3 ms·
It's been difficult for me to visualize the 6D phase space of the design. I'm starting to see the particles lie on something like a deforming 4D shell that main
by pontifier 6y ago
It's been difficult for me to visualize the 6D phase space of the design. I'm starting to see the particles lie on something like a deforming 4D shell that maintains it's volume in 6 dimensions.
Edit (further description of the 4D shell under the Liouville theorem):
When the plasma has large spatial volume, the momentum of particles at any point creates a 1D line forming an empty 4D shell. When all particles enter the 1D spatial focus the particle velocities there are essentially random and have large variation in all 3 spatial dimensions. Essentially a 4D sphere with only 1 dimension in space.
The result is a morphing 4D shell that collapses all particles into a focus with 0 volume once per period.
- pontifier 6y agoActually... On further visualization the plasma seems to just form a 4D sphere that rotates and translates in 6 dimensions. The flatness of the 2 "missing" dimensions corresponds to the quality of the focus and synchronization of the system, so they are not going to ever be completely missing. The focus is like what you'd get if you were looking at slices of a solid ball. You'd see a point grow into a large circle, then shrink again to a point. It's basically the view on the left side of the simulation on my website. The right side of the simulation video shows a different cross section. The x axis there is the one dimension of the 4D sphere that stays in 3 space.