Theoretical modelling of the magnetic-field-penetration in a plasma opening switch experiment

Fast magnetic field penetration into a positive-polarity plasma-opening-switch (POS) of 100 ns duration time has been recently measured. The measurements provide the temporal and spatial evolution of the magnetic field in the plasma. We present theoretical results for the magnetic field evolution based on the Hall model for fast magnetic field penetration into a cylindrical plasma of inhomogeneous density [1], and compare them with the experiment. This model allows for magnetic field penetration into most of the plasma for both positive and negative switch polarities as long as fast magnetic field penetration along the electrodes occurs. The evolution of the magnetic field depends on various parameters. These parameters are the switch polarity, the plasma density profile and the time-varying field values in the vicinity of the electrodes and at the plasma-vacuum boundaries. The magnetic field near the electrodes is unknown experimentally. We assume its shape and time dependence based on previous theoretical models and numerical simulations. The other parameters, namely the plasma density profile and the field values at the plasma-vacuum boundaries, are taken from the measurements. The model yields an analytical solution under some simplifications that are possibly valid for this experiment. The theoretical results appear to fit well the spatial and temporal magnetic field values obtained experimentally, and provide an explanation for the fast magnetic field penetration.