Abraham–Lorentz force

Summary

In the physics of electromagnetism, the Abraham–Lorentz force (also known as the Lorentz–Abraham force) is the recoil force on an accelerating charged particle caused by the particle emitting electromagnetic radiation by self-interaction. It is also called the radiation reaction force, the radiation damping force, or the self-force. It is named after the physicists Max Abraham and Hendrik Lorentz. The formula although predating the theory of special relativity, was initially calculated for non-relativistic velocity approximations was extended to arbitrary velocities by Max Abraham and was shown to be physically consistent by George Adolphus Schott. The non-relativistic form is called Lorentz self-force while the relativistic version is called the Lorentz–Dirac force or collectively known as Abraham–Lorentz–Dirac force. The equations are in the domain of classical physics, not quantum physics, and therefore may not be valid at distances of roughly the Compton wavelen

Official source

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications

Related people

Related units

Related concepts

Related courses

Related lectures

Energetics of turbulence generated by chiral MHD dynamos

An asymmetry in the number density of left- and right-handed fermions is known to give rise to a new term in the induction equation that can result in a dynamo instability. At high temperatures, when a chiral asymmetry can survive for long enough, this chiral dynamo instability can amplify magnetic fields efficiently, which in turn drive turbulence via the Lorentz force. While it has been demonstrated in numerical simulations that this chiral magnetically driven turbulence exists and strongly affects the dynamics of the magnetic field, the details of this process remain unclear. The goal of this paper is to analyse the energetics of chiral magnetically driven turbulence and its effect on the generation and dynamics of the magnetic field using direct numerical simulations. We study these effects for different initial conditions, including a variation of the initial chiral chemical potential and the magnetic Prandtl number, PrM. In particular, we determine the ratio of kinetic to magnetic energy, Υ, in chiral magnetically driven turbulence. Within the parameter space explored in this study, Υ reaches a value of approximately 0.064–0.074–independently of the initial chiral asymmetry and for PrM=1. Our simulations suggest, that Υ decreases as a power law when increasing PrM by decreasing the viscosity. While the exact scaling depends on the details of the fitting criteria and the Reynolds number regime, an approximate result of Υ(PrM)=0.1 Pr−0.4M is reported. Using the findings from our numerical simulations, we analyse the energetics of chiral magnetically driven turbulence in the early Universe.

TAYLOR & FRANCIS LTD2019

Dynamo instabilities in plasmas with inhomogeneous chiral chemical potential

We study the dynamics of magnetic fields in chiral magnetohydrodynamics, which takes into account the effects of an additional electric current related to the chiral magnetic effect in high-energy plasmas. We perform direct numerical simulations, considering weak seed magnetic fields and inhomogeneities of the chiral chemical potential mu(5) with a zero mean. We demonstrate that a small-scale chiral dynamo can occur in such plasmas if fluctuations of mu(5) are correlated on length scales that are much larger than the scale on which the dynamo growth rate reaches its maximum. Magnetic fluctuations grow by many orders of magnitude due to the small-scale chiral dynamo instability. Once the nonlinear backreaction of the generated magnetic field on fluctuations of mu(5) sets in, the ratio of these scales decreases and the dynamo saturates. When magnetic fluctuations grow sufficiently to drive turbulence via the Lorentz force before reaching maximum field strength, an additional mean-field dynamo phase is identified. The mean magnetic field grows on a scale that is larger than the integral scale of turbulence after the amplification of the fluctuating component saturates. The growth rate of the mean magnetic field is caused by a magnetic alpha effect that is proportional to the current helicity. With the onset of turbulence, the power spectrum of mu(5) develops a universal k(-1) scaling independently of its initial shape, while the magnetic energy spectrum approaches a k(-3) scaling.

AMER PHYSICAL SOC2022

In this thesis, the development, design, fabrication and characterization of three innovative laser beam shaping, homogenizing and speckle reduction devices are reported. Typical beam shaping devices are static and not easily adaptable to a large variety of optical setups. Furthermore, the main issues when shaping coherent light are diffraction effects, speckle patterns, interferences and wavelength dependency. The devices presented in this work solve these issues. The main subjects discussed are beam shaping of coherent light and speckle reduction. Beam shaping and speckle reduction are important in many applications like laser machining, illumination, laser displays and photolithography. The first device presented is a dynamic diffuser and homogenizer for line generation. The 1D linear diffuser consists of a large single crystal silicon membrane of 5x5, 10x10 or 15x15 mm2 areas and having a thickness of 5 μm to 10 μm. This optical surface has a 100 % fill factor. The goal is to deform the membrane in one dimension only so that the light is also diffused in one dimension. The free standing continuous silicon membrane has a bridge type configuration. The actuation of the device is made electromagnetically at resonance by the use of the Lorentz force. Stiffening beams are fabricated below the membrane to decouple the 1D and 2D modes and to prevents 2D dynamic deformations. The device is fabricated on SOI wafer using standard microfabrication technologies. The devices are characterized using a laser doppler vibrometer (LDV) and a goniometer. The LDV measurements have shown that 1D and 2D modes can be excited separately. The diffusion angle is tunable between 0 to 22 mrad. The device is used to smooth out the interference effects created by a static 1D beam shaping optical element. The relative optical power efficiency of is 99.8 %. The device is capable to sustain high optical load of at least 140 W/cm2. It is now being tested in an industrial environment with high power CO2 laser for sealing glass capillaries. The second device presented is a 2D dynamic diffuser. It has to fulfill several characteristics, namely to diffuse light with small and tunable angle with high efficiency, reduce the speckle contrast and interference patterns, have a simple driving and packaging scheme and handle high optical power. A device with a 5x5 mm2 optical surface is designed, fabricated and characterized. The mirror is made of a thin and large deformable a-Si membrane which is supported by an array of posts. The disposition of the posts determines how the membrane is deformed in smaller sub-reflecting elements. A periodic and a pseudo random arrangements of the post arrays are designed. Electrostatic actuation is used to deform the membrane. The whole v deformable mirror is fabricated over a scanning stage. Out of plane resonant comb drive actuators are used to actuate the scanning stage. The diffusion of the light is performed by the deformation of the membrane while the homogenization of the beam profile is accomplished by the simultaneous scanning of the whole deformed membrane. Optical simulations are successfully used to predict the optical properties of the diffuser and to set the requirements for the electro-mechanical part of the device design. The fabrication process is using parylene-C as a refilling material and as a sacrificial layer to enable the fabrication of a 100 % fill factor deformable mirror. The membrane is continuous and release hole free. It is aluminum coated and showed an absolute optical power efficiency of 81 % in the actuated state. The high optical power handling of the device could not be tested. Nevertheless , the material of the device is silicon and the stage is connected with large springs to the frame for high heat conductivity. The pseudo random devices showed ability to shape an incoming beam regardless of its intensity profile into a output beam having a Gaussian profile. Besides, the diffusion angle is small and tunable between 0 to 10 mrad FWHM. The periodic devices is able to transform an incoming Gaussian beam into a super Gaussian intensity profile. Finally, the dynamic diffuser is capable of reducing the speckle contrast of a laser beam projected on a diffusing screen. The speckle contrast is reduced from 0.7 to 0.21 using the device alone and it is reduced to 0.11 when the dynamic diffuser is used in combination with a static diffuser. Tunable diffusion angle, smoothing of interferences, tunable beam shaping and speckle re- duction is realized while keeping the degree of freedom of the device to a minimum. By taking advantage of the optical design of the pseudo random diffuser, only one control electrode is needed to deform the membrane and one signal is used to scan the diffuser. The result is a very compact device, simple actuation and a straightforward packaging schemes. The last device presented is a very small footprint speckle reduction device. A simple actuation scheme using comb drive actuators and four folded springs enable large in plane displacement of a random phase plate. 180 μm of in plane displacement is achieved with a driving voltage as low as 29 V. The speckle contrast is reduced to 0.21 when the device is translating at 314 Hz. A comprehensive study of the diffuser characteristics is made to understand the surface parameters of the diffuser that influence directly the performances on the speckle reduction. The surface profile of the binary height has to be well defined to insure a phase shift of π. This very small device is a good candidate for integration in any portable device where speckle reduction is needed.

EPFL2012