiently long that the equilibrium concentration of 13sXe (Eq 1 16) is present In this case the xenon concentration increases considerably above its equilibrium value since it is no longer being removed by thermal neutron capture The 135Xe is being produced by the decay of the equilibrium concentration of 1 3 5 1 (6 3 hr) and being lost by its own 9 2 hr beta decay 1 he net result is shown in big 18, where the poisoning is plotted as a function of time after shutdown from equilibrium for several values of the thermal neutron flux The t = 0 values of Fig 18 are obtained from the equilibrium curve shown in Fig 17 The 1 35Xe poisoning builds up to a maximum after shutdown For low values of the flux, the time to reach maximum poisoning is only a few hours For the higher flux values normally encountered in power-reactor operation, the poisoning reaches a maximum about 10 hr after shutdown The value of the poisoning does not return to its preshutdown value until 30 or 40 hr after shutdown

As Fig 1 8 shows, the value of the poisoning at maximum can be many times the equilibrium (before shutdown) value The excess reactivity required to overcome the maximum poisoning may be more than is available in power reactor, particularly if the fuel has been depicted by prior operation If this is the case, then the reactor shutdown time has to be limited to less than a few hours or more than 30 or 40 hr must be allowed

The full shutdown from equilibrium shown in Fig 1 8 is not the only situation of practical interest Often the power level is cut back or increased by some fraction of full power Initially the 13SXe concentration has a value corresponding to the initial power level, after the change in power level, the l35Xe concentration changes until it reaches a new equilibrium value corresponding to the final power level Figures 1 9 and 110 show the time to reach the maximum poisoning following a step decrease or a step increase of the thermal-neutron flux (which is directly proportional to the reactor power level) Figure 1 9 shows, for example, that a 50% cutback from 4 X 1013 neutrons tin 2 see creates a maximum,35Xt poisoning about 23,000 see (6 4 hr) after the cutback In the reverse process, Fig 1 10 shows that when the flux level is doubled from 2 X 1013 neutrons cm 2 sec ‘, the maximum 13,;Xe poisoning effect occurs about 1 1,600 see (3 2 hr) after the increase 1 rom the initial values of the neutron flux, the initial equilibrium concentration of 13sXe and 1 3,I, and the value at the time the maximum effect occurs, the maximum poisoning or maximum reduction in 5k/k tan be calculated

(b) Samarium-149 * In 1 13% of the fissions of 2 3 5 U

(or 0 66% of 2 3 3 U fissions, or 1 9% of 2 3 9 Pu fissions), one

•Numerical data used in this section are from Ref 7
of the fission fragments has a mass number 149 Some of the fissions form 149Pmand others form 149Nd

Fission -> 1 49Pm(54 hr) 1 49Sm(stahle)

1 ission 149Nd(2 hr) 149Pm(54 hr) 149Sm(stable)

Because the ‘49Nd half-life is small compared to the 1 49Pm half life, the first chain above is a good approxinta tion for both chains As noted earlier, 149Sm strongly absorbs theimal neutrons I he other nuclides in the chain are not anomalous m this respect

The rate of change of the 149Sm concentration is just equal to its production rate from 149Pm decay minus its rate of loss from thermal neutron capture (which converts it to stable 1 50Sm)

= ^Pm (Pm) — (Sm)aSm<A (121)

where (Pm) and (Sm) are the concentrations of l49Pm and l49Sm, respectively, Apm is the decay constant of 149Pm = 3 56 X 10 6/scc, a<,m is the thcrnul-ncutron — eipture cross section of 149Sm = 50,000 barns = 5 X 10 20 cm2, and ф is the thermal neutron flux (neutrons cm 2 see *) Note that, unlike 13sXe, the 149Sm is removed only when it captures thermal neutrons The rate of change of 149Pm is its production rate from fission (neglecting the intermediate 149Nd) minus its loss by beta decay (loss by neutron capture is negligible)

YHm0Zf — Apm (Pm) (1 22)

where (Pm) is the concentration (atoms/cm3) of l49Pm, Ypm is the yield of 149Pm in fission, and 2f is the macroscopic thermal-neutron-fission cross section of the nuclear fuel

When a power reactor has been operating at a steady state (k = 1) for many hours, the equilibrium concentra­tions of 149Pm and 149Sm (from Eqs. 1.21 and 1.22) are

Ypm02f

^Pm

Xp

m (Ptn)eq _ Yp m £f ^Sm 0 ^Sm

Note that the equilibrium concentration of 149Pm is proportional to the thermal-neutron flux, 0, while the equilibrium concentration of 149Sm is independent of the flux.

The equilibrium 149Sm poisoning (Eq 1.18) is

P(teq) = poisoning of 1 9Sm at equilibrium concentration _ (Sm)eqOsm _ Ypm2f<Jgm _

which is also independent of the thermal-neutron flux Substituting into Eq. 1.24 the values of the yields and the fission/absorption cross section ratios gives

These correspond approximately to 5k/k values of —0.96% for 23SU, -0 58% for 23 3 U, and -7.7% for 23 9Pu Comparison of the equilibrium value of 1 4 9 Sm poisoning in 23 5 U-fueled reactors with the equilibrium values of 1 35Xe poisoning (Fig. 1.7) shows the former to be only about one-fourth of the latter.

When a power reactor that has been operating at steady state (k = 1) for some hours is shut down, the concentra­tion of 149Sm increases from its initial (t = 0) value by the creation of 1 4 9 Sm from 1 4 9 Pm decay

1 4 9 Sm cone, after shutdown

= 1 49Sm cone, at shutdown + (1 — e kPm()

X 1 49Pm cone, at shutdown (1 25)

Since the half-life of 14 9Pm is 54 hr, the 1 4 9 Sm concentra­tion is increased by one-half the 149Pm shutdown concen­tration during the first 54 hr after shutdown After a few hundred hours the 149Sm concentration is equal to the sum of the 149Sm concentration at shutdown and the 149Pm concentration at shutdown.

When a power reactor has been operating at a steady state (k = 1) and at constant flux for a few hundred hours, both the 149Pm and 149Sm concentrations have their
equilibrium values (Eq 1.23). If the reactor is then (at t = 0) shut down, the 149Sm concentration builds up according to Eq. 1.25. Substitution of the equilibrium concentrations into Eq. 1.25 gives

149Sm cone, after shutdown from equilibrium

= (Sm)Cq [1 + (0C7Sm/Xpm)(l — e ЛРт’)1 = (Sm)cq [1 + 1.40 X 1O"140

X (1 — e’^Pmt)] (1.26)

where ф is the thermal-neutron flux m neutrons cm 2 sec 1 and Xpm is the disintegration constant of 149Pm (= 3 56 X 10 6/sec = 0.693/54 hr). It is apparent that the poisoning effect of 1 49Sm becomes quite important in high flux operation A shutdown from operation at a flux of 1014 can increase the poisoning effect by a factor of 1 + 1.40, or 2 40 times the equilibrium poisoning (Eq. 1.24), if the shutdown continues for a few hundred hours. Sufficient excess Sk/k must be available to compen­sate for this poisoning when the reactor is started up.

(c) Fuel Burnup. During the operation of a nuclear power reactor, fuel (23 5 U, 2 33 U, or 23 9Pu) is continually being burned up (l e., fissioned) so the remaining fuel becomes depleted in the fissionable nuclide. The effect of this burnup, or depletion, is to reduce the reactivity available to compensate for fission-product poisoning or for other reactivity-reducing effects Eventually the depletion becomes intolerable, and the reactor has to be refueled

At a point in the reactor fuel where the thermal — neutron flux is ф, the absorption of neutrons decreases the concentration of fissile material (23SU, 2 3 3 U, or 2 3 9 Pu) exponentially with time

Fuel cone at time t

= (Fuel cone at t = 0) exp (—ста f0 ф dt) (1 27)

where cra is the neutron absorption cross section of the fissile material The neutron flux is assumed to vary with time (For convenience the integral can be written as 0dv t, where 0dv is the average flux during the time from t = 0 to t = t )

The fractional burnup is defined as the change in fuel concentration divided by the initial concentration. From bq 1.27 it follows that

Fractional burnup = F = 1 — e <7a<*>ivt (1 28)

As an example, the fractional burnup of 2 3 5 U in three months (7.8 X 106 sec) in a powei reactor with an average thermal-neutron flux at the fuel of 5 X It)1 3 neutrons cm 2 sec 1 is 1 — exp I(—685 barns)(5 X It)1 3 )(7 8 X 1 06 cm"2)] = 1 — exp (—0 267), or 0 234, i. e, a fractional burnup of 23.4%.

Figure 1 11 shows the relation between the fractional burnup of fuel and the resulting loss in reactivity 5k/k For a 23 4% burnup, the loss in reactivity is about 2 7% This is to be compared with the reactivity loss of 4.9% (see discussion after 1 q 1 20) attributable to equilibrium xenon poisoning at the same average neutron flux and the 1% (see discussion after fq 1 24) loss in reactivity from samarium poisoning

I ig 1 11 Poisoning as function of fractional fuel burnup (1 rom J Л1 I Ltrr. г Rinleat Re, и tm Contsol / ngmeenng, p 199, D Van Nostraud Company, Inc Princeton, N J, 1963 )

In any actual power reactor, calculations of burnup must take into account many factors not considered in the foregoing. These include the presence of fertile material (23 8 U or 2 3 2lh) in the fuel, the energy and spatial distributions of neutron flux, the geometry and composi­tion of the fuel elements, and the operating history of the reactor. The data presented here are intended to provide a semi-quantitative indication of the effect of fuel depletion on the reactivity that is needed for instrumentation system design.

(a) Pulsation Dampeners. Dampeners may be included in sensing take-off lines and are available in stainless-steel construction in %-in. and V2-in. pipe sizes. (In Fig. 4.22 item 14 is a typical pressure dampener.) One design consists
of a sintered stainless-steel disk or cylinder held in a stainless-steel body; another a captive stainless-steel pin in an orifice opening. Plugging may present a problem; so periodic cleaning may be required. Some sensors have electronic dampening of the output signal to avoid a mechanical dampener.

(b) Diaphragm Seals. Stainless-steel diaphragm seals can be used when a sensor is not corrosion resistant or is subject to possible contamination. The space between the sealing diaphragm and the sensor is filled with a suitable liquid whose pressure duplicates that on the process side of the diaphragm. Fluids satisfactory for temperatures up to 350°F service are common. The seals are usually assembled m the factory to ensure a complete fill. Diaphragm seals are commonly used on Bourdon tubes and in force-balance capsules involving minimum displaced volume. Excessive displacement may involve an error arising when the spring rate of the seal diaphragm is added to the measured pressure. A seal diaphragm is part of the design in F’ig. 4.17.

(c) Overpressure Devices. Pressures in excess of the normal design rating of the sensor may be encountered. For such emergencies a self-operating shut-off valve may be installed between the take-off and the sensor and set to close at preset point to protect the sensor. Stainless-steel guards are available in У4-іп. and У2-іп. pipe sizes for operation up to 9000 psi.

(d) Siphons. Siphons or loops in take-off piping are used to keep hot fluids from contacting the sensor mechanism, which has usually been calibrated at ambient. Performance tests on the sensor indicate the maximum temperature that can be tolerated. The strain-gage sensor in Fig. 4.17 includes coolant connections.

6- 3.1 Reactor Excitation

To determine the dynamic characteristics of a system, one must measure variables that are changing with time

(from the standpoint of reactor hardware). Also, although this table shows more periodic devices than random devices used as externally induced excitation, a trend in recent years to increased use of random excitation must be noted.

For externally excited experiments, a variety of methods is used (see Table 6.10) Except for the occasional use of on-line electronic analyzer methods, most experi­ments do not give transfer functions until the recorded data are processed off-line. Both electronic analyzers and digital computers are used for this processing.

As noted m Table 6.8, the excitation may be sinusoidal or pseudorandom and either a control rod or some other plant control device may be used to excite the system In

Furthermore, the variations must have the following properties

1. Amplitudes sufficient to override unwanted effects that could reduce accuracy.

2. A sufficiently long duration or a sufficient number of repetitions to provide the desired accuracy

3. Frequencies in the ranges to be investigated

If the intrinsic variations, or random noise, of a system are used, the system is said to be self-excited. On the other hand, a system is said to be externally excited if a perturbation is introduced by a signal-generating device. In both instances transducers responsive to the variations of interest provide the experimental data.

Table 6.9 lists the kinds of excitation that have been used to date. The relative popularity of the various forms of excitation (Tables 6.6 and 6.8) is indicated somewhat arbitrarily by the number of dynamics experiments that have used each form. Transfer functions and related functions have been emphasized in Tables 6.6 and 6.8 Many other* dynamics tests (such as valve-position changes in power plants, rod drops, positive-period tests, and Rossi-alpha coincidence counting) are not represented even though they may be somewhat related to the tests discussed here. With this understanding the predominance of self­excitation experiments indicated in Table 6.9 can be attributed, at least in part, to their experimental simplicity

‘These tests may be used to measure specific effects rather than to extract transfer functions sinusoidal excitation the transfer function between the excitation variable (such as the reactivity of a control rod) and the system output variable (such as the reactor power) may be obtained at the excitation frequency by any one of the following approaches

1. Using the separately measured fundamental fre­quency amplitudes and phases of input and output, applying Eq 6.1 or Table 6.1.

2. Applying the appropriate electronic gain and phase to the output and using it to “null out” the input signal (see Sec. 6-5.2).

3. Cross-correlating the input and output signals, using Eq 6.9 in digital processing or Table 6.1 in continuous processing (see Sec. 6-5.4)

The last approach is commonly used at present.

Center rod, in 8-rod bank, in

Peak reactivity % for
1-in peak stroke

Figure 6.5 shows typical rod-oscillator test results for a boiling-water reactor. In such tests one is interested in the difference between the at-power transfer function and the zero-power transfer function for this can determine the feedback, H, in Eq 6 17. In addition, the height and width of the resonance (in this example at со = 7 radians/sec) are of interest because they indicate the extent to which an instability of self-sustained oscillations is being approached In pseudorandom excitation you attempt to introduce all frequencies in the band of interest into the system at once rather than sequentially as in sinusoidal testing. In the commonly used binary excitation, an input control signal has two values, such as +1 and —1, however, ternary signals (having values +1, 0, and —1) have been suggested112 Rather than letting the duration of +1 and —1 values be determined by an ideal random process, it is more

advantageous to use a repetitive almost-random signal,41 such as that shown in Fig 6 6

In analyzing data in pseudorandom excitation experiments, you obtain the cross-correlation function by either on-line or off-line integration

: fT/2 x(t) y(t + r) dt

T •’-T/2 2 using the time^hifted product of the input variable, x(t), and the output variable, y(t). Figure 6.7 shows a typical experimental result. Using the relations in Table 6.1, you obtain the transfer function from Pxy(f), the Fourier transform of CXy(r)

(6.20)

With x(t) perfectly random, it can be shown that Cxy(r) in Eq 6.19 is the system impulse-response function41 and Px(f) in Eq. 6.20 is a constant. The transfer function in Fig. 6.7 was obtained in this manner.

It is not usual to measure transfer functions by pulse or step excitation, although this is possible.59 In the method the quotient of Fourier amplitudes is taken from an analysis of the input and the output signals to obtain the transfer function However, it is preferable to have a series of pulses or steps, such as pseudorandom excitation, because the added signal energy helps overcome unwanted noise.

2-3.1 Structural Design*

In common with other reactor instruments, nuclear radiation detectors must be rugged This entails con­struction features that should be recognized by the user

The mechanical design is determined by the require­ments of the manufacturing process, by the realities of handling and installation, and by the rigors of the environ­ment in which it is to function During construction, a gas ionization detector must withstand the mechanical stresses when it is evacuated before being filled with gas It must also withstand the high temperature and vacuum used in the outgassing process After it is filled with gas, the detector must be able to withstand the pressure and temperature changes in the reactor environment These requirements in themselves are sufficient to ensure a high degree of rugged ness

The detector must also withstand mishandling and possible abuse during shipping and installation Some applications may require that the detector be moved during operation or between operating periods Unless the accel erations associated with movements are very small, the detector must have electrodes with exceptional mechanical stability to prevent vibration This must be ensured by proper design, e g, including adequate electrode supports

The detector environment is frequently subject to changes m temperature and pressure and to vibration or mechanical noise Differential thermal expansion within the detector is minimized by using materials with similar thermal expansion coefficients, by providing adequate constraints, or by permitting relative motion Any of these methods may make the detector microphomc The high voltage and considerable mterelectrode capacitance of the detector greatly enhance the generation of microphonics This tendency can be minimized by careful design of the electrode assembly

2-3.2 Materials of Construction

The choice of materials of construction for a gas ionization detector is a compromise between radiological, mechanical, and thermal requirements For example, in a light structure made of materials of low atomic number, both the self-absorption and the buildup of detector radioactivity are reduced Reduction of both of these effects is desirable in all nuclear radiation detectors However, such a structure is not optimum for a gamma detector, gamma detection is based on generation of Compton scattered (recoil) electrons, a process that is most efficient in heavier structures made of materials with high

atomic number Moreover, a light structure may not meet the requirements for detector ruggedness

The primary criterion in materials selecting is to maximize the generation of the signal Selecting materials to maximize sensitivity to incident gammas involves dif­ferent considerations from those involved in selecting materials for a neutron detector

In ionization chambers for gamma detection, construction is very important Sensitivity to incident gammas is maximized by increasing the thickness of chamber walls and electrodes, by using structural materials of high atomic number, and by using high density gases of high atomic number There are optimum values for most design features For example, chamber-wall thickness must not be so great that self-shielding causes excessive gamma attenuation In fact, wall thickness need not greatly exceed the range of the most energetic Compton electrons Gas pressure should not be so great as to cause excessive recombination of the ion pairs that are generated by the passage of Compton electrons through the gas The ma terials selected for a gamma chamber should have low cross sections for reaction with any neutrons that may accom pany the incident gammas Moreover, it is preferable that any neutron reactions that do occur should generate a minimum of energetic ionizing radiations Figures 2 15 and 2 16 show the effect of material selection and construction features

On the other hand, if the ionization chamber is designed for maximum neutron sensitivity (with minimum gamma sensitivity), neutron-sensitive materials, і e, ma­terials that create ionizing radiations when exposed to

neutrons must be used The choice is influenced by consideration of the mechanical, thermal and radiation properties of the neutron sensitive material

(a) Physical Methods. Condensation and Fractional Vaporization. Separation of condensable vapors, generally in groups. Identification and quantitative evaluation is performed by other methods. Curves of vapor pressure vs. temperature of possible components must be known.

Fractional Distillation. Separation, identification, and quantitative evaluation of condensable hydrocarbons even in complex mixtures.

Adsorption or Absorption and Desorption (Chromatog­raphy). Separation, identification, and quantitative evalua­tion of many gases and vapors even in complex mixtures.

Diffusion. Separation of hydrogen and some isotopes.

Thermal Diffusion. Separation of some isotopes.

Electric Discharge. Separation of nomomzable gases.

(b) Chemical Methods. Selective Absorption, Separa­tion and quantitative evaluation of gases and vapors already known. There is a need for selective reagents. Quantitative analysis can be accomplished by (1) volumetric or baro­metric methods, (2) gravimetric methods, (3) titrimetric methods, (4) electrical conductivity, (5) colorimetry, or (6) calorimetry.

(c) Combustion Analysis. Fractional Combustion Sep­aration, identification, and quantitative evaluation, mainly of H2, CO, and hydrocarbons

Complete Combustion. Quantitative evaluation of H2, CO, and hydrocarbons.

(d) Absorption of Electromagnetic Radiation. Mag­netic Susceptibility. Quantitative evaluation of 02, NO, C102, and N02, not mixed with each other. Mainly used for 02

Visible. Quantitative evaluation of colored gases, not mixed with each other (N02, Cl, etc.)

Ultraviolet, Quantitative evaluation of 03,N0,C6H6, C6Hs(CH3),etc.

Infrared. Identification and selective quantitative eval­uation of CO, C02, hydrocarbons, NH3, S02 , S03, etc.

Visible Spectroscopy Identification of various sub­stances, quantitative evaluation doubtful.

Ultraviolet Spectroscopy. Identification of various substances, quantitative evaluation doubtful.

Infrared Spectroscopy. Identification and quantitative determination of H20, CO, C02, hydrocarbons, organic compounds, etc. Can detect composition of highly diluted mixtures.

Mass Spectrometry. Identification and quantitative evaluation of a large number of substances. Precise and capable of detecting composition of highly diluted mix­tures.

(e) Hydrogen Determination. The determination of hydrogen is normally the last to be performed. When all other constituents have been determined, the remaining gas can be considered as a binary mixture. Analysis for hydrogen can then be performed by one of the following methods

Sonic Analyzer. The velocity of sound, S, is related to the molecular weight of the gas through which it is propagating

where R = gas constant

T = absolute temperature к = ratio of specific heats (k = cp/cv) m = molecular weight

Two sound waves of identical frequency are passed through two similar tubes, one filled with a reference gas and the other with the mixture. Different sound velocities in the two tubes result in a phase difference between the two waves reaching the ends of the tubes. This difference is used to compare the velocity of sound in the two gases. The mean molecular weight of the mixture can be derived, and the hydrogen content can thus be calculated.

Interferometry (Optical). A monochromatic light beam is split and passed through two identical tubes, one filled with a reference gas and the other with the mixture. Usually the reference gas chosen is the major constituent in the binary mixture. Because of the difference in the velocity of light in the two gases, the light beams emerge with a difference in phase and can be made to produce interference bands. The spacing of the bands is related to the relative concentrations of the components of the gas mixture and the refractive indices of the sample and the reference gas

Pa Pb nab = niy+nby

where паь = refractive index of a binary mixture (A + B) na and nj, = refractive indices of the components A and В P = pressure of the gas mixture Pa and P(, = partial pressures of the components

When the refractive index of the mixture is known, the partial pressure of one component can be deduced and hence the concentration can be estimated. Interferometers are capable of great accuracy provided they are used with skill and provided pressure and temperature corrections are applied.

Thermal Conductivity. In binary mixtures thermal conductivity can vary linearly with the concentration of one component Absolute evaluation of thermal conduc­tivity is very difficult, and normally only relative values are determined. Eor this purpose a hot wire Wheatstone bridge is used. Sample gas passes through a cell that contains a resistance wire. A second cell containing a compensating resistance is filled with a reference gas, which is usually the major constituent in the mixture. The heat-loss difference between the two arms, due to the different thermal conductivities of the gases, unbalances the bridge The bridge output must be calibrated against standard gas mixtures.

This method is highly suitable for hydrogen because the thermal conductivity of hydrogen is considerably higher than that of other gases The thermal conductivities of some gases relative to normal air at 0°C are air = 1, H2 = 7, CH4 = 1.27, CO = 0.96, and C02 = 0.59.

Diffusion. Hydrogen could be determined by taking advantage of its high diffusivity through porous dia­phragms. The method is time-consuming, but its accuracy is good.

When the analysis for hydrogen is required in a mixture containing more than two components, other methods must be used.

Combustion Analysis. If the gas mixture contains no hydrocarbons, hydrogen may be estimated by measuring the water formed by oxidation. Actually, hydrogen is usually found mixed with other hydrogenated combustible gases that also produce water on oxidation. If there are no more than two other hydrocarbons, the identity of which must be known, combustion analysis is still possible provided carbon dioxide is also estimated. This requires the solution of three equations.

Other Methods. Hydrogen is also determined by gas chromatography and mass spectrometry. Infrared spectros­copy cannot be used since hydrogen has no absorption bands in the region of the spectrum.

(f) Oxygen Determination. Paramagnetic Analyzer. A continuous stream of gas is passed through an annular tube and crossed by a transverse connection tube The latter is wound with a heating spiral, one end of which passes through a strong magnetic field. Any oxygen molecules in the gas are attracted toward the magnet more from the left side of the transverse tube than from the right. Warm molecules are less susceptible to the effect of the magnet. As a result continuous flow is established through the transverse tube. The gas flow through the transverse connection depends upon the oxygen concentration. The temperature gradient along the heater winding depends upon gas flow. Therefore, oxygen concentration is mea­sured by temperature gradient.

Electrochemical Gas Analyzer. A heated zirconium oxide tube sets up a current when there are different concentrations of oxygen in two gases that flow inside and outside the tube. The unknown gas is passed inside the tube, and the reference gas (air) is passed outside the tube. The electrical output of the tube is proportional to the logarithm of the ratio of the oxygen concentration of the two gases. The advantages of the method are that it is accurate, requires no fuel, is unaffected by high S02 or S03 concentrations, is unaffected by high C02 concentra tions, reads net 02 , and has a fast response.

(g) Summary of Methods Used for Gas Analysis. Та Ые 4.23 summarizes the various methods that may be used for gas analysis. Instrumental procedures for gas analysis tend to supersede classical laboratory methods. Laboratory methods are often used as standard references. Instruments are used as the ordinary tools of the investigation.

Eor simple analysis (C02, CO, 02, H2, and CH4), the nondispersive infrared analyzer, the magnetic oxygen ana­lyzer, and the sonic analyzer for hydrogen are suitable. For mixtures of increased complexity, chromatography is rec­ommended. It is economical and quick. It can fractionate mixtures into single or groups of components, which can be useful before applying infrared or mass spectrometry.

(h) Mass Spectrometry. The material to be studied is subjected to an ionizing process, separated according to mass by electromagnetic means, and the resulting mass spectrum is analyzed, quantitatively and qualitatively, by comparing it with the spectra of known calibrating mate­rials.

Ions are produced by four methods (1) electron bombardment, in which the unknown, if it is gaseous, is bombarded in an evacuated chamber by electrons, (2) direct emission of ions from the surface of some solid materials by heating a filament that is covered with a thin layer of the material to be analyzed, (3) the crucible method, in which materials (e. g., halides) are evaporated from a small furnace, and subsequently the vapor is ionized by electron bombardment, and (4) the spark method, in which a high-voltage spark between electrodes of the material to be analyzed yields ions of that material. Positive ions are accelerated by electric fields between a system of electrodes. Ions are focused in their passage through slits or apertures in the electrodes. The ion source in a mass

•From G Tine, Gas Sampling and Chemical Analysis in Combustion Processes, p 86, Pergamon Press, Inc, New York, 1961 tAbbreviations i d = instrumental delay (sec)

A = particularly suitable method В = possible method Aj = undifferentiated estimation A2 = estimation of formaldehyde only T A = trace analysis

f s = analysis can be performed also on flowing streams

$The actual sample sizes, time consumptions, and accuracies depend upon the particular apparatus that is used and, in many instances, upon the gas to be detected §Only suitable for binary mixtures of known components

spectrometer is a combination of the region where the ions are generated (this region usually has an electron gun to provide the electron bombardment) and the ion-accelera­ting region.

The ions are separated by one of these four basic methods a magnetic analyzer (masses separate according to their momenta in a magnetic field), a time-of-flight analyzer (ions with same kinetic energy but different masses have velocities inversely proportional to the square root of the mass and become separated if injected into a field-free “drift” region), a linear-accelerator analyzer (accelerated ions are segregated by electrostatic deflection), and an ion-resonance analyzer (ions move in a region where a radiofrequency electric field is set up at right angles to a magnetic field and, if the frequency is in resonance with the spiralling ions, the ions spiral out of the field and are collected)

Formulas for computing the expected variation due to the statistical nature of an experiment are vital in optimum planning. Table 6.16 contains formulas useful in ascertain­ing the precision of the various functions involved in noise analysis. The meaning of the fractional-error formulas is that, if many values of a function were determined (at a particular f or t), 68 3% would he within the average ± this fractional error

In all cases the error varies inversely as the square root of the measuring time and inversely as the square root of either the bandwidth, B, or the resolution, Af

В = upper frequency limit of P(f), which is approximately constant from 0 to В and thereafter near zero (6.43)

or

В = if C(r) is approximately C(0)e t/T(- (6 44)

1

Af = — for the ideal and hamming windows of Tm

Fig 6 16 (6 45)

 

(6 48) (6 49)

 

1 (N/M)4

 

N_ 2T

 

1 MAt

 

(6 50)

 

or

Af = 7t times the half-power bandwidth of a

sharply tuned circuit (6.46)

The half-power bandwidth is also defined as the resonant frequency divided by the so-called resonance Q

The above pertains primarily to continuous frequency analysis, however, there is also statistical error associated with sinusoidal excitation experiments because random
where N is the number of data points, T/At, and M is the maximum number of lag intervals, rm/At If, when these equations are applied, it is found that some of the parameters so determined are not readily attainable (if, for example, too many digits are required), then obviously suitable compromises must be made between the limita­tions of the analysis and the desired results In continuous analysis one evidently optimizes just Af and T of Eqs 6.48 and 6 50 somewhat independently of the fmax selected.

An illustration of selections made in an ion-chamber noise analysis90 of the Experimental Boiling Water Reactor to measure a resonance at 1.7 Hz is

N= 3331 Fractional error in P(f) = 03

M = 300 fmax = 10 Hz

At = 0 05 sec fmm = Af = 0 067 Hz

Fission chambers are most commonly used as in-core neutron flux sensors They are the backbone of the in-core neutron detection systems in the majority of boiling-water reactors (see Vol 2, Chap 16, Sec 16 2) The fission chamber is used as the neutron sensor in most traveling m core probe systems for both pressurized water reactors and boiling water reactors

Fission chambers feature relatively slow burnup of the uranium liner They provide satisfactory operation in all three basic modes (1) the pulse-counting mode, (2) the mean square-voltage mode, and (3) the mean-current (d-c) mode (see Chap 5, Sec 5 5, and Chap 2, Sec 2 2) In core fission chambers are thus suitable for use in source-range channels (where pulse counting is required because of the low value of the neutron flux) in the intermediate-range channels (where mean square voltage techniques extend the operating range), and in the power-range channels (where mean current techniques provide accurate power measure ments for both fixed sensors and traveling probes) For each of these modes of operation, the optimum design is different with respect to size, materials, fill gas pressure, emitter—collector gap dimensions, neutron sensitivity, etc

Just as m out-of core neutron detectors, both the neutron and the gamma fluxes contribute to the total output of an in core fission chamber Many of the design parameters which may be changed to achieve a specific neutron-sensitivity characteristic also affect the gamma sensitivity Since the output signal attributable to incident gamma radiation is not unambiguously related to the reactor power level, the design of an in-core fission chamber is optimum if at the end of detector life the ratio of the output current due to neutron flux to the output current due to gamma radiation is still acceptable

The mam design parameters that can be varied to meet the specific requirements for an in-core fission chamber are (1) the physical form of the uranium used, (2) the enrich­ment of the uranium, (3) the surface area and thickness of the uranium, (4) the type of fill gas used, (5) the fill-gas pressure, (6) the dimensions of the gap between the emitter and the collector, and (7) the dimensional tolerances Each of these is discussed below

(a) Uranium Form Two basic types of in-core fission chambers have been developed and manufactured One type incorporates an enriched uranium oxide layer plated on the inside of the detector housing that forms the outside wall of the sensitive volume (see Fig 3 1) The second type

contains a machined sleeve of enriched uranium—aluminum alloy at the outer surface of the sensitive volume (see Fig 3 2) The more carefully the weight and thickness of the uranium coating or uranium—aluminum sleeve are controlled, the more accurately the neutron sensitivity of the detector can be controlled The majority of commercial detectors are manufactured with a ±20% tolerance on initial neutron sensitivity Under very special circumstances a ±5% tolerance on initial neutron sensitivity can be achieved by carefully controlling the uranium plating process or the uranium—aluminum alloy machining

(b) Uranium Enrichment. Because the enrichment of the uranium in a neutron sensor has no effect on the gamma sensitivity (total mass of uranium is constant), the best way to increase the signal-to-noise ratio is to increase the enrichment of the uranium used in the sensor Fully enriched uranium provides the maximum neutron sensi­tivity while maintaining the same gamma sensitivity.

(c)

Uranium Surface Area. For a given total mass of the enriched uranium layer, the neutron sensitivity of an in-core fission chamber depends on the surface area of the uranium. Surface area is varied by changing the chamber diameter and length. The gamma sensitivity also varies when the chamber geometry is changed. Consequently, there is a combination of sensor diameter and length which yields the highest signal-to-noise ratio.

(d) Type of Fill Gas. Argon is the most commonly used fill gas. It has all the desired properties (chemically inert, good thermal conductivity, low thermal-neutron cross section, and suitable ionization properties). Other com­monly used fill gases are helium and nitrogen or mixtures of argon and nitrogen.

Chemical inertness is desirable since a gas that is not inert may combine with chamber materials (particularly in presence of an intense nuclear radiation field) and thus reduce the gas available for ionization. High thermal conductivity is desirable to remove heat developed in the chamber by the signal-generating processes. If the thermal — neutron cross section is high, the fill gas will be depleted by nuclear transformation; in addition, neutrons absorbed by the fill gas are not available for reaction with the uranium.

(e) Fill-Gas Pressure. Neutron and gamma sensitivities of an in-core fission chamber are directly proportional to the fill-gas pressure as long as the range of fission fragments and gamma photons is greater than the gap between the emitter and collector. Most in-core fission chambers operate at several atmospheres pressure to achieve higher neutron and gamma sensitivities. Because both the gamma and neutron sensitivities are similarly increased, detector life is not appreciably affected by varying the fill-gas pressure.

(f) Emitter—Collector Gap. Of all the factors involved in in-core fission-chamber design, the most critical is the sizing of the gap between the neutron-sensitive emitter and the positively charged collector. Since the ionization current is a function of the number of fill-gas atoms, a large gap produces a large detector current. This characteristic is especially important at low flux levels, such as those existing in the source range. At higher flux levels the gap must be reduced to ensure detector saturation [Sec. 3-3.1(h)] up to and exceeding the highest neutron flux the detector is designed for.

(g) Dimensional Tolerances. As noted earlier, the accuracy of initial detector sensitivity is directly related to the dimensional tolerances applied to the neutron-sensitive material and to the emitter—collector gap. Because so many of the characteristics of in-core fission chambers are related directly to dimensions, the effects of tolerance accumula­tion are extremely important and must be carefully considered.

(h) Operating Characteristics. In-core fission chambers exhibit most of the operating characteristics of out-of-core neutron sensors. As pointed out in Chap. 2, Sec. 2-2.1, variation of chamber voltage provides three regions of detector performance: the low-voltage (presaturation) re­gion, the plateau (saturation) region, and the multiplication region. The exact shape of the current—voltage curve depends on chamber construction parameters.

In view of this characteristic behavior of fission chambers, it follows that the voltage applied to the chamber should be high enough to keep it on the plateau region at or above the highest radiation flux in which it is expected to operate. If there is any question about the chamber voltage required to achieve saturated operation, it is preferable to err on the high side, since the chamber current is proportional to the incident radiation flux in both the saturation and multiplication regions but not in the presaturation region. For most in-core fission chambers being used in power reactors today, the neutron flux never exceeds 2 X 1014 neutrons cm"2 sec 1 , so an operating voltage of 125 volts d-c is sufficient to guarantee saturated operation. Figure 3.3 shows saturation curves for a typical in-core fission chamber.

The ideal detector plateau would be flat, but this is never achieved. Below 1013 neutrons cm"2 sec the plateau has a slope that is generally attributable to detector-cable leakage current. As the neutron flux in­creases, the plateau starting voltage (the low end of the plateau) increases and the multiplication starting voltage (the low end of the multiplication region) decreases. When the neutron flux increases to the point where the plateau starting voltage equals the multiplication starting voltage, the plateau disappears. This point is generally defined as the upper flux limit of the detector.

It is more important for an in core fission chamber operating in the mean square voltage mode[4] to stay in the plateau region than for one operating in the pulse counting mode or the mean current (d c) mode This results from the fact that the signal is a function of chamber current squared rather than chamber current alone Figure 3 4 shows that as a result the plateau starting voltage of a mean square voltage chamber is somewhat higher and the multiplication starting voltage somewhat lower than a d-c chamber

In the mean square voltage mode of operation, adjust ment of the chamber voltage must be related to the band pass of the signal amplifier into which the chamber operates Pulses from the chamber are distributed in energy in accordance with the power frequency spectrum curves in Fig 3 5 The breaks in the curves occur at the frequencies corresponding to the ion collection time, T, and the electron collection time, Te Reducing the chamber voltage shifts the entire power frequency spectrum curve to lower frequencies because the time required to collect the ions and electrons in the chamber increases

The power frequency spectrum curve is divided into two distinct regions, the low-power range and the high power range At low reactor power the low pulse frequency

allows ample time for both the ions and electrons to be collected in the chamber At high reactor power the pulse frequency is so high that the ions are not collected, only electrons are collected The break in the curve occurs at the point where the transition from the collection of ions plus electrons to the collection of electrons alone is made

Fig 3 5—Mean square voltage chamber performance char acteristics T, = ion collection time Te = electron collection time SV = saturation voltage and RV = reduced voltage

The best plateau characteristics in both the low power and high power ranges are obtained when the band pass of the amplifier is designed to be within the flat portion of the power frequency spectrum curve at saturated chamber voltage Improper setting of the chamber voltage shifts the frequency of the power frequency spectrum curve and drives the amplifier response off the flat portion of the curve Typical breakpoints in the low power and high power band-pass amplifier are defined in Vol 2, Chap 18, Sec 18-2 3(c)

There are three major factors creating nonlinear opera­tion of in core fission chambers (1) gas migration between the active and the inactive volumes of the chamber owing to temperature differences, (2) operation in the presatura­tion region, and (3) operation in the multiplication region A change in reactor power level always causes gas migration in an in-core fission chamber Gas migration decreases the chamber sensitivity as reactor power increases and vice fission chambers used to monitor reactor power from below source level to above the overpower trip level

Operating Range of Pulse Counting Fission Cham hers I he normal operating range of an in core pulse­counting fission chamber is from 101 to 109 neutrons cm [5] [6] sec 1 The lower limit is determined bv the statistics of pulse counting The variations in the neutron counting

versa When the sensor is operated in the presaturation region, a further decrease in sensitnity occurs because the chamber current is not linear with neutron flux

In the saturation region the chamber current is linear with neutron flux, so the only source of nonlinearity is gas migration In the multiplication region the decrease in current due to gas migration is counteracted b the increase in multiplication due to the gas migration It mav be desirable to set the chamber voltage somewhere in the multiplication region rather than in the saturation region to obtain maximum linearity on chambers with large gas migration sensitivity of a pulse counting fission chamber noted in Table З 1 result from anations m gamma flux at the detector The integral bias curves Fig 3 7, show the reduction in neutron counting sensitivity as the gamma exposure rate increases from 10s to 2 5 X 107 R/hr while the neutron flux remains constant Figure 3 7 also demon strates the importance of the proper discriminator setting Any discriminator setting less than 3 would result in operation to the left of the plateau at higher gamma leyels yvith attendant errors in count rate information At a neutron flux of 5 X 1()2 neutrons cm 2 sec 1 the chamber indicates approximately 1 count/sec, someyvhat less than is desirable for statistical confidence Accordingly, the neu tron source m the reactor should be sized to provide from 2 to 10 counts/sec

The upper limit of the pulse counting chamber is determined by the 1 MHz bandwidth of the signal amplifier and the 300-nsec rise time and collection time of the

chamber pulses. At a true random input of 106 counts/sec, the counting loss is 23% of the true count rate. Since the pulse-counting chamber has a neutron counting sensitivity of greater than 103 counts/sec per unit flux (1 neutron cm-2 sec 1 ) in a 105 R/hr gamma field, the upper limit of
the neutron flux is 109 neutrons cm”2 sec 1 at 106 counts/sec.

When the in-core neutron flux exceeds 101 0 neutrons cm"2 sec 1 , the pulse-counting chamber should be removed from the core to prevent depletion of the fissionable material.

Operating Range of Mean-Square-Voltage Fission Cham­bers. The operating range of the mean-square-voltage fission chamber is 108 to 1013 neutrons cm"2 sec"1. The lower limit is set by the detector noise resulting from alpha emission from the uranium coating, prompt gamma radia­tion, and delayed neutrons at low reactor start-up levels. When the neutron flux is 108 neutrons cm"2 sec 1 or greater, the neutron-flux signal exceeds the noise signal.

The upper limit of the range of a mean-square-voltage chamber is reached when the plateau starting voltage becomes equal to the multiplication starting voltage, as described in Sec. 3-3.1(h). Because the plateau is shorter for chambers operating in the mean-square-voltage mode, the upper limit of their range is lower than the same chamber operating in the mean-current (d-c) mode.

When the in-core flux exceeds 1011 neutrons cm"2 sec 1 , the mean-square-voltage chamber should be removed from the core to prevent depletion of the uranium.

Operating Range of Mean-Current (d-c) Fission Cham­bers. The operating range of in-core fission chambers used in the mean-current mode is from less than 1012 neutrons cm”2 sec 1 to greater than 1014 neutrons cm”2 sec"1. The lower limit is set primarily by the leakage current in the ceramic-insulated cable. The upper limit is reached when the plateau starting voltage is equal to the multiplication starting voltage. Because mean-current (d-c) chambers normally provide the signals that initiate reactor overpower trip and are calibrated against a reactor heat balance, they

must have good linearity over at least one decade of their operating range

(j) Traveling In-Core Fission Chambers. The design requirements for traveling in-core fission chambers are the same as those for fixed in-core mean-current chambers except that the traveling chambers must withstand the rigors of periodic insertion into and withdrawal from the core The traveling in core fission chambers have the same requirements for operating range and linearity as the fixed in-core mean-current chambers Table 3 2 summarizes the characteristics of traveling in-core fission chambers com­monly used in power reactors Figure 3 8 shows a typical traveling m-core probe The helically wound outer sheath of the drive cable engages the drive gears to move and position the sensor

5- 4.1 Introduction

In the power-range channels, neutron-flux-measuring circuits monitor the neutron flux when the reactor is operating at or nea. full power. The channels provide information necessary for either manual or automatic control of the reactor

The power-range channels cover linearly one decade of power, thus providing a much finer control of power level than is possible with the logarithmic channels The system provides a linear display of power level over a wide range, the range being changed by switching

A power-range channel, shown in Fig 5 18, consists of a CIC, high-voltage supply, linear picoammeter, and readout and control signals Each of these items is discussed in the following paragraphs.

5- 4.2 Sensor

A CIC with the same characteristics as those used in the intermediate-level channel is used [see Sec. 5-3.2(a) and the discussion of CIC’s in Chap. 2, Sec 2-2 2].

5- 4.3 High-Voltage Supplies

See Sec 5-3.2(b).

5- 4.4 Linear Picoammeter

The signal from the CIC is monitored by a linear picoammeter with either manual or automatic range con­trol. In a manually operated unit, the current range is predetermined and normally provides an accurate indica­
tion of power level only for the highest two decades of power. Figure 5 19 shows an automatic range-changing picoammeter that gives continuous coverage from a few watts to full power The unit automatically changes range on an increasing and decreasing signal at the range set points

The basic current-measuring device of the picoammeter is an electrometer with appropriate feedback resistors to determine the range of operation. The electrometer, shown schematically m Fig 5.20, consists of a very high input impedance operational amplifier.

5- 4.5 Readout Indication

Signals generated from the picoammeter are presented to the operator in several ways The range is indicated by readout lamps, the level is displayed on meters and recorders marked 0 to 100% The level can also be displayed on a digital readout unit

5- 4.6 Control and Safety Circuits

Alarm units are provided in the picoammeter for initiating a. reactor shutdown if the power level exceeds a predetermined maximum value The alarm unit is described in Sec 5 2.4(e) The relays are connected in a two-out-of — three sequence to increase system reliability against single failures causing reactor shutdown (see Chap. 11)

5- 4.7 Calibration and Checkout

As with the other channels described in this chapter, a built-in test source is provided to check the system response from the picoammeter The test source also provides a means for setting and checking the alarm units