The Importance of Accurate Computation of Secondary Electron Emission for Modeling Spacecraft Charging

Secondary electron emission is a critical contributor to the current balance in spacecraft charging. Spacecraft charging codes use a parameterized expression for the secondary electron yield δ(Eo) as a function of incident electron energy Eo. Simple 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 recall classical models for the range R(Eo): a power law expression of the form b1Eon1, and a more general empirical bi-exponential expression R(Eo) = b1Eo n1+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 d(Eo→∞)). In most models, the yield is the result of an integral along the path length of incident electrons. Special care must be taken when computing this integral. An improved fourth-order numerical method is presented and compared to the standard secondorder method. A critical step in accurately characterizing a particular spacecraft material is the determination of the model parameters in terms of the measured electron yield data. 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