Nonlinear Dynamics Of Charged Particle Research Articles

Nonlinear dynamics of charged particle slipping on rough surface with periodic force

This paper deals with two types of period-doubling bifurcation phenomena in a particle system, where the charged particle slips on rough surface with periodic force. The charged particle system is characterized by a two-dimensional nonlinear mapping, i.e., the Fermi–Ulam model (FUM) with dissipation. Based on the dissipative FUM, theoretical investigations are performed to identify the two types of period-doubling bifurcations with the assist of eigenvalue analysis approach and further to reveal their underlying mechanisms of the particle system as the strength of the periodic force for the particle system increases. Finally, bifurcation diagram and the maximum Lyapunov exponent are employed to analyze the dynamical evolution of bifurcation behaviors in the particle system quantitatively. These results are helpful for the in-depth understanding of transport mechanism of charged particle system.

Nonlinear dynamics of charged particles in an oblique electromagnetic wave

We study dynamics of a charged particle under action of an electromagnetic wave that propagates obliquely to a background uniform magnetic field. The dynamics is described by a slow–fast Hamiltonian system. We show that long-term dynamics is dominated by phenomena of capture of particle into resonance with the wave and escape from this resonance, as well as of scattering on resonance. We find that the variation of the particleʼs kinetic energy on the time interval between capture and escape is bounded and accumulated in the motion along the background field. We discuss possible applications of the obtained results.

Do phase portraits resist current sheet bifurcation?

We investigate the non-linear dynamics of charged particles in the double-humped current sheets that develop in the Earth’s magnetotail. Using Poincaré surfaces of section, we examine the various dynamical regimes that occur in a sharp field reversal and compare them to those obtained in single-humped current sheets. We demonstrate that bifurcation of the magnetotail current sheet does not alter the overall phase portrait structure which is characterized by three distinct regimes, viz., trapped, quasi-trapped, and transient. The phase portraits in single- and double-humped current sheets are not strictly identical though. A greater abundance of trapped particles and a distortion of the transient orbit domain are obtained in the latter case. In contrast, numerical simulations performed with an asymmetrical double-humped current distribution reveal considerable modification of the phase portrait with an expansion of the stochastic regime and a drastic reduction of the transient one. The degree of asymmetry in double-humped current sheets accordingly appears as a primary parameter to characterize the nonadiabatic behavior of charged particles.

Dynamics of charged particles in bifurcated current sheets: The κ ≈ 1 regime

We examine the nonlinear dynamics of charged particles in the double‐hump current sheets that develop during the late growth phase of substorms. We focus on particles for which the adiabaticity parameter κ (defined as the square root of the minimum curvature radius to maximum Larmor radius ratio) is of the order of unity. We show that as in the case of a simple parabolic field reversal, the magnetic moment scattering experienced by these particles may be described as the result of perturbation of the gyromotion by an impulsive centrifugal force. Here however the double‐hump structure of the current sheet leads to two successive centrifugal perturbations, which has a significant impact on the net change of magnetic moment. In a single‐hump current sheet, three distinct regimes of magnetic moment variations are obtained for a given value of κ, namely, systematic enhancement at small pitch angles, negligible change at large pitch angles, and in between either damping or enhancement depending upon gyration phase. In contrast, in a double‐hump current sheet, repeated application of this three‐branch pattern can lead to magnetic moment damping for particles that previously experience magnetic moment enhancement and vice versa. The gyrophase gain both during and between the centrifugal impulses is found to play an essential role in the net magnetic moment change. In particular, in contrast to single‐hump current sheets, the κ ≈ 1 limit may be characterized by quasi‐adiabatic behavior with negligible variations of the magnetic moment.

Application of the matrizant method to calculate the third-order aberration coefficients for a sector magnetic field including fringing-field effects

The matrizant method is used to study the nonlinear dynamics of charged particles in magnetic sector analyzers. The calculations of matrizants (transfer matrices) allow for both fringing-field effects due to the stray field and higher harmonics of the sector magnetic field (up to the third order). For the rectangular distribution of the field components along the optical axis, analytical expressions for the aberration coefficients (including dispersion ones) are derived up to the third order. In the simulation of real fields with a nonzero stray-field width, the smooth distribution of the field components is employed. The aberration coefficients for this distribution were calculated by means of a conservative numerical method.

Nonlinear dynamics of charged particles interacting with combined ac-dc electromagnetic fields

A nonlinear Lorenz model describing interactions between charged particles and combined ac-dc electromagnetic fields is studied for various combinations of frequencies, field strengths and relative angle (θ) between the ac and dc magnetic fields. Strong directional effects on the magnitude and location of resonant particle motion are observed when θ is varied and the regular resonance windows in the aligned field ( θ = 0) and linear version of the model studied previously by Durney etaal., break up to form irregular and less well pronounced regions of large and small particle displacements when nonlinearities are taken into account. The length of time takne to achieve resonant behaviour also becomes larger and more variable when nonlinearities are present. The possible relevance of these effects to interactions between electromagnetic fields and biological media is briefly discussed.

Nonlinear dynamics of charged particles in the magnetotail

An important region of the Earth's magnetosphere is the nightside magnetotail, which is believed to play a significant role in energy storage and release associated with substorms. The magnetotail contains a current sheet which separates regions of oppositely directed magnetic field. Particle motion in the collisionless magnetotail has been a long‐standing problem. Recent research from the dynamical point of view has yielded considerable new insights into the fundamental properties of orbits and of particle distribution functions. A new framework of understanding magnetospheric plasma properties is emerging. Some novel predictions based directly on nonlinear dynamics have proved to be robust and in apparent good agreement with observation. The Earth's magnetotail may serve as a paradigm, one accessible by in situ observation, of a broad class of boundary regions with embedded current sheets. This article reviews the nonlinear dynamics of charged particles in the magnetotail configuration. The emphasis is on the relationships between the dynamics and physical observables. At the end of the introduction, sections containing basic material are indicated.