Hey, I was searching terms related to a similar idea and came across this post.
Steve, I think you are on to something here. I had a similar concept (though smaller in scale) that I have been toying with for the past ten years. It is nice to see someone else exploring the concept of a spherical compression wave collapsing towards the centroid.
A couple points though…
A smaller sphere will have a higher resonant frequency, which means a higher pressure wave amplitude from the initial displacement.
Using the Ideal Gas Law (specifically the molecular adaptation) you can calculate the temperature from isentropic compression at the peak pressure as the wave travels towards the centroid. When that temperature passes the threshold for fusion, that is the active region of the device. The confinement time can be taken as the amount of time a particle with that much kinetic energy will take to cross the active region. Density can be cross-checked at the same time with the IGL.
One thing to remember is that we cannot just assume that the macroscopic image of a wavefront is accurate, we need to consider the brownian motion of the particles themselves, traveling in a direction generally towards the centroid, but still bouncing against each other as the wave collapses.
The actual resonant frequency of the sphere will have to be experimentally determined, as the conditions at the pressure wave vary so greatly as the temperature and density rises that calculating it precisely will be difficult.
I did the relevant math at one time to calculate the active region for a small sphere with a pure hydrogen fuel gas, but due to a computer error I lost the final version. One of these days I will revisit the draft I have and try to re-locate the mathematic errors I know are there and re-write the whole thing.
Maybe by discussing our 2 concepts and their similarities and differences we can get a better mental handle on the physics involved.
Merlyn_x
Magical Engineer and Technical Metaphysicist