# Electron Energy Loss Spectroscopy and Surface Vibrations by H. Ibach

By H. Ibach

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83) small. For the same reason an extra high-current load of the monochromator, which may result in charging, should be avoided. Furthermore, the angular spread of the incoming beam may deteriorate at higher input currents. 2 without a substantial gain in the monochromatic current. Finally, the output current is a very broad function of the input current near the mathematical optimum. Therefore, by reducing the input current substantially, one looses only a small and technically unimportant amount of the monochromatic current.

When 2yR » s, an increase in the current density j0 simply leads to an linear increase in yR, so a smaller fraction of the electrons get through the entrance slit as the cathode brightness is increased. If one considers the case of laminar flow between two parallel plates, where the electrons are accelerated from zero kinetic energy to a fixed energy E, then a result similar to Eq. 44) is obtained, but with a prefactor smaller by a factor of 2/9. The pass current estimated from Eq. 44) is, at low kinetic energies, much smaller than the theoretical limit expected from the maximum emissity of the cathode.

In this chapter, we now carry the problem one step further to take into account the influence of space-charge effects on the transmission. We do this by a method that treats the space-charge effect as a first-order perturbation; by this term, we mean that for a given pair of conjugate trajectories of electrons with the pass energy E0, we calculate the effective space charge through use of the trajectory equations without space charge. In a second step, we study the influence ofthat space charge on the trajectory equations, and this finally allows us to calculate the transmission as a function of the input current.