Reply To: Where are Japan and China in funding Focus?

[Steve Ivy]

“the slight asymmetry would introduce Rayleigh-Talyor like instabilities way before the compressive wave could reach the centre. So peak density & temperature would be far lower than needed.”

James, I did quite a bit of reading before on Rayleigh-Talyor instabilities (and I just did a quick review today on them) and whatever might be the limiting factor here I
really don’t think Rayleigh-Taylor would be the problem.

http://en.wikipedia.org/wiki/Rayleigh–Taylor_instability

I quote…

“Rayleigh–Taylor instability,is an instability of an interface between two fluids of different densities, which occurs when the lighter fluid is pushing the heavier “fluid.[1]”

You see in the case of a converging spherical shock wave the higher density material takes the form of an ever denser shell that is approaching a much less dense center. It is dense pushing sparse, not sparse pushing dense, hence it is not a problem (or at least it’s not a RT problem.)

Picture the situation some few pico-seconds before the shock-wave reaches the center…

Here I have made a formula as a sketch that explains the basic sort of density distribution I expect with respect to radius
This is a decent on line function plotter… http://rechneronline.de/function-graphs/

10*(1/(x-10)^2)*sin(3x)+3
With x-axis set to (-10 to 0) and with y-axis set to (-25 to 25)

I am assuming the following for the purposes of the illustration

1) Initial density of the material is “3”
Trace = density as a function of of distance from the center at r=0 some point in time after the system has already reached a steady oscillatory state.

So this is a snapshot of the approaching pressure wave/high density wave after the steady state oscillation has been established so the density at the center will rapidly swing back and forth between a very sparse and cold minimum and a very hot and dense maximum.

Since there really isn’t much material in the center there really isn’t much of anything to push back against the approaching high density shock wave.

You might say that if there isn’t anything there there will not be anything to fuse?

I concede that.

But I say the area that really should interest us is not the exact center of the sphere but rather that small bit of material on the leading edge of the traveling wave, like a surfer riding riding in on a giant wave that is forced through a narrowing inlet between cliffs and who is rising rapidly (and is speeding up dramatically) because the wave he is riding has no place to go but up.

You mention that just increasing the sphere’s diameter will not help presumably because it would make the system resonant frequency lower and thus there would be a slower change in pressure at the center allowing what instabilities there are more time to do their damage.

As I mentioned (I believe the wave velocity at the center is not a constant related to the diameter of the sphere) but instead is a variable and it effectively limited only to the amount of stored momentum in the system. So a small sphere with a very high mechanical Q could match a large one with a low Q but a large one with a large Q would be the most interesting case.

Using the case of sonoluminescence, you would have a converging wave in a liquid with a bubble of vapor in the center.

In my example you could have anything (solid, liquid, gas, plasma) but for ease just imagine it is a gas for the moment and then consider plasmas (both charged and
neutral ones next.)

Such a system would see a wave that would have made it a very thin gas at one instant just before the next approaching wave reaches the center. It’s like the
sonoluminescence case but I think much more stable because you get rid of that annoying dancing bubble of aspherical gas floating in the center trying to rise up
due to it’s buoyancy.

“jamesr” said…

“If it were that simple, the spherical implosive method of detonating plutonium bombs, would also work for fusion. To ignite a fusion burn wave at the centre of a
spherically compressed volume you need the compression, heating and ignition to occur faster than any of the instabilities have time to develop. The instability grows
exponentially in time, but is proportional to the size of the initial perturbation. Or in other words your large sphere being driven at the outside would have generate a
spherical wave front perfect to less than one atom width.”

James, I don’t think even the best H-Bombs achieved that level of precision. I don’t think you make a case that it is necessary.

“By increasing the size of the sphere to increase the ratio of driving oscillation to proposed peak oscillation in the centre, the wave takes longer to reach the centre and so reduces the tolerance on the spherical accuracy. The exponential growth of the instability will always be faster then the cubic growth in geometric scaling.”

As addressed earlier, I believe the bounding factor on center speed is not system diameter but rather system momentum. Spherical asymmetries are a real concern
but I think manageable ones. Trick is to drive the wall evenly!

“On the other hand if by some miracle you could get it to work – having that much fusionable fuel in a sphere would make a very big bomb.”

Now there you are touching on something I ponder upon with some real apprehension!

There probably is a maximum size beyond which this system might become a bomb which is why I propose that experts study it rather than simply having amateurs
build it. It might not be safe!!!

Beyond that I know it might seem ludicrous, but I am worried that it might even be possible that such a system (made suitably large and effective) could start producing little molecular sized chunks of neutronium or even black holes after each compression and that they might fall to the center of the earth and there begin
to coalescent into something of real concern.

Thanks – Steve