The "projectile" being accelerated in a plasma coaxial railgun is a complex mixture: besides plasma, it contains solid particles of fuse, liquid and vapor metal. Materials accelerated are not limited to the fuse metal, the rail material through ablation also contributes to them. For such a situation "plasma focusing" is a simplified term, borrowed from electron beams in vacuum technology (and electron lenses) where the Busch's theorem describes the tendency of electrons to approach the axis (or to focus) in the presence of radial and axial components of magnetic fields and under the assumption that on the time scale of interest, the ions remain essentially motionless. The present work is the first in a series of papers trying to classify and to explain a larger spectrum of problems affecting a mixture of metals in different states (solid, liquid, and vapor) in which magnetic fields, transient diffusion, and other phenomena may be used to contain or focus a flowing stream under thermal expansion. The main variable used in experiments to affect the focusing was the topology of magnetic fields, temporal and spatial. Emphasis was given to the effects of penetration of magnetic field in the bulk of the "projectile" being accelerated. Experiments were conducted on a 0.5-m coaxial railgun with inner and outer coaxial radii of 0.25 and 0.31 in., respectively. The rails were constructed from stock sizes of copper pipe with a CVD tungsten coating on the inner rail surface to minimize arc damage during the shots. External magnetic fields were applied to a 3-mg metallic vapor arc accelerated with a 250 kA capacitive discharge. Plasma characteristics were measured with magnetic pick-up coils and langmuir probes. Confinement and focusing of the arc was examined with break screens and metal deposition analysis.