Low temperature high current ion beams and laminar flows

Abstract

Self-consistent Vlasov-Poisson equilibria for the extraction of ions with low temperature T i are discussed, with comparison to the laminar flow case T i = 0, in two dimensional diodes. Curvilinear coordinates aligned with laminar beam flow lines are extended to the low ion temperature case, with a reduced current density j d , expressed with cathode integrals. This generalizes one-dimensional interpolation between rays along the cathode coordinate to multidimensional integrations, including also the momentum components, so that j d is free from the granularity defect and noise, typical of standard ray tracing approach. A robust numerical solution procedure is developed, which allows studying current saturated extraction and drift tube effects. A discussion of particle initial conditions determines the emission angles and shows that temperature effect at beam edge is partly balanced by the focus electrode inclination. Results for a typical diode are described, with detail about normalized emittance, here taken strictly proportional to the x − p x phase space area, for a beam with non uniform velocities.