Ions that are moved by electric fields in gases follow quite exactly the electric field lines since these ions have substantially lost their kinetic energies in collisions with gas atoms or molecules and so carry no momenta. Shaping the electric fields appropriately the phase space such ion beams occupy can be reduced and correspondingly the ion density of beams be increased.
IntroductionIon clouds can be shaped by electric fields only in so far as is allowed by Liouville's theorem [1], which states that the magnitude of the phase space occupied by an ion beam, which moves in vacuum, can not be changed. Ion beams that move in gases do not have this limitation, since they move substantially along electric field lines between collisions with gas atoms or molecules. However, ion clouds that move in gases increase their volumes over time by diffusion, so that the clouds' lateral and longitudinal dimensions increase with the square root of time. Consequently, ion beams cannot easily be focused to fine points, but wide ion beams can be transformed to narrow ones with increased ion densities.