The Onset and Growth of Current-Driven Pinch Instabilities in Liquid Metal Columns: Linear and Nonlinear Numerical Approaches

The linear pinch (or Z-pinch) instability, in which a current is driven through a conducting fluid or plasma in cylindrical geometry, is a well-known phenomenon in the plasma community. However, the instability in liquid metals has received little attention. The objective of the present study is to investigate and quantify the onset and growth of pinch instabilities in liquid metal columns. For this, a linear instability spectral code and nonlinear simulations using the FreeMHD package are used, and their results are compared. The instability of axisymmetric (m=0) and higher order (m>0) growth modes is considered in a variety of parametric configurations including axial perturbation wavelengths and current intensity. In addition, upper bounds on growth rates are identified to predict effective growth rates in experiments and applications. Computational findings are compared to preliminary results from a conducting liquid metal pinch experiment. These results provide further insight into the growth and nonlinear behavior of pinched liquid metal columns, potentially informing improved application designs using such configurations.