How do the atoms and electrons move around space when the solar core presses them into a dense plasma? It takes a lot of intelligence to compute the center of the sun. As far as I imagine, it's compressed by the hand of gravity and high energy fusion radiation wants to escape one way or the other. Perhaps there are convective forces, perhaps the protons and the neutrons get knocked around at millions of meters per second. Do fusion generator researchers have a considerable body of work for the micro and macro measurements of the material? Can you give me an idea of what happens there to the various elements?
 A: 
Perhaps there are convective forces, perhaps the protons and the
neutrons get knocked around at millions of meters per second

At the densities seen in the sun, the mean free path of these particles is tiny. They continually collide with other particles. It takes about 100,000 years for a photon to get out of the core of the sun.
In contrast, fusion devices here on Earth typically work at the density of a pretty good vacuum. In these situations, the particles are free to move about. In fact, that's the main problem, they would typically leave the plasma and not react. This is the purpose of the huge magnets seen on most fusion designs, which keep the charged particles inside the reactor long enough to undergo a fusion reaction.
The alternative solution is the NIF approach, which compresses the fuel to even greater densities than the sun, about ten times. In this case, the resulting fuel mass is tiny, so while the particles within are acting similar to those inside the sun and colliding all the time, they're only travelling a few micrometers before they get to the edge of the fuel.
Current computing power allows us to simulate only a toy model of these systems, but it continues to improve. Someday I expect we'll be able to model this down to the individual electrons.
