Integral transport approach for molecular processes in inertial electrostatic devices

An inertial electrostatic device (IEC) consists of a chamber containing nearly transparent, concentric wire grids with a high voltage difference between them. Typical UW IEC experiments run at moderate pressures, ~0.3 Pa (~2 mtorr), so atomic and molecular processes can be important. Ions created in a source region pass through the anode grid primarily as an arbitrary mixture of D⁺, D₂ ⁺, and D₃ ⁺ ions and, while being accelerated radially by the electrostatic potential, interact with the background gas to produce a source of cold ions (D⁺ and D₂ ⁺) through interactions with the background D₂ gas. These cold ions are accelerated by the potential and produce additional cold ions through interactions with the background gas. A 1-D model for the effect of various molecular and atomic processes (charge exchange, ion impact ionization, and dissociative processes) between deuterium ions (D⁺, D₂ ⁺, and D₃ ⁺) and the background gas on the performance of spherical, gridded IEC devices has been developed. This formalism includes the bouncing motion of ions in the potential well and sums over all generations of cold ions. This leads to a set of coupled Volterra integral equations, which are solved numerically to yield the energy spectrum of the ion and fast neutral flux; the resulting neutron production rate is calculated. Recent improvements in the model, including non-zero ion birth velocities from dissociation reactions, will be discussed. Comparison with experimental data for the Wisconsin IEC devices will be presented.