592 BELL SYSTEM TECHNICAL JOCRNAL 



curves for t/, and r,. cross o\cr. Ihe optimum bow offset is then the value 

 which provides the minimum value at the crossover. From the theory 

 given earlier it is possible to compute these curves. If we had analytical 

 expressions for the motion of the tuner with temperature and for the varia- 

 tion of frequency with gap spacing it should be possible to obtain completely 

 theoretical curves. 



As a test of the theory of heating and cooling it is sufficient to use the 

 experimental curves for the motion of the tuner with temperature and the 

 variation of frequency with gap spacing in conjunction with the heating 

 and cooling curves of Figs. 79 and 80 calculated from equations (F^.l) and 

 (13.2). The value of A' which must be determined in order to obtain 

 numerical values from the curves of Figs. 79 and 80 may be determined 

 from Fig. 84 by using the relationship 



,, Pa - Pb 



K = 



n - n 



where Pa and Pb are the bombardment power inputs corresponding to anode 

 temperatures Ta and Tb ■ There is no ready means for directly determining 

 the heat capacity C. However, if one point on either the heating or cooling 

 curves is fitted to the experimental data the value of C may be determiined 

 and the remainder of the points computed. The results of such a computa- 

 tion are show^n by the dashed lines in Fig. 85. In view of the restrictive as- 

 sumptions of a uniform anode temperature and the neglect of all conduction 

 cooling the agreement in general form is reasonably good. 



The W.E. 2K45 includes a number of advances in reflex oscillator tech- 

 nique over the 2K25. It will be observed in Figs. 76 and 77 that the electron 

 optical system employed in the gun differs from that used in the 2K25. In 

 the 2K25 a gun producing a rectilinear beam was employed. In the 2K45 

 the gun consists of a concave cathode surrounded by a cylindrical electrode 

 and a focussing anode. The design of this type of gun was originated by 

 Messrs. A. L. Samuel and A. E. Anderson at these laboratories. The design 

 is such as to produce a radial focus beam which converges into the cylindrical 

 section of the focussing anode, /fter the beam enters the focussing anode 

 its convergence is decreased by its own space charge, and the beam passes 

 through the grids at api)ro.\imately the condition of minimum diameter. 

 J^etwecn the second grid and the repeller the beam continues to diverge 

 radially on the outbound and return trij)s. \ he intention of the design is 

 that the beam shall ha\ e diverged sufficiently so that the maximum possible 

 fraction will recross the gap within a ring having an inner diameter equal 

 to the first grid and outer diameter equal to the second jzrid. Fnder these 

 conditions only a small fraction of the beam will return into the cathode 

 region, the remainder being captured on the su])p()rt of the first grid after tlic 



