Abstract
A two-lens optical system entails two beams: a crossover beam and a Kohler illumination beam. We observed that upon varying the excitation corresponding to the first lens from large to small values, the crossover beam changed to a Kohler illumination beam with increased brightness. We derived new calculation formulas for the Kohler illumination beam. Brightness B and beam current Ib can be expressed as B = Bco (ϕco/ϕ)2 and Ib = Bco (παϕco)2/4, where Bco, ϕco, ϕ, and α denote the crossover beam brightness, crossover beam size, Kohler illumination beam size, and beam semi-angle, respectively; additionally, ϕco and ϕ are obtained at the same first lens excitation. These two equations were experimentally validated. We obtained a brightness of 2.05 × 108 A/cm2 sr using a beam energy and an emission current of 20 keV and 54 µA, respectively. Notably, this value surpasses the Langmuir limit of 4.11 × 105 A/cm2 sr by 499 times.
Highlights
We showed2 that for a convex cathode or curved trajectories, beams with brightness higher than the Langmuir limit were obtainable
The Langmuir limit, defined by Langmuir, was first obtained from1dI′ = I0AdA′ cos Θ/πr2, (1)where A is the emission area, r is the distance from A, and Θ is the angle between r and the optical axis
The ratios of maximum to minimum brightness were measured as 717, 403, and 310 for beam energies of 10 keV, 20 keV, and 30 keV, respectively. These results indicate that the brightness was not conserved when lens excitation was varied
Summary
We showed2 that for a convex cathode or curved trajectories, beams with brightness higher than the Langmuir limit were obtainable. The maximum brightness values for beam energies of 10 keV, 20 keV, and 30 keV were observed to be, respectively, 143, 208, and 92.1 times higher than the Langmuir limit, and these experiments were performed using a cathode with a large curvature.
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