Welding: Processes, Quality, and Applications by Richard J. Klein

By Richard J. Klein

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142 *106 N L  200 (76) where HV = 60 keV is the energy of the electrons, NL is the number of the line, presenting in the bitmap, shown on Figure 32, the beam. This bitmap shows the converted into light current distribution transferred through the slit at beam scan at two slits, as this is displayed at the insertion of Figure 31. The beam current is 10 mA. The integral current distributions in nine cross-sections from the X-axis and respectively the Y-axis distributions, corresponding to equal focus positions, are investigated.

Note, that (57) is just the geometrical properties of an ellipse. (57) Design of High Brightness Welding Electron Guns and Characterization… 29 Figure 13. Determination of emittance ellipse by Twiss parameters Coefficient (or Twiss parameter) β characterize changes of the beam envelope. Its definition could be written in terms of second order moments of distribution function: x  There the brackets x2 x . (58) means an average value, performed over the beam particles distribution. Respectively  is a measure of the average declination of electron trajectories from the beam axis: x  x' 2 x , (59) .

For example, in unlimitedly wide electron beam going along the axis between two perpendicular to this axis equi-potential planes, situated on a distance l from each other, the potential distribution U(z) has minimum in the middle between these planes. From integrating eq. 10-6 [AV-3/2]. e. a virtual cathode is formed. This abrupt decrease of the potential is physically connected with slowing down of the electrons and considerable increase of the space charge. 10- [AV-3/2] are reached, then the potential in the middle between the equi-potential planes jumps to 0,75U and the normal current flow is restored.

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