Sec. 4-2] ELECTRICAL TRANSDUCERS 221 



polarity), M the gas-volume flow velocity in cubic meters per second, 

 t the collection time in seconds, and C the capacitance to ground 

 (shield) of the cylinder A. 



The method has been used in atmospheric-electricity studies to 

 determine the space charge, i.e., the local concentration of excess 

 charge in the air; excess-charge concentrations from 3.3 x 10~ 12 to 



160 x 10 -12 coulomb/m 3 have been measured. 1 



4-2. Space Charges 



Space charge is the local concentration of positive ions n + or of 

 electrons and negative ions n~ in a medium. 



The classical transducer for the space-charge determination in 

 highly ionized gases is the Langmuir probe (4-21). 



The space charge in atmospheric air is defined as the local excess 

 concentration of ions of one polarity. It can be determined by 

 measuring the concentration of ions of either polarity, n + and n~, 

 with the Gerdien counter (4- 1 2a) and forming the difference n + - - n~. 

 Alternatively, the Brown excess-ion counter (4-126) can be used; its 

 output is directly proportional to the space charge as defined above. 



In cases where the space is well localized and the geometry of the 

 electric field is well defined, the space charge can be determined from 

 electric-field measurements (4-5). 



4-21. Langmuir Probes 



In highly ionized gases, with a concentration of ions larger than 

 10 8 per cubic centimeter, the space charges and the space potential 

 can be found from the voltage-current characteristics of a probe 

 inserted in the ionized gas (plasma). 



The probe arrangement is shown in Fig. (4-2)1. Figure (4-2)2a 

 illustrates the usual voltage-current characteristic. If the probe 

 potential E p is highly negative with respect to the plasma potential 

 (point A), electrons will not be able to reach the probe; only a con- 

 stant positive ion current i + , independent of the probe potential, is 

 noted. 



If the probe potential is made less negative (point B), some elec- 

 trons will reach the probe, and with further reduction of the negative 

 potential, the electron current (obtained by deducting the ion current 

 i + from the total current i) will increase exponentially. By plotting 

 the logarithm of the electron current density, j = (i/a), to the probe 



1 J. G. Brown, Terrestrial Magnetism and Atm. Elec, 35, 1 (1930), and 38, 



161 (1933). 



