Fission-chamber-compensated self-powered detector for in-core flux measurement and reactor control
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to nuclear reactors. More particularly, the present invention relates to a self-powered detector for in-core measurement of local reactor power level and neutron flux density. 
     2. Description of the Prior Art 
     Present day fission chambers that are used in the core of a nuclear reactor contain a ceramic seal between the chamber and its integral coaxial cable. The purpose of this seal is to maintain a constant quantity of gas in the fission chamber in order to provide a neutron sensitivity that is independent of the temperatures of the chamber and its integral cable. A majority of these seals develop leaks during the exposure interval 10 21  to 10 22  nvt, after which interval the chamber loses its desirable property of temperature-independent neutron sensitivity. The chamber then suffers from a larger nonlinearity with reactor power level, a change in sensitivity after a cold start-up, and, in the case of bottom-entry detectors, a change in sensitivity after a change in rod bank position or in power level. 
     Self-powered neutron detectors do not depend upon the gas in the sensitive region for their current output. Accordingly, no seal is required between the detector and its integral cable. Thus, neutron sensitivity is independent of the temperature of the detector and that of its integral cable. Such detectors are useful for measuring local power level or neutron flux density after the reactor has been in a steady state for several minutes, but, because of their slow speed of response, they do not give correct readings immediately after a power level change. They cannot be used to provide a warning or a scram signal if the reactor power level becomes too high, as in-core fission chambers are often called upon to do in water reactors. 
     For example, after a step change in local neutron flux density, the output of a rhodium self-powered detector changes 61% of the flux density change in one minute, 82% in two minutes, 90% in three minutes, 96% in five minutes, and 98% in ten minutes. It is readily apparent the detector-based reading can be in serious error for the first five or ten minutes of operation. Such dilatory response is undesirable in a nuclear reactor. 
     Pertinent prior art publications include: U.S. Pat. No. 2,874,304, entitled &#34;Ionization Chamber&#34;, issued to Lichtenstein on Feb. 17, 1959; U.S. Pat. No. 3,043,954, entitled &#34;Fission Chamber Assembly&#34;, issued to Boyd et al. on July 10, 1982; U.S. Pat. No. 3,565,760, entitled &#34;Nuclear Reactor Power Monitor System&#34;, issued to Parkos et al. on Feb. 23, 1971; U.S. Pat. No., 4,103,166, entitled &#34;Method and Apparatus for Monitoring the Output of a Neutron Detector&#34;, issued to Neissel et al. on July 25, 1978; U.S. Pat. No. 3,760,183, entitled &#34;Neutron Detector System&#34;, issued to Neissel on Sept. 18, 1973; and the publications Dynamic Compensation of Rhodium Self-Powered Neutron Detectors, Banda et al., IEEE Transactions on Nuclear Science, Vol. NS-23, No. 1 (February 1976), and A Pena-Detector Flux-Measure System With A Fast Response, Johnstone, Research Reactors Div., U.K.A.E.A. Research Group, Atomic Energy Research Establishment (March 1971). So far as any of the above-mentioned patents might be considered necessary, either in whole or in part, to assist or enable one skilled in the art to practice the herein disclosed invention, they are hereby incorporated into this patent application by reference. 
     SUMMARY OF THE INVENTION 
     The present invention provides in combination a rhodium self-powered detector, a seal-less fission chamber, and appropriate electronic circuitry for combining the outputs of the self-powered detector and of the fission chamber in such a way that the combined output is always proportional to the local reactor power level or neutron flux density. The self-powered detector and fission chamber are located in close proximity to each other or can be combined as one unit as shown in U.S. Pat. No. 3,760,183, &#34;Neutron Detector System&#34;, J. P. Neissel. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram of a first preferred embodiment of the present invention; 
     FIG. 2 is a graph plotting the output of amplifier 12, shown in FIG. 1, as a function of time; 
     FIG. 3 is a graph plotting the output of differentiating circuit 15, shown in FIG. 1, as a function of time; 
     FIG. 4 is a graph plotting the output of differentiating circuit 17, shown in FIG. 1, as a function of time; 
     FIG. 5 is a graph plotting the output of summing amplifier 18, shown in FIG. 1, as a function of time; and 
     FIG. 6 is a block diagram of another preferred embodiment of the present invention. 
    
    
     DETAILED DESCRIPTION OF A PREFERRED AND ALTERNATE EMBODIMENT 
     The preferred embodiment of the present invention is shown in FIG. 1, including a rhodium self-powered neutron detector 11, an amplifier 12, a seal-less fission chamber 13, an amplifier 14, a differentiating circuit 15 with time constant T 1  /ln 2 (determined by a capacitor C1 and a resistor R1, where T 1  is the half-life of the ground state of Rh 104 ), an amplifier 16, a differentiating circuit 17 with time constant T 2  /ln 2 (determined by a capacitor C2 and a resistor R2, where T 2  is the half-life of the isometric state of Rh 104 ), and a summing amplifier 18. The outputs of amplifier 12, differentiating circuit 15, and differentiating circuit 17, after a step in flux density, are shown in FIGS. 2, 3, and 4, respectively, and their sum, or the output of summing amplifier 18, is shown in FIG. 5. 
     The self-powered detector 11 can be considered as the primary signal source and, in fact, it is the only signal source under steady-state conditions. Fission chamber 13 supplies only the transient information that is missing from the self-powered-detector signal for a short time after a neutron flux level change. Accordingly, the output signal produced by the present invention is only subject to the fission-chamber errors inherent and persistent in prior art devices for a short time after a neutron flux density change. 
     Another preferred embodiment of the invention that has certain advantages (discussed below) over the embodiment shown in FIG. 1, is shown in FIG. 6 and includes a rhodium neutron detector 21, amplifier 22, a seal-less fission chamber 23, an amplifier 26, an amplifier 24, a first differentiating circuit 25 with a time constant T 1  /ln 2 (determined by a capacitor C3 and resistor R3, where T 1  is the half-life of the ground state of Rh 104 ), a second differentiating circuit 27 with a time constant T 2  /ln2 (determined by a capacitor C4 and a resistor R4, where T 2  is the half-life of the isomeric state of Rh 104 ), and a summing amplifier 28. 
     The fission chamber should preferably contain a regenerative sensitive coating consisting of a mixture of U 234  and U 235 . It may or may not contain a gas seal between the chamber and cable volumes. 
     The center conductor of a cylindrical rhodium self-powered neutron detector, such as detector 11 or 21 consists of 100% Rh 103 . In a neutron flux, some of the Rh 103  atoms transmute to the ground state of Rh 104  which then decay by beta emission to stable Pd 104  ; and some of the Rh 103  atoms transmute to the isomeric or metastable state of Rh 104  which then decay be isomeric transition to the ground state of Rh 104 . Hence the equations describing the numbers of isomeric-state and ground-state Rh 104  atoms are: ##EQU1## where N 4m  =number of isomeric-state Rh 104  atoms 
     N 4  =number of ground-state Rh 104  atoms 
     N 3  =number of Rh 103  atoms 
     t=time 
     φ=neutron flux density 
     σ 4m  =cross section for the reaction Rh 103  (n,γ)Rh 104m   
     σ 4  =cross section for the reaction Rh 103  (n,γ)Rh 104   
     λ 4m  =decay constant for RH 104m   
     λ 4  =decay constant of Rh 104 , and 
     Rh 104m  represents the isomeric-state of Rh 104 . 
     Loss of Rh 103  due to burnup is neglected in this analysis of transient response. In addition, the detector current is given by 
     
         I.sub.1 =Kλ.sub.4 N.sub.4 +K.sup.1 φ            (3) 
    
     where the first term on the right represents the current produced by the beta particles emitted during decay of Rh 104  and the second term represents a prompt current produced by prompt neutron reactions in the detector and its environment. 
     These three equations can be solved for I 1  for the case of a step function in φ 1 , i.e., for ##EQU2## and the solution is ##EQU3## where ##EQU4## Notice that c is a calculable constant. 
     The current at time zero is ##EQU5## which is referred to as the prompt neutron sensitivity, S p . The current after several hours is ##EQU6## which is referred to as the sum of the prompt neutron sensitivity, S p , and the delayed neutron sensitivity, S D . Thus, the current for t≧0 is ##EQU7## and the output of amplifier 12 (or 22) is ##EQU8## where G 12  =transimpedance of amplifier 12 (or 22). 
     But the desired output voltage is ##EQU9## and this can be obtained by adding to V 12 , in the summing amplifier 18 (or 28), the following voltages which are obtained from the fission chamber 13 or 23 according to FIG. 1 or 6, respectively: ##EQU10## Referring to the embodiment of FIG. 1, we can write ##EQU11## where G 14  =transimpedance of amplifier 14 
     G 16  =transimpedance of amplifier 16, and 
     S 13  =neutron sensitivity of fission chamber 13. 
     So for perfect compensation, ##EQU12## and ##EQU13## which are obtained by combining equation (12) with equation (14-1), and equation (11) with equation (13-1). Referring to the embodiment of FIG. 6, we can write ##EQU14## So for perfect compensation, ##EQU15## and ##EQU16## which are obtained by combining equation (12) with equation (14-6), and equation (11) with equations (13-6) and (5). Note that, with the embodiment of FIG. 1, amplifiers 12, 14, and 16 must be adjusted as S D  and S 13  change due to burnup; with FIG. 6, only amplifiers 22 and 26 must be adjusted, since the voltage gain of amplifier 24 is a calculable constant. Accordingly, the embodiment of FIG. 6 is initially easier to calibrate. 
     For perfect compensation, the output of amplifier 14 must be, from equation (11), ##EQU17## and the output of amplifier 16 must be from equation (12), ##EQU18## At steady state, the output of amplifier 12 is from equation (9), ##EQU19## Therefore, for perfect compensation, ##EQU20## from (17) and (19) and ##EQU21## from (18) and (19). 
     The adjustment procedure for the present invention is as follows: 
     At steady state: 
     1. Adjust amplifier 12 (or 22) to obtain the desired output from amplifier 18 (or 28). 
     2. For the case of the embodiment of FIG. 1, adjust amplifier 14 so its output is ##EQU22##  and adjust amplifier 16 so its output is ##EQU23## 3. For the case of the embodiment of FIG. 6, adjust amplifier 26 so the output of amplifier 24 is ##EQU24## Note: the values of the constants used above are: ##EQU25## where c is calculated from ##EQU26## and S D  /(S p  +S D ) is reported in the literature by Banda &amp; Nappi, in the article &#34;Dynamic Compensation of Rhodium Self Powered Neutron Detectors&#34;, IEEE Trans. Nucl.Sci. NS-23, 311-316 (1976). It should be understood that the Banda et al article is not considered essential to a full and complete understanding of the present invention. Rather, the present invention is considered fully disclosed by the present patent application. 
     Fission chamber sensitivity changes after a cold startup--and, in the case of bottom-entry detectors, after a change in power level or rod bank position--are very slow, requiring hours to reach completion. These slow fission-chamber current changes produce essentially, as a result, zero voltage output at the outputs of the differentiating circuits 15 (25) and 17 (27). Essentially zero error is produced in the output of summing amplifier 18 (28). 
     Whenever the potential fission-chamber contribution to the total signal differs from the values given by Equations (11) and (12) above, the output after a rapid neutron flux change can be in error. The error in the potential fission-chamber contribution can be present after a cold startup, and, in the case of bottom-entry detectors, after a change in power level or rod bank position. The error can be caused by improper adjustment of amplifiers 14 and 16, in the case of the embodiment of FIG. 1, or of amplifier 26, in the case of the embodiment of FIG. 6. 
     Table I, below, shows the output error, expressed as a percentage of the correct output, for a step change in power level from 80% to 100% of full power, vs. time after the step, for the cases of: 
     (1) potential fission-chamber contribution too small by 10%; 
     (2) potential fission-chamber contribution too large by 10%; and 
     (3) no fission-chamber contribution. 
     
                       TABLE I                                                     
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OUTPUT ERROR AFTER POWER-LEVEL CHANGE                                     
FROM 80% TO 100% OF FULL POWER                                            
       Error In Potential Fission-Chamber Contribution                    
TIME     -10%         +10%     -100%                                      
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 0       -1.86%       +1.86%   -18.60%                                    
10 sec.  -1.60%       +1.60%   -16.00%                                    
20 sec.  -1.38%       +1.38%   -13.79%                                    
40 sec.  -1.03%       +1.03%   -10.31%                                    
 1 min.  -0.78%       +0.78%    -7.78%                                    
 2 min.  -0.36%       +0.36%    -3.61%                                    
 3 min.  -0.19%       +0.19%    -1.95%                                    
 5 min.  -0.09%       +0.09%    -0.90%                                    
10 min.  -0.04%       +0.04%    -0.35%                                    
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     Table II, below, shows the output error, expressed as a percentage of the correct output, for an exponential power level increase from 100% of full power and at a 10-second period vs. time after the start of the increase, for the cases of: 
     (1) potential fission-chamber contribution too small by 10%; 
     (2) potential fission-chamber contribution too large by 10%; and 
     (3) no fission-chamber contribution. 
     
                       TABLE II                                                    
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OUTPUT ERROR AFTER START OF 10-SECOND PERIOD                              
POWER-LEVEL INCREASE FROM 100% OF FULL POWER                              
       Error In Potential Fission-Chamber Contribution                    
TIME     -10%         +10%     -100%                                      
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0        0            0        0                                          
1 sec.   -0.88%       +0.88%    -8.78%                                    
2 sec.   -1.66%       +1.66%   -16.61%                                    
3 sec.   -2.36%       +2.36%   -23.59%                                    
4 sec.   -2.98%       +2.98%   -29.81%                                    
5 sec.   -3.54%       +3.54%   -35.36%                                    
6 sec.   -4.03%       +4.03%   -40.30%                                    
7 sec.   -4.47%       +4.47%   -44.70%                                    
8 sec.   -4.86%       +4.86%   -48.63%                                    
9 sec.   -5.21%       +5.21%   -52.13%                                    
10 sec.  -5.52%       +5.52%   -55.24%                                    
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     As can be seen from Tables I and II above and from FIG. 5, the present invention provides a linear power level measurement while also providing rapid response to detected changes in power level resulting from changes in reactor power level, changes in sensitivity after a cold start-up, and, in the case of bottom-entry detectors, changes in sensitivity after a change in rod bank position or power level. Accordingly, the present invention solves the problems of rapid response and precision measurement of in-core flux for nuclear reactor control. 
     The foregoing was provided for purposes of illustration and example. It will be appreciated that various equivalent embodiments of the invention can be produced depending on the specific reactor in which the invention is used. Therefore, the scope of the invention should be limited only by the breadth of the claims.