Asymptotic Analysis of Electron Emission Mechanisms in a Collisional Crossed-Field Gap

Crossed-field devices (CFDs) in which the magnetic field is perpendicular to the electric field are important in high-power applications [1]. It is crucial to maximize the current in these devices, motivating assessments of the limiting current (LC) [2]. Introducing collisions to account for imperfect vacuum eliminates magnetic insulation and alters the LC [3].

While the goal is to operate at the LC, this may not always be the case. Since many CFDs use thermionic cathodes [1], it becomes necessary to assess transitions between thermionic emission (TE), field emission (FE), and the LC using “nexus theory” [4].

This study incorporates collisions into CFD nexus theory. We demonstrate the prior asymptotes for TE, FE, and vacuum LC [4] while introducing the transition to the CFD collisional LC [3]. The agreement between the exact and asymptotic solutions for various magnetic fields, temperatures, and collision frequencies will be demonstrated and discussed.

[1] M. Pearlman, D. Smithe, C. Roark, M. Worthington, J. Watrous, A. L. Garner, and J. Browning, IEEE Trans. Electron Devices 69, 7053-7058 (2022).

[2] P. J. Christenson, Ph.D. dissertation (University of Michigan, 1996).

[3] L. I. Breen, K. L. Cartwright, A. M. Loveless, and A. L. Garner, Phys. Plasmas 31, 092108 (2024).

[4] A. M. Loveless, A. M. Darr, and A. L. Garner, IEEE Trans. Plasma Sci. 50, 2609-2620 (2022).