Measurement of shot voltage used to deduce the magnitude of secondary thermionic emission

Abstract

The electric current passing from filament to anode of a thermionic valve is a stream of individual electrons; the passage and arrival of each of these will cause a disturbance among the electrons already on the anode. Hence the current which passes through the circuit connecting the anode to the kathode will contain ripples which are due to the arrival on the anode of individual electrons. The electrons arrive with random phase distribution, and hence the circuit receives a succession of shock impulses. There will be a fluctuating potential difference across the circuit, and the mean square value of this can be measured after adequate amplification. The root mean square value of this potential difference is commonly termed the shot voltage, because the pattering of the electrons on the anode has been likened to the pattering of small shot on a target. The shot voltage will depend on the rate of arrival of the electrons and on the characteristics of the circuit which they shock into excitation. The shot voltage was predicted by Schottky in 1918, and measured roughly by Hartmann in 1921. Schottky developed an expression for the magnitude of the shot voltage and, according to him, it should be proportional to the charge on an electron. Schottky’s formula was tested experimentally by Hull and Williams. They used a lightly damped circuit having a natural frequency of about 10 6 c/s, and their measurements yielded a value for e which agreed with Millikan’s value to within ⅓%. A further set of measurements were made by Williams and Vincent where the receiving circuit was a graphite line drawn on a glass tube, and thus formed a system aperiodic to its fundamental mode. They observed the shot voltage by a selective amplifier, which gave appreciable response only to frequencies near 120 k. c./s. With this apparatus they obtained a value for e which agreed with Millikan’s value to closer than one part in a thousand. Williams and Huxford made a further series of measurements with improved apparatus, and again obtained the correct value for e ; they used an amplifier which had appreciable response only between 112 and 121 k. c./s.