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Asymptotic analysis of ultra-relativistic charge

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Asymptotic analysis of ultra-relativistic charge. / Burton, David A.; Gratus, Jonathan; Tucker, Robin W.
In: Annals of Physics, Vol. 322, No. 3, 03.2007, p. 599-630.

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Burton DA, Gratus J, Tucker RW. Asymptotic analysis of ultra-relativistic charge. Annals of Physics. 2007 Mar;322(3):599-630. doi: 10.1016/j.aop.2006.05.009

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@article{362bce0252a6452687bf1b100aa0aa3a,
title = "Asymptotic analysis of ultra-relativistic charge",
abstract = "This article offers a new approach for analysing the dynamic behaviour of distributions of charged particles in an electromagnetic field. After discussing the limitations inherent in the Lorentz–Dirac equation for a single point particle a simple model is proposed for a charged continuum interacting self-consistently with the Maxwell field in vacuo. The model is developed using intrinsic tensor field theory and exploits to the full the symmetry and light-cone structure of Minkowski spacetime. This permits the construction of a regular stress-energy tensor whose vanishing divergence determines a system of non-linear partial differential equations for the velocity and self-fields of accelerated charge. Within this covariant framework a particular perturbation scheme is motivated by an exact class of solutions to this system describing the evolution of a charged fluid under the combined effects of both self and external electromagnetic fields. The scheme yields an asymptotic approximation in terms of inhomogeneous linear equations for the self-consistent Maxwell field, charge current and time-like velocity field of the charged fluid and is defined as an ultra-relativistic configuration. To facilitate comparisons with existing accounts of beam dynamics an appendix translates the tensor formulation of the perturbation scheme into the language involving electric and magnetic fields observed in a laboratory (inertial) frame.",
keywords = "Radiation reaction, Ultra-relativistic particle beams, Accelerated charge, Non-neutral charge",
author = "Burton, {David A.} and Jonathan Gratus and Tucker, {Robin W.}",
note = "The final, definitive version of this article has been published in the Journal, Annals of Physics 322 (3), 2007, {\textcopyright} ELSEVIER.",
year = "2007",
month = mar,
doi = "10.1016/j.aop.2006.05.009",
language = "English",
volume = "322",
pages = "599--630",
journal = "Annals of Physics",
issn = "0003-4916",
publisher = "ELSEVIER ACADEMIC PRESS INC",
number = "3",

}

RIS

TY - JOUR

T1 - Asymptotic analysis of ultra-relativistic charge

AU - Burton, David A.

AU - Gratus, Jonathan

AU - Tucker, Robin W.

N1 - The final, definitive version of this article has been published in the Journal, Annals of Physics 322 (3), 2007, © ELSEVIER.

PY - 2007/3

Y1 - 2007/3

N2 - This article offers a new approach for analysing the dynamic behaviour of distributions of charged particles in an electromagnetic field. After discussing the limitations inherent in the Lorentz–Dirac equation for a single point particle a simple model is proposed for a charged continuum interacting self-consistently with the Maxwell field in vacuo. The model is developed using intrinsic tensor field theory and exploits to the full the symmetry and light-cone structure of Minkowski spacetime. This permits the construction of a regular stress-energy tensor whose vanishing divergence determines a system of non-linear partial differential equations for the velocity and self-fields of accelerated charge. Within this covariant framework a particular perturbation scheme is motivated by an exact class of solutions to this system describing the evolution of a charged fluid under the combined effects of both self and external electromagnetic fields. The scheme yields an asymptotic approximation in terms of inhomogeneous linear equations for the self-consistent Maxwell field, charge current and time-like velocity field of the charged fluid and is defined as an ultra-relativistic configuration. To facilitate comparisons with existing accounts of beam dynamics an appendix translates the tensor formulation of the perturbation scheme into the language involving electric and magnetic fields observed in a laboratory (inertial) frame.

AB - This article offers a new approach for analysing the dynamic behaviour of distributions of charged particles in an electromagnetic field. After discussing the limitations inherent in the Lorentz–Dirac equation for a single point particle a simple model is proposed for a charged continuum interacting self-consistently with the Maxwell field in vacuo. The model is developed using intrinsic tensor field theory and exploits to the full the symmetry and light-cone structure of Minkowski spacetime. This permits the construction of a regular stress-energy tensor whose vanishing divergence determines a system of non-linear partial differential equations for the velocity and self-fields of accelerated charge. Within this covariant framework a particular perturbation scheme is motivated by an exact class of solutions to this system describing the evolution of a charged fluid under the combined effects of both self and external electromagnetic fields. The scheme yields an asymptotic approximation in terms of inhomogeneous linear equations for the self-consistent Maxwell field, charge current and time-like velocity field of the charged fluid and is defined as an ultra-relativistic configuration. To facilitate comparisons with existing accounts of beam dynamics an appendix translates the tensor formulation of the perturbation scheme into the language involving electric and magnetic fields observed in a laboratory (inertial) frame.

KW - Radiation reaction

KW - Ultra-relativistic particle beams

KW - Accelerated charge

KW - Non-neutral charge

U2 - 10.1016/j.aop.2006.05.009

DO - 10.1016/j.aop.2006.05.009

M3 - Journal article

VL - 322

SP - 599

EP - 630

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

IS - 3

ER -