Secondary electron emission under magnetic constraint: from Monte Carlo simulations to analytical solution

Abstract

The secondary electron emission process is essential for the optimal operation of a wide range of applications, including fusion reactors, high-energy accelerators, or spacecraft. The process can be influenced and controlled by the use of a magnetic field. An analytical solution is proposed to describe the secondary electron emission process in an oblique magnetic field. It was derived from Monte Carlo simulations. The analytical formula captures the influence of the magnetic field magnitude and tilt, electron emission energy, electron reflection on the surface, and electric field intensity on the secondary emission process. The last two parameters increase the effective emission while the others act the opposite. The electric field effect is equivalent to a reduction of the magnetic field tilt. A very good agreement is shown between the analytical and numerical results for a wide range of parameters. The analytical solution is a convenient tool for the theoretical study and design of magnetically assisted applications, providing realistic input for subsequent simulations.

Comment on “Effects of an oblique magnetic field on sheath formation in the presence of electron emission”

“…The same dependence has been calculated using a Monte Carlo simulation (Figure 3b in ref. [2]). While the curve corresponding to cosine angular distribution is identical in the two papers, the two curves supposed to correspond to the same isotropic distribution are different.…”

“…For comparison, the three curves are plotted in Figure 1: 1—cosine, the same curve in both refs. [1,2], 2—isotropic in ref. [2], and 3—isotropic in ref.…”

“…Reduction rate of the secondary electron inflow α as a function of the magnetic field angle θ B for three angular distributions: 1—cosine (the same curve in both refs. [1,2]), 2—isotropic in ref. [2], and 3—isotropic in ref.…”

“…Since curve 1 is the same in both refs. [1,2], it means that the cosine angular distribution has been identically defined in the two articles. The difference between the curves 2 and 3 comes from the improper definition of the isotropic angular distribution in ref.…”

“…Returning to Figure 1, the difference between the curves 2 and 3 is that the isotropic distribution in ref. [2] has been defined with respect to the solid angle (correct isotropic distribution) while in ref. [1] it has been defined with respect to the polar angle (false isotropic distribution).…”