TRAVELING-WAVE TUBES 



31 



but discontinuity effects are also important. However, a suitably defined 

 helix impedance is of some interest. 



Figure 3.7 presents the impedance as defined on a voltage-power basis. 

 The peak "transverse" voltage Vt is obtained by integrating the radial elec- 

 tric field from the radius a of the helically conducting sheet to oo . The 

 "transverse" characteristic impedance Kt is defined by the relation 



P = (mvVKd 



80 

 70 

 60 

 50 

 40 



30 



20 

 X. 



>|o 

 Ij, 10 



6 



5 



0.4 0.6 O.S 1.0 2 3 4 5 6 7 S 10 20 30 



Fig. 3.7 — Curves giving the variation of transverse impedance, Kt , with ya. 



The impedance is found to be given by 



noil 



© 



(yay 



h'r^)''' 



/o/o) 



+ 



(rJ('+'/f:)<^-«^''-"'^r 



(3.10) 



The /'s and K's are modified Bessel functions of argument ya. 

 ' The dashed line on Fig. 3.7 is a plot of 30/70 vs. ya. It may be seen that, 

 lor large values of ya, very nearly 



Kt = i^/my/m^O/ya) 



(3.11) 



