GENERAL CIRCUIT CONSIDERATIONS 



229 



Suppose we wanted to improve on such circuits by reducing the stored 

 energy. An obvious procedure would be to cut away most of the fiat opposed 

 surfaces as shown in Fig. 5.5. This reduces the energy stored between the 

 resonator walls, but results in energy storage outside of the open edges, 

 energy associated with a "fringing lield." 



Going to an extreme, we might consider an array of closely spaced very 

 fine wires, as shown in Fig. 5.6. Here there are no opposed fiat surfaces, 

 and all of the electric field is a fringing field; we have 

 reached an irreducible minimum of stored energy in 

 paring down the resonator. 



The structure of Fig. 5.6 has not been analyzed 

 exactly, but that of Fig. 5.7 has. InFig. 5.7, wehave 

 an array of fine, closely spaced half-wave wires be- 

 tween parallel planes.* This should have roughly 

 twice the stored energy of Fig. 5.6, and we will esti- 

 mate (Er/ff^Py^ for Fig. 5.6 on this basis. We obtain 

 in Appendix III: 



For the half-wave wires. 



i^/^^pyi' = 6.20 {v/vgy^ 



(5.25) 



Fig. 5.6— Quarter-wave 

 wires, which have a min- 

 imum of stored energy. 



and hence for the quarter-wave wires, approximately 



(£V/52p)i/3 = 7_8i (^,/i,Ji/3 (5.26) 



As we have noted, (v/c), which appears in the expression for {E-f^-Py^ 

 for the sinusoidal field impressed at radius a and in (5.24) and (5.25), is a 



Fig. 5.7 — Half-wave wires between parallel planes. The stored energy can be calculated 

 for this configuration, assuming the wires to be very fine. The circuit does not propagate a 

 wave unless added coupling is provided. 



function of the accelerating voltage. Figure 5.8 makes a comparison be- 

 tween the sinusoidal field impressed at a radius a, curve A ; the flat resona- 

 tors, either circular or square, B; the half-wave wires, C; and the quarter- 



* There is no transverse magnetic wave propagation along such a circuit unless extra 

 coupling or loading is provided. Behavior of nonpropagating circuits in the presence of an 

 electron stream is considered in Section 4 of Chapter XTV. 



