Guiding-centre transformation of the radiation–reaction force in a non-uniform magnetic field

In this paper, we present the guiding-centre transformation of the radiation–reaction force of a classical point charge travelling in a non-uniform magnetic field. The transformation is valid as long as the gyroradius of the charged particles is much smaller than the magnetic field non-uniformity length scale, so that the guiding-centre Lie-transform method is applicable. Elimination of the gyromotion time scale from the radiation–reaction force is obtained with the Poisson-bracket formalism originally introduced by Brizard (Phys. Plasmas, vol. 11, 2004, 4429–4438), where it was used to eliminate the fast gyromotion from the Fokker–Planck collision operator. The formalism presented here is applicable to the motion of charged particles in planetary magnetic fields as well as in magnetic confinement fusion plasmas, where the corresponding so-called synchrotron radiation can be detected. Applications of the guiding-centre radiation–reaction force include tracing of charged particle orbits in complex magnetic fields as well as the kinetic description of plasma when the loss of energy and momentum due to radiation plays an important role, e.g. for runaway-electron dynamics in tokamaks.

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Radiation-reaction force on a moving mirror

Journal de Physique I ◽

10.1051/jp1:1993237 ◽

1993 ◽

Vol 3 (11) ◽

pp. 2151-2159 ◽

Cited By ~ 10

Author(s):

Claudia Eberlein

Keyword(s):

Reaction Force ◽

Radiation Reaction ◽

Radiation Reaction Force

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The two-body problem: an effective-one-body approach

10.1093/oso/9780198786399.003.0056 ◽

2018 ◽

Author(s):

Nathalie Deruelle ◽

Jean-Philippe Uzan

Keyword(s):

Body Problem ◽

Equations Of Motion ◽

Reaction Force ◽

Kerr Black Hole ◽

Radiation Reaction ◽

Spherically Symmetric ◽

Geodesic Motion ◽

Two Body Problem ◽

Symmetric Spacetime ◽

Radiation Reaction Force

This chapter presents the basics of the ‘effective-one-body’ approach to the two-body problem in general relativity. It also shows that the 2PN equations of motion can be mapped. This can be done by means of an appropriate canonical transformation, to a geodesic motion in a static, spherically symmetric spacetime, thus considerably simplifying the dynamics. Then, including the 2.5PN radiation reaction force in the (resummed) equations of motion, this chapter provides the waveform during the inspiral, merger, and ringdown phases of the coalescence of two non-spinning black holes into a final Kerr black hole. The chapter also comments on the current developments of this approach, which is instrumental in building the libraries of waveform templates that are needed to analyze the data collected by the current gravitational wave detectors.

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Theoretical Optimization of Cascading Magnets’ Structure for Oxygen Enrichment by Gradient Magnetic Fields

Volume 9: Heat Transfer, Fluid Flows, and Thermal Systems, Parts A, B and C ◽

10.1115/imece2009-12141 ◽

2009 ◽

Author(s):

Fengchao Li ◽

Li Wang ◽

Ping Wu ◽

Shiping Zhang

Keyword(s):

Magnetic Field ◽

Magnetic Fields ◽

Magnetic Flux ◽

Oxygen Concentration ◽

Uniform Magnetic Field ◽

Oxygen Enrichment ◽

Gradient Magnetic Field ◽

Length Direction

Oxygen molecules are paramagnetic while nitrogen molecules are diamagnetic. In the same gradient magnetic field, the magnetizing forces on oxygen molecules are stronger than those on nitrogen molecules, which in opposite directions. The intercepting effect on oxygen molecules by gradient magnetic field can be used for oxygen enrichment from air. The structure, which is called multi-channel cascading magnets array frame in the paper, are optimized by additional yokes. By comparison of distributions of magnetic field in multi-channel array without yokes and that with yokes, the additional yokes can eliminate the differences among different magnetic spaces in multi-channel cascading magnets’ arrays and enhances the magnetic flux densities in spaces. Joining magnets together in the length direction can make the air stay longer in the ‘magnetic sieve’ and raise the oxygen concentration of air flowing out from the optimized multi-channel cascading magnets’ arrays. The inside additional yoke can used to avoid the gradient magnetic field at the joints of the magnets and get near uniform magnetic field along length direction. The optimized multi-channel cascading magnets’ array frames can effectively promote the development of oxygen enrichment from air by “magnetic sieve”.

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Spin-1/2 Particles under the Influence of a Uniform Magnetic Field in the Interior Schwarzschild Solution

Universe ◽

10.3390/universe7120467 ◽

2021 ◽

Vol 7 (12) ◽

pp. 467

Author(s):

Fayçal Hammad ◽

Alexandre Landry ◽

Parvaneh Sadeghi

Keyword(s):

Magnetic Field ◽

Magnetic Fields ◽

Total Mass ◽

Uniform Magnetic Field ◽

Energy Levels ◽

Relativistic Wave Equation ◽

Relativistic Wave ◽

Schwarzschild Solution ◽

Relativistic Regime ◽

The Magnetic Field

The relativistic wave equation for spin-1/2 particles in the interior Schwarzschild solution in the presence of a uniform magnetic field is obtained. The fully relativistic regime is considered, and the energy levels occupied by the particles are derived as functions of the magnetic field, the radius of the massive sphere and the total mass of the latter. As no assumption is made on the relative strengths of the particles’ interaction with the gravitational and magnetic fields, the relevance of our results to the physics of the interior of neutron stars, where both the gravitational and the magnetic fields are very intense, is discussed.

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Synchrotron Radiation Spectra

Publications of the Astronomical Society of Australia ◽

10.1017/s1323358000013291 ◽

1972 ◽

Vol 2 (3) ◽

pp. 142-144 ◽

Cited By ~ 1

Author(s):

L. J. Gleeson ◽

K. C. Westfold

Keyword(s):

Magnetic Field ◽

Synchrotron Radiation ◽

Energy Distribution ◽

Power Law ◽

Uniform Magnetic Field ◽

Charged Particles ◽

Radiation Spectra ◽

Field Lines

In this paper we give an account of the corrections that must be made to the formula for the emissivity ηf due to a power-law energy distribution of ultrarelativistic charged particles in a uniform magnetic field B0 in directions well away from the field lines when the effects of upper and lower cut-off values E2 and E1 in the energy distribution are not negligible.

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The Magnetic Fields of Pulsars

Symposium - International Astronomical Union ◽

10.1017/s0074180900236292 ◽

1974 ◽

Vol 64 ◽

pp. 187-187

Author(s):

D. M. Sedrakian

Keyword(s):

Magnetic Field ◽

Angular Velocity ◽

Magnetic Fields ◽

Relative Motion ◽

Kinematic Viscosity ◽

Charged Particles ◽

Normal Fluid ◽

Inertia Effects ◽

Generation Mechanisms ◽

Image Position

Two generation mechanisms of magnetic fields in pulsars are considered.If the temperature of a star is more than 108K, the star consists of a normal fluid of neutrons, protons and electrons. Because the angular velocity of pulsars is not constant dω/dt ≠0, inertia effects can occur, and generate magnetic fields through the relative motion of charged particles with different masses. The kinematic viscosity of electrons is 30 times larger than that of protons; hence electrons move with the crust, but the proton-neutron fluid will move relative to the electrons. The magnetic momentum can be calculated by the following formula where Meff = Mp + Mn(Nn/Np), R = radius of the star, σ = conductivity. For typical neutron stars we have dω/dt~ 10-8 s-2, R~106 cm, σ~1029 s-1 and we get a magnetic field of the order of 1010 G.

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