Generating particle beams of controlled dimensions and divergence: I. Theory of particle motion in aerodynamic lenses and nozzle expansions

A particle beam is produced when a particle-laden gas expands through a nozzle into a vacuum. This work discusses the theoretical basis of a novel method for producing highly collimated and tightly focused particle beams. The approach is to pass the particle-laden gas through a series of axisymmetric contractions and enlargements (so-called aerodynamic lenses) before the nozzle expansion. Particles are moved closer to the axis by a lens if the particle sizes are less than a critical value and particles can be confined very closely to the axis by using multiple lenses in series. Since particles close to the axis experience small radial drag forces, they stay close to the axis during nozzle expansion and therefore form a narrow particle beam downstream. The major effects that limit the minimum beam width are Brownian motion and lift forces on particles during the nozzle expansion. Simple theoretical models are developed in this work to estimate the minimum particle beam width set by these effects. While the Brownian-motion effects occur for all types of particles, the lift-force effects only occur for nonspherical particles but are often much greater than the Brownian-motion effects.