In the present analysis we study the dynamics of charged particles under the action of slowly modulated electromagnetic carrier waves. With the use of a high-frequency laser mode along with a modulated static magnetic wiggler, we show that the ensuing total field effectively acts as a slowly modulated high-frequency beat-wave field typical of inverse free-electron laser schemes. This effective resulting field is capable of accelerating particles in much the same way as space-charge wake fields do in plasma accelerators, with the advantage of being more stable than plasma related methods. Acceleration occurs as particles transition from ponderomotive to resonant regimes, so we develop the ponderomotive formalism needed to examine this problem. The ponderomotive formalism includes terms that, although not discussed in the usual applications of the approximation, are nevertheless of crucial importance in the vicinity of resonant capture. The role of these terms is also briefly discussed in the context of generic laser-plasma interactions.

Spatially modulated electrostatic fields can be designed to efficiently accelerate particles by exploring the relationships between the amplitude, the phase velocity, the shape of the potential, and the initial velocity of the particle. The acceleration process occurs when the value of the velocity excursions of the particle surpasses the phase velocity of the carrier, as a resonant mechanism. The ponderomotive approximation based on the Lagrangian average is usually applied in this kind of system in non-accelerating regimes. The mean dynamics of the particle is well described by this approximation far from resonance. However, the approximation fails to predict some interesting features of the model near resonance, such as the uphill acceleration phenomenon. A canonical perturbation theory is more accurate in these conditions. In this work, we compare the results from the Lagrangian average and from a canonical perturbation theory, focusing in regions where the results of these two approaches differ from each other.

In the present analysis, we study effects of the radiation reaction (RR) on the dynamics of charged particles submitted to the action of localized longitudinal high-frequency carriers travelling at the speed of light. As the wave's crests and troughs keep overtaking particles, dissipative RR forces tend to drag particles alongside the wave in an effort to reduce the relative wave–particle speed. Particles of course never reach the phase velocity of the wave, but are instead driven to an ever-growing velocity, towards the speed of light, while in the wave localization region. We developed a modified average Hamiltonian formalism capable of describing the intricacies of the corresponding dynamics. The modified formalism agrees with simulations and is of particular usefulness in the study of optimum values for the localization length and maximum wave amplitude.

Nine gold-plated costume jewelries bought in the street market of Porto Alegre and from Chinese websites were investigated through Particle-Induced X-ray Emission (PIXE) and Rutherford Backscattering Spectrometry (RBS) in order to verify their elemental composition and distribution. The analyzed costume jewelries were made of Cu-based alloys with Ni, Zn, Sn and Al. Elements such as Ag, Al, Bi, Cd, Co and Fe were found in minor amounts in some particular samples. Through RBS, it was possible to distinguish the bulk from the gold-plated layer. Toxic elements as Ni and Cd were found in at least one sample. The high concentration of Ni comes from the bulk Cu-alloy below the Au layer. In this case, the Au acts as a protective layer separating the Ni from the user’s skin.

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