WAVl'; I'KOP AC A ri(».\ ALOXc; \\ KI.KCTKOX Hi: \ M 



101) 



Vr 



3.6 

 3.4 

 3.2 

 3.0 

 2.8 

 2.6 

 2.4 

 2.2 

 2.0 

 1.8 



0.8 



yb 



Fig. 2 — Comparison between space-charge wavelengths for cylindrical beams 

 with Brillouin flow and those with rectilinear (confined) flow, respectively. 



of the rectilinear beam. The 12 independent variables of (56-57) are re- 

 duced to 6 by expressing He and Ee in terms of E, and H^ , respectively. 

 The latter, however, require 2 arbitrary constants for a complete descrip- 

 tion in region 11, making a total of 8 constants to be determined. 



The eliminant of the 8 boundary-value equations can be written as a 

 TM wave-admittance equation at the beam surface: 



where 



8 = 



6n = 



8o + RF 



hjyh) _jc^e li(yh) - 8-K,iyh) 

 7 /o(7^) + 8-Ko(yb) 



Io(yh) 



K;{ya) LV ya 



ka cot i/' 



Ki{ya)h{ya) - Ko(ya)To(ya) 



(58) 



(59) 



(00) 



