Modes of confinement

3) - Magnetic confinement (p 1 - 2 - 3 - 4 )

As the plasma does not seem to want to cooperate, physicists have come up with scenarios where we create a transport barrier in the plasma, to retain the particles in its centre and obtain a more effective confinement.
Today, the H mode, an operating mode with good confinement and a reference for machines of the next generation, is solidly established, and research is well underway on alternative scenarios of called "advanced tokamaks".

d) Modes of confinement

As the theoretical comprehension of radial diffusion phenomena remains limited, many experimental studies on confinement have been carried out in the major machines worldwide. This has led to a very great database being compiled, from which empiric laws have been determined, expressing confinement time as a function of the main machine and plasma parameters, rather like the way that we resorted in wind tunnel studies to establish some laws of fluid mechanics. This is of crucial importance to be able to extrapolate the performance in confinement to a next generation machine.

The first scaling law of this type, established in ohmic operation, i.e. without additional power, showed in particular an increase in confinement time with the major radius of the machine. Operation with additional power, indispensable to raise the plasma temperature to the necessary conditions for the future reactor, was then studied. It was found that the confinement deteriorated compared to the values when the power coupled to the plasma was increased.

The H mode

Nevertheless, it was noticed that under certain conditions, confinement was abruptly improved above a power threshold but still not as good as in ohmic operation. This enhanced confinement was called H mode (for "High confinement") in contrast to the confinement mode obtained below the power threshold, called L mode (for "Low confinement"). It enables improvement of confinement times by a factor of nearly 2 in comparison with L mode. The discovery of this mode of enhanced confinement, on the ASDEX machine in the eighties, was crucial to thermonuclear fusion, and the H mode is still today the reference scenario for the next step machine ITER.

You see opposite the database used in establishing the scaling rule for confinement time in H mode, showing the agreement between experimental results from the different machines (in ordinates) and the result of the scaling law of scale (in abscissa).

This empiric law forecosts:

an increase of confinement time with the machine major radius and the plasma current (which explains in part why JET, the largest of present machines, obtains the best performance)
deterioration with additional power coupled to the plasma

For the next generation tokamak ITER, an extrapolation based on the scaling law established from results on present machines predicts a confinement time around 5 secs, which will permit to attain the goals fixed for the project (amplification factor Q=10) . It is worth noting that the threshold power at the transition from L mode to H mode depends, amongst other things, on the size of the machine, resulting in a very large figure in the case of ITER.

The stabilising mechanisms, enabling the transition to H mode have not been completely elucidated and are the subject of a number of both theoretical and experimental studies. If the H mode was originally found by accident, we know today that stabilisation of turbulence, which is the cause of confinement deterioration, is obtained thanks to a differential in the poloidal rotation velocity of the different magnetic surfaces (the fact that rotation velocity varies greatly from one surface to another is called velocity shear). Indeed, the magnetic surfaces are in rotation under the influence of the plasma electric fields. A modification of these electric fields causes velocity shear, preventing turbulence from developing. A transport barrier is set up at the plasma edge, retaining heat and particles in its core. The most characteristic point of these scenarios is the appearance of strong gradients in the plasma edge, leading notably to the creation of a pressure pedestal in the plasma, proportional to its density and temperature. The red curve representing the H mode on the drawing below is steeper in the edge zone than in the corresponding green curve in L mode.

Nevertheless, let us not imagine that the situation is calm: these very steep gradients at the edge lead to specific instabilities in the H mode, which we call ELMs (for Edge Localised Modes). The plasma pressure profile relaxes periodically towards less steep slopes (black dotted line under the red curve on the diagram). Then the barrier rebuilds itself, the profile steepens again before collapsing at the following ELM. As a consequence, large particles and heat blasts escape from the plasma at each ELM, imposing strong constraints on vacuum chamber components.

The L mode is also not at rest, with instabilities in the centre called sawteeth (dotted line under the green curve in the centre): the central temperature drops abruptly when it reaches a limit, before rising gradually up to the next sawtooth where the phenomenon repeats itself. We now know, however, how to avoid sawteeth, due to many experimental and theoretical studies, working in the domains of plasma parameters (current, magnetic field, additional power) where the phenomenon does not occur. This is not yet the case for ELMs in H mode: the identification of the mechanisms leading to this phenomenon is a very active area of research.

Other enhanced modes of confinement

In addition to the H mode, there are other modes of enhanced confinement, and particularly at the end of the nineties we saw the rise of the called " advanced tokamak " scenarios, in which performance is achieved thanks to very delicate control of current and electric field profiles in the pulse, generating internal transport barriers (or ITB for Internal Transport Barriers) in a more control region than in the case of H mode, as we see on the diagram above. These scenarios, promising but difficult to implement on account of the retroaction to be carried out on the current profile, are still in the exploratory stage.

On Tore Supra, other modes of enhanced confinement involving internal transport barriers are being explored, as shown by the curve opposite. They are obtained by using specific heating scenarios, whose stabilising influence on the plasma diminishes transport phenomena. Confinement time can thus be increased up to a factor of 2 over L mode (see the H parameter, which translates confinement improvement compares to L mode). We have for example the LHEP modes (for Lower Hybrid Enhanced Performance) obtained with hybrid frequency heating, and other modes obtained with ion cyclotron frequency heating, used in ICRH mode (for Ion Cyclotron Resonant Heating) or FWEH (pour Fast Wave Electron Heating).

On other machines like Textor in Germany, another mode of improved confinement, RI mode (for Radiation Improved), was obtained by injecting well chosen impurities into the plasma, to benefit from another stabilising effect (density peaking). It allows to reach performances close to those of the H mode, while having the advantage of reducing the heat load on plasma facing components.