Blackbody Radiation

  • #1
Even by taking low numbers for the surface area and emissivity of the plasma, the radiation would be extremely high due to high temepreatures in magnetic confinement fusion.

So how is blackbody radiation countered in magnetic confinement?

Answers and Replies

  • #2
Well the plasma is a highly ionized 'gas' so it is not like a solid blackbody radiator. The issue is EM radiation due to recombination and cyclotron radiation due to the fact that electrons are flying in all directions in a magnetic field. But basically, this energy is lost from the plasma and impinges on the first wall which is heated. Therefore the first wall and confinement chamber must be cooled. The heat can then be transferred to some type of energy recovery system or power conversion system, e.g. steam Rankine cycle. However the conversion efficiency of a Rankine cycle is likely to be low. On the other hand, recovering every little bit helps in the economics of a fusion power plant.

It might be possible to conceive of some photovoltaic system based on recent developements in carbon nanotubes at GE.

The other complication can be a hard neutron flux in the case of a fusion reaction such as DT which produces neutrons.
  • #3
Thank you.
  • #4
To answer your question you need to answer the following:
- for the temperatures considered (say 5 keV) what is the black body spectrum
- for the wavelength involved in this BB spectrum, is the plasma transparent or not ? (taking the size of the plasma into account, meters)
I guess that the plasma is transparent in these wavelength range, because the wavelength involved are very short.
Note however that such a plasma will not be transparent for all wavelength. Wave propagation in plasma is a rather complicated -but fascinating- subject.
A an application, several experimental techniques are used to measure plasma temperatures from its BB emission: electron-cyclotron radiation for example.
  • #5
additional comments

The densities of tokamak plasmas are typically around 10^20 m^-3.

These plasmas are very hot, fully ionised. But they are not very dense, something close to a technical vacuum. In addition, higher temperatures imply faster particles and reduced collisionality. Therefore, collisions between electrons are not very frequent, as compared to 'usual' materials. Conductivity is high and resistivity is low. For example, a tokamak plasma can typically sustain a 1 Mega-Amps current induced from a 1 Volt force (a few m² section and 20 m cirumference). The collisions have nearly no impact on wave propagation, specially at high frequencies. Therefore collisions, or resistivity of the plasma is not an efficient wave damping mechanism in tokamak plasmas, actually extremely negligible.

In addition, plasmas do not "perturb" much wave propagations as long as the wave frequencies are higher than the "plasma frequency". For the density considered in tokamaks, this corresponds to typically 100 GHZ. For a 5 keV plasma, the maximum emission for the black-body radiation would fall in the PETA-Herz range (PHz), the soft x-rays region. This frequency is 1 million times higher than the tokamak plasma frequency. In this range, and even well below, the electrons cannot "react" to the wave and just let it propagate, like in vacuum. There is no need to talk about the ions, which are >1000 times more heavy and really frozen at these frequencies.

The only remaining mechanism that may allow an high frequency electromagnetic wave to be absorbed is collision-less damping called "Landau damping". Electrons with a velocity close to the wave velocity can "surf" on the wave and trap energy from. But, since the wave is nearly not pertubed by the plasma, it propagates at the speed of the light. Therefore only electrons moving close to the speed of light in the wave direction could interact with the wave and steal some energy. These are called 'relativistic' electrons. It is easy to check that with a temperature of 5 keV, there are very few relativistic electrons in the Boltzman distribution. Therefore, the Landau damping is extremely small for waves above the plasma frequency.

Finally, if you remember that the emissivity is simply given by 1-exp(-a L), where a is the attenuation factor (m-1) and L the dimension of the plasma (m), you can easily understand that the emissivity above the plasma frequency is extremely small. Probably smaller than any value you had tried.

Below the plasma frequency things are more interesting, but also more complicated. There are numerous resonances where energy can be absorbed and therefore also emitted. Landau damping is again the main absorption mechanism.
An example is the electron-cyclotron resonance. It can be used to measure plasma temperature, when this resonnance occurs above the plasma frequency (harmonics can also be used). In tokamak plasma, the ECE emission (electron-cyclotron emission) are often emitted in the BB conditions. It is funny to note that ECE measuring devices are usually calibrated in laboratory by exposition to a oven at typically 1000°C which represents only 0.1 ev, at least 50000 times lower that the plasma temperature. The ECE detector are then coupled to a lock-in amplifier, otherwise they would not be able to detect temperatures as low as 1000°C.

Ions may also come in the play, like for ion-cyclotron waves. But a difference is that wavelengths are typically in the cm range or larger within the plasma, and the frequencies are rather low in the 100 MHz range. This is because the ion trajectories in tokamak magnetics fields are spirals with typical radius in the cm range. Their propagation is more difficult to analyse than ECE because of the magnetic field homogenities that play on a scale comparable to the wavelengths. In addition, in the vacuum the wavelengths are larger than meters. In principle these waves could offer a mean to measure ion temperatures. But this is on the border of feasibility and the interpretation is difficult because of the explained characteristics.

Finally note that there are radiations emitted from the plasma in the high frequency / transparency range of frequency. But the intensity is not given by the BB spectrum, because of the transparency (emitted radiations have no chance to get re-absorbed and thermodynamic equilibrium cannot be reached). For example, soft X-rays are actually emitted and are also used to measure plasma temperatures. The interpretation of these measurements is not based on the BB spectrum but on the individual particle emission theory combined with plasma density.
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