Public Outreach: "Chaos & Plasma"

Eddies in flatland:
2-dimensional turbulence

One area of work in our research group is the investigation of turbulence and structure formation in magnetised plasmas. These have a special feature: turbulent eddies and flows are essentially two-dimensional. Many properties and structures are similar to those of wind and weather. This is because the atmosphere of the Earth and many planets can also be described analogously as a quasi two-dimensional fluid.

As a rule, turbulence in most liquids and gases is three-dimensional. Vortices usually take the form of tornado tubes and always break down into smaller and smaller vortices.

However, thin layers, such as the Earth's atmosphere or soap films and the skin of soap bubbles, are exceptions. There, small flat vortices can organise themselves into large, stable structures and currents. A prominent example are the colourful bands and the Great Red Spot on Jupiter.

In a strong magnetic field, hot plasma gas also behaves like a layered liquid: large-scale flows and long-lasting, coherent structures form from chaotic, turbulent vortices. With the help of theoretical investigations, numerical simulations on high-performance computers and comparison with experiments, we want to understand the structure formation in such complex systems.

De Fluminibus

The scientific study of the dynamics of fluids has a long tradition at the University of Innsbruck. This is shown by the dissertation by Johann Baptist Zeiler von Zeilheim from 1767:

(Physico-hydraulic treatise on the course of currents, to which supplements are added from general philosophy)

From the contents of the first part:

De regulari fluminum cursu

§.1 Fluidum est corpus, cujus partes levissime inter se cohaerentes impulsui externo facile cedunt, & facilime inter se moventur.

§.2. Si partes majore quantitate collectae, su nativo pondere, seu motu intestino, sese ad superficiem horizonti parallelam componant, Fluidum liquidum dicitur. COROLL. Farinae pulvisculi in cumulum collecti, lapides minutissimi triti, nubes ex tenuissimis vaporibus collecta, flamma, fumus &c. Fluida sunt: at vinum, lac, mercurius, aqua &c. simul liquida. Quamvis Fluidum et Liquidum promiscue usurpari solet.

D. Joan. Bapt. Paulus Zeiler de Zeilheim: De cursu fluminum. Oeniponti: Litteris Wagnerianis, MDCCLXVII. contemporary paperback. Latin. XVI+118 PP. With 3 plates. (Ex libris Alexander Kendl)

Tornado, vortices and smoke rings

A Fluid (Liquid, Gas or Plasma) forms vortices when there are very different speeds in close proximity to each other.

Vortices can occur, for example, behind fast-moving objects such as cars or aeroplanes, in the lee of buildings or on the edge of fast currents.

A Smoke ring is a circularly curved vortex that forms at the edge of an opening from which a gas flows out at high speed. Who can create the most beautiful ring with the large smoke drum?

With sufficient thermal lift (Convection) and lateral winds, funnel-shaped Small drums or Tornadoes can be created in the air. The physical principle can be easily understood using the giant tornado machine!

When water flows from a basin into a drainage pipe, Whirlpool is created. Competition: Who can transfer the water between two plastic bottles the fastest? The winner will be the one who creates the strongest water vortex by turning it correctly!

Chaos pendulum

The movement of the Magnetic pendulums and Doppelpendels shows deterministic chaos:

With only slightly different initial conditions (different deflection), the movements are completely different after a short time, seemingly random and unpredictable.

Chaotic systems are unstable: small changes can be amplified enormously (especially exponentially), large changes can be damped.

Turbulent flows In liquids, gases and plasmas are examples of deterministic chaos in complex dynamic systems with many Degrees of freedom.

The Weather and the confinement of Fusion plasmas are also essentially determined by Chaos and Structure formation.

Video recording of our large plasma ball.

Plasma ball and plasma tube

Lightning To touch: the Plasma ball generates luminous filaments and flashes through electrical discharges between the inner Electrode and the glass wall with a high-frequency alternating field of approx. 30 kHz and several kilovolts.

The glow of the plasma is created by Recombination of Neon and Xenon, which were generated by fast Electrons (~ 20'000 K) in the flash filaments by ionisation.

Touching the glass surface changes the Electrical capacity of the sphere at this point, and the electric field thus is intensified and "magically" attracts the flashes. The principle behind this is similar to the capacitive Touchscreens on smartphones or tablets.

Due to the high electric field strength outside the sphere (~ 500 volts/metre at a distance of 1 m), Fluorescent tubes glow "by themselves".

Our plasma sphere was made by glass artisan Bernd Weinmayer in Tyrol and is the most popular eye-catcher among our exhibits.

Magnetic levitation: symbolic illustration of the forces of magnetic fields, which are also used to keep plasmas that are hundreds of millions of degrees hot away from the walls of the experiments in fusion research.

Magnetic confinement of plasmas

Force is exerted on moving electrically charged particles via a Magnetic field. An illustrative example of the strength of this force is the magnetic Levitation, in which objects can be held in suspension with the help of ring-shaped currents (in coils, in diamagnetic materials or in permanent magnets).

The electrically charged components of Plasmas, Electrons and Ions, can also be confined by the magnetic Lorentz force. Strong toroidal magnetic fields, which are generated by current-carrying Coils and are enclosed in a ring, are particularly suitable for confining hot plasmas (~ 100 million K).

However, this alone is not sufficient for particle confinement. Because the field strength decreases outwards in a pure ring field, the particles would quickly be driven against the wall.

Permanent confinement of the plasma is only possible by twisting the field lines. The field lines circulating in the ring span "magnetic surfaces" nested inside each other like onion skins, in which the density and temperature are constant.

This principle is used in experiments on magnetic confinement of plasmas of the type Tokamak or Stellarator, which are used to investigate the possible utilisation of Fusion energy in Power stations.

However, instabilities and turbulence generate a transport of plasma to the outside, resulting in a loss of heat and particles.

To efficiently generate energy through fusion reactions, however, the plasma must remain well confined for a sufficiently long time. Understanding and controlling turbulence in plasmas are therefore important tasks in fusion research.