Speaker
Description
Vacuum breakdown is an important limitation in the performance of many technical devices, such as high-voltage circuit breakers and particle accelerators. Field emission, the process through which electrons are emitted from a cold cathode under a strong electric field, is a necessary step in the development of breakdown. The average electric field in the gap between electrodes in breakdown experiments is insufficient to lead to field emission - enhancement of the applied electric field by a factor of $~10^2$ or higher is needed for breakdown to occur. Various theories of enhanced field emission have been proposed, such as mobile dislocations [1], plasmons [2] or nonmetallic electron emission [3], but the exact processes that lead to field emission from cold electrodes in vacuum are still not well understood. As breakdown develops, other mechanisms come into play, such as the transition from field to thermionic emission, vaporisation, ionisation of the metal vapour and production of plasma and deformation of the electrode's surface.
A phenomenological description of field emission is used in this work. The surface electric field and the resulting emission current is given by the Fowler-Nordheim formula, from which the field enhancement factor - the ratio between the macroscopic (applied) electric field and the microscopic (enhanced) electric field - in a field emission centre can be determined. Simulations were done for a 2D axially symmetric, cylindrical copper cathode using COMSOL Multiphysics, using a numerical model that builds upon the works in [4, 5]. The surface electric field was increased over a time interval of 10 ns, until a maximum effective electric field of $10$ GV/m was reached, and a limitation on the circuit's current was imposed, analogous to having an external circuit that containing a ballast, so that the maximum current would not rise to values much higher than around 30 A.
Calculations for a field emission centre with a radius of $1\,\mu $m show that during the first 5 ns, the current is zero and there is no heating. Then, as the field enhancement factor and consequently the electric field increase, there is a rise in the emission current density and the total current, and the cathode starts heating up. When high enough currents are reached, the external circuit has the effect of slightly lowering the effective electric field; the current continues to rise, but at a slower rate, and the temperature keeps increasing. Finally, after about 13 ns, we transition into the thermionic regime, the emission current density increases dramatically, the contribution from the sheath electric field leads to an overall increase of the field on the surface of the cathode, and the cathode heats up quickly, reaching the critical temperature of copper in less than 1 ns.
By varying the field emission centre radius, it was determined that field emission centres with radius of order of $1 \, \mu$m are the most favourable for breakdown. Field emission centres that are larger (e.g., $\sim10\, \mu $m) than this lead to emission current densities that are too low to lead to breakdown, and the total current, which is limited by the external circuit, would need to be much higher. Smaller field emission centres ($\sim100$ nm) lose heat too quickly, and a steady state is reached at a temperature that is too low.
In addition to this, calculations taking into account hydrodynamics and surface deformation were done. Comparing the simulated current with experimental current oscillograms, such as in [6], the simulated current is in reasonable agreement with the experimental data. The final results are to be presented at the conference.
References:
[1] E. Z. Engelberg, J. Paszkiewicz, R. Peacock, S. Lachmann, Y. Ashkenazy, and W. Wuensch, “Dark current spikes as an indicator of mobile dislocation dynamics under intense dc electric fields,” Phys. Rev. Accel. Beams, vol. 23, p. 123501, Dec 2020.
[2] W. Wuensch in 8th International Workshop on Mechanisms of Vacuum Arcs, (Padova, Italy), 2019.
[3] R. Latham and N. Xu, “‘Electron pin-holes’: the limiting defect for insulating high voltages by vacuum, a basis for new cold cathode electron sources,” Vacuum, vol. 42, no. 18, pp. 1173–1181,1991.
[4] H. T. C. Kaufmann, M. D. Cunha, M. S. Benilov, W. Hartmann, and N. Wenzel, “Detailed numerical simulation of cathode spots in vacuum arcs: Interplay of different mechanisms and ejection of droplets,” Journal of Applied Physics, vol. 122, p. 163303, 10 2017.
[5] N. Almeida, H. Kaufmann, and M. Benilov, “Phenomenological description of vacuum breakdown,” in 10th International Workshop on the Mechanisms of Vacuum Arcs (Hybrid MeVArc 2022, Sept. 18 - 22, 2022, Chania, Greece), pp. 27–31, 2022.
[6] W. Wuensch, “Advances in the Understanding of the Physical Processes of Vacuum Breakdown,” 5 2013.
Acknowledgements
IPFN activities were supported by FCT - Fundação para a Ciência e Tecnologia, I.P. by project references UIDB/50010/2020, UIDP/50010/2020 and LA/P/0061/2020 and by European Regional Development Fund through the Operational Program of the Autonomous Region of Madeira 2014-2020 under project PlasMaM1420-01-0145-FEDER-000016.
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