Physics puzzle: A 1 radius 7 billion K temp. ball is activated inside Jupiter

[jcarper]

Physics puzzle: A 1" radius 7 billion K temp. ball is activated inside Jupiter...

Physics puzzle:

A 1" radius, 7 billion K temp. fireball is activated inside Jupiter...from an artificially induced fission reaction of .04kt. It is activated deep enough into Jupiter to be under 40,000,000 bars pressure, let's assume at 90% depth near the center in the midst of liquid metallic hydrogen, just outside the ammonia, methane, water-ice shell surrounding the nickel-iron core.

Assume a temporary fusion reaction takes place. (Is this possible?) Does it "blow-out of" the planet or does is "blow up" the planet?

What are the implications?

 

[Drakkith]

Have you tried running the numbers and seeing how the fusion would occur?

 

[qraal]

7 billion K from fission? Don't think so.

 

[jcarper]

I don't have the knowledge to run the fusion calcs. However, think about Nagasaki for instance. In 1-millionth of a sec temps exceeded 10 million degrees, this was considering a reaction that exceeded 5 billion bars at detonation and went into 1 bar territory. It took only 1millionth of a sec for a small percentage of fissioned material of 1.2kg (of of 7) to do 22kt detonation. (in this small amount of time the hold pressure was overcome).

Now consider the hold pressure of our scenario under 40 million bars, the containment time is tremendous and could easily surpass 1 billion K using only .04kt with 100% fission rate.

Also, compare a fusion ball of the sun's inner 30%. It has an enormous volume to surface area ratio of about 70,000 to 1. Our theoretical fusion ball has a beginning ratio of far below .33 to 1. This ratio helps HOLD IN the fusion reaction and therefore would require much fewer bars of pressure to hold it than originally estimated. ?

 

[qraal]

I don't have the knowledge to run the fusion calcs. However, think about Nagasaki for instance. In 1-millionth of a sec temps exceeded 10 million degrees, this was considering a reaction that exceeded 5 billion bars at detonation and went into 1 bar territory. It took only 1millionth of a sec for a small percentage of fissioned material of 1.2kg (of of 7) to do 22kt detonation. (in this small amount of time the hold pressure was overcome).

Now consider the hold pressure of our scenario under 40 million bars, the containment time is tremendous and could easily surpass 1 billion K using only .04kt with 100% fission rate.

Also, compare a fusion ball of the sun's inner 30%. It has an enormous volume to surface area ratio of about 70,000 to 1. Our theoretical fusion ball has a beginning ratio of far below .33 to 1. This ratio helps HOLD IN the fusion reaction and therefore would require much fewer bars of pressure to hold it than originally estimated. ?

I was wrong when I said fission couldn't reach ~7 billion K. In raw kinetic terms the fission products have a temperature of ~2.5 trillion K, but that doesn't last. Collisions with the rest of the unfissioned mass will "cool it down" i.e. share the energy. Question is just how long any fusion conditions generated would last, how much fusion would occur and whether that would start a fusion burn-wave, thus producing a detonation. The real problem is what kind of fusion fuels can reasonably be expected inside Jupiter. The core is probably convective and well mixed, so the easiest fusing deuterium won't be available in high concentration. A fission detonation is thus unlikely to trigger a burn.

 

[Drakkith]

As qraal said, the products cool off quickly. The pressure in the core isn't nearly high enough to cause enough of a fusion reaction to sustain it against the cooling of the explosion as it propagates outward.