SOME RESULTS OX CVLIXDKICAL CAVITY RESOXATORS 427 



We liave calculated and give in Table III values of r, e, E and s for several 

 values of c and for a few modes of special interest. For three cases, "TE 01, 

 "TM 11 and "TM 11, we have determined an empirical formula to fit the 

 calculated values of ^. These are also given in Table III. 



TE Modes 



TABLE II. Elliptic Cylinder Fields 



Et = —k i/ ^ S((c, r])J((c, sin k-.iZ cos cot 



r •Y/t2 _ \ 



Er, = k A/- S(,{c, ri)j'({c, t) sin k:i z cos ut 



y e 1 



\/>^ - 1 

 ^j = ^3 >5'^(c, t])] \{c, f) cos k>, z sin wt 



H.q = kz S({c, ri)J((c, ^) COS kiZ sin wt 



q 



11 z = klSfic, Ti)J(,{c, t) sin hz sin ut 



TM Modes 



\/^2 — 1 



E^ = —kz Siic, ri)J({c, sin k^z cos ut 



Q 



■\/ 1 ~2 



■Et, = —^3 S'((c, r))J({c, sin ^3 3 cos wt 



1 



Ez = k'l S((c, 7))J ({c, l) cos hz cos (Jit 



H^ = —k 4 / - S'((c, ri)Jp{c, i:) cos ^3 z sin coi 



/-y/t2 _ J 

 - "S^Cc, j/jZ/Cc, $) cos h z sin wi 



Notes: 



Derivatives are with respect to ^ and 77. 



Sf and // carry prefixed superscripts, e or 0, since they may be either even or odd. 



q = Co Vl^ — rf' c = coki 



Kl = «3 = 7" «- = ^1 + «j 



a L 



2co is distance between foci of ellipse. 

 a is the semi major diameter of the ellipse, 

 r^ „, is the value of c$ that makes 



J l{c,^) — for ^-^ modes 

 J'^ifyO = for TE modes. 



