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An understanding of material phase transitions in megaampere pulsed-power–driven exploding conductors is important for predicting the growth of hydrodynamic instabilities in magneto-inertial fusion concepts. This study analyzes phase transitions in electrical conductor explosions using 1D Lagrangian and 2D arbitrary Lagrangian–Eulerian resistive magnetohydrodynamic simulations to show that micrometer-scale surface roughness can lead to the electrothermal instability (ETI), a feedback effect that concentrates resistive heating and leads to early melting and ablation. Simulations of the Mykonos electrothermal instability II (METI-II) experiment show melting begins 19% sooner for machined rods with micrometer-scale surface roughness than for rods without these features. The surface magnetic field is 41 T around the initial region of melt, representing a lower magnitude than both the 86 T from 1D simulations and the 85 T threshold reported elsewhere. In 2D simulations with micrometer-scale surface roughness, temperature measurements indicate the critical point temperature of aluminum is reached 17% faster in comparison with 1D simulations. Values from 2D simulations with surface roughness align with predictions from ETI theory, and the observed temperature redistribution further supports the ETI as an underlying mechanism. Simulation results are validated against experimental photonic Doppler velocimetry data. This study shows 1D simulations are adequate to model conductors with sub-micrometer-scale surface roughness in this high-energy-density regime; however, 2D or 3D simulations are required to capture the full range of physics for accurately describing phase transitions in conductors with micrometer-scale or larger surface roughness. [ABSTRACT FROM AUTHOR]