A brightness exceeding simulated Langmuir limit

When an excitation of the first lens determines a beam is parallel beam, a brightness that is 100 times higher than Langmuir limit is measured experimentally, where Langmuir limits are estimated using a simulated axial cathode current density which is simulated based on a measured emission current. The measured brightness is comparable to Langmuir limit, when the lens excitation is such that an image position is slightly shorter than a lens position. Previously measured values of brightness for cathode apical radii of curvature 20, 60, 120, 240, and 480 μm were 8.7, 5.3, 3.3, 2.4, and 3.9 times higher than their corresponding Langmuir limits, respectively, in this experiment, the lens excitation was such that the lens and the image positions were 180 mm and 400 mm, respectively. From these measured brightness for three different lens excitation conditions, it is concluded that the brightness depends on the first lens excitation. For the electron gun operated in a space charge limited condition, some of the electrons emitted from the cathode are returned to the cathode without having crossed a virtual cathode. Therefore, method that assumes a Langmuir limit defining method using a Maxwellian distribution of electron velocities may need to be revised. For the condition in which the values of the exceeding the Langmuir limit are measured, the simulated trajectories of electrons that are emitted from the cathode do not cross the optical axis at the crossover, thus the law of sines may not be valid for high brightness electron beam systems