Magnetic vector potential | EPFL Graph Search

In classical electromagnetism, magnetic vector potential (often called A) is the vector quantity defined so that its curl is equal to the magnetic field: \nabla \times \mathbf{A} = \mathbf{B}. Together with the electric potential φ, the magnetic vector potential can be used to specify the electric field E as well. Therefore, many equations of electromagnetism can be written either in terms of the fields E and B, or equivalently in terms of the potentials φ and A. In more advanced theories such as quantum mechanics, most equations use potentials rather than fields. Magnetic vector potential was first introduced by Franz Ernst Neumann and Wilhelm Eduard Weber in 1845 and in 1846, respectively. William Thomson also introduced vector potential in 1847, along with the formula relating it to the magnetic field. Magnetic vector potential The magnetic vector potential A is a vector field, defined along with the electric potential ϕ (a scalar field)

Magnetic force microscopy contrast formation and field sensitivity

Johannes Schwenk

The magnetic force microscope (MFM) is an established experimental tool for imaging stray fields with high spatial resolution and sensitivity. The MFM contrast can however contain contributions from the sample topography, variations in the surface Kelvin potential and magnetic contributions arising from grain-to-grain variations of the areal density of the magnetic moment, apart from the contrast generated by the micromagnetic pattern of the sample. Differential imaging techniques can be used to disentangle these contrast contributions. The calibration of the response of the MFM tip on different spatial wavelengths of the field allows a quantitative determination of the magnetic vector field in the plane parallel to the sample surface scanned by the tip. Generally, the tip becomes less sensitive for smaller spatial wavelengths. Obtaining a high spatial resolution thus requires a high measurement sensitivity that can be obtained by MFM operation in vacuum and by using & nbsp;high-quality factor cantilevers. As a result, field sensitivities better than 80 mu T/root Hz can be obtained, even with low magnetic moment tips.

2022

Carbon Nanotubes

Jaap Kroes

This thesis studies carbon nanotubes using state-of-the-art computational methods. Using large-scale quantum-mechanical calculations, based on density-functional-theory, we investigate several important aspects of the physics and chemistry of single-walled-nanotubes. The focus is on the effect of defects, namely adparticles and vacancies, on the structural, electronic and dynmical properties of the nanotubes. We also present preliminary results of simulations exploring a possible route for the formation of SWNTs from graphene nanoflakes. Adparticles include atomic hydrogen, oxygen, sulfur at different concentrations as well as nitrogen--oxides. Chemisorption of hydrogen as well as oxygen and isoelectronic species results in the formation of clusters on the sidewall, with characteristic structures corresponding to characteristic signatures in the electronic spectra. Especially in the case of oxygen, we find that relatively high energy barriers separate different structures: this shows that not only thermodynamically favored configurations are relevant for the understanding of oxygen chemisorption but the presence of traps cannot be neglected. The fingerpint of these traps is confirmed by scanning-tunneling spectroscopy. Trends with size and chirality of the nanotubes and oxygen coverage are studied in detail and also explained in terms of simple chemical descriptors. The importance of large-scale atomistic models is also emphasized to obtain convergent results and thus reliable predictions, and comparison is made of results we obtain using different gradient-corrected exchange-correlation functionals and in part with hybrid functionals. The study of nitrogen-oxides faces the difficulty to correctly represent physisorption, also with empirically corrected gradient-corrected exchange-correlation and hybrid functionals. Still our calculations of vibrational frequencies of different molecules on the sidewall, once compared with experiment, are able to distinguish the specific species observed in infrared spectra. Part of our work is centered on the comparison of widely used classical potentials (reactive force fields) with DFT results. Specifically we use them to study hydrogen and oxygen chemisorption, and especially examine the validity of several different force-fields for the description of the structure and energetics of single and double vacancies. In all cases, we find rather limited agreement with DFT results, showing the intrinsic difficulty to represent the subtle and intrinsic quantum effects governing the physico-chemical behavior of carbon nanotubes. Still, the wealth of results we have obtained might be useful for an improvement of these classical schemes for a specific application or other semi-classical models.

EPFL2014

Rapid 3-D Magnetic Integral Field Computation of Current-Carrying Finite Arc Segments With Rectangular Cross Section

Basile Kawkabani, Frédéric Michael Maurer

The computation of 3-D magnetic fields is a demanding task in the analysis of electrical machines and other electromagnetic devices. In this context, integral field calculation provides a smooth solution, high precision and resolution, "on-demand"-calculation, and an origin-based formulation of the magnetic field and the magnetic vector potential. However, conventional elliptic methods lead to huge parallelizable computing efforts and significant errors. In this article, a 3-D generic current-carrying arc segment with rectangular cross section is studied. A new analytic formulation is proposed to speed up the computation of magnetic fields and reduce the error by more than three orders of magnitude. In addition, the proposed magnetic vector potential expression has a similar accuracy as numerical integration. In fact, a significant reduction of the error level has been showcased clearly with respect to the existing approaches. This article is promising for improving the design methodology and optimization of large superconducting dipole magnets or arched end-winding geometries of large electrical machines.

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Carbon Nanotubes

Jaap Kroes

EPFL2014