GUIDED WAVK 1'U<)1'A(;AT1()\ TllUOl (;II <;^ i;()MA(i.\HTI(' MKDIA. 11 943 



noii-i'cciprocity will occur. It is understandable that this double function 

 of the magnetization (conversion to elliptic polarization plus creation 

 of (lit'fereiices in permeal)ility) leads to higher order effects. Ilowev'er, 

 inasmuch as for tlie ferrite and plasma the magnetization can produce 

 large changes, the re(iuirement of elliptic polarization in zero magnetic 

 field cannot l)e regarded as essential in practice. These considerations are 

 demonstrated by a simple example in Section 2.2. 



The (Unices considered in this paper actually are such that the electric 

 or the magnetic held vector in the plane normal to the held is ellipti(;ally 

 polarized even in the absence of the gyromagnetic medium. For example, 

 the magnetic lines of force of the TEio mode in a rectangular waveguide 

 form two sets of closed loops in a plane parallel to the wide sides (see 

 Fig. 2) and repeating every wavelength. This pattern moves bodily 

 down the guide with the phase velocity of the mode, so that an observer 

 stationary at any point not at the center or at the narrow walls of the 

 guide sees a magnetic field rotating at the signal frequency and tracing 

 out a generally elliptic path. The sense of the rotation is opposite on 

 opposite sides of the center plane, and depends on the propagation direc- 

 tion. The conditions outlined in the previous paragraph are therefore 

 satisfied; introduction of a ferrite slab magnetized as in Fig. 1(a) will 

 yield first order non-reciprocal effects. 



The problems considered here are such that the electromagnetic 

 fields do not ^'ary in the direction of magnetization. Under these condi- 

 tions the field can be split into a TE and TM field satisfying different 

 wave equations. In general, the two fields are coupled through the bound- 

 ary conditions. Most of the paper is devoted to the analysis of the non- 

 reciprocal helix, a problem that has recently gained importance in 

 connection with high power traveling- wave-amplifiers. The conventional 

 amplifier suffers from a limitation on its maximum useful gain; waves 

 reflected from the output end will make the tube "sing" above a certain 

 critical gain. Ferrites offer the possibility of preferentially suppressing 

 these ])ackward waves and so of increasing the permissible gain by a 

 large amount.* In section 2.3 the "fiat" helix (one of infinite radius) is 

 considered. For the slow^ waves employed in practice a rather complete 

 treatment is possible in this case of planar geometry. In Section 3 the 

 cylindrical helix is treated. Inasmuch as the solutions involve functions 

 for which no extensive tables exist, the treatment has to be more sketchy. 



* ]\Iore speeificallj-, in high-power traveling-wave tubes the large beam cur- 

 rent employed may t)e above the critical value required forlnickward wave os- 

 cillations due to sjiatial harmonics of the helix structure. In such cases the larger 

 attenuation of tjackward waves will permit a higher beam current and therefore 

 stable amjjlification to higher power levels. 



