APPENDIX G CONFINED-FLOW FOCUSING OF A RELATIVISTIC BEAM where the subscripts c and o, respectively, denote the cathode and the entrance to the interaction region. is the relativistic factor , where is the beam speed and c is the speed of light, so that the focusing field and corresponding solenoid power are reduced by a factor from the non- relativistic value. In the derivation of Equation (G-l) the self-magnetic field of the beam in- creases the focusing force by a factor , but the angular velocity of the beam also falls, by a factor . In a 60 kW 0. 2-microperveance beam, for example, the voltage is 39 kV, is 0. 37, and is 0. 963, so that nearly 4 percent of the solenoid power is saved in comparison with a nonrelativistic beam of the same length and charge density. The equilibrium condition for a relativistic beam (reference 26 of Section 4)
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