Like other fluids, plasma can sustain shocks (discontinuities in density, velocity, and temperature) when the fluid velocity is greater than the local sound speed. However, there are numerous effects which enrich the physics involved in plasma shock formation, including the pile-up of magnetic fields, strong radiative cooling, and two-fluid effects. As well as the astrophysical relevance of these effects in laboratory experiments, they also impact shocks formed in imploding magnetised fusion concepts, and form an excellent test-bed for validating numerical codes.

Magnetic Field Pile-up

One of the first projects the PUFFIN group undertook (during 2021, when the Pandemic made travel to carry out new experiments difficult) was to reanalyse data from a series of experiments on the MAGPIE generator at Imperial College London, which looked at the formation of a 3D bowshock through the interaction of a super-sonic plasma with a blunt obstacle (a b-dot probe). Using MHD shock theory and detailed 3D MHD simulations (using the GORGON code developed by Prof. Jeremy Chittenden at Imperial College London), we were able to explain the different shock opening angles parallel and perpendicular to the magnetic field in terms of the magnetic field pile-up around the obstacle.

Radiative cooling

Plasmas are hot, and so emit copious amounts of electromagnetic radiation across the spectrum, especially in the extreme-ultra-violet and X-rays regions. This strong cooling can trigger an instability when the cooling leads to a local increase in density which in turn increases the cooling rate. The scale of this instability also depends on the rate of thermal conduction, which smooths out temperature gradients, and as the thermal conduction in a plasma is significantly different parallel and perpendicular to the local magnetic field, this creates anisotropic instabilities.

We observed these instabilities in data taken during experiments on MAGPIE in which a super-sonic tungsten plasma flow collided with a large planar conducting obstacle. The data was taken in 2016 and 2017, but it was only during 2020-2023 that we had sufficient time to analyse it in detail, in a paper published by Dr Stefano Merlini in 2023. There is a great deal of rich physics in these experiments still to be explored, and the long timescales on PUFFIN may prove useful for observing the growth of these instabilities in plasmas with lower cooling rates, for which the atomic physics is easier to model.

Oblique shocks

In a planar geometry, the angle between a shock and sloping target (such as the sharp nosecone of a fighter jet) depends only on the Mach number and the adiabatic index of the fluid. By measuring the shock angle from two angled targets in the same field of view, we can therefore calculate the plasma adiabatic index directly. This is interesting, because this adiabatic index can be far from the ideal gas value of 5/3 when ionisation and radiation are taken into account. Graduate student (and now Dr) Rishabh Datta proposed a series of experiments to study this which were funded through ZNetUS on the COBRA facility at Cornell in July 2024. After a few attempts with different targets, we settled on the “crocodile” whose upper and lower jaws are at different angles. Analysis of this data is ongoing!

Further reading