. The Bell System technical journal . ^dV^]^Fr-j- \(X a t \ BEAM FORMATION WITH ELECTRON GUNS 395. Fig. 6 — Curves showing the current density variation with radius in a beamI which has been dispersed by thermal velocities. Here r« is the nominal beam radius,I r is the radius variable, and <t is the standard deviation defined in equation 17. A family of curves with this ratio, Fr, as parameter has been reproduced: from the Hines-Cutler paper and appears here as Fig. 7. Using this no-tation, (25) becomes dV ^ Vr,/{2V.) j^ Frdi^ 27reo r or d rdz^ jn_ lo Fr^ Fr 27r€0 (27,7a)3/2 J. J. (27) wher
. The Bell System technical journal . ^dV^]^Fr-j- \(X a t \ BEAM FORMATION WITH ELECTRON GUNS 395. Fig. 6 — Curves showing the current density variation with radius in a beamI which has been dispersed by thermal velocities. Here r« is the nominal beam radius,I r is the radius variable, and <t is the standard deviation defined in equation 17. A family of curves with this ratio, Fr, as parameter has been reproduced: from the Hines-Cutler paper and appears here as Fig. 7. Using this no-tation, (25) becomes dV ^ Vr,/{2V.) j^ Frdi^ 27reo r or d rdz^ jn_ lo Fr^ Fr 27r€0 (27,7a)3/2 J. J. (27) where we have made use of the dc electron drift velocity to make dis-tance the independent variable instead of time, and have defined aquantity K which is proportional to gun perveance. We can now apply(27) to the motion of both the outer (edge) non-thermal electron andthe cr-electron. From (26) we see that Fr, and Fg depend only on re/a] 396 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956 12 11 10 a LLI< u B 1 z zo ^ Fr = ^ ^ /^ ^ ^ ^ /^ / rz ^ / >>
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Keywords: ., bookcentury1900, bookdecade1920, booksubjecttechnology, bookyear1
