- Accepted Paper
Vacuum breakdown: Phenomenological description and hydrodynamical modeling of crater formation
Phys. Rev. Accel. Beams - Accepted 16 October, 2026
DOI: https://doi.org/10.1103/tmcm-pkrj
Phys. Rev. Accel. Beams - Accepted 16 October, 2026
DOI: https://doi.org/10.1103/tmcm-pkrj
Vacuum breakdown in high-field environments remains a fundamental limit for the operation of high-voltage devices, yet the physical transition from localised field emission to a macroscopic arc is not fully understood. We present a unified numerical study describing the full lifecycle of breakdown on copper cathodes, from its onset within a characteristic activation time, to the formation of surface craters. By integrating the Murphy-Good emission formalism with experimental current-voltage transients, we demonstrate that breakdown initiation is reproduced for emitting regions with radii of order $1% %TCIMACRO{}% %BeginExpansion % %EndExpansion $. Sites outside this “Goldilocks” range either fail to trigger thermal runaway or produce currents inconsistent with observed data. Our model shows that this runaway leads to an explosive vaporisation of the cathode, generating a dense plasma cloud that drives the transition to a vacuum arc. By employing the level-set method to track hydrodynamic surface deformation, we find that the resulting ion-driven energy fluxes induce cratering over a $100% %TCIMACRO{}% %BeginExpansion % %EndExpansion $ timescale, with morphologies in good qualitative agreement with post-mortem experimental data. Furthermore, we identify a distinct sheath voltage threshold ($% %TCIMACRO{}% %BeginExpansion % %EndExpansion $) for the occurrence of secondary microexplosions. These results suggest that high-field breakdown is a deterministic sequence of electro-thermal and hydrodynamic events, providing a theoretical framework for the transition between field emission and the low-voltage arc regime.
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