Power Density of the Sun's Core.

[valleysheep]

Hi guys,

I've recently stumbled on an interesting article highlighting a point by james jean that a pinhead of 1mm (I took this to mean that it was a box of 1mm sides so 1E-9m³ volume) heated to 15 million kelvin, sun's core, could kill a person 84 miles away.

I tried working this out using stefan-boltzmann's law of [itex]\sigma[/itex]T^4 then an inverse square law. It seemed like a sensible working coming to an answer of ~400,000 W/m² at the point the person is standing (84 miles away). This is all assuming a vacuum. As a side point would it still happen if it wasn't a vacuum ?

I have also read that the power density of the sun is 276.5W/m³ at the sun's core, which sort of throws a wrench in the plan.

So i guess i am missing something here which is why i need some help :P.

My last concern is that if we were to harness fusion power by what ever means, magnetic containment etc) wouldn't the temperatures reached cause massive damage to the surround area. I first thought that the entire surrounding would absorb the radiated heat.

Thanks for your time in advance. I also apologise for any incredibly poor physics used in this post.

 

[Bill_K]

You're comparing two quite different things. What you calculated is the thermal energy density, which the sun's core has simply by virtue of being hot. This stays pretty much where it is. The second number, 276.5W/m³, is the power generated by the fusion of hydrogen to helium. This is what must eventually escape the sun's surface.

 

[valleysheep]

Right ok.

What temperatures would a reactor reach such as the JET project ? Can't seem to find this anywhere.

 

[mfb]

The pinhead would kill you, if it keeps its temperature for more than some microseconds with magic.

As a side point would it still happen if it wasn't a vacuum ?

keV X-rays and air... we would need the absorption coefficient.

What temperatures would a reactor reach such as the JET project ?

Of the order of 100 million K. Fusion experiments cannot reach the pressure (and therefore density) of stars and ~100W/m^3 would be a poor fusion yield, therefore those disadvantages are compensated with a higher temperature. Luckily the plasma is not a dense black body with that temperature, so the emitted radiation power is not too high.

 

[valleysheep]

How exactly does the plasma differ from that plasma within the star ? I am guessing as you've stated the density would be different. Also why wouldn't the 100million K temperature not just destroy the surroundings ? (I suppose i should look up a more in depth layout of the reactor to see the size of the actual plasma rings etc)

 

[Astronuc]

Right ok.

What temperatures would a reactor reach such as the JET project ? Can't seem to find this anywhere.

Interestingly the Culham site does not provide JET's plasma parameters with respect to temperature. There is one paper that discusses some initial results with an electron temperature of about 5 keV (~5.8 million K) and an ion temperature of 3 keV (~1.75 million K), which is rather cold, and average electron densities of 1 to 4 E19 /m³.

The site does report on their MAST spherical tokamak, which has had temperatures of about 23 million K with a particle density of about 1 E20 /m³.
http://www.ccfe.ac.uk/MAST.aspx

The target for ITER is apparently 100 million K.

The European Fusion Development Agency has or had a website that gave some background on JET and ITER. The site may have been replaced by the site for Fusion for Energy.

http://fusionforenergy.europa.eu/understandingfusion/

The temperature at the center of the sun is about 15 million K, but the density (and pressure) is orders of magntides greater than those that can be achieved with terrestrial plasmas. The limits are due to limits on magnetic field strength and strength of structural materials.
http://fusionforenergy.europa.eu/understandingfusion/

The particle densities of terrestrial plasmas are on the order of 1E19 to 1E20 /m³, while hydrogen densities in the sun and similar stars are on the order of 160000 kg/m³ or particle densities on the order of 1E32 /m³ resulting in pressures on the order of 340 billion atm (1 atm = pressure of Earth's atmosphere at sea level).
http://fusedweb.llnl.gov/cpep/chart_pages/5.plasmas/sunlayers.html
http://solarscience.msfc.nasa.gov/interior.shtml
http://image.gsfc.nasa.gov/poetry/ask/a11354.html

The power radiating from the plasma can be handled by high temperature materials. It is the fact that the densities of terrestrial plasmas are so low that the thermal burden on the first wall is limited to several 100s K.

 

[valleysheep]

Ahhhh awesome, thanks for the final explanation astronuc and for the links. Thanks to Bill_K and mfb as well. Problem solved :P.