588 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1954 



tion is about 1,000 gauss. It will therefore be consistent with the neglect 

 of anisotropy to assume that the applied frequency is such that p is less 

 than unity and this will be done hereafter. 



2.2 Ion clouds or plasmas 



Since these are considered in much less detail in these papers, their 

 physical properties are stated only briefly here. 



Instead of a tensor relationship between B and, H we now have one 

 between the displacement vector D and the electric field E. If the mag- 

 netizing field is along the z axis, we have 



D^ = eE^ — jrjEy , 



Dy = j-qEx + eEy , and (6) 



D, = €,E^ . 



If the medium consists of equal densities R of positive ions and elec- 

 trons, and if collisions and thermal velocities are neglected, e and t] can 

 be calculated for weak ac disturbances Ee^'^^ from the equation of motion 



V = 1 Ee"^' + y[v X H], 

 ~ m 



where v is the velocity vector of the electron and y = cuo/m, in the usual 

 notation. When this equation is solved and the abbreviations 



uo = \y\ Ho; (T = —; q = — ; ^p = zr 



0)0 CO meo 



are introduced, one obtains, from the fact that the total current is 

 joicoE + Rv, the heavy ions being assumed stationary, 



(7) 

 a- — L 



e^ = €o(l - q^), 



where eo is the dielectric constant of vacuum. The waveguide theory will 

 involve the parameters 



2 2 



VE = - = I - jz ^TT" ^ , and 



e (X- -\- q- - I 



