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An electron gun must be able to draw a sufficient current and accelerate the electrons to the desired speed. The first part of an electron gun geometry presents unique design challenges because the emitted electron speeds are usually lowest there, and therefore the space charge density is quite high. The Pierce electron gun design uses electrodes with a particular shape to counteract the Coulomb repulsion between electrons in the beam. As a result, the electrons in the beam propagate in straight lines. The emitted electrons at the cathode are assumed to be space charge limited; the initial thermal distribution of electron velocities is neglected.