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Lets say we have 1 gram of plasma (Argon) at 1 million kelvin confined in a vacuum with electromagnets. If we keep the magnets on but shut down the device that heated the plasma, how long will it take for it to cool off?

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One rough way that comes to mind would be to calculate radiated power according to the Stefan-Boltzmann law, assuming that the plasma is so dense it radiates as black body. –  Ján Lalinský Aug 22 '14 at 6:55

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Since your plasma is in a vacuum environment, the only way for it to loose energy is by radiation (conduction transfer through the magnets are neglected). You have thus to consider which bodies are surrounding your plasma and which radiative model is the best ton consider for them. I guess you can consider a black body with the simple Stefan equation.

The most common model is the NEC (net emission coefficient). Take a look at this article chich describes quite precisely the Argon plasma radiation exchange. With the NEC and P1 model you can take in account the emitted power and the absorbed energy by the plasma itself.

Once you get the power emitted by the plasma, I think you just have to integrate the energy balance equation to get the amount of energy lost over the time. Then you have to consider the temperature evolution of this plasma, and figure out when it actually stop existing (its temperature equals surrounding temperature? I don't know...). This can be quite tough because the temperature field isn't uniform (but maybe you can start with a uniform one to get first results).

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Thanks! Although I was hoping for an approximation. "The plasma may last 30 min" for example. :D –  Pema Aug 22 '14 at 9:05
Sorry I just realized this article is in french... If I get an idea of the duration I'll tell you by the day. –  Nicolas Berteloot Aug 22 '14 at 9:20

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