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Center for Nonlinear Studies |
Predicting gas breakdown is critical for plasma formation and avoiding device damage. Paschen’s law (PL), driven by Townsend avalanche, is well known in plasma physics. For micro- and nanoscale gaps, the increased electric fields strip electrons from the cathode by field emission (FE), reducing the breakdown voltage. Further reducing the gap distance results in charge buildup at the cathode prohibits additional emission. Introducing a perpendicular magnetic field, as common in crossed-field amplifiers and accelerators, changes this behavior. In this seminar, we describe theoretical linkages of these phenomena and extensions to more realistic geometries.
We first describe a matched asymptotic analysis that unifies field emission and PL to derive analytic equations showing that the breakdown voltage scales linearly with gap distance when FE drives breakdown and apply this theory to microscale experiments with cathode surface roughness and nanoscale experiments at both vacuum and atmospheric pressure. We demonstrate that nanoscale breakdown may occur from a space-charge dominated condition rather than directly from field emission. We discuss this behavior in the context of “nexus theory,” which is a theoretical framework linking various electron emission mechanisms, including space-charge limited, field, thermionic, photo-, and quantum space-charge limited emission.
We next describe approaches to extend electron emission physics to nonplanar geometries by using variational calculus (VC) to extremize the current in the gap, conformal mapping of the space-charge electric potential, and Lie point symmetries. We further derive a relationship between the charge-free and space-charge limited potential that yields the space-charge-limited current density (SCLCD) for multidimensional diodes for any geometry and apply it to arrays of sharp tips.
We conclude by emphasizing the importance of the spatial dependence of the space-charge-limited and charge-free electric potential in these calculations. We show how collision frequency and magnetic field alter the charge-free electric potential and, by extension, the SCLCD.
Bio: Dr. Allen Garner received the B.S. degree (with high honors) in nuclear engineering from the University of Illinois, Urbana-Champaign, in 1996. He received an M.S.E. in nuclear engineering from the University of Michigan in 1997, an M.S. in electrical engineering from Old Dominion University in 2003, and a Ph.D. in nuclear engineering from the University of Michigan in 2006. He was an active duty Naval officer from 1997 to 2003 and is currently a Captain in the United States Navy Reserves. From 2006 to 2012, he was an electromagnetic physicist at GE Global Research Center. He joined Purdue University in 2012, where he is currently Professor and Graduate Program Chair in Nuclear Engineering.
Prof. Garner has been awarded two Meritorious Service Medals, the Navy and Marine Corps Commendation Medal, and five Navy and Marine Corps Achievement Medal. He also received the 2021 and 2024 Purdue School of Nuclear Engineering Outstanding Research Award, 2019 Outstanding Faculty Mentor of Engineering Graduate Students, and 2016 IEEE NPSS Early Achievement Award.
Host: Chengkun Huang (T-5)