Secondary-electron emission effects in a 1D ELM model studied with Gkeyll

The 1D ELM heat pulse problem of Havl{\'i\v{c}kov\'a} et al (PPCF 54: 045002) is generalized to include secondary electron emission (SEE), an important factor since the secondary electron emission coefficient $\delta$ varies widely for different wall materials, ranging from $\delta <\sim 0.5$ for lithium to $\delta >1$ for standard high-$Z$ metals at large $T_e$. For moderate collisionality regimes, analysis and gyrokinetic simulation with the Gkeyll code show an enhancement of the electron heat flux by $\sim(1-\delta)^{-1}$, a large enhancement for $\delta$ approaching unity. In very collisionless regimes, this enhancement is reduced as secondary electrons escape the plasma before isotropizing in pitch angle.