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## Main Question or Discussion Point

I'm interested in the general topic of the luminosity of plasmas. I would expect that this topic would come up most often in astrophysics, so that's where I'm posting the question as to get the best shot at getting an answer.

I'm interested in applying the information in a rather unusual way, though. Basically, I want to be able to guess within 1-2 orders of magnitude the amount of heat radiated by hypothetical ultra-high temperature, thrust, and ISP rocket exhausts.

The most reasonable exhausts would probably

a) pure hydrogen

b) "fusion exhaust" (the exact composition could vary, though all variants would include helium).

So if I knew some thermodynamic quantities like pressure and temperature, is there any reasonably simple way to roughly (1-2 orders of magnitude) figure out the rate at which the plasma would lose energy?

Black body laws gives me radiated power as the fourth power of the temperature, but I'm pretty sure this is not a sufficiently good approximation, that real plasmas will radiate a lot less.

If the radiated power went as the 4th power temperature , and since ISP should scale as sqrt(temperature) for a simple rocket, every doubling of the ISP would increase the cooling problem by a factor of 2^8 = 256.

However, while the black-body approximation is simple, I don't think it's reasonable.

I'm interested in applying the information in a rather unusual way, though. Basically, I want to be able to guess within 1-2 orders of magnitude the amount of heat radiated by hypothetical ultra-high temperature, thrust, and ISP rocket exhausts.

The most reasonable exhausts would probably

a) pure hydrogen

b) "fusion exhaust" (the exact composition could vary, though all variants would include helium).

So if I knew some thermodynamic quantities like pressure and temperature, is there any reasonably simple way to roughly (1-2 orders of magnitude) figure out the rate at which the plasma would lose energy?

Black body laws gives me radiated power as the fourth power of the temperature, but I'm pretty sure this is not a sufficiently good approximation, that real plasmas will radiate a lot less.

If the radiated power went as the 4th power temperature , and since ISP should scale as sqrt(temperature) for a simple rocket, every doubling of the ISP would increase the cooling problem by a factor of 2^8 = 256.

However, while the black-body approximation is simple, I don't think it's reasonable.