IMPEDANCE PROPERTIES OF ELECTRON STREAMS 



An 



and as /o — /a'o it is clear that 



Z) < 0. 



(10) 



Hence, since the discriminant in general is negative (8) has three 

 real roots. Two of these are positive and one negative. A double 

 root occurs for /q = /a'o, and the value of this root is clearly T = Tr' 

 For currents smaller than the Kipp current there are two positive 

 roots Ti and T^ such that Ti < Tr and T^ > Tk- 



Thus it becomes evident that space charge conditions corresponding 

 to the roots T^ result in a negative capacitance. Interpreted in terms 



CATHODE 



O O 



O S! 



o o 



Fig. 3 — Schematic of a space charge grid tube. 



of Fig. 2, the roots Ti correspond to the upper branch a^ and the 

 roots 7^2 to the lower branch y^. Hence, it is evident that space 

 charge corresponding to the lower branch has a negative dielectric 

 constant. 



Consider next the system pictured schematically in Fig. 3. It 

 differs basically from that in Fig. 1 in that a negatively polarized 

 grid has been interposed between the planes a and h of Fig. 1. The 

 arrangement shown in Fig. 3 may be considered to be equivalent to 

 a space charge grid tube with the accelerating grid Gi and control 

 grid Gi. The grid Gi is assumed to be by-passed to the cathode for 

 a-c. The planes indicated by 2 and 3 are imaginary planes located 



