Electrostatic-elastoplastic simulations of copper surface under high electric fields

Abstract

Maximizing the performance of modern linear accelerators working with high gradient electromagnetic fields depends to a large extent on ability to control breakdown rates near metal surfaces in the accelerating structures. Nanoscale voids, presumably forming in the surface layers of metals during the technological processing, can be responsible for the onset of the growth of a surface protrusion. We use finite element simulations to study the evolution of annealed copper, single crystal copper and stainless steel surfaces that contain a void under high electric fields. We use a fully coupled electrostatic-elastoplastic model in the steady state. Gradually increasing the value of an external electric field, we analyze the relationship of surface failure and depth of the void for the chosen materials with different elastoplastic properties. According to our results, the stainless steel and single crystal copper surfaces demonstrate the formation of well-defined protrusions, when the external electric field reaches a certain critical value. Among the three materials, annealed copper surface starts yielding at the lowest electric fields due to the lowest Young’s modulus and yield stress. However, it produces the smallest protrusions due to a significant strain hardening characteristic for this material.