Shown below are three early animated gif results from a simulation of ion beam formation at the end of a plasma column. The plasma is confined in a cylindrical opening in the conducting wall of a plasma chamber. Beam is extracted by the strong electric field of an adjacent grounded "puller" electrode (not shown). The extraction potential is made visible by a family of equipotential surfaces (9.5, 9.0 ..) kV spacing. The wall of the hole is at 10 keV.

The total charge density is displayed by a false color plot, with logarithmic scale (a factor e between colors: magenta = 10.0, blue = 3.7, cyan = 1.35, ..).

The top plot has the plasma electrons switched off. A sequence of increasing proton beam densities is shown, doubling between frames (2, 4, .. 256). The ion path is shown by tracking 24 rays from left to right. Ions have zero temperature and are launched from the left at 20 eV kinetic energy. The number of rays surviving is shown upper right, all 24 at density 2, falling to 7 at density 256 (arbitrary units).

Note the rapid drop in density as ions accelerate in the extraction field. The beam is so sharply focussed by the extraction field at low density that the density change in initial acceleration is masked. Space charge blowup drives a portion of the beam into the wall at all but the lowest density. The position (axis left is at -86, 0), value of the highest potential, and the density there (relative to a maximum of 10) are shown. The potential on the hole axis at the left is seen to grow to 770 eV and is not linear in density.

When electrons are added (kT = 20 eV), a nearly neutral plasma forms near the region of highest potential. This plot has proton density of 75, and the e/p fraction at the highest potential point of 96%. The sequence shows oscillation in the shape of the end of the plasma column as self-consistency is approached by Vlasov iteration. The plasma potential in this example is 93 eV, and the electron density at the wall is about 10% of the highest density on axis.

In the final example, the ion density is fixed at 256, and the electron fraction is gradually increased from 0 to 98.8%. The plasma potential fall from 770 eV to 150 eV, and the plasma extrudes into the hole. Note the shape of the end of the plasma column and the sheath formation which buffers the plasma electrons from the wall. Note also that the proton beam maintains fairly uniform density profile throughout the sequence, while tripling in intensity as the number of rays surviving grows from 7 to 12.

The final 8 frames, 4 at 98.4% and 4 at 98.8% show stages in the Vlasov iteration. The position of the end of the plasma column in unstable at this high ion density as there is a region of negative dEz/dz.