CIRCULAR CYLINDER CAVITY RESONATOR 35 



length in the Appendix, where it is denoted by Fi{x). Table II of the Ap- 

 pendix gives its values (for ( — \, 2 and 3) and also those of G({x) where 



Fi{x) = -\ogG({x) (11) 



Thus (10) becomes 



-log sin (d = log [x Jt{x)/G({x)] + C (12) 



and the final equation for the current streamlines is 



[xJt{x)/Gl{x)] sin (d ^ C (13) 



where C is a parameter as before. 



It is not difficult to show that G({x)/Jc{x) has zeros at the zeros of J((x). 

 For these values of x, sin €6=0 whatever the value of C, and all stream- 

 lines converge on (or diverge from) 2(m points on the end plate. 



The flow lines of (13) are orthogonal to the family (8) and could readily 

 be drawn in this manner. However, better accuracy is obtained by plotting 

 (13). 



End Plate: Distributions 



The 32 attached plates show the distribution of current in the end plates 

 of a circular cylinder cavity resonator for a number of modes. 



In the first set of 21, the scaling is such that the diameters of the figures 

 are proportional to those of circular waveguides which would have the 

 same cutoff frequency. This group is of particular interest to the wave- 

 guide engineer. 



In a second group of 11, the scaling is such as to make the outside diam- 

 eters of the cylinders uniform. This group is of particular interest to a 

 cavity designer. 



This distribution is a vector function of position; that is, at each point in 

 the end plate the surface current has a different direction of flow and a dif- 

 ferent magnitude or intensity. The variation in current intensity is repre- 

 sented by ten degrees of background shading. The lightest indicates re- 

 gions of least current intensity and the darkest greatest intensity. The 

 direction of current flow is shown by streamlines. Streamlines are lines 

 such that a tangent at any point indicates the direction of current flow at 

 that point. 



The modes represented are the 



r£ 01, 02, 03 TM 01,02, 03 



r£ 11, 12, 13 TM U, 12, 13 



TE 21, 22, 23 TM 21, 22 



TE3l,32 TM3l,32 



