Electromagnetism

Summary

In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interactions of atoms and molecules. Electromagnetism can be thought of as a combination of electrostatics and magnetism, two distinct but closely intertwined phenomena. Electromagnetic forces occur between any two charged particles, causing an attraction between particles with opposite charges and repulsion between particles with the same charge, while magnetism is an interaction that occurs exclusively between charged particles in relative motion. These two effects combine to create electromagnetic fields in the vicinity of charged particles, which can accelerate other charged particles via the Lorentz force. At high energy, the weak force and electromagnetic force are unified as a single electroweak force. The electromagnetic force is responsible for

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https://en.wikipedia.org/wiki/Electromagnetism

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Ce cours introduit les lois fondamentales de l'électricité et les méthodes permettant d'analyser des circuits électriques linéaires, composés de résistances, condensateurs et inductances. On commencera par le régime continu pour passer ensuite au régime alternatif sinusoïdal, monophasé et triphasé.

The topics covered by the course are concepts of fluid mechanics, waves, and electromagnetism.

The course first develops the basic laws of electricity and magnetism and illustrates the use in understanding various electromagnetic phenomena.

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The Large Hadron Collider (LHC) has been producing pp collisions at 7 and 8 TeV since 2010 and promises a new era of discoveries in particle physics. One of its experiments, the Large Hadron Collider beauty (LHCb) experiment, was constructed to study CP violation in the B meson system. In addition to B physics, new Physics beyond the Standard Model can also be searched for at this single-arm forward spectrometer. With the different sub-detectors and the high resolution of the tracking system, the LHCb detector has the ability to search for heavy, long-lived and charged particles, which are predicted by extensions of the Standard Model. One of these extensions, the minimal Gauge Mediated Supersymmetry Breaking (mGMSB), proposes such a particle, named stau (τ~) - the SUSY bosonic counterpart of the heavy lepton tau (τ). The theory proposes that the staus may be pair-produced in pp collisions or in the decays of heavier particles, and have only electromagnetic interactions with the atoms of the medium like the muons. Therefore, we expect that at the energy of the LHC these particles can be produced if they do exist and that we have a chance to discover them at LHCb, as well as at the other experiments of the LHC. This thesis is dedicated to the search for stau pairs produced in pp collisions at the centre-of-mass energies √s = 7 and 8 TeV in the LHCb detector. For this purpose, we generated the stau pairs with seven different particle masses ranging from 124 to 309 GeV/c2 and simulated their path through the LHCb detector, as well as their muon background from the decays Z0, γ∗ → μ+μ−. Based on the results from the simulation, a set of cuts are then defined to select the stau pairs. Some muon pairs at high energies will also pass the selection cuts. Thus, to separate the stau pairs from the muon pairs, the Neural Network technique has been used. A first Neural Network has been used to distinguish the stau tracks from the muon tracks using their signals left in the sub-detectors: the VELO silicon detector, the electromagnetic calorimeter, the hadron calorimeter and the RICH detectors. Then, two methods to select the stau pairs have been developed: the first one is based on the product of the two responses from the first Neural Network (NN1) for the two tracks, the second one employs a second Neural Network to separate the stau pairs from the muon pairs by using the above product of the two NN1 responses and the invariant mass of pair. Finally, a favourable region for the staus finding has been defined and the expected numbers of stau and muon pairs in this region have been evaluated. The training of the Neural Network has been achieved with the Monte Carlo variables, then the trained Neural Network has been used to classify the data. The data used in our work were collected by the LHCb experiment in 2011 and 2012 and correspond to integrated luminosities of 1 fb−1 at √s = 7 TeV and of 2 fb−1 at √s = 8 TeV. No significant excess of signal has been observed. Upper limits at 95% CL on the cross section for stau pair production in pp collisions at √s = 7 and 8 TeV have been computed by using the profile likelihood method, which is derived from the well known Feldman and Cousins method.

EPFL2013

Backreaction of electromagnetic fields and the Schwinger effect in pseudoscalar inflation magnetogenesis

Oleksandr Sobol

We study magnetogenesis in axionlike inflation driven by a pseudoscalar field phi coupled axially to the electromagnetic (EM) field (beta/M-p)phi F-mu nu(F) over tilde mu nu with dimensionless coupling constant beta. A set of equations for the inflaton field, scale factor, and expectation values of quadratic functions of the EM field is derived. These equations take into account the Schwinger effect and the backreaction of generated EM fields on the Universe expansion. It is found that the backreaction becomes important when the EM energy density reaches the value rho(EM) similar to (root 2 epsilon/beta)rho(inf) (epsilon is the slow-roll parameter and rho(inf) is the energy density of the inflaton) slowing down the inflaton rolling and terminating magnetogenesis. The Schwinger effect becomes relevant when the electric energy density exceeds the value rho(E) similar to alpha(-3)(EM)(rho(2)(tot)/M-p(4)), where rho(tot) = 3H(2)M(p)(2) is the total energy density and alpha(EM) is the EM coupling constant. For large beta, produced charged particles could constitute a significant part of the Universe energy density even before the preheating stage. Numerically studying magnetogenesis in the alpha-attractor model of inflation, we find that it is possible to generate helical magnetic fields with the maximal strength 10(-15) G, however, only with the correlation length of order 1 pc at present.

2019

Influence of backreaction of electric fields and Schwinger effect on inflationary magnetogenesis

Oleksandr Sobol

We study the generation of electromagnetic fields during inflation when the conformal invariance of Maxwell's action is broken by the kinetic coupling f(2)(phi)F mu nu F mu nu of the electromagnetic field to the inflaton field phi We consider the case where the coupling function f(phi) decreases in time during inflation and, as a result, the electric component of the energy density dominates over the magnetic one. The system of equations which governs the joint evolution of the scale factor, inflaton field, and electric energy density is derived. The backreaction occurs when the electric energy density becomes as large as the product of the slow-roll parameter. and inflaton energy density,rho(E) similar to epsilon rho(inf). It affects the inflaton field evolution and leads to the scale-invariant electric power spectrum and the magnetic one which is blue with the spectral index n(B) = 2 for any decreasing coupling function. This gives an upper limit on the present-day value of observed magnetic fields below 10(-22) G. It is worth emphasizing that since the effective electric charge of particles e(eff) = e/f is suppressed by the coupling function, the Schwinger effect becomes important only at the late stages of inflation when the inflaton field is close to the minimum of its potential. The Schwinger effect abruptly decreases the value of the electric field, helping to finish the inflation stage and enter the stage of preheating. It effectively produces the charged particles, implementing the Schwinger reheating scenario even before the fast oscillations of the inflaton. The numerical analysis is carried out in the Starobinsky model of inflation for the powerlike f proportional to a(a) and Ratra-type f = expo(beta phi/M-p) coupling functions.

2018

EPFL2013