Chapter Three - Transporting charged particle beams in static fields

The model of the generalized effective potential of the quadrupole field is considered. The model is based on the stability limit of the charged particles' oscillations in the composition of the high-frequency and static quadrupole electric fields. The representation of the polyharmonic oscillations in the variable fields by harmonic oscillations in the field of the generalized effective potential is approximate. Its accuracy increases at the stability limits. With the use of the model the problem of ion oscillations' excitation under the superposition on the quadrupole RF field of the static quadrupole and homogeneous electric fields is solved.

On Landau damping in models of Langmuir turbulence

Chapter 4 Transporting Charged Particles in Radiofrequency Fields

Chapter 3 Transporting Charged Particle Beams in Static Fields

The generalized form of Madey’s [Nuovo Cimento B 50, 64 (1979)] theorem is derived. The obtained results are used to analyze the influence of inhomogeneous electric and magnetic fields on an interaction between a beam of charged particles and a packet of electromagnetic waves. The presence of the external static fields can lead not only to the change in the damping rate of the wave packet but also to the reversal of the effect sign that is the pumping of the packet by the beam. The expression for the beam–waves energy transfer can be generalized to take into account ponderomotive forces. This interaction is illustrated by several examples: the interaction of the electron beam with Langmuir soliton, the interaction in the magnetic field with parabolic profile, and in the magnetic mirror with linear profile of the field.

This chapter is concerned with introducing a number of model problems, based on the relativistic motion of charged particles in static electric and magnetic field configurations. It discusses that these configurations include uniform dipole magnetic fields, uniform electric fields, quadrupole magnetic and electric fields, superpositions of uniform electric and magnetic fields, periodic magnetic dipole field or magnetic undulator. It explains that these model problems also allowed this chapter to introduce some rudimentary examples of analyses that are based on both relativistic and Hamiltonian formalisms. It adds that these analyses will help form the basis of more complex investigations of charged particle motion.

A new photoelectron spectrometer has recently been used to analyze the energy and spatial distribution of photoelectrons produced by multiphoton ionization of rare gases. It is based on the analysis of the image obtained by projecting the expanding electron cloud resulting from the ionization process onto a two-dimensional position sensitive detector by means of a static electric field. In this article, we present the principle of this imaging spectrometer and the relevant equations of motion of the charged particle in this device, together with an inversion method that allows us to obtain the energy and angular distribution of the electrons. We present here the inversion procedure relevant to the case where the electrostatic energy acquired in the static field is large as compared to the initial kinetic energy of the charged particles. A more general procedure relevant to any regime will be described in a following article.

In semiconductor physics, a wealth of new phenomena are obtained from the application of static external fields. Whereas the most striking phenomena arise in transport, the optical properties are also radically modified by static fields. As in the case of optical fields, the properties of a system subject to a static magnetic field are determined by the interaction of the particles with this field. This interaction gives rise to the formation of new eigenstates at the one- or two-particle level, which in turn results in a direct response to the magnetic field as well as in a modified response to other external perturbations, such as optical fields. We shall not discuss the first aspect, which concerns the magnetic properties of the system, but instead shall focus on the second aspect in this chapter. Classically, charged particles orbit around the magnetic-field axis, in the case of free electrons with the cyclotron frequency w 0c = eB/m.1 The corresponding confinement of the motion in quantum mechanics leads asymptotically (for large fields) to one-dimensional behavior in bulk semiconductors and is zero-dimensional for quantum wells in a perpendicular field. Both cases share many features with one- and zero-dimensional material systems, which can be realized in quantum wires and quantum dots, respectively. The analogy is indeed very close as long as we consider properties for which the center-of-mass motion of electron-hole pairs is negligible, an assumption usually valid for optical transitions.KeywordsStatic Magnetic FieldLandau LevelLower Landau LevelMagnetie FieldCoherent Pair StateThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The wave propagation characteristics in a stationary unbounded plasma in a static arbitrary magnetic field are reviewed. If the plasma is drifting, a Lorentz transformation can be made to obtain the ω-k relations in the reference frame where the plasma is moving. The transformation is a simple one for the slow waves with non-relativistic drift velocities. The modified waves for the drifting plasma have an important bearing on the instability of the transverse modes in a system of a drifting plasma in a plasma. The dispersion for bounded (cylindrical geometry) plasmas is studied, where the propagation vector is along the z-axis. The salient features of these waves are obtained by studying the circularly symmetric mode. The general features predicted by the quasi-static approximation are verified and the exact and quasi-static solutions are compared. The range of validity of the quasi-static approximation is determined and the h-values are plotted. As the radius becomes larger these modes evolve into the plane wave cases of the unbounded plasma. When a fast beam of charged particles, electrons, ions or a plasma, traverses a stationary plasma in a magnetic field, there is a possibility of unstable transverse modes of propagation. If the drifting particles are either electrons or ions, the circularly polarized waves exhibit an instability over a very narrow frequency range near the ion and electron cyclotron frequencies respectively. When a plasma drifts through a plasma, in addition to the instabilities noted above, there can be an instability near zero frequency, and the growth condition is determined. For typical parameter values these transverse modes have greater growth constants than the longitudinal mode. These unstable transverse modes have possible applications in the generation of high frequencies, and are possible explanations for various instabilities in the ionosphere.

Quantum simulations made using Floquet methods show that a charged particle can exchange energy with an oscillating potential barrier in discrete quanta ħω, where ω is the frequency of oscillation. However, this exchange is classically forbidden because no other mass is included in the model, so that energy and momentum could not both be conserved in the absorption or emission of a photon. We define a semiclassical mechanism for these inelastic processes in which a photon may be absorbed by a charged particle moving against an intense static electric field, or emitted when the particle moves with this field. In this model, the particle has an energy loss Q in photon absorption, and an energy gain Q in photon emission. Then the particle travels a short distance at constant momentum until the energy increment Q is made up by the interaction with the static electric field, after which the particle resumes classical motion with the initial energy plus or minus exactly one quantum. We use the energy–time uncertainty relation to determine the minimum value for the static electric field that is required for this process, and this value is typical of the experimental conditions for laser-assisted scanning tunneling microscopy and laser-assisted field emission where the exchange of quanta is found to occur.

Champs electriques statiques induits par une onde lumineuse dans les milieux ionises

Electron Beams and Microwave Vacuum Electronics

Chapter 2 Language of Aberration Expansions in Charged Particle Optics

We study the quantization of a charged particle motion without spin inside a flat box under a static electromagnetic field. Contrary to Landau’s solution with constant magnetic field transverse to the box and using Fourier transformation, we found a full solution for the wave function which is different from that one given by Landau, and this fact remains when static electric field is added. However, the Landau’s levels appear in all cases.

While considering the non separable solution for the quantum problem of the motion of a charged particle in a flat surface of lengths Lx and Ly with transversal static magnetic field B and longitudinal static electric field E, the quantum current, the transverse (Hall) and longitudinal resistivities are estimated for the state n = 0 and j = 0.We noticed that the transverse resistivity is proportional to an integer number, due to the quantization of the magnetic flux, and longitudinal resistivity can be zero for times t \(\gg\) LxB/cE. Additionally, a modified quantization of the magnetic flux is discovered utilizing a modified periodicity of the eigenfunction, allowing for IQHE and FQHE of any filling factor of the form v = k/l, with k, l \(\in\) \({Z}\).