Magnetized Plasmas

A magnetized plasma is defined as having the energy density of the magnetic field in the plasma greatly exceed the energy density associated with the hydrodynamic pressure. In this case, the force due to pressure gradients can be ignored to a large extent and the plasma motion is mainly the result of magnetic forces.

A theory by Woltjer in the 1950’s and elaborated by B. Taylor in the 1970’s proposed that a magnetized plasma with negligible hydrodynamic pressure would self-organize into a specific lowest energy state while preserving a topological quantity called the magnetic helicity. The helicity is a measure of magnetic linkages like the links on a chain. This Woltjer-Taylor relaxation theory provides a good initial explanation into the shapes of many lab and naturally occurring plasmas such as spheromaks (a fusion plasma confinement concept) and the solar corona.

While the Woltjer-Taylor model explains the configuration a plasma would like to attain, it does not explain how it achieves this configuration, that is the model does not explain what happens. A goal of the Bellan research group has been to discover the underlying mechanism of Woltjer-Taylor relaxation. In recent years, we have discovered that a central assumption of the relaxation model, namely that the plasma slowly evolves from one equilibrium state to another is in fact not true. What happens in reality is that the plasma is far from equilibrium and there exist fast dynamic processes. In particular, the plasma automatically self-organizes into a high-velocity, highly collimated jet that in contrast to the Woltjer-Taylor assumption develops significant pressure gradients. These jets are essentially the same as the astrophysical jets shooting out from new-born stars but are 20 orders of magnitude smaller in both time and duration.

We have been studying these jets and have found that they develop some remarkable instabilities. First the jet develops what is called a kink instability wherein the jet tries to coil up, and then an enormous effective gravity from the kinking (a billion G’s) instigates a completely different kind of instability which is called a Rayleigh-Taylor instability. The Rayleigh-Taylor instability chokes the jet and causes yet other types of instability which are now being studied. Another feature under study is that the choking of the jet creates large electric fields that accelerate particles to high energy.

The jets, kinking, Rayleigh-Taylor instability, and creation of energetic particles are relevant to astrophysical, solar, and fusion plasmas and we are engaging these communities with the results of our experiments.

Since many of these observations were not predicted by any theory we are developing new theoretical models to explain the experimental observations and are scaling the theories to other situations (astrophysics, etc.) to see what these new ideas imply for these other situations.

We are also using the jets to study an issue relevant to magnetized target fusion which is a controlled thermonuclear scheme where an imploding conducting shell adiabatically compresses a magnetized plasma to the density and temperature required for fusion. Instead of using a conduction shell we are having the magnetically driven jet slam into a target cloud. A change of frames would have the target cloud slam into the magnetized jet which is the same as the shell compress a magnetized plasma. By measuring the change of temperature and density in the jet we can follow the adiabatic compression process and, in principle, determine the dimensionality of this compression.