218 INSTRUMENTATION IN SCIENTIFIC RESEARCH [Chap. 4 



beam energy expressed in electron-volts, then the beam-current can 

 be found from 



. CE 



-E 



t 



where C is the capacitance to ground of the cage. 



The charged plate and the Faraday cage permit the measurement 



of a charge as small as 10 3 to 10 4 electrons. 1 Large errors are likely to 



occur from inadequate insulation. 



The charged plate and the Faraday cage can be used to measure 



the velocity distribution in a beam of charged particles. For this 



purpose an opposing potential is 

 applied to the cage, and the beam 

 current is measured as a function 

 of this potential. The arrangement 

 is shown in Fig. (4- 1 )4a for electron 

 beams. With increasing voltage 

 — E an increasing number of elec- 

 trons are unable to enter the cage 

 and the current decreases as shown 

 in Fig. (4-1)46. The differentiation 

 of this curve furnishes the velocity 

 distribution curve shown in Fig. 

 <4-l)4c. 



4-12. Gas-flow Systems 



a. Gerdien Ion Collector. This 

 system is used primarily for the 

 determination of the number and 

 the concentration of ions in gases 

 (air) but can also be used for the 

 measurement of ion mobility and 

 air conductivity. The system is 

 illustrated schematically in Fig. 

 (4-1)5 and consists of a cylindrical capacitor, the external cylinder 

 being grounded and the internal electrode C charged to a voltage E. 

 Air containing ions is drawn through the capacitor; the ions are 

 attracted toward the electrode C and cause in the external circuit 

 a current which is proportional to n, the concentration of ions, i.e., 

 the number of ions per cubic meter, to their charge q and to the 



1 O. Klemperer, "Einfuhrung in die Elektronik," p. 30, J. Springer Verlag, 

 Berlin, 1933. 



•Increasing neg. potential 

 of the cage 



Number of 

 electrons 



(c) 



Velocity, e volts 



Fig. (4-1)4. Application of the Faraday 

 cage for the determination of electron 

 velocity distribution: (a) circuit dia- 

 gram; (b) voltage-current characteris- 

 tic; (c) differentiated voltage-current 

 characteristic. 



