222 INSTRUMENTATION IN SCIENTIFIC RESEARCH [Chap. 4 



versus the probe voltage E v , Fig. (4-2)26, a straight line a is obtained. 

 The slope of this line depends upon the electron temperature tr 

 ( assuming a Maxwell velocity distribution) so that t~ can be found 



R. 



rom 





dE a 



k d log J" 



(1) 



If the probe potential is made less negative, the electron current 

 will be equal to the ion current, so that the total current is zero 



Fig. (4-2)1. Langmuir probe: C, 

 cathode; A, anode of discharge 

 tube; E D , discharge voltage source; 

 P, probe; probe potential adjusted 

 by varying voltage source E; S, ion 

 sheath formed in front of negatively 

 biased probe. 



Fig. (4-2)2. Voltage-current charac- 

 teristic of the Langmuir probe. 



(point G). With further reduction of the negative probe potential, 

 the slope /5 of the log i versus E v characteristic changes. The bend of 

 the characteristic occurs when the probe potential is equal to the 

 space potential E s . At this point, provided no collision occurs in 

 the sheath, the electron current is approximately 



H- 



aen' 



27T?n~ 



(2) 



where e is the charge, m the mass of the electron, and k the Boltzmann 

 constant. The quantity a is the area on the plasma side of the sheath 

 covering the probe; with a plane probe, a is approximately equal to 

 the surface area of the probe. The electron concentration n~ can be 

 computed from Eq. (2). The positive-ion concentration n + is about 



