Non relativistic limit of the Landau-Lifshitz equation: A new equation

G. Ares de Parga; S. Domínguez-Hernández; E. Salinas-Hernández

doi:10.1016/j.aop.2016.02.012

Non relativistic limit of the Landau-Lifshitz equation: A new equation

G. Ares de Parga, S. Domínguez-Hernández, E. Salinas-Hernández

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

It is shown that Ford equation is not adequate in general to describe the motion of a charged particle including the reaction force in the non relativistic limit. As in General Relativity where a post-Newtonian method is developed in order to describe the gravitational effects at low velocities and small energies, an extra term inherited from Special Relativity must be added to the Ford equation. This is due to that the new term is greater than the reaction force in many physical situations. The Coulombic case is analyzed showing the necessity of including the new term. Comparison with General Relativity results is analyzed. The Vlasov equation to first order in 1/c² is proposed for the constant electric and magnetic fields.

Original language	English
Pages (from-to)	45-65
Number of pages	21
Journal	Annals of Physics
Volume	369
DOIs	https://doi.org/10.1016/j.aop.2016.02.012
State	Published - 1 Jun 2016

Keywords

Ford equation
Landau-Lifshitz equation
Radiation reaction
Vlasov equation

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10.1016/j.aop.2016.02.012

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title = "Non relativistic limit of the Landau-Lifshitz equation: A new equation",

abstract = "It is shown that Ford equation is not adequate in general to describe the motion of a charged particle including the reaction force in the non relativistic limit. As in General Relativity where a post-Newtonian method is developed in order to describe the gravitational effects at low velocities and small energies, an extra term inherited from Special Relativity must be added to the Ford equation. This is due to that the new term is greater than the reaction force in many physical situations. The Coulombic case is analyzed showing the necessity of including the new term. Comparison with General Relativity results is analyzed. The Vlasov equation to first order in 1/c2 is proposed for the constant electric and magnetic fields.",

keywords = "Ford equation, Landau-Lifshitz equation, Radiation reaction, Vlasov equation",

author = "{Ares de Parga}, G. and S. Dom{\'i}nguez-Hern{\'a}ndez and E. Salinas-Hern{\'a}ndez",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",

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T1 - Non relativistic limit of the Landau-Lifshitz equation

T2 - A new equation

AU - Ares de Parga, G.

AU - Domínguez-Hernández, S.

AU - Salinas-Hernández, E.

PY - 2016/6/1

Y1 - 2016/6/1

N2 - It is shown that Ford equation is not adequate in general to describe the motion of a charged particle including the reaction force in the non relativistic limit. As in General Relativity where a post-Newtonian method is developed in order to describe the gravitational effects at low velocities and small energies, an extra term inherited from Special Relativity must be added to the Ford equation. This is due to that the new term is greater than the reaction force in many physical situations. The Coulombic case is analyzed showing the necessity of including the new term. Comparison with General Relativity results is analyzed. The Vlasov equation to first order in 1/c2 is proposed for the constant electric and magnetic fields.

AB - It is shown that Ford equation is not adequate in general to describe the motion of a charged particle including the reaction force in the non relativistic limit. As in General Relativity where a post-Newtonian method is developed in order to describe the gravitational effects at low velocities and small energies, an extra term inherited from Special Relativity must be added to the Ford equation. This is due to that the new term is greater than the reaction force in many physical situations. The Coulombic case is analyzed showing the necessity of including the new term. Comparison with General Relativity results is analyzed. The Vlasov equation to first order in 1/c2 is proposed for the constant electric and magnetic fields.

KW - Ford equation

KW - Landau-Lifshitz equation

KW - Radiation reaction

KW - Vlasov equation

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U2 - 10.1016/j.aop.2016.02.012

DO - 10.1016/j.aop.2016.02.012

M3 - Artículo

SN - 0003-4916

VL - 369

SP - 45

EP - 65

JO - Annals of Physics

JF - Annals of Physics

ER -

Non relativistic limit of the Landau-Lifshitz equation: A new equation

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Keywords

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