Exact Solution of the Relativistic Equation of Motion of a Charged Particle Driven by an Elliptically Polarized Electromagnetic Shaped Pulse Propagating Along a Static and Homogeneous Magnetic Field

Ondarza, R.; Gómez, Federico

doi:10.1109/tps.2004.826117

Cited by 9 publications

(2 citation statements)

References 16 publications

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“…For instance, in plasma physics, this problem is concerned with the mechanics of particle acceleration, when heating and radioactive effects are taken into account, see Ref. [35]. This kind of studies are based on the numerical integration of Eq.…”

Section: Discussionmentioning

confidence: 99%

Equations of motion of a relativistic charged particle with a curvature depending actions

Arreaga-Garcia,

Morales

2013

Preprint

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We present an introduction to the study of a relativistic particle moving under the influence of its own Frenet-Serret curvatures. With the aim of introducing the notation and conventions used in this paper, we first recall the action of a relativistic particle.We then suggest a mathematical generalization of this action in the sense that now the action may include terms of the curvatures of the world line generated by the particle in Minkowski space-time. We go on to develop a pedagogical introduction to a variational calculus which takes advantage of the Frenet-Serret equations for the relativistic particle. Finally, we consider a relativistic particle coupled to an electromagnetic field that is moving under the influence of its own Frenet-Serret curvatures. Within this frame based on the Frenet-Serret basis, we obtain the equations of motion for several curvature dependent actions of interest in physics. Later, as an illustration of the formalism developed, we consider the simplest case, that of a relativistic particle when no geometrical action is included, in order to show (i) the equivalence of this formalism to the Newton's second law with the Lorentz force and (ii) the integrability in the case of a constant electromagnetic field.

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Section: Discussionmentioning

confidence: 99%

Equations of motion of a relativistic charged particle with a curvature depending actions

Arreaga-Garcia,

Morales

2013

Preprint

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“…The previous studies[ [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]] on the topic have not considered the effect of radiation reaction in this scheme. The radiation reaction (or radiative friction) is a recoil force acting on the accelerating (retarding) particle as a result of emission of radiation and can in turn influence the motion of the particle.…”

Section: Introductionmentioning

confidence: 99%

Radiation reaction effect on laser driven auto-resonant particle acceleration

2015

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The effects of radiation reaction force on laser driven auto-resonant particle acceleration scheme are studied using Landau-Lifshitz equation of motion. These studies are carried out for both linear as well as circularly polarized laser fields in the presence of static axial magnetic field. From the parametric study, a radiation reaction dominated region has been identified in which the particle dynamics is greatly effected by this force. In the radiation reaction dominated region the two significant effects on particle dynamics are seen viz., (1) saturation in energy gain by the initially resonant particle, (2) net energy gain by a initially non-resonant particle which is caused due to resonance broadening. It has been further shown that with the optimum choice of parameters this scheme can be efficiently used to produce electrons with energies in the range of hundreds of TeV. The quantum corrections to the Landu-Lifshitz equation of motion have also been taken into account. The difference in the energy gain estimates of the particle by the quantum corrected and classical Landu-Lifshitz equation are found to be insignificant for the present day as well as upcoming laser facilities.

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Adiabatic formulation of charged particle dynamics in an inhomogeneous electro-magnetic field

2013

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The relativistic motion of a charged particle is studied in an inhomogeneous field of finite duration laser pulse. An inhomogeneity in a laser field is due to the spatial variation of laser intensity. Such a variation in laser intensity is characteristic of focused and de-focused laser beams. In the presence of an inhomogeneity, the problem becomes non-integrable and hence particle dynamics can not be derived exactly. In the present work considering a slow variation in the laser intensity, it is shown that the particle dynamics is associated with an adiabatic invariant. It is further found that the adiabatic invariant itself evolves and in a typical example changes such that the adiabaticity parameter attains a value of order unity. Thus higher orders of invariance are required for specifying the particle dynamics in terms of an adiabatic invariant. An adiabatic formalism is derived using the Lie transform perturbation method for calculating the higher orders of invariance and to obtain the evolution of the adiabatic invariant. The estimates of energy gained by a particle considering focused laser field are obtained by solving the equation of motion numerically. On comparing the results of a numerical experiment with theoretical predictions, it is found that the energy estimates improve on taking into account higher orders of invariance predicted by the present theory.

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Exact Solution of the Relativistic Equation of Motion of a Charged Particle Driven by an Elliptically Polarized Electromagnetic Shaped Pulse Propagating Along a Static and Homogeneous Magnetic Field

Cited by 9 publications

References 16 publications

Equations of motion of a relativistic charged particle with a curvature depending actions

Equations of motion of a relativistic charged particle with a curvature depending actions

Radiation reaction effect on laser driven auto-resonant particle acceleration

Adiabatic formulation of charged particle dynamics in an inhomogeneous electro-magnetic field

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