Consider a channel which contains a logarithmic integrator of the Cooke-Yarborough type with a basic section as shown in Figure 2-1, containing eight sections with the frequency break­points spaced one decade apart and the time constants one decade apart.

Tk

If the ratio of —— is constant over all sections and equal to 0. 0256, and the frequency

Tk. 6

break points are established to provide 0 to 10 volts for a range of 0. 1 to 10 counts/sec input,

Table 2-1 is a tabulation of the fractional standard deviation and average output voltage as a

function of the input count rate obtained by the use of Equations (2-17) and (2-18).

TABLE 2-1

FRACTIONAL STANDARD DEVIATION AND AVERAGE OUTPUT VOLTAGE AS A FUNCTION OF INPUT COUNT RATE____________________________________________

♦Based on the single diode pump relationship

inaccurate at the end point.

If a trip or alarm is provided at 5 x 10° counts/sec then the number of erg’s between the trip or alarm point and the average output voltage is given by

sT — S

cr.

where

n = number of оg’s between ST and S, and S™ = trip or alarm point.

A tabulation of n as a function of count rate is given in Table 2-2.

TABLE 2-2

TABULATION OF n AS A FUNCTION OF COUNT RATE

can be substituted into Equation (2-25) to produce the tabulation (Table 2-3) of the average rate of crossings over the trip level, ST.

R

*Trip point at 5×10 counts/sec

5

If the counting channel is to be operated in the region near lxlO cps with a trip setting at

c

5×10 cps, the digest of Table 2-3 (shown in Table 2-4) illustrates the average number of spurious trips possible in this region.

AVERAGE TIME BETWEEN TRIPS AS A FUNCTION OF COUNT RATE Count Rate (sec’*) Average Time Between Trips

It is shown in Table 2-4 that the average time to trip changes very rapidly for a very small increment of change in the reading, especially since the scale is logarithmic and covers seven decades.

In order that a smaller operating range not be required, the response time of the

logarithmic integrator may be made slower and the average time between trips at the region of

5 . .

lxlO counts/sec can be made much more tolerable.

In Equation (2-25) the part of the function which varies rapidly is the exponential, which is

a function of the number of root mean-square fluctuations between the operating point and the trip

‘ °S

or alarm point. From Equation (2-18) it is seen that the fractional standard deviation — is

s

directly proportional to. ‘ where

Tk is the frequency break, and is the time constant break.

For the counting channel considered in the previous analysis, the time constant breaks and response time (measured) as a function of к and rate are listed in Table 2-5.

FRACTIONAL STANDARD DEVIATION AND AVERAGE OUTPUT VOLTAGE
AS A FUNCTION OF INPUT COUNT RATE

From Table 2-2a and the proposed log integrator circuit constants, the average number of crossing-per-unit time over the trip level is tabulated in Table 2-‘3a. . , •

0,09

Count Rate (sec"1) n Tk

To qualify the in-core cable for use in the in-core startup systems, cable samples were tested in an operating reactor. D-c electrical characteristics were measured before insertion and at intervals after insertion.

5. 4. 1 Cable Samples And Processing

A single sample of each of two types of cable was irradiated. Both short-term and long­term effects were noted. One cable consisted of a 0. 018-inch-diameter center wire of stainless — steel-clad copper (Sylvania Oxalloy 28). GE quartz fiber, 150 2/2, initially manufactured with a Dow-Corning 1053 binder (a silicone compatible binder), and an outer braid of 0. 004-diameter Type-304 stainless steel wire. The braid outer diameter was 0. 070 to 0. 076 inch. The second cable was identical to the first except that Owens-Corning S-994 glass (S-glass) fiber, 150 1/2 with silicone compatible binder, was used instead of quartz fiber. .

The binder is coated on the quartz and S-glass fibers at the time of their manufacture.

The coating, by providing lubrication, increases the strength and flexing tolerance of the fibers.

It would be virtually impossible to otherwise fabricate the cable; however, the binder must be completely removed before the cables can be used at high temperature and/or in intense radiation fields.

♦The photos at the amplifier input were of poor quality for reproduction, so photos taken with a terminating resistance of 2700 ohms were substituted for them. This results in a pulse whose slow component has a faster decay time but which otherwise has the same general appearance as that at the 5000-ohm amplifier input resistance.

The binder, being an organic material in nature, decomposes when heated to a high temperature and/or exposed to high radiation. Spme of the. decomposition products are carbon­aceous and can degrade the insulation, resistance to the point where thfe’cable is unusable.

■x The cables are cleaned by the cable manufacturer by baking them in air at 850°F for 8 hours. This treatment removes all the organic components that could cause difficulty in reactor service.

For purposes of this test, the cable samples were drawn into 1/8-inch-o. d.. Type-304 stainless steel tubes. The tubes were seal-welded on the end to be irradiated, and terminated with a hermetic electrical connector on the other end. Before the final seal weld was made, the tubes were evacuated to 0. 1 micron while at a temperature of 800°F. The tubes were then backfilled with reactor grade argon at 1 atmosphere, and sealed.