294 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 9 



mass analyses. They have, therefore, been wholly replaced by vacuum- 

 tube amplifiers which provide the requisite sensitivity and also permit less 

 sensitive meters and recording instruments to be used. Most frequently, 

 the first stage of an amplifying system is an electrometer- type vacuum tube 

 coupled directly to the ion-collecting electrode of the mass spectrometer. 

 These tubes usually contain four elements and are designed to draw very 

 small grid currents and to operate with plate potentials of only 7 to 20 volts. 

 The input signal is applied to the second grid, or what is normally the screen 

 grid. Several electrometer tubes with very high sensitivities and suitable 

 characteristics have been designed especially for this type of application. 

 The FP-54 [12] is the most sensitive of these tubes and can be used for con- 

 tinuous indication of ion currents as small as 10 -15 amp. Several other elec- 

 trometer tubes are also available such as the Vx-41 [13] and the 38, 954, and 

 959 [19] which, though somewhat less sensitive, are, under some conditions, 

 more stable. 



The output from the electrometer tube may be used directly to drive a 

 sensitive galvanometer, or the signal can be further amplified by successive 

 stages of d-c amplification. 



The signal voltage driving the grid of the electrometer tube is derived 

 from the voltage E developed across a grid resistor of the order of 10 8 to 

 10 11 ohms through which the ion current passes to ground. The maximum 

 sensitivity that can be achieved in circuits of this type is limited by the 

 average voltage e produced in the resistor by thermal agitation. This is 

 given [14-16] approximately by the relation 



e 1 = brTRAf 



where T = absolute temperature 



A/ = frequency band passed by amplifying system 

 Assuming that the minimum detectable ion current i is that which produces 

 across the resistance R a voltage equal to e, then 



i = 1.29 X 10- 



R 



Although it is apparent that the signal-to-noise ratio can be improved by 

 using a high input resistance, values of R greater than 10 11 ohms are difficult 

 to obtain and still more difficult to maintain at a constant value. Variations 

 in temperature and particularly in surface resistance are sometimes difficult 

 to control and, together with variation in the effective resistance with signal 

 voltage, may lead to drift and transient changes in the sensitivity of the 

 instrument. More important still is the tendency of some resistors to 

 polarize, thus introducing a long signal decay time. The band-pass fre- 



