446 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1957 



magnetization m and RF magnetic field hP in the cavity should be sim- 

 ple. All three conditions can be satisfied if a thin ferrite disc is placed 

 against the endwall of the cavity (Fig. 3). Noting that the tangential 

 component of the magnetic field intensity is continuous at the plane 

 face of the disc we have: 



7 • 7 



nir = Xmhr — JMe 



me = jKhr + Xmhe 



Inserting (A3) into (Al) we find the additional magnetic energy stored 

 in the disc 



Wj'^ =^ [ [x.Xhr%'* + /l«%°*) +JK{hr%'* - /l,0/l,0*)] dv (A4) 

 Z Jvi 



In order to evaluate (A4) we use the fact that the TEm-mode can be 

 expressed as the sum of two circularly polarized modes rotating in 

 opposite directions 



Thus, we have 





hri.2 = B — Ji{kcr)e^^' cos ^z 



rCr. 



(A5) 



he J = ±jB y^ J,{Kr)e'^^' cos ^z (A6) 



hzi,2 = BJiikcrje"^^^ sin ^z 



Eri.2 = zhB^ MKr)e'^'' sin ^z 



Eei.2 = jB ^" J,'(kcr)e^'' sin ^z 

 kc 



amplitude factor 



Bessel function of the first kind 



propagation constant in the ^-direction 



propagation constant in the r-direction 



propagation constant in free space 



length of cavity 



wavelength in free space 



radius of cavity 



wavelength in the cavity 



first zero of the derivative of Ji 



(A7) 



