Progress on the electro-thermo-mechanical instability and its role as seed on plasma instabilities

Significance 

Instabilities are the result of any disturbance that may occur in a physical parameter of a system such as density, temperature, magnetic or electric field, or current. When, a large pulsed current passes through an electrical conductor, the resulting flow of electrons generates a magnetic field around the conductor, while the metallic target is heated and expands due to Joule heating. Magnetic pressure and resulting compressive forces tend to compress the conductor. The current conductor interaction leads to a phenomenon known as instability generation and growth. There are several factors that can contribute to instability growth in electrical conductors, including the duration and magnitude of the current pulse, the geometry and material properties of the conductor, and the presence of an external magnetic field that might interact with the current. To mitigate the effects of instability growth, scientists study and design conductors covered by dielectric coating materials. Additionally, they can use specialized tools and simulations to model the behavior of pulsed currents and optimize conductor designs to minimize the risk of instability growth. Indeed, the growing interest in instability growth can also be attributed to the need to understand the seed mechanisms associated to instabilities generation in non-stationary plasma systems. Most studies have identified this problem as a big obstacle to applications of conductors and plasmas thus needs to be addressed urgently.

Conductive targets interacting with strong pulsed currents and associated magnetic fields have four distinct characteristic cases: single-wire Z-pinch configuration, Z-pinch wire arrays, magnetic flyer plate experiments and magnetically driven pulsed power liners. Study of instabilities in non-stationary plasma systems, such as the Magneto-Rayleigh–Taylor (MRT), has attracted large interest due to their importance in potential plasma applications like laser-driven inertial fusion energy and magnetized pulsed-power liners. Moreover, electro-thermal instability has drawn significant research attention because it is a promising seed mechanism for the MRT instability.

In a recent proof-of-principle study, the existence of a relatively new instability named electro-thermo-mechanical (ETM) instability was demonstrated before the conductor’s melting phase. This developed instability enabled computational simulations and experiments from the solid to the final plasma phase. For the first time, a single cylindrical metallic target heated by a pulsed current was studied, and the physical model simulations and experimental results were in good agreement. The imposed boundary conditions, in synergy with the Joule heating of the current-carrying surface and the temperature dependence of the electrical resistivity as well as the magnetic pressure and the resulting compressive stresses, produce longitudinal and radial thermal shocks that trigger temperature fluctuations and consequently displacement variations along the conductor in the solid regime.

Herein, a team of researchers from Hellenic Mediterranean University/Institute of Plasma Physics & Lasers: Dr. Evaggelos Kaselouris, Mr. Alexandros Skoulakis, Professor Vasilis Dimitriou, Professor Ioannis Fitilis, Professor John Chatzakis, Professor Makis Bakarezos, Professor Nektarios Papadogiannis and led by Professor Michael Tatarakis presented new important advances in the exploration of the ETM instability in the solid elastic regime. Specifically, ETM instability was studied as a potential seed of magneto-hydro-dynamic instabilities observed in the plasma phase following the well-established perturbation theory. Their work is currently published in the journal, Plasma Physics and Controlled Fusion.

The authors demonstrated the whole evolution dynamics of the instability amplitude from the solid to plasma phase as well as phase transitions through experiments, simulations and analytical solutions. The resulting and sustained axial wavelength modes in the plasma phase were in the range of values of the axial perturbations of the ETM instability developed in the elastic phase and determined by the derived dispersion equation. The results of the advanced 3D multiphysics finite element method (FEM) and boundary element method (BEM) simulations were used to validate the analytical study, and a remarkable agreement was obtained.

The instability pathway from the solid to plasma phase was effectively monitored by combining multiphysics FEM-BEM-MHD simulations with experiments. The results revealed the importance of considering the material’s thermoelastic properties and adding a full thermoelastic Cauchy stress tensor in generating ETM instability in the solid thermoelastic region before melting. Furthermore, the results suggested the significance of understanding the role of ETM instability as a seeding mechanism for the observed instabilities in the plasma phase.

In summary, the study explored the ETM instability in the solid elastic phase for the case of the electrically exploded conductor in the skin effect mode. The findings confirmed the importance and crucial role of ETM instability as a seed mechanism for growing instability modes in the plasma phase. In a statement to Advances in Engineering, the lead and corresponding author, Professor Michael Tatarakis explained that the study provided a better understanding of instability growth in electrical conductors.

Progress on the electro-thermo-mechanical instability and its role as seed on plasma instabilities - Advances in Engineering
Schematic representation of birth and growth of the ETM instability

Reference

Kaselouris, E., Skoulakis, A., Dimitriou, V., Fitilis, I., Chatzakis, J., Bakarezos, M., Papadogiannis, N, & Tatarakis., M. (2022). Progress on the electro-thermo-mechanical instability and its role as seed on plasma instabilities. Plasma Physics and Controlled Fusion, 64(10), 105008.

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