electron streams in a diode 843 



3.2 The A-c. Components of the Electron Stream 



We now return to the a-c. equations for the electron stream, (29) and 

 (30). In (29), the arbitrary function AiS) must obviously involve an ex- 

 ponential function oijcot, and it must therefore be of the form 



A{S) = Ae^-^ (40) 



where A is an arbitrary constant. Then the substitution of (26) gives 



A{S) =A exp. [y« (/ + f^) + I e'"'] (41) 



The term in q/I is a second-order term that may be neglected, and -=- can 

 be replaced by its value from (39) that is, 



^ = '-^-r (42) 



where r is the d-c. transit time to any coordinate x. The resultant exponential 



factor in -y- can then be included in the arbitrary constant A, and this 



gives 



A{S) = Ae''''^'-'^ (43) 



The substitution of this function in (29) now gives the following relation 

 for the amplitudes of the a-c. components 



« = ^,--_M5_JLi (44) 



The arbitrary function B{S) may be treated in a similar manner, and (30) 

 then gives the complex amplitude of the conduction current density 



,=i^(.-.f^).-_^^, (45) 



where B is another arbitrary constant. 



The substitution of this value of q in (25) and (44) also gives the ampli- 

 tudes of electron velocity and electric intensity. 



= -L[.-.f]e- + i[l+-^] 



(47) 



