Solar Furnace Suns Concentration

I'll be the first to admit that I'm moving into territory that I'm
unfamiliar with, and that extrapolating is a dangerous business.
What I'd like to see is how to bring 20 MW of energy into a
spherical chamber of about about 15 ft diameter.

I got these figures from an electric arc furnace of about similar
dimensions, and it is using that energy to melt steel scrap and
Directly reduced iron.

So for lack of any specific information, which I couldn't find on
the internet, I'm assuming comparability between an electric arc
furnace and a solar oven. At an energy density of 1,370
watts/meter^2, and using the surface area of half a sphere as an
approximation of the surface area of a parabola (My calculus is too
rusty to figure out the parabola area question - anyone want to give
it a try) I've figured out that I'd need a dish of diameter of 300
feet, to concentrate 20 MW of power, which I believe is around
15,000 suns.

Now that's a whole lot of honking energy, and this facility isn't
floating in space, so I can't put the chamber oven at the focal
point of the dish - therefore, the energy has to be transported to
the oven, without melting the tunnel it's going through. I'm
envisioning the dish being on the roof and tracking the sun during
the lunar day. The oven would be in the smelting facility, so the
energy beam would need to be directed ~ 90 degrees down into the
tunnel at lunar sunrise and sunset.

Can anybody correct the flaws in my logic, math, or science please.
Don't completely rewrite the scenario. I want to place 136,000 lbs
into the chamber, which is roughly 782 ft^3 of regolith. I want to
process that in one hour.

What would a better design be to accomplish the material handling
requirements of this solar oven?

> 15,000 suns, as you are using it is ambiguous. At the distance of
Earth,
> the Sun delivers what is called the solar constant, 1360 watts per
meter
> squared. A large mirror could focus the energy to raise it to
much higher
> values, but the temperature would be ~ 6,000 K max. No known
material
> remains solid (or liquid or gaseous) at that temperature, but
becomes a
> plasma (ionized). I don't know if this helps or not. Sincerely,
Jay
> Huebner
>
> Is it possible to direct a beam of 15,000 suns from the focal
point
> of a parabolic mirror down a path into a furnace chamber?
>
> I know the easiest solution is to have the focal point be right in
> the furnace chamber but I'm trying to look at the issue of the
> layout of a materials processing facility and it would be easier
to
> design the workflow if the beam could be channeled into the
furnace.