Flux magnétique | EPFL Graph Search

Le flux magnétique ou flux d'induction magnétique, souvent noté \Phi, est une grandeur physique mesurable caractérisant l'intensité et la répartition spatiale du champ magnétique. Cette grandeur est égale au flux du champ magnétique \vec{B} à travers une surface orientée \vec{S}. Ce flux est par définition le produit scalaire de ces deux vecteurs (voir définition mathématique ci-dessous). Son unité d'expression dans le Système international d'unités est le weber (unité homogène à des volts-secondes). Définition mathématique thumb|right|300px|Visualisation d'une surface circonscrite par une bobine à trois spires. Par définition, le flux du champ magnétique \vec{B} à travers un élément infinitésimal de surface orienté \vec{\mathrm{d}S} est le produit scalaire de ces deux vecteurs : :\mathrm{d}\Phi = \vec{B}\cdot\vec{\mathrm{d}S} = |\vec B|\cdot|\vec {\mathrm{d} S}|\cdot\cos\theta où \t

Magnetism and metal-organic self-assembly of rare-earth atoms on decoupling layers

Sébastien Reynaud

This thesis presents investigations of magnetic and structural properties of two dimensional metal-organic frameworks and of single atoms, both adsorbed on decoupling layers grown on metal surfaces, with focus on rare earth elements.We first report on a series of attempts at realizing self-assembled metal-organic networks on different decoupling layers, probed by scanning tunneling microscopy. The aim is to produce regular structures with high surface filling factors such that the magnetic properties of the rare earth atoms in the metal-organic networks can be investigated by X-ray ensemble measurements. The combinations of three molecular ligands (QDC, BDA, ZnTPyP) on three insulating layers (MgO, NaCl, graphene) with Tb as rare earth are reported. Of the three decoupling layers, only graphene is found to allow the synthesis of metal-organic structures. We successfully synthesized large islands of a rare earth-QDC coordination complex, with a majority of fivefold coordination of the rare earth atoms. The same structure is reproduced with Dy and Er.X-ray absorption spectroscopy, X-ray magnetic circular and linear dichroism measurements are then carried out on the Dy- and Er-QDC/gr/Ir(111) networks. Compared to single atoms on gr/Ir(111), both Dy and Er change their

4f

occupancy from 4

f^n

4f^{n-1}

and change their easy axis of magnetization. Both species are paramagnetic when incorporated into the metal-organic structure. The last part of the thesis is devoted to the study of Dy, Ho, and Gd on NaCl thin films. All three atoms display

4f

occupancy of the gas phase. The top-Cl adsorption site is determined with scanning tunneling microscopy. The magnetic properties are probed with X-ray absorption spectroscopy, X-ray magnetic circular and linear dichroism. Ho and Gd are paramagnetic. Dy has out-of-plane anisotropy with open hysteresis at non zero magnetic field. However, thermally assisted quantum tunneling of the magnetization prevents remanence at zero field.

EPFL2022

Bootstrap current compensation with electron-cyclotron waves in 3D reactor-size configurations

Sergi Ferrando I Margalet

In magnetic confinement devices, the inhomogeneity of the confining magnetic field along a magnetic field line generates the trapping of particles (with low ratio of parallel to perpendicular velocities) within local magnetic wells. One of the consequences of the trapped particles is the generation of a current, known as the bootstrap current (BC), whose direction depends on the nature of the magnetic trapping. The BC provides an extra contribution to the poloidal component of the confining magnetic field. The variation of the poloidal component produces the alteration of the winding of the magnetic field lines around the flux surfaces quantified by the rotational transform ι. When ι reaches low rational values, it can trigger the generation of ideal MHD instabilities. Therefore, the BC may be responsible for the destabilisation of the configuration. This thesis is divided into two parts. In the first part, we present a self-consistent method to calculate the BC and assess its effect on equilibrium and stability in general 3D configurations. This procedure is applied to two reactor-size prototypes (both with plasma volumes ∼ 1000m3): a quasi-axisymmetric (QAS) system and a quasi helically symmetric (QHS) system with magnetic structures that develop BC in opposite directions. The BC increases with the plasma pressure, therefore its relevance is enhanced when dealing with reactor-level scenarios. The behaviour of both prototypes at reactor level values of β ≡ (kinetic plasma pressure)/(magnetic pressure) is assessed, as well as its alteration of the equilibrium and stability. In the QAS prototype, BC-consistent equilibria have been computed up to β = 6.7% and the configuration is shown to be stable up to β = 6.4%. Convergence of self-consistent BC calculations for the QHS case is achieved only up to β = 3.5%, but the configuration is unstable for β ≥ 0.6%. The relevance of symmetry breaking modes of the Fourier expansion of the confining magnetic field on the generation of BC is studied for each prototype. This proves the close relationship between magnetic structure and BC. Having established the potentially dangerous implication of the BC, principally, in reactor prototypes, a method to compensate its harmful effects is proposed in the second part of the thesis. It consists of the modelling of the current driven by externally launched ECWs within the plasma to compensate the effects of the BC. This method is flexible enough to allow the identification of the appropriate scenarios in which to generate the required CD depending on the nature of the confining magnetic field and the specific plasma parameters of the configuration. Both the BC and the CD calculations are included in a self-consistent scheme which leads to the computation of a stable BC+CD-consistent MHD equilibrium. This procedure is applied in this thesis to simulate the required CD to stabilise the QAS and QHS prototypes introduced in the first part. The estimation of the input power required and the effect of the driven current on the final equilibrium of the system is performed for several relevant scenarios and wave polarisations providing various options of stabilising driven currents. Several scenarios have been devised for each prototype in order to drive current at the appropriate location and with the desired direction. Different polarisations and launching conditions have been employed to this purpose. In particular, a HFS launched X2 ECW with an input power of 1.5MW has been shown to drive sufficient current to maintain the rotational transform below the critical value 2/3 at β = 6.4% for the QAS reactor. Correspondingly, in the QHS reactor, an X3-mode ECW of 100KW was sufficient to drive the current required to push the rotational transform below unity near the magnetic axis at β = 3%. Thus, stabilisation of BC-driven instabilities with externally launched ECWs has been achieved for both contrasting configurations. The method proposed in this thesis allows also the utilisation of EBW in the generation of CD. The possible advantages of EBCD for compensation studies are described as well as their possible application to the two prototypes under consideration. The BC+CD procedure is particularly interesting to investigate new magnetic geometries as potential candidates for fusion reactors. With this numerical tool, it is possible to assess the implications of their consistent BC when operating at reactor level. It also allows to quantify how much power would be required to maintain the system MHD stable in these circumstances. Nevertheless, this method is flexible enough to be applicable to any configuration.

EPFL2006

Possibilities and limitations of using Preisach model for hysteresis in superconductors

Marten Sjöström

Superconductors of type-II are partially penetrated by magnetic flux, where the pinning of flux tubes constitutes a memory that gives rise to a hysteresis. However, the hysteresis gradually disappears when a transport current approaches the critical current. This paper investigates what possibilities and limitations the Preisach model has to describe this hysteresis. Previous results are complimented by demonstrating the limitation to higher harmonics, the computation of an inverse model including an inductive part, and by modelling the gradual disappearing hysteresis with a saturation.

2001