Field electron emission, or electron tunneling through a potential barrier under the influence of a strong electrostatic field, is of broad interest to the accelerator physics community. For example, it is the source of undesirable dark currents in resonant cavities, providing a limit to high-field operation. The classical approach to field electron emission is the Fowler-Nordheim (FN) framework, which incorporates a simplified surface potential and various assumptions. Here we build a more realistic model using the potential and charge densities derived from a density-functional theory (DFT) calculation. We examine the correction factors associated with each model assumption. Compared to the FN framework, our results can be extended up to 80 GV/m, a limit that has been reached in laser-induced strong field emission scenarios.

Hydroiodic acid (HI) treated - reduced graphene oxide (rGO) ink/conductive polymeric composites are considered as promising cold cathodes in terms of high geometrical aspect ratio and low field emission (FE) threshold devices. In this study, four simple, cost-effective, solution-processed approaches for rGO-based field effect emitters were developed, optimized and compared; rGO layers were coated on a) n+ doped Si substrate, b) n⁺-Si/P3HT:rGO, c) n⁺-Si/PCDTBT:rGO and d) n⁺-Si/PCDTBT:PC₇₁BM:rGO composites, respectively. The fabricated emitters were optimized by tailoring the concentration ratios of their preparation and field emission characteristics. In a critical composite ratio, FE performance was remarkably improved compared to the pristine Si, as well as n⁺-Si/rGO field emitter. In this context, the impact of various materials, such as polymers, fullerene derivatives, as well as different solvents on rGO function reinforcement and consequently on FE performance upon rGO-based composites preparation was investigated. The field emitter consisted of n⁺-Si/PCDTBT:PC₇₁BM(80%):rGO(20%)/rGO displayed a field enhancement factor of ∼2850, with remarkable stability over 20h and low turn-on field in 0.6V/μm. High-efficiency graphene-based FE devices realization paves the way towards low-cost, large-scale electron sources development. Finally, the contribution of this hierarchical, composite film morphology was evaluated and discussed.

The structure and phenomena arising from charge transfer in cold field emission modus in a single closed carbon nanotube under cold field emission conditions were studied. By studying microphotographs in various microscopes - AFM, SEM, TEM it was found inhomogeneities in the form of two types of superlattices. The conductivity of the emitter section of a nanodiode circuit with an emitter made of an individual closed carbon nanotube (CNT) and arrays of closed CNTs was studied. High values of cold field emission were observed, as well as nonlinearity and anomalies of the current-voltage characteristic (I-V characteristics), which manifested themselves in the form of peaks at low and high current values. Peaks in the CVC have distinct areas of negative differential conductivity. It is argued, that the anomalously high currents in the I–V characteristics of cold field emission of electrons from a nanoemitter made of closed CNTs can be associated with a sharp increase in the density of electron states at energies near the van Hove singularity.

For a linear ordinary differential equation (ODE in short) of the third order, results are presented that supplement the theory of conjugate points and extremal solutions by W. Leighton, Z. Nehari, M. Hanan. It is especially noted the sensitivity of solutions to the initial data, which makes their numerical study difficult. Similar results were obtained for the third-order nonlinear equations of the Emden-Fowler type.

This work introduces the mathematical framework of the novel “First-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations (1st-CASAM-NODE)” which yields exact expressions for the first-order sensitivities of NODE decoder-responses to the NODE parameters, including encoder initial conditions, while enabling the most efficient computation of these sensitivities. The application of the 1st-CASAM-NODE is illustrated by using the Nordheim-Fuchs reactor dynamics/safety phenomenological model, which is representative of physical systems that would be modeled by NODE while admitting exact analytical solutions for all quantities of interest (hidden states, decoder outputs, sensitivities with respect to all parameters and initial conditions, etc.). This work also lays the foundation for the ongoing work on conceiving the “Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations (2nd-CASAM-NODE)” which aims at yielding exact expressions for the second-order sensitivities of NODE decoder-responses to the NODE parameters and initial conditions while enabling the most efficient computation of these sensitivities.