A Detailed Analysis of Beam Formation 

 with Electron Guns of the Pierce Type 



By W. E. DANIELSON, J. L. ROSENFELD,* and J. A. SALOOM 



(Manuscript received November 10, 1955) 



The theory of Cutler and Hines is extended in this paper to permit an 

 analysis of heam-spreading in electron guns of high convergence. A lens 

 correction for the finite size of the anode aperture is also included. The Cutler 

 and Hines theory was not applicable to cases where the effects of thermal 

 velocities are large compared with those of space charge and it did not include 

 a lens correction. Gun design charts are presented which include all of these 

 effects. These charts may he conveniently used in choosing design parameters 

 to produce a prescribed beam. 



CONTENTS 



1 . Introduction 377 



2. Present Status of Gun Design; Limitations 378 



3. Treatment of the Anode Lens Problem 379 



A. Superposition Approach 379 



B. Use of a False Cathode 382 



C. Calculation of Anode Lens Strength by the Two Methods 383 



4. Treatment of Beam Spreading, Including the Effect of Thermal Electrons 388 



A. The Gun Region 388 



B. The Drift Region 392 



5. Numerical Data for Electron Gun and Beam Design 402 



A. Choice of Variables 402 



B. Tabular Data 402 



C. Graphical Data, Including Design Charts and Beam Profiles 402 



D. Examples of Gun Design Using Design Charts 403 



6. Comparison of Theory with Experiment 413 



A. Measurement of Current Densities in the Beam 413 



B. Comparison of the Experimentally Measured Spreading of a Beam with 

 that Predicted Theoretically 416 



C. Comparison of Experimental and Theoretical Current Density Distri- 

 butions where the Minimum Beam Diameter is Reached 418 



D. Variation of Beam Profile with T 418 



7. Some Additional Remarks on Gun Design 418 



* Mr. Rosenfeld participated in this work while on assignment to the Labora- 

 tories as part of the M.I.T. Cooperative Program. 



375 



