Integrodifferential models of electron transport for negative ion sources

Abstract

Thanks to the presence of a transverse magnetic flux density ($B_{x}$ and $B_{y}$ where $z$ is the extraction axis), the undesired extraction of electrons from a negative ion source is reduced and it is due to collisions. The electron transport is studied with a kinetic model, including Vlasov–Poisson effects and atomic collisions. The integrodifferential equations (IDE) resulting from a reduction to a one-dimensional problem (1-D) by integration on characteristic orbits are strongly affected by the trapped orbits, as here evaluated; a kernel calculation with a partial wave approximation is introduced. Dependencies from the local drift velocity $v_{d}$ and effective Larmor radius $L_{e}$ are found. Solutions are investigated in simple cases with a constant electron current (no additional electron production). Equilibrium solution and electron conductivity are analytically obtained. Presheath solutions are discussed; the approximated conversion to differential equations that are adequate for presheath only (with moderated electric field gradient $E_{z,z}>-eB_{x}^{2}/m$) and their numeric solutions coupled to Poisson equation are reported, and compared to iterative IDE solutions. Examples with different values of $L_{e}$ and mean free path (mfp) ratio are described.