Importance of Accurate Computation of Secondary Electron Emission for ModelingSpacecraft Charging
The secondary electron yield is a critical process in establishing the charge balance in spacecraft charging and the subsequent determination of the equilibrium potential. Spacecraft charging codes use a parameterized expression for the secondary electron yield δ(Eo) as a function of incident electron energy, Eo. A critical step in accurately characterizing a particular spacecraft material is establishing the most efficient and accurate way to determine the fitting parameters in terms of the measured electron yield data and physics-based theoretical models. Simple two- or three- step physics models of the electron penetration, transport and emission from a solid are typically expressed in terms of the incident electron penetration depth at normal incidence or range R(Eo), and the mean free path of the secondary electron, λ(E). We review the models for δ(Eo) derived from various forms of the range expression R(Eo), including the Sternglass model based on the Bethe expression for the stopping power R= λ(Eo)~Eo/ln(Eo), several power law expressions of the form R(Eo)=b1Eon1 with different n1, and a more general empirical bi- exponential expression R(Eo)=b1Eon1+b2Eon2. Expressions are developed that relate the theoretical fitting parameters (λ, b1, b2, n1 and n2) to experimental terms (the energy Emax at the maximum secondary electron yield δmax, the first and second crossover energies E1 and E2, and the asymptotic limits for δ(Eo→∞)). In most models, the yield is the result of an integral along the path length of incident electrons. Special care must be taken in computing this integral. An improved fourth-order numerical method is presented, and its effectiveness is shown to be a significant improvement as compared to standard second- order methods. The fitting procedures and range models are applied to several measured data sets to compare their effectiveness in modeling the function δ(Eo) over the full range of incident energies, and in particular for determining crossover energies and critical temperatures.
Sébastien Clerc and JR Dennison, “Importance of Accurate Computation of Secondary Electron Emission for ModelingSpacecraft Charging,” Proceedings of the 9th Spacecraft Charging Technology Conference, (Epochal Tsukuba, Tsukuba,April 4-8, 2005), 8 pp.