Flow shear stabilizes rotating tokamak plasmas

The extremely hot plasma inside a tokamak nuclear fusion reactor ‘floats’ in a magnetic field to avoid contact with the walls. Plasma rotation has several different effects on the plasma stability, succinctly summarized in a comprehensive analytical stability criterion derived in the following publication:

Stability of localized modes in rotating tokamak plasmas
J. W. Haverkort and H. J. de Blank. Plasma Physics and Controlled Fusion, vol. 53, nr. 4, p. 045008. © 2011 DOI: 10.1088/0741-3335/53/4/045008

Besides well-known terms arising from the Kelvin-Helmholtz, magneto-rotational, and Rayleigh-Taylor instabilities, the criterion also contains two stabilizing terms due to rotation. One was described in an earlier post. Another less effect was discovered to be due the Coriolis force also responsible for the circulating weather patterns in the earth atmosphere.

For certain conditions (See Eq. 3) the stabilizing influence of flow shear outweighs other destabilizing effects, allowing differential rotation to have a positive effect on tokamak stability.

Flow shear stabilization of rotating plasmas due to the Coriolis effect
J. W. Haverkort and H. J. de Blank. Physical Review E, vol. 86, 016411. © 2012 The American Physical Society DOI: 10.1103/PhysRevE.86.016411

Rotating tokamak plasma oscillates like atmosphere

Tokamak simulation

If you move an air parcel up in a quiet atmosphere its density will be higher than that of the air surrounding it so that it will fall back. The frequency of the resulting oscillation is called the Brunt–Väisälä frequency. The hot ionized plasma, inside the donut-shaped nuclear fusion tokamak, typically rotates around its central axis. The resulting centrifugal forces, similar to the effect of gravity, cause similar oscillations as in the atmosphere.

Through this effect rotation stabilizes and helps to keep the hot plasma confined. See also another post for a second positive effect of rotation.

The Brunt-Väisälä Frequency of Rotating Tokamak Plasmas
J. W. Haverkort, H. J. de Blank, and B. Koren

Journal of Computational Physics,
© 2012 DOI: 10.1016/j.jcp.2011.03.016

Electrical charge can be sustained in a highly conducting fluid


Magnetohydrodynamics of insulating spheres
J. W. Haverkort, T. W. J. Peeters

A widespread notion in the field of ‘ideal’ magnetohydrodynamics describing highly conducting fluids there can be no electrical charge accumulation. Any nonzero charge will quickly redistribute over a short enough time-scale to be irrelevant. One can however easily show that in the presence of a magnetic field Lorentz forces can act to sustain a finite charge density, see equation 3.  This charge and the associated electric field have a distinct influence on the current distribution and the resulting forces on non-conducting inclusions and bubbles in a conducting fluid as shown in the above picture and explained in the paper.


Magnetic field shape forces bubbles out of liquid metals

In the industrial processing of metals, magnetic fields are often used to stir or break liquid metals, calm free surfaces, influence turbulence properties and remove unwanted inclusions.

Even though bubbles and solid inclusions in liquid metals may not conduct electricity themselves, because the surrounding metal does, some interesting magnetohydrodynamic effects arise, like the electromagnetic Archimedes force, and electromagnetically induced drag.

In a continuous caster, liquid steel enters a mold and slowly turns into a solid slab. Under the influence of unwanted flow patterns small bubbles or inclusions can be trapped into the steel, forming elongated ‘blowholes’ after rolling the steel slabs. To suppress unwanted liquid steel flows enormous electromagnets fully surrounding the casting mold. Currents induced by the flow though this magnetic field generate Lorentz forces that brake the flows.

Through computer simulations we discovered a new effect on gas bubbles in the submerged entry nozzle of a continuous caster. We show that, depending on the shape of the magnetic field, the so-called electromagnetic Archimedes force can force  Argon bubbles radially outwards. This effect may be used improving the anti-clogging capacity of gas.

Magnetohydrodynamic Effects on Insulating Bubbles and Inclusions in the Continuous Casting of Steel
J. W. Haverkort and T. Peeters