Magnetic confinement

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

The magnetic trap that confines the particles is not so easy to achieve: the plasma does not like it and tries to counter the magnetic field imposed on it...

b) Stability of confinement

Thanks to the tokamak configuration, we manage to confine the particles by compensating the pressure of the plasma, which tries to spread like a gas, by magnetic pressure. Unfortunately, such equilibrium, if quite easy to achieve, may become unstable, i.e. a small disturbance is likely to grow over time and, in certain cases, lead to total loss of confinement: this is what we call disruption. In other cases, it is just a partial loss of confinement, which does not result in the sudden shutdown of the pulse, but which considerably degrades its performance.

For example, we see here experimentally the image of a magnetic equilibrium perturbation on JET. The flow surfaces seen by X ray imaging should match the theoretical flow surfaces (in black on the figure), as is the case at the start of the demonstration opposite. But a state of instability develops, and disturbs the arrangement in the magnetic configuration. This ends up in a disruption...

Disruptions

A disruption may have many consequences. Any sudden decrease in current and/or magnetic fields induces mirror currents and /or magnetic fields in the components around the machine. These components are then subjected to what may be considerable forces. The higher the initial plasma current, (and we often count in Mega Amperes in the tokamaks) the shorter time it takes to disappear; the more sudden the current variation, the more serious the disruption is. Tokamaks are thus designed to be able to withstand such events (we use non-magnetic materials, the structure of the machine is very robust, the different parts in contact are electrically insulated and the components are carefully attached inside the chamber). Apart from these mechanical forces, all the energy contained in the plasma is also transferred over a short time to the components of the vacuum chamber, which are thus designed to withstand these extreme peaks of heat. Finally, disruption also has consequences on the experimental programme. It is generally difficult to restart the machine directly after a disruption, and it is often necessary to resort to conditioning pulses before being able to resume experimentation. Even if disruptions are still a part of everyday life of present tokamaks, which are still at the stage of being research instruments, it is clear that there is an interest in trying to avoid them, particularly by studying the stability of magnetic equilibria

Watch the film "Instabilities" (gif, 1600 kb)

Instabilities

The study of stability of magnetic equilibria is called magneto-hydro-dynamics (MHD for the initiated). This complex name simply covers the notion of fluid (hydro) in movement(dynamics) in a magnetic field (magneto), which applies very exactly to what happens inside a tokamak. To want to confine a hot plasma in an immaterial container formed by the magnetic field lines is a bit like wanting to contain a gas under pressure in a tyre inner tube. Another comparison, which we often hear from physicists to show the difficulty, is to a ring of jam (graphic representation of the plasma) that must be confined by using sticky tape. More seriously, by going back to the image of a tyre inner tube, MHD helps to optimisetube characterisation (geometry, rubber thickness) so that it will withstand the gas pressure without bursting, leaking or kinking. We will call b the ratio of the plasma kinetic pressure (proportional to its density and temperature) to the confinement magnetic pressure (proportional to the intensity of the magnetic field). For the " inner tube " not to burst, the magnetic confinement must be stronger than the plasma pressure forces , i.e. the ratio must be smaller than 1. Practically, we find that this limit in b is much lower than 1, of the order of few percentage, because of the appearance of instabilities. This notably limits the maximum density that may be obtained, since the plasma kinetic pressure is directly proportional to it.

To understand the notion of equilibrium stability, the simplest analogy is that of a marble rolling on a corrugated surface. Depending on the geometry of the surface, the equilibrium of the marble will be stable, meta-stable or unstable, as shown below.

The mechanisms of instability in plasma physics are nearly unlimited. Some instabilities are comparable to examples borrowed from fluid mechanics, as the Rayleigh Taylor’s instability, which consists of superposing two fluids with the heaviest on top. Imagine for example a vessel in which you pour water and then carefully add oil over the top. The system is then in a state of meta-stable equilibrium. The slightest nudge will provoke a change with the heavier fluid dropping to the bottom, which corresponds to a stable equilibrium.

Another type of instability are kink instabilities, which occur when a current parallel to the magnetic field cause twisting of the filed lines, recalling the effect obtained if we twist a rope too much: the rope twists out and kinks. Other instabilities are really proper to plasma physiscs and have no equivalent in other domains.