7(50 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 



wlicre r is the aiicxie vollajijc and W Is the initial voltage through which 

 the electrons must travel l)efore they can ionize. 



The ions produced in the space by this process flow back toward the 

 cathode. The ion current ip resulting from this process is 



= io(e^ '» - 1 



ioie-' "» - 1) (8) 



As mentioned above, new electrons are released at the cathode by posi- 

 tive ions, neutral atoms excited to a metastable state, and photons gen- 

 erated in the gas. These secondary processes can be grouped together by 

 defining a coefficient y as the number of new electrons released at the 

 cathode by all of these processes for each positive ion generated in the 

 cathode-anode space. Thus each electron passing from cathode to anode, 

 on the average, results in the release of M new electrons where 



M = 7(e-''^*' - 1) (9) 



Each new electron from the cathode is also amplified in the gas so that 

 after n multiplication cycles, the electron current at the anode is^ 



in = ioe^''" ''\l + ill + ^/2 + • • • + M-) 



(10) 



When M is less than unity and n -^ x (the eciuilibrium state), (10) re- 

 duces to a steady state value of 



. _ ioe ° (11) 



* 1 - M 



Since the current is dependent on the initial current iu , the discharge 

 is said to be non-self-sustaining. This corresponds to the portion AB 

 of the curve of Fig. 2. 



If the applied voltage is made high enough, the multiplication factor 

 approaches unity, the current of (11) becomes independent of the initial 

 current, and the tube is said to have broken down. This condition cor- 

 responds to the horizontal portion BC of Fig. 2. To control this break- 

 down voltage, the cathode secondary emission coefficient 7 and the gas 

 ionization coefficient rj must be controlled. 



The secondary emission coefficient is highly sensitive to the surface 

 conditions of the cathode. Pure metals such as molybdenum are often 

 preferred to coated surfaces because they permit highly stable and repro- 

 ducible emission. With the cathode surface determined, the breakdown 

 voltage can be adjusted by changing the gas filling and tube geometry. 

 Fig. 3 show^s the breakdown voltage for a tube having parallel-plane 



