Charged Particle Beam Optics Research Articles

Quantum mechanics of bending of a nonrelativistic charged particle beam by a dipole magnet

Quantum mechanics of bending of a nonrelativistic monoenergetic charged particle beam by a dipole magnet is studied in the paraxial approximation. The transfer map for the position and momentum components of a particle of the beam between two transverse planes at different points on the curved optic axis of the system is derived starting with the nonrelativistic Schrödinger equation. It is found that the quantum transfer map contains the classical transfer map as the main part and there are tiny quantum correction terms. The negligibly small quantum corrections explain the remarkable success of classical mechanics in charged particle beam optics.

Hamilton's optical–mechanical analogy in the wavelength-dependent regime

Hamilton's optical–mechanical analogy between the trajectory of material particles in potential fields and the path of light rays in media with continuously variable refractive index played an important role in the development of Schrödinger's wave mechanics. We shall examine how the Hamilton's analogy between charged-particle beam optics and light beam optics is extended to the wavelength-dependent regime. Brief accounts of the quantum prescriptions of charged-particle beam optics along with the non-traditional prescriptions of light beam optics are also presented. These prescriptions have been instrumental in seeing the analogy in the wavelength-dependent regime.

The Foldy–Wouthuysen transformation technique in optics

We describe the standard Foldy–Wouthuysen transformation technique along with its applications in optics and the new results it leads to. The use of the Foldy–Wouthuysen transformation technique is central in the non-traditional prescriptions of Helmholtz optics and Maxwell optics, respectively, resulting in the wavelength-dependent modifications of light beam optics, even at the paraxial level. It is further shown that the wavelength-dependent modifications in the newly developed formalisms of light beam optics are in close anology with the quantum theory of charged-particle beam optics.

Current accumulation for a self magnetic field calculation in a finite-element gun code

We describe a novel current accumulation algorithm for the three-dimensional self magnetic field calculation in a charged-particle beam optics code. The current source is a charged-particle beam represented by a collection of numerically-integrated current-carrying rays. We compute the magnetic vector potential using edge basis functions and the curl-curl formulation of the finite-element method. The current accumulation algorithm takes advantage of a novel particle tracker that happens to be ideal for this application. We show that our source vector is compatible with the singular finite-element matrix, even with modest numerical integration errors. Thus, a conjugate gradient matrix solver works well, with no need for additional gauge conditions. We confirmed this behavior in a series of numerical tests on a small problem with incomplete linear and quadratic basis functions on a variety of element shapes.

Beam optics applications: quantumlike versus classical-like domains

A review of the charged-particle beam optics in terms of recently developed approaches within both classical-like and quantumlike frameworks is presented. On the basis of the mutual connection of optics and mechanics, a brief overview of the quantumlike approach to electron optics is presented. In particular, the main results of the optical applications of the thermal wave model in phase space are given within the Wigner-Weyl picture. Furthermore, the tomographic approach in both classical-like and quantumlike domains in terms of the marginal-probability distribution is also presented. In particular, possible applications of the tomographic approach to optical problems with aberrations for accelerators are put forward. Some aspects of using quantumlike systems in quantum computing projects are discussed.

Iron-free permanent magnet systems for charged particle beam optics

The strength and astounding simplicity of certain permanent magnet materials allow a wide variety of simple, compact configurations of high field strength and quality multipole magnets. Here we analyze the important class of iron-free permanent magnet systems for charged particle beam optics. The theory of conventional segmented multipole magnets formed from uniformly magnetized block magnets placed in regular arrays about a circular magnet aperture is reviewed. Practical multipole configurations resulting are presented that are capable of high and intermediate aperture field strengths. A new class of elliptical aperture magnets is presented within a model with continuously varying magnetization angle. Segmented versions of these magnets promise practical high field dipole and quadrupole magnets with an increased range of applicability.

Correction of charged particle beam optics by a programmed electrostatic wire array

Theoretical and experimental results are reported on a method for the correction of aberrations in optical elements for high-power ion beams. The approach involves the use of arrays of wires immersed in large diameter beams. Individually controlled voltages are applied to the wires, resulting in local transverse deflections of beam particles. With regard to wire survivability and voltage requirements, the method appears feasible for application to high-intensity negative ion beams. A formalism is described for the calculation of optimum wire voltages to achieve a specified beam angular correction in a Cartesian geometry. The results of the calculations were tested in modeling experiments using an 8-keV electron beam. The experimental array consisted of 46 wires and boundary plates with independent applied voltages up to 3 kV. Voltage profiles for one-dimensional focusing, two-dimensional focusing, and beam steering were studied. The observed particle deflections and beam emittance growth due to the facet lens effect are in agreement with predictions.