Electron Emission Theories for Multiple Mechanisms and Device Configurations

Adam M Darr, Purdue University

Abstract

Electron emission plays a vital role in many modern technologies, from plasma medicine to heavy ion beams for fusion. An accurate theoretical model based upon the physics involved is critical to efficient operation of devices pushing the boundaries of complexity. The interactions between different electron emission mechanisms can severely alter device performance, especially when operating in extreme conditions. This dissertation studies electron emission from the perspectives of increasing geometric and physical mechanism complexities One half of this dissertation derives new relations for space-charge limited emission (SCLE) in non-planar geometries. SCLE is the maximum stable current that may be produced by electron emission before the electric field of the electrons themselves self-limits further emission. In planar devices, this is modeled by the well-established Child-Langmuir (CL) equation. The Langmuir-Blodgett (LB) equations remain the most commonly accepted theory for SCLE for cylindrical and spherical geometries after nearly a century; however, they suffer from being approximations based on a polynomial series expansion fit to a nonlinear differential equation. I derive exact, fully analytic equations for these geometries by using variational calculus to transform the differential equation into a new form that is fully and exactly solvable. This variational approach may be extended to any geometry and offers a full description of the electric field, velocity, and charge density profiles in the diode. SCLE is also an important mechanism for characterizing the operation of devices with an external magnetic field orthogonal to the electric field. This “crossed-field” problem decreases the limiting current as electrons travel longer, curved paths, effectively storing some charge in the gap (moving parallel to the emitter). At a critical magnetic field called the Hull cutoff, electron paths become so tightly curved that the circuit can no longer be completed, a condition called magnetic insulation. Crossed-field SCLE has been accurately modeled in planar devices by Lau and Christenson. Using the variational approach, I replicate their planar results and extend the calculation to cylindrical geometry, a common choice for magnetron devices. Further, I derive additional equations with simplified assumptions that, for the first time, provide an analytic description of experimental results below the Hull cutoff field. Following this I incorporate a series resistor: device resistance (or impedance) changes non-linearly with current and voltage, so I couple Ohm’s Law (OL) to all the models of crossed-field devices. For devices just below the Hull cutoff, I predict analytically and show in simulation novel bi-modal behavior, oscillating between magnetically insulated and non-insulated modes. With crossed-field device assessment, the variational calculus approach to space-charge may be used for numerous applications, including high power microwave sources, relativistic klystron devices, heavy ion beams, Hall thrusters, and plasma processing. The other half of this dissertation derives analytic theories to solve for emission current with three or more electron emission mechanisms simultaneously. In addition to the CL law, SCLE may also occur in neutral, non-vacuum diodes, modeled by the Mott-Gurney (MG) equation. These are the two limiting mechanisms I study; the other major modality of electron emission is direct electron production, the source of current in the device. Electrons are ejected when impelled by high temperature or electric field at the emission surface.

Degree

Ph.D.

Advisors

Garner, Purdue University.

Subject Area

Physics|Electromagnetics|Mathematics

COinS