The goal of "the Octavio" is to create a virtual cathode without consuming a lot of power.
Ideally it would have the same effect as the polywell, but with less electrons hitting the magrid and without needing enormous currents through the coils.
Why do the coils in the polywell need to carry such a high current?
Because in the polywell the magnetic fields of the opposite coils are canceling each other, electrons are not always hitting the grid because of a magnetic field very close to the grid, the rest of the magnetic field is canceled, it works but it is very inefficient. For "the real thing" big and superconducting coils are needed, if that would be enough.
So I started to think about a configuration where there is no direct cancellation of magnetic fields.
When using six coils in a cube like configuration like the polywell, there will always be asymmetry if the magnetic fields are not canceling each other.
After thinking about all kinds of configurations, hallbach spheres, doughnut shaped configurations etc, the conclusion was that the most simple symmetric configuration where there is no direct cancellation of magnetic fields is the octahedron.
You can see a drawing of a spherical octahedron with the direction of the currents on the top-left of this blog.
Just like the polywell it will be at a high positive electric potential and surrounded by electron guns (8 for the octavio), the electrons entering the Octavio core should create a virtual cathode in the center.
The following picture shows the direction of the magnetic fields, in the center of the core the magnetic field is zero:
So why did he not try it?
I don't know why Bussard didn't try such a configuration, but I think that the "Octavio core" alone would not create a virtual cathode.
When electrons travel from the electron guns through the sphere triangles of the core, the magnetic field is the strongest at the center of the sphere triangles of the core. It could be strong enough to create beam focusing. Strong enough to make the electrons "follow" the field lines (actually they a spiraling around the field lines, but if the magnetic field is strong enough, the spiral radius is small enough to think of it as electrons "following" the field lines).
If you imagine the magnetic field lines, you can see that the beam would diverge near the center and focus again when traveling past the center. Maybe this could still create a virtual cathode. However, the field lines are diverging in the outward direction outside the core, so electrons would start circling around the wires of the grid when they leave the core. Also, electrons will loose energy when they change direction or when the are spiraling (brehmsstrahlung) and when they slow down their orbital radius around the magrid coil wires will become smaller, until they hit the grid, effectively creating a substantial negative space charge which will cancel the electric field created by the virtual cathode.
When I have build the core, I will measure the effect of magnetic fields on the grid current, but unless I'm completely wrong (which is quite possible) there won't be any useful virtual cathode with only the core.
PS: Because the core is made of 8 sphere triangles it's called the "Octavio", the name was taken from the book "The Light Fantastic" by Terry Pratchett, in which the Octavio is a book with 8 spells.