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Turbulence phenomena in plasmas   

Do not go away with the idea that plasmas are calm environments. Under the influence of electromagnetic field fluctuations, everything moves around inside, a bit like water bubbling to boiling point.


We have seen that the proper working of a thermonuclear reactor requires that the plasma interior be very hot and dense (see Lawson criterion). Strong gradients (the difference between the centre and the edge) of temperature and density are thus developed.

We can show theoretically and experimentally that by increasing the gradients, we increase the level of the electromagnetic field fluctuations way beyond usual the values that one would observe if the plasma were in thermal equilibrium.

This is a very common phenomenon, which one can observe in fluids in everyday life. If we start to heat water on a stove, we can see the convective motion that appears shortly afterwards. By increasing the heat, this motion becomes gradually more and more violent and irregular. We talk in terms of turbulence.

The effect of turbulence, in plasmas as well as in water, is the increase of matter and energy transport. In the operating conditions of the tokamaks, the combined effect of electric and magnetic fields fluctuations is the cause of "anomalous" transport. The fluctuating electric field gives rise to amplification of particle movement across field lines. The magnetic fluctuations cause distortion in the field lines. The  energy and matter losses are associated with particles, which move freely along field lines.

The films opposite clearly show fluctuations in the electric field obtained by numerically solving the equations governing turbulent dynamics. We can clearly observe in frame (a) the continuous formation and destruction of vortexes. Frame (b) shows the corresponding level of temperature. You can see the plumes of hot plasma coming out and cold plumes going in. This is an example of the mechanism of abnormal transport.

The use of very powerful computers to solve  plasma dynamics equations is a very active domain of research, with applications in meteorology for example.


Watch the film "Density evolution" (mpg, 2723 kb)
Watch the film "Density evolution" (mpg, 2723 kb)Watch the film "Density evolution" (mpg, 2723 kb)


Watch the film "Potential fluctuation" (mpg, 1759 kb)
Watch the film "Potential fluctuation" (mpg, 1759 kb)Watch the film "Potential fluctuation" (mpg, 1759 kb)


Watch the film "Pressure evolution" (mpg, 2193 kb)
Watch the film "Pressure evolution" (mpg, 2193 kb)Watch the film "Pressure evolution" (mpg, 2193 kb)
We can see heat losses caused by turbulence

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