950 



THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1954 



as the permeability matrix of the ferrite. The equations of motion for 

 the plasma* lead to the expressions 



€i = €0 (1 - q^), 



e = €o 



V = ^0 



*eff 



1 + 

 2 



go- 

 cr^ - 1' 



- r?' 



(7^ - 1 



(10) 



eo 



/I 2\2 2 



(1 - gr) - 0- 



(1 - g2) _ ,2 



where o- is now the ratio of the cyclotron resonance frequency; 



e I jLto 



1 



2^ 



He 



in a field Ho , to the applied frequency and q is the ratio of the plasma 

 frequency to applied frequency; Ceff behaves ^\'ith magnetic field in much 

 the same waj^ as Meff • It is a constantly decreasing function of a and is 

 negative between \ a \ = 1 — q^ and | o- | = Vl — gS going to infinity 

 at the latter value. The left and right handed dielectric constants, 

 e — 17 and e + 77 are given by eo[l — q/(l — o-)]andeo[l — q /(I -\- a)]. 



2.2. Examples of Non-reciprocal Systems 



We now discuss briefly three examples of non-reciprocal systems as 

 illustrations of particular points. As an example of a system which can 

 be analyzed ^^ery easily and completely we consider a plasma occupying 

 the region, x > and bounded at .r = by a sheet of constant impedance. 

 This impedance is to depend upon frecjuency but not on the propagation 

 constant. It will be written as j\^iJLo/eoZ{oo) where no and eo are free space 

 values. A practical realization of such a sheet might consist of a very 

 large number of similar fins of negligible thickness and separation, 

 parallel to the ?/-axis and attached normally to a conducting plane x = 

 constant. The fields between separate fins are uncoupled and E, is uni- 

 form between fins. For such an arrangement, Z(co) = tan o^y/eofj-'oXo > 



* See Section 2.2 of Part I. 



