Exact solution to the Landau-Lifshitz equation in a constant electromagnetic field

Yaremko, Yurij

doi:10.1063/1.4820131

Cited by 13 publications

(10 citation statements)

References 29 publications

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“…As a check, we note that for a constant electric field, a = 0, and p ⊥ = 0, the LL solution ( 9) and the Lorentz solution (4) agree, and also solve the LAD equation. This is consistent with the literature result that there is 'no radiation reaction for hyperbolic motion' [35][36][37]; there is though radiation [35, 38, p. 399].…”

Section: Longitudinal Polarisationsupporting

confidence: 92%

“…Many authors have found exact solutions to the LAD and/or LL equations in a number of field configurations, including fields depending only on time [28], constant electromagnetic fields [36,52,53], rotating electric fields [5,53,54], the Coulomb potential in the nonrelativistic limit [55], and plane waves [45,46]. These works, the majority of which predate the RFD hypothesis, contain implicit support for it.…”

Section: Discussionmentioning

confidence: 99%

“…II.A]. Further, although the exact solution of LAD is not known even in a general constant field, its asymptotic behaviour is known [56], namely the particle worldline becomes confined to an eigen-2-plane of the field tensor; the same holds for the exact solution of LL 1 [36].…”

Section: Discussionmentioning

confidence: 99%

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Exact solutions in radiation reaction and the radiation-free direction

Ekman,

Heinzl,

Ilderton

2021

Preprint

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We present new exact solutions of the Landau-Lifshitz and higher-order Landau-Lifshitz equations describing particle motion, with radiation reaction, in intense electromagnetic fields. Through these solutions and others we compare the phenomenological predictions of different equations in the context of the conjectured 'radiation-free direction' (RFD). We confirm analytically in several cases that particle orbits predicted by the Landau-Lifshitz equation indeed approach the RFD at extreme intensities, and give time-resolved signals of this behaviour in radiation spectra.

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Section: Longitudinal Polarisationsupporting

confidence: 92%

Section: Discussionmentioning

confidence: 99%

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Exact solutions in radiation reaction and the radiation-free direction

Ekman,

Heinzl,

Ilderton

2021

Preprint

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“…A study of the numerical properties of the LL system in a constant magnetic field is presented in [20], and analytical solutiond of the LL equation in constant fields appear in [21] and [22]. We note that each component of the LL acceleration is equivalent to the numerator in the corresponding EFO accelerations, Eq.…”

Section: B Motion Parallel To a Constant Electric Fieldmentioning

confidence: 99%

Radiation reaction and limiting acceleration

Price,

Formanek,

Rafelski

2021

Preprint

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We investigate the strong acceleration properties of the radiation reaction force and identify a new and promising limiting acceleration feature in the Eliezer-Ford-O'Connell model: in the strong field regime, for many field configurations, we find an upper limit to acceleration resulting in a bound to the rate of radiation emission. If this model applies, strongly accelerated particles are losing energy at a much slower pace than predicted by the usual radiation reaction benchmark, the Landau-Lifshitz equation, which certainly can not be used in this regime. We explore examples involving various 'constant' electromagnetic field configurations and study particle motion in a light plane wave as well as in a material medium.

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“…It is known that the eigenvalues of the matrix F = F µ ν = F µρ g ρν , are the roots of the fourthdegree polynomial with invariants (1/2)F µν * F µν = ( E, B) and (1/2)F µν F µν = (B 2 − E 2 ) in the coefficients (for example see [56,57]). Therefore, the eigenvalues of the matrix Λ = −2eF are the roots of the equation…”

Section: Eigenvalues Of Electromagnetic Tensor For Constant Fieldsmentioning

confidence: 99%

Dirac particle with memory: Proper time non-locality

Tarasov

2020

Physics Letters A

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A generalization of the standard model of Dirac particle in external electromagnetic field is proposed. In the generalization we take into account interactions of this particle with environment, which is described by the memory function. This function takes into account that the behavior of the particle at proper time can depend not only at the present time, but also on the history of changes on finite time interval. In this case the Dirac particle can be considered an open quantum system with non-Markovian dynamics. The violation of the semigroup property of dynamic maps is a characteristic property of dynamics with memory. We use the Fock-Schwinger proper time method and derivatives of non-integer orders with respect to proper time. The fractional differential equation, which describes the Dirac particle with memory, and the expression of its exact solution are suggested. The asymptotic behavior of the proposed solutions is described. PACS 45.10.Hj Perturbation and fractional calculus methods PACS 03.65.Yz Decoherence; open systems; quantum statistical methods PACS 11.90.+t Other topics in general theory of fields and particles

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Exact solution to the Landau-Lifshitz equation in a constant electromagnetic field

Cited by 13 publications

References 29 publications

Exact solutions in radiation reaction and the radiation-free direction

Exact solutions in radiation reaction and the radiation-free direction

Radiation reaction and limiting acceleration

Dirac particle with memory: Proper time non-locality

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